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Analysis | Engineering | Engineering
Analysts in the field of engineering look at requirements, structures, mechanisms, systems and dimensions. Electrical engineers analyse systems in electronics. Life cycles and system failures are broken down and studied by engineers. It is also looking at different factors incorporated within the design. |
Analysis | Mathematics | Mathematics
Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.
Florian Cajori explains in A History of Mathematics (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:
The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in [appended to] Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."
The analytic method is not conclusive, unless all operations involved in it are known to be reversible. To remove all doubt, the Greeks, as a rule, added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions.
James Gow uses a similar argument as Cajori, with the following clarification, in his A Short History of Greek Mathematics (1884):
The synthetic proof proceeds by shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded. The Greeks distinguished theoretic from problematic analysis. A theoretic analysis is of the following kind. To prove that A is B, assume first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be known a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible, then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem. Problematic analysis is applied in all cases where it is proposed to construct a figure which is assumed to satisfy a given condition. The problem is then converted into some theorem which is involved in the condition and which is proved synthetically, and the steps of this synthetic proof taken backwards are a synthetic solution of the problem. |
Analysis | Psychotherapy | Psychotherapy
Psychoanalysis – seeks to elucidate connections among unconscious components of patients' mental processes
Transactional analysis
Transactional analysis is used by therapists to try to gain a better understanding of the unconscious. It focuses on understanding and intervening human behavior. |
Analysis | Signal processing | Signal processing
Finite element analysis – a computer simulation technique used in engineering analysis
Independent component analysis
Link quality analysis – the analysis of signal quality
Path quality analysis
Fourier analysis |
Analysis | Statistics | Statistics
In statistics, the term analysis may refer to any method used
for data analysis. Among the many such methods, some are:
Analysis of variance (ANOVA) – a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts
Boolean analysis – a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis
Cluster analysis – techniques for finding groups (called clusters), based on some measure of proximity or similarity
Factor analysis – a method to construct models describing a data set of observed variables in terms of a smaller set of unobserved variables (called factors)
Meta-analysis – combines the results of several studies that address a set of related research hypotheses
Multivariate analysis – analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis
Principal component analysis – transformation of a sample of correlated variables into uncorrelated variables (called principal components), mostly used in exploratory data analysis
Regression analysis – techniques for analysing the relationships between several predictive variables and one or more outcomes in the data
Scale analysis (statistics) – methods to analyse survey data by scoring responses on a numeric scale
Sensitivity analysis – the study of how the variation in the output of a model depends on variations in the inputs
Sequential analysis – evaluation of sampled data as it is collected, until the criterion of a stopping rule is met
Spatial analysis – the study of entities using geometric or geographic properties
Time-series analysis – methods that attempt to understand a sequence of data points spaced apart at uniform time intervals |
Analysis | Business | Business
Financial statement analysis – the analysis of the accounts and the economic prospects of a firm
Financial analysis – refers to an assessment of the viability, stability, and profitability of a business, sub-business or project
Gap analysis – involves the comparison of actual performance with potential or desired performance of an organization
Business analysis – involves identifying the needs and determining the solutions to business problems
Price analysis – involves the breakdown of a price to a unit figure
Market analysis – consists of suppliers and customers, and price is determined by the interaction of supply and demand
Sum-of-the-parts analysis – method of valuation of a multi-divisional company
Opportunity analysis – consists of customers trends within the industry, customer demand and experience determine purchasing behavior |
Analysis | Economics | Economics
Agroecosystem analysis
Input–output model if applied to a region, is called Regional Impact Multiplier System |
Analysis | Government | Government |
Analysis | Intelligence | Intelligence
The field of intelligence employs analysts to break down and understand a wide array of questions. Intelligence agencies may use heuristics, inductive and deductive reasoning, social network analysis, dynamic network analysis, link analysis, and brainstorming to sort through problems they face. Military intelligence may explore issues through the use of game theory, Red Teaming, and wargaming. Signals intelligence applies cryptanalysis and frequency analysis to break codes and ciphers. Business intelligence applies theories of competitive intelligence analysis and competitor analysis to resolve questions in the marketplace. Law enforcement intelligence applies a number of theories in crime analysis. |
Analysis | Policy | Policy
Policy analysis – The use of statistical data to predict the effects of policy decisions made by governments and agencies
Policy analysis includes a systematic process to find the most efficient and effective option to address the current situation.
Qualitative analysis – The use of anecdotal evidence to predict the effects of policy decisions or, more generally, influence policy decisions |
Analysis | Humanities and social sciences | Humanities and social sciences |
Analysis | Linguistics | Linguistics
Linguistics explores individual languages and language in general. It breaks language down and analyses its component parts: theory, sounds and their meaning, utterance usage, word origins, the history of words, the meaning of words and word combinations, sentence construction, basic construction beyond the sentence level, stylistics, and conversation. It examines the above using statistics and modeling, and semantics. It analyses language in context of anthropology, biology, evolution, geography, history, neurology, psychology, and sociology. It also takes the applied approach, looking at individual language development and clinical issues. |
Analysis | Literature | Literature
Literary criticism is the analysis of literature. The focus can be as diverse as the analysis of Homer or Freud. While not all literary-critical methods are primarily analytical in nature, the main approach to the teaching of literature in the west since the mid-twentieth century, literary formal analysis or close reading, is. This method, rooted in the academic movement labelled The New Criticism, approaches texts – chiefly short poems such as sonnets, which by virtue of their small size and significant complexity lend themselves well to this type of analysis – as units of discourse that can be understood in themselves, without reference to biographical or historical frameworks. This method of analysis breaks up the text linguistically in a study of prosody (the formal analysis of meter) and phonic effects such as alliteration and rhyme, and cognitively in examination of the interplay of syntactic structures, figurative language, and other elements of the poem that work to produce its larger effects. |
Analysis | Music | Music
Musical analysis – a process attempting to answer the question "How does this music work?"
Musical Analysis is a study of how the composers use the notes together to compose music. Those studying music will find differences with each composer's musical analysis, which differs depending on the culture and history of music studied. An analysis of music is meant to simplify the music for you.
Schenkerian analysis
Schenkerian analysis is a collection of music analysis that focuses on the production of the graphic representation. This includes both analytical procedure as well as the notational style. Simply put, it analyzes tonal music which includes all chords and tones within a composition. |
Analysis | Philosophy | Philosophy
Philosophical analysis – a general term for the techniques used by philosophers
Philosophical analysis refers to the clarification and composition of words put together and the entailed meaning behind them. Philosophical analysis dives deeper into the meaning of words and seeks to clarify that meaning by contrasting the various definitions. It is the study of reality, justification of claims, and the analysis of various concepts. Branches of philosophy include logic, justification, metaphysics, values and ethics. If questions can be answered empirically, meaning it can be answered by using the senses, then it is not considered philosophical. Non-philosophical questions also include events that happened in the past, or questions science or mathematics can answer.
Analysis is the name of a prominent journal in philosophy. |
Analysis | Other | Other
Aura analysis – a pseudoscientific technique in which supporters of the method claim that the body's aura, or energy field is analysed
Bowling analysis – Analysis of the performance of cricket players
Lithic analysis – the analysis of stone tools using basic scientific techniques
Lithic analysis is most often used by archeologists in determining which types of tools were used at a given time period pertaining to current artifacts discovered.
Protocol analysis – a means for extracting persons' thoughts while they are performing a task |
Analysis | See also | See also
Formal analysis
Metabolism in biology
Methodology
Scientific method
Synthesis (disambiguation) – list of terms related to synthesis, the converse of analysis |
Analysis | References | References |
Analysis | External links | External links
Category:Abstraction
Category:Critical thinking skills
Category:Emergence
Category:Empiricism
Category:Epistemological theories
Category:Intelligence
Category:Mathematical modeling
Category:Metaphysics of mind
Category:Methodology
Category:Ontology
Category:Philosophy of logic
Category:Rationalism
Category:Reasoning
Category:Research methods
Category:Scientific method
Category:Theory of mind |
Analysis | Table of Content | Short description, Science and technology, Chemistry, Types of Analysis, Isotopes, Computer science, Engineering, Mathematics, Psychotherapy, Signal processing, Statistics, Business, Economics, Government, Intelligence, Policy, Humanities and social sciences, Linguistics, Literature, Music, Philosophy, Other, See also, References, External links |
Abner Doubleday | short description | Abner Doubleday (June 26, 1819 – January 26, 1893) was a career United States Army officer and Union major general in the American Civil War. He fired the first shot in defense of Fort Sumter, the opening battle of the war, and had a pivotal role in the early fighting at the Battle of Gettysburg. Gettysburg was his finest hour, but his relief by Maj. Gen. George G. Meade caused lasting enmity between the two men. In San Francisco, after the war, he obtained a patent on the cable car railway that still runs there. In his final years in New Jersey, he was a prominent member and later president of the Theosophical Society.
In 1908, 15 years after his death, the Mills Commission declared that Doubleday had invented the game of baseball, although Doubleday never made such a claim. This claim has been thoroughly debunked by baseball historians.Kirsch, pp. xiii–xiv. |
Abner Doubleday | Early years | Early years
Doubleday, the son of Ulysses F. Doubleday and Hester Donnelly, was born in Ballston Spa, New York, in a small house on the corner of Washington and Fenwick streets. As a child, Abner was very short. The family all slept in the attic loft of the one-room house. His paternal grandfather, also named Abner, had fought in the American Revolutionary War. His maternal grandfather Thomas Donnelly had joined the army at 14 and was a mounted messenger for George Washington. His great-grandfather Peter Donnelly was a Minuteman. His father, Ulysses F., fought in the War of 1812, published newspapers and books, and represented Auburn, New York, for four years in the United States Congress.Beckenbaugh, pp. 611–612. Abner spent his childhood in Auburn and later was sent to Cooperstown to live with his uncle and attend a private preparatory high school. He practiced as a surveyor and civil engineer for two years before entering the United States Military AcademyTagg, pp. 25–27. in 1838. He graduated in 1842, 24th in a class of 56 cadets, and was commissioned a brevet second lieutenant in the 3rd U.S. Artillery.Eicher, p. 213. In 1852, he married Mary Hewitt of Baltimore, the daughter of a local lawyer.Texas Handbook |
Abner Doubleday | Early commands and Fort Sumter | Early commands and Fort Sumter
thumb|Major Robert Anderson and his officers at Fort Sumter, South Carolina
200px|right|thumb|Doubleday photo displayed at Fort Sumter National Monument in Charleston harbor
thumb|200px|Fort Sumter Medal bearing the likeness of Major Robert Anderson which was presented to Abner Doubleday
Doubleday initially served in coastal garrisons and then in the Mexican–American War from 1846 to 1848 and the Seminole Wars from 1856 to 1858. In 1858, he was transferred to Fort Moultrie in Charleston Harbor serving under Colonel John L. Gardner. By the start of the Civil War, he was a captain and second in command in the garrison at Fort Sumter, under Major Robert Anderson. He aimed the cannon that fired the first return shot in answer to the Confederate bombardment on April 12, 1861. He subsequently referred to himself as the "hero of Sumter" for this role. Of note, although Doubleday did not invent baseball, by sheer coincidence the Fort Sumter Garrison Flag (or Storm Flag) has the star pattern arranged in a diamond shape, which by that time in history, was the shape of the baseball infield. |
Abner Doubleday | Brigade and division command in Virginia | Brigade and division command in Virginia
Doubleday was promoted to major on May 14, 1861, and commanded the Artillery Department in the Shenandoah Valley from June to August, and then the artillery for Major General Nathaniel Banks's division of the Army of the Potomac. He was appointed brigadier general of volunteers on February 3, 1862, and was assigned to duty in northern Virginia while the Army of the Potomac conducted the Peninsula Campaign. His first combat assignment was to lead the 2nd Brigade, 1st Division, III Corps of the Army of Virginia during the Northern Virginia Campaign. In the actions at Brawner's farm, just before the Second Battle of Bull Run, he took the initiative to send two of his regiments to reinforce Brigadier General John Gibbon's brigade against a larger Confederate force, fighting it to a standstill. Personal initiative was required since his division commander, Brig. Gen. Rufus King, was incapacitated by an epileptic seizure at the time. He was replaced by Brigadier General John P. Hatch.Langellier, pp. 43, 45, 49. His men were routed when they encountered Major General James Longstreet's corps, but by the following day, August 30, he took command of the division when Hatch was wounded, and he led his men to cover the retreat of the Union Army.
Doubleday again led the division, now assigned to the I Corps of the Army of the Potomac, after South Mountain, where Hatch was wounded again. At Antietam, he led his men into the deadly fighting in the Cornfield and the West Woods, and one colonel described him as a "gallant officer ... remarkably cool and at the very front of battle." He was wounded when an artillery shell exploded near his horse, throwing him to the ground in a violent fall. He received a brevet promotion to lieutenant colonel in the regular army for his actions at Antietam and was promoted in March 1863 to major general of volunteers, to rank from November 29, 1862.Eicher, p. 703. At Fredericksburg in December 1862, his division mostly sat idle. During the winter, the I Corps was reorganized and Doubleday assumed command of the 3rd Division. At Chancellorsville in May 1863, the division was kept in reserve. |
Abner Doubleday | Gettysburg | Gettysburg
thumb|Birthplace in Ballston Spa
thumb|right|Doubleday and his wife, Mary
At the start of the Battle of Gettysburg, July 1, 1863, Doubleday's division was the second infantry division on the field to reinforce the cavalry division of Brigadier General John Buford. When his corps commander, Major General John F. Reynolds, was killed very early in the fighting, Doubleday found himself in command of the corps at 10:50 am. His men fought well in the morning, putting up a stout resistance, but as overwhelming Confederate forces massed against them, their line eventually broke and they retreated back through the town of Gettysburg to the relative safety of Cemetery Hill south of town. It was Doubleday's finest performance during the war, five hours leading 9,500 men against ten Confederate brigades that numbered more than 16,000. Seven of those brigades sustained casualties that ranged from 35 to 50 percent, indicating the ferocity of the Union defense. On Cemetery Hill, however, the I Corps could muster only a third of its men as effective for duty, and the corps was essentially destroyed as a combat force for the rest of the battle; it would be decommissioned in March 1864, its surviving units consolidated into other corps.
On July 2, 1863, Army of the Potomac commander Maj. Gen. George G. Meade replaced Doubleday with Major General John Newton, a more junior officer from another corps. The ostensible reason was a false report by XI Corps commander Major General Oliver O. Howard that Doubleday's corps broke first, causing the entire Union line to collapse, but Meade also had a long history of disdain for Doubleday's combat effectiveness, dating back to South Mountain. Doubleday was humiliated by this snub and held a lasting grudge against Meade, but he returned to division command and fought well for the remainder of the battle. He was wounded in the neck on the second day of Gettysburg and received a brevet promotion to colonel in the regular army for his service. He formally requested reinstatement as I Corps commander, but Meade refused, and Doubleday left Gettysburg on July 7 for Washington.Coddington, pp. 690–691.
Doubleday's staff nicknamed him "Forty-Eight Hours" as a compliment to recognize his tendency to avoid reckless or impulsive actions and his thoughtfulness and deliberateness in considering circumstances and possible responses.Barthel, p. 127 In recent years, biographers have turned the nickname into an insult, incorrectly claiming "Forty-Eight Hours" was coined to highlight Doubleday's supposed incompetence and slowness to act. |
Abner Doubleday | Washington | Washington
Doubleday assumed administrative duties in the defenses of Washington, D.C., where he was in charge of courts martial, which gave him legal experience that he used after the war. His only return to combat was directing a portion of the defenses against the attack by Confederate Lieutenant General Jubal A. Early in the Valley Campaigns of 1864. Also while in Washington, Doubleday testified against George Meade at the United States Congress Joint Committee on the Conduct of the War, criticizing him harshly over his conduct of the Battle of Gettysburg. While in Washington, Doubleday remained a loyal Republican and staunch supporter of President Abraham Lincoln. Doubleday rode with Lincoln on the train to Gettysburg for the Gettysburg Address and Col. and Mrs. Doubleday attended events with Mr. and Mrs. Lincoln in Washington. |
Abner Doubleday | Postbellum career | Postbellum career
After the Civil War, Doubleday mustered out of the volunteer service on August 24, 1865, reverted to the rank of lieutenant colonel, and became the colonel of the 35th U.S. Infantry in September 1867. He was stationed in San Francisco from 1869 through 1871 and he took out a patent for the cable car railway that still runs there, receiving a charter for its operation, but signing away his rights when he was reassigned. In 1871, he commanded the 24th U.S. Infantry, an all African-American regiment with headquarters at Fort McKavett, Texas. He retired in 1873.
In the 1870s, he was listed in the New York business directory as a lawyer.
Doubleday spent much of his time writing. He published two important works on the Civil War: Reminiscences of Forts Sumter and Moultrie (1876), and Chancellorsville and Gettysburg (1882), the latter being a volume of the series Campaigns of the Civil War. |
Abner Doubleday | Theosophy | Theosophy
In the summer of 1878, Doubleday lived in Mendham Township, New Jersey, and became a prominent member of the Theosophical Society. When two of the founders of that society, Helena Blavatsky and Henry Steel Olcott, moved to India at the end of that year, he was constituted as the president of the American body. |
Abner Doubleday | Death | Death
thumb|right|Doubleday's tombstone in Arlington National Cemetery
Doubleday died of heart disease in Mendham Township on January 26, 1893. Doubleday's body was laid in state in New York's City Hall and then was taken to Washington by train from Mendham, and was buried in Arlington National Cemetery in Arlington County, Virginia. He was survived by his wife. |
Abner Doubleday | Baseball | Baseball
Although Doubleday achieved minor fame as a competent combat general with experience in many important Civil War battles, he is more widely known as the supposed inventor of the game of baseball, in Elihu Phinney's cow pasture in Cooperstown, New York, in 1839.
The Mills Commission, chaired by Abraham G. Mills, the fourth president of the National League, was appointed in 1905 to determine the origin of baseball. The committee's final report, on December 30, 1907, stated, in part, that "the first scheme for playing baseball, according to the best evidence obtainable to date, was devised by Abner Doubleday at Cooperstown, New York, in 1839." It concluded by saying, "in the years to come, in the view of the hundreds of thousands of people who are devoted to baseball, and the millions who will be, Abner Doubleday's fame will rest evenly, if not quite as much, upon the fact that he was its inventor ... as upon his brilliant and distinguished career as an officer in the Federal Army."Kirsch, p. xiii.
However, there is considerable evidence to dispute this claim. Baseball historian George B. Kirsch has described the results of the Mills Commission as a "myth". He wrote, "Robert Henderson, Harold Seymour, and other scholars have since debunked the Doubleday-Cooperstown myth, which nonetheless remains powerful in the American imagination because of the efforts of Major League Baseball and the Hall of Fame in Cooperstown." At his death, Doubleday left many letters and papers, none of which describe baseball or give any suggestion that he considered himself a prominent person in the evolution of the game, and his New York Times obituary did not mention the game at all. Chairman Mills himself, who had been a Civil War colleague of Doubleday and a member of the honor guard for Doubleday's body as it lay in state in New York City, never recalled hearing Doubleday describe his role as the inventor. Doubleday was a cadet at West Point in the year of the alleged invention and his family had moved away from Cooperstown the prior year. Furthermore, the primary testimony to the commission that connected baseball to Doubleday was that of Abner Graves, whose credibility is questionable; a few years later, he shot his wife to death and was committed to an institution for the criminally insane for the rest of his life.Kirsch, pp. xiii–xiv. Part of the confusion could stem from there being another man by the same name in Cooperstown in 1839.Morris, Peter. But Didn't We Have Fun. Ivan R. Dee Publishing. 2008
Despite the lack of solid evidence linking Doubleday to the origins of baseball, Cooperstown, New York, became the new home of what is today the National Baseball Hall of Fame and Museum in 1937.
There may have been some relationship to baseball as a national sport and Abner Doubleday. While the modern rules of baseball were formulated in New York during the 1840s, it was the scattering of New Yorkers exposed to these rules throughout the country, that spread not only baseball, but also the "New York Rules", thereby harmonizing the rules, and being a catalyst for its growth. Doubleday was a high-ranking officer, whose duties included seeing to provisions for the US Army fighting throughout the south and border states. For the morale of the men, he is said to have provisioned balls and bats for the men."Bats, Balls, and Bullets". Essay by George B. Kirsch Civil War Times Illustrated. May 1998, pp. 30-37 |
Abner Doubleday | Namesakes and honors | Namesakes and honors
thumb|right|Abner Doubleday monument in Ballston Spa
Doubleday's men, admirers, and the state of New York erected a monument to him at Gettysburg. There is a obelisk monument at Arlington National Cemetery where he is buried.
Doubleday Field is a 9,791-seat baseball stadium named for Abner Doubleday, located in Cooperstown, New York, near the Baseball Hall of Fame. It hosted the annual Hall of Fame Game, an exhibition game between two major league teams that was played from 1940 until 2008. It has hosted the Hall of Fame Classic since 2009.
The Auburn Doubledays are a collegiate summer baseball team based in Doubleday's hometown of Auburn, New York.
Doubleday Field at the United States Military Academy at West Point, New York, where the Army Black Knights play at Johnson Stadium, is named in Doubleday's honor.
The Abner Doubleday Little League and Babe Ruth Fields in Ballston Spa, New York, the town of his birth. The house of his birth still stands in the middle of town and there is a monument to him on Front Street.
A sign at the Doubleday Hill Monument, erected in Williamsport, Maryland, to commemorate Doubleday's occupation of a hill there during the Civil War, claims he invented the game in 1835.
Mendham Borough and Mendham Township, New Jersey has held a municipal holiday known as "Abner Doubleday Day" for numerous years in the General's honor and commissioned a plaque near the site of his home in the borough in 1998, even though the borough was known as Mendham Township back then.
In 2004, the Abner Doubleday Society erected a monument to Doubleday in Iron Spring Park, Ballston Spa, near his birthplace. |
Abner Doubleday | See also | See also
List of American Civil War generals (Union)
William Webb Ellis, sometimes apocryphally credited with inventing rugby football |
Abner Doubleday | Notes | Notes |
Abner Doubleday | References | References
Gomes, Michael. "Abner Doubleday and Theosophy in America: 1879–1884". Sunrise, April/May 1991.
"Doubleday, Abner" in The Handbook of Texas. |
Abner Doubleday | Further reading | Further reading
Silkenat, David. Raising the White Flag: How Surrender Defined the American Civil War. Chapel Hill: University of North Carolina Press, 2019. . |
Abner Doubleday | External links | External links
Defense of Madame Blavatsky
Baseball Hall of Fame
Photo of Abner Doubleday and wife Mary, taken by Mathew Brady, owned by University of Michigan Museum of Art
Ulysses Freeman Doubleday – McLean County Museum of History
Category:1819 births
Category:1893 deaths
Category:American military personnel of the Mexican–American War
Category:Burials at Arlington National Cemetery
Category:People from Auburn, New York
Category:People from Ballston Spa, New York
Category:People of New York (state) in the American Civil War
Category:Union army generals
Category:United States Military Academy alumni
Category:Writers from New York (state)
Category:New York (state) Republicans
Category:American Theosophists
Category:People from Mendham Township, New Jersey |
Abner Doubleday | Table of Content | short description, Early years, Early commands and Fort Sumter, Brigade and division command in Virginia, Gettysburg, Washington, Postbellum career, Theosophy, Death, Baseball, Namesakes and honors, See also, Notes, References, Further reading, External links |
America's National Game | short description | right|thumb
America's National Game is a book by Albert Spalding, published in 1911, that details the early history of the sport of baseball. It is one of the defining books in the early formative years of modern baseball.
Much of the story is told first-hand; since the 1850s, Spalding had been involved in the game, first as a pitcher and later a manager and club owner. Later he branched out to become a leading manufacturer of sporting goods.
In addition to his personal recollections, he had access to the records of Henry Chadwick, the game's first statistician and archivist. Much of his early history of the game is considered to be reliable. Spalding was, however, said to aggrandize his role in the major moments in baseball's history. Early editions of the book include quality full-page photo-plates of important players. |
America's National Game | See also | See also
History of baseball |
America's National Game | References | References
Category:1911 non-fiction books
Category:Baseball books |
America's National Game | Table of Content | short description, See also, References |
Amplitude modulation | short description | thumb|right|250px|An audio signal (top) carried by a carrier signal using amplitude modulation (middle) and frequency modulation (bottom).|alt=Animation of audio, AM and FM modulated carriers.
Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the amplitude (signal strength) of the wave is varied in proportion to that of the message signal, such as an audio signal. This technique contrasts with angle modulation, in which either the frequency of the carrier wave is varied, as in frequency modulation, or its phase, as in phase modulation.
AM was the earliest modulation method used for transmitting audio in radio broadcasting. It was developed during the first quarter of the 20th century beginning with Roberto Landell de Moura and Reginald Fessenden's radiotelephone experiments in 1900. This original form of AM is sometimes called double-sideband amplitude modulation (DSBAM), because the standard method produces sidebands on either side of the carrier frequency. Single-sideband modulation uses bandpass filters to eliminate one of the sidebands and possibly the carrier signal, which improves the ratio of message power to total transmission power, reduces power handling requirements of line repeaters, and permits better bandwidth utilization of the transmission medium.
AM remains in use in many forms of communication in addition to AM broadcasting: shortwave radio, amateur radio, two-way radios, VHF aircraft radio, citizens band radio, and in computer modems in the form of quadrature amplitude modulation (QAM). |
Amplitude modulation | Foundation | Foundation
In electronics, telecommunications and mechanics, modulation means varying some aspect of a continuous wave carrier signal with an information-bearing modulation waveform, such as an audio signal which represents sound, or a video signal which represents images. In this sense, the carrier wave, which has a much higher frequency than the message signal, carries the information. At the receiving station, the message signal is extracted from the modulated carrier by demodulation.
In general form, a modulation process of a sinusoidal carrier wave may be described by the following equation:AT&T, Telecommunication Transmission Engineering, Volume 1—Principles, 2nd Edition, Bell Center for Technical Education (1977)
.
A(t) represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its angular frequency , and the instantaneous phase deviation . This description directly provides the two major groups of modulation, amplitude modulation and angle modulation. In angle modulation, the term A(t) is constant and the second term of the equation has a functional relationship to the modulating message signal. Angle modulation provides two methods of modulation, frequency modulation and phase modulation.
In amplitude modulation, the angle term is held constant and the first term, A(t), of the equation has a functional relationship to the modulating message signal.
The modulating message signal may be analog in nature, or it may be a digital signal, in which case the technique is generally called amplitude-shift keying.
For example, in AM radio communication, a continuous wave radio-frequency signal has its amplitude modulated by an audio waveform before transmission. The message signal determines the envelope of the transmitted waveform. In the frequency domain, amplitude modulation produces a signal with power concentrated at the carrier frequency and two adjacent sidebands. Each sideband is equal in bandwidth to that of the modulating signal, and is a mirror image of the other. Standard AM is thus sometimes called "double-sideband amplitude modulation" (DSBAM).
A disadvantage of all amplitude modulation techniques, not only standard AM, is that the receiver amplifies and detects noise and electromagnetic interference in equal proportion to the signal. Increasing the received signal-to-noise ratio, say, by a factor of 10 (a 10 decibel improvement), thus would require increasing the transmitter power by a factor of 10. This is in contrast to frequency modulation (FM) and digital radio where the effect of such noise following demodulation is strongly reduced so long as the received signal is well above the threshold for reception. For this reason AM broadcast is not favored for music and high fidelity broadcasting, but rather for voice communications and broadcasts (sports, news, talk radio etc.).
AM is also inefficient in power usage; at least two-thirds of the power is concentrated in the carrier signal. The carrier signal contains none of the original information being transmitted (voice, video, data, etc.). However its presence provides a simple means of demodulation using envelope detection, providing a frequency and phase reference to extract the modulation from the sidebands. In some modulation systems based on AM, a lower transmitter power is required through partial or total elimination of the carrier component, however receivers for these signals are more complex because they must provide a precise carrier frequency reference signal (usually as shifted to the intermediate frequency) from a greatly reduced "pilot" carrier (in reduced-carrier transmission or DSB-RC) to use in the demodulation process. Even with the carrier eliminated in double-sideband suppressed-carrier transmission, carrier regeneration is possible using a Costas phase-locked loop. This does not work for single-sideband suppressed-carrier transmission (SSB-SC), leading to the characteristic "Donald Duck" sound from such receivers when slightly detuned. Single-sideband AM is nevertheless used widely in amateur radio and other voice communications because it has power and bandwidth efficiency (cutting the RF bandwidth in half compared to standard AM). On the other hand, in medium wave and short wave broadcasting, standard AM with the full carrier allows for reception using inexpensive receivers. The broadcaster absorbs the extra power cost to greatly increase potential audience. |
Amplitude modulation | Shift keying | Shift keying
A simple form of digital amplitude modulation which can be used for transmitting binary data is on–off keying, the simplest form of amplitude-shift keying, in which ones and zeros are represented by the presence or absence of a carrier. On–off keying is likewise used by radio amateurs to transmit Morse code where it is known as continuous wave (CW) operation, even though the transmission is not strictly "continuous". A more complex form of AM, quadrature amplitude modulation is now more commonly used with digital data, while making more efficient use of the available bandwidth. |
Amplitude modulation | Analog telephony | Analog telephony
A simple form of amplitude modulation is the transmission of speech signals from a traditional analog telephone set using a common battery local loop.AT&T, Engineering and Operations in the Bell System (1984) p.211 The direct current provided by the central office battery is a carrier with a frequency of 0 Hz. It is modulated by a microphone (transmitter) in the telephone set according to the acoustic signal from the speaker. The result is a varying amplitude direct current, whose AC-component is the speech signal extracted at the central office for transmission to another subscriber. |
Amplitude modulation | Amplitude reference | Amplitude reference
An additional function provided by the carrier in standard AM, but which is lost in either single or double-sideband suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control (AGC) responds to the carrier so that the reproduced audio level stays in a fixed proportion to the original modulation. On the other hand, with suppressed-carrier transmissions there is no transmitted power during pauses in the modulation, so the AGC must respond to peaks of the transmitted power during peaks in the modulation. This typically involves a so-called fast attack, slow decay circuit which holds the AGC level for a second or more following such peaks, in between syllables or short pauses in the program. This is very acceptable for communications radios, where compression of the audio aids intelligibility. However, it is absolutely undesired for music or normal broadcast programming, where a faithful reproduction of the original program, including its varying modulation levels, is expected. |
Amplitude modulation | ITU type designations | ITU type designations
In 1982, the International Telecommunication Union (ITU) designated the types of amplitude modulation:
DesignationDescriptionA3Edouble-sideband a full-carrier – the basic amplitude modulation schemeR3Esingle-sideband reduced-carrierH3Esingle-sideband full-carrierJ3Esingle-sideband suppressed-carrierB8Eindependent-sideband emissionC3Fvestigial-sidebandLincompexlinked compressor and expander (a submode of any of the above ITU Emission Modes) |
Amplitude modulation | History | History
thumb|One of the crude pre-vacuum tube AM transmitters, a Telefunken arc transmitter from 1906. The carrier wave is generated by 6 electric arcs in the vertical tubes, connected to a tuned circuit. Modulation is done by the large carbon microphone (cone shape) in the antenna lead.
thumb|One of the first vacuum tube AM radio transmitters, built by Meissner in 1913 with an early triode tube by Robert von Lieben. He used it in a historic voice transmission from Berlin to Nauen, Germany. Compare its small size with the arc transmitter above.
Amplitude modulation was used in experiments of multiplex telegraph and telephone transmission in the late 1800s. However, the practical development of this technology is identified with the period between 1900 and 1920 of radiotelephone transmission, that is, the effort to send audio signals by radio waves. The first radio transmitters, called spark gap transmitters, transmitted information by wireless telegraphy, using pulses of the carrier wave to spell out text messages in Morse code. They could not transmit audio because the carrier consisted of strings of damped waves, pulses of radio waves that declined to zero, and sounded like a buzz in receivers. In effect they were already amplitude modulated. |
Amplitude modulation | Continuous waves | Continuous waves
The first AM transmission was made by Canadian-born American researcher Reginald Fessenden on December 23, 1900 using a spark gap transmitter with a specially designed high frequency 10 kHz interrupter, over a distance of at Cobb Island, Maryland, US. His first transmitted words were, "Hello. One, two, three, four. Is it snowing where you are, Mr. Thiessen?". Though his words were "perfectly intelligible", the spark created a loud and unpleasant noise.
Fessenden was a significant figure in the development of AM radio. He was one of the first researchers to realize, from experiments like the above, that the existing technology for producing radio waves, the spark transmitter, was not usable for amplitude modulation, and that a new kind of transmitter, one that produced sinusoidal continuous waves, was needed. This was a radical idea at the time, because experts believed the impulsive spark was necessary to produce radio frequency waves, and Fessenden was ridiculed. He invented and helped develop one of the first continuous wave transmitters – the Alexanderson alternator, with which he made what is considered the first AM public entertainment broadcast on Christmas Eve, 1906. He also discovered the principle on which AM is based, heterodyning, and invented one of the first detectors able to rectify and receive AM, the electrolytic detector or "liquid baretter", in 1902. Other radio detectors invented for wireless telegraphy, such as the Fleming valve (1904) and the crystal detector (1906) also proved able to rectify AM signals, so the technological hurdle was generating AM waves; receiving them was not a problem. |
Amplitude modulation | Early technologies | Early technologies
Early experiments in AM radio transmission, conducted by Fessenden, Valdemar Poulsen, Ernst Ruhmer, Quirino Majorana, Charles Herrold, and Lee de Forest, were hampered by the lack of a technology for amplification. The first practical continuous wave AM transmitters were based on either the huge, expensive Alexanderson alternator, developed 1906–1910, or versions of the Poulsen arc transmitter (arc converter), invented in 1903. The modifications necessary to transmit AM were clumsy and resulted in very low quality audio. Modulation was usually accomplished by a carbon microphone inserted directly in the antenna or ground wire; its varying resistance varied the current to the antenna. The limited power handling ability of the microphone severely limited the power of the first radiotelephones; many of the microphones were water-cooled. |
Amplitude modulation | Vacuum tubes | Vacuum tubes
The 1912 discovery of the amplifying ability of the Audion tube, invented in 1906 by Lee de Forest, solved these problems. The vacuum tube feedback oscillator, invented in 1912 by Edwin Armstrong and Alexander Meissner, was a cheap source of continuous waves and could be easily modulated to make an AM transmitter. Modulation did not have to be done at the output but could be applied to the signal before the final amplifier tube, so the microphone or other audio source didn't have to modulate a high-power radio signal. Wartime research greatly advanced the art of AM modulation, and after the war the availability of cheap tubes sparked a great increase in the number of radio stations experimenting with AM transmission of news or music. The vacuum tube was responsible for the rise of AM broadcasting around 1920, the first electronic mass communication medium. Amplitude modulation was virtually the only type used for radio broadcasting until FM broadcasting began after World War II.
At the same time as AM radio began, telephone companies such as AT&T were developing the other large application for AM: sending multiple telephone calls through a single wire by modulating them on separate carrier frequencies, called frequency division multiplexing. |
Amplitude modulation | Single-sideband | Single-sideband
In 1915, John Renshaw Carson formulated the first mathematical description of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device creates a sideband on both sides of the carrier frequency. Passing the modulated signal through another nonlinear device can extract the original baseband signal. His analysis also showed that only one sideband was necessary to transmit the audio signal, and Carson patented single-sideband modulation (SSB) on 1 December 1915. This advanced variant of amplitude modulation was adopted by AT&T for longwave transatlantic telephone service beginning 7 January 1927. After WW-II, it was developed for military aircraft communication. |
Amplitude modulation | Analysis | Analysis
thumb|391x391px|Illustration of amplitude modulation
The carrier wave (sine wave) of frequency fc and amplitude A is expressed by
.
The message signal, such as an audio signal that is used for modulating the carrier, is m(t), and has a frequency fm, much lower than fc:
,
where m is the amplitude sensitivity, M is the amplitude of modulation. If m < 1, (1 + m(t)/A) is always positive for undermodulation. If m > 1 then overmodulation occurs and reconstruction of message signal from the transmitted signal would lead in loss of original signal. Amplitude modulation results when the carrier c(t) is multiplied by the positive quantity (1 + m(t)/A):
In this simple case m is identical to the modulation index, discussed below. With m = 0.5 the amplitude modulated signal y(t) thus corresponds to the top graph (labelled "50% Modulation") in figure 4.
Using prosthaphaeresis identities, y(t) can be shown to be the sum of three sine waves:
Therefore, the modulated signal has three components: the carrier wave c(t) which is unchanged in frequency, and two sidebands with frequencies slightly above and below the carrier frequency fc. |
Amplitude modulation | Spectrum | Spectrum
thumb|400px|Figure 2: Double-sided spectra of baseband and AM signals.|alt=Diagrams of an AM signal, with formulas
A useful modulation signal m(t) is usually more complex than a single sine wave, as treated above. However, by the principle of Fourier decomposition, m(t) can be expressed as the sum of a set of sine waves of various frequencies, amplitudes, and phases. Carrying out the multiplication of 1 + m(t) with c(t) as above, the result consists of a sum of sine waves. Again, the carrier c(t) is present unchanged, but each frequency component of m at fi has two sidebands at frequencies fc + fi and fc – fi. The collection of the former frequencies above the carrier frequency is known as the upper sideband, and those below constitute the lower sideband. The modulation m(t) may be considered to consist of an equal mix of positive and negative frequency components, as shown in the top of figure 2. One can view the sidebands as that modulation m(t) having simply been shifted in frequency by fc as depicted at the bottom right of figure 2.
thumb|200px|right|Figure 3: The spectrogram of an AM voice broadcast shows the two sidebands (green) on either side of the carrier (red) with time proceeding in the vertical direction.|alt=Sonogram of an AM signal, showing the carrier and both sidebands vertically
The short-term spectrum of modulation, changing as it would for a human voice for instance, the frequency content (horizontal axis) may be plotted as a function of time (vertical axis), as in figure 3. It can again be seen that as the modulation frequency content varies, an upper sideband is generated according to those frequencies shifted above the carrier frequency, and the same content mirror-imaged in the lower sideband below the carrier frequency. At all times, the carrier itself remains constant, and of greater power than the total sideband power. |
Amplitude modulation | Power and spectrum efficiency | Power and spectrum efficiency
The RF bandwidth of an AM transmission (refer to figure 2, but only considering positive frequencies) is twice the bandwidth of the modulating (or "baseband") signal, since the upper and lower sidebands around the carrier frequency each have a bandwidth as wide as the highest modulating frequency. Although the bandwidth of an AM signal is narrower than one using frequency modulation (FM), it is twice as wide as single-sideband techniques; it thus may be viewed as spectrally inefficient. Within a frequency band, only half as many transmissions (or "channels") can thus be accommodated. For this reason analog television employs a variant of single-sideband (known as vestigial sideband, somewhat of a compromise in terms of bandwidth) in order to reduce the required channel spacing.
Another improvement over standard AM is obtained through reduction or suppression of the carrier component of the modulated spectrum. In figure 2 this is the spike in between the sidebands; even with full (100%) sine wave modulation, the power in the carrier component is twice that in the sidebands, yet it carries no unique information. Thus there is a great advantage in efficiency in reducing or totally suppressing the carrier, either in conjunction with elimination of one sideband (single-sideband suppressed-carrier transmission) or with both sidebands remaining (double sideband suppressed carrier). While these suppressed carrier transmissions are efficient in terms of transmitter power, they require more sophisticated receivers employing synchronous detection and regeneration of the carrier frequency. For that reason, standard AM continues to be widely used, especially in broadcast transmission, to allow for the use of inexpensive receivers using envelope detection. Even (analog) television, with a (largely) suppressed lower sideband, includes sufficient carrier power for use of envelope detection. But for communications systems where both transmitters and receivers can be optimized, suppression of both one sideband and the carrier represent a net advantage and are frequently employed.
A technique used widely in broadcast AM transmitters is an application of the Hapburg carrier, first proposed in the 1930s but impractical with the technology then available. During periods of low modulation the carrier power would be reduced and would return to full power during periods of high modulation levels. This has the effect of reducing the overall power demand of the transmitter and is most effective on speech type programmes. Various trade names are used for its implementation by the transmitter manufacturers from the late 80's onwards. |
Amplitude modulation | Modulation index | Modulation index
The AM modulation index is a measure based on the ratio of the modulation excursions of the RF signal to the level of the unmodulated carrier. It is thus defined as:
where and are the modulation amplitude and carrier amplitude, respectively; the modulation amplitude is the peak (positive or negative) change in the RF amplitude from its unmodulated value. Modulation index is normally expressed as a percentage, and may be displayed on a meter connected to an AM transmitter.
So if , carrier amplitude varies by 50% above (and below) its unmodulated level, as is shown in the first waveform, below. For , it varies by 100% as shown in the illustration below it. With 100% modulation the wave amplitude sometimes reaches zero, and this represents full modulation using standard AM and is often a target (in order to obtain the highest possible signal-to-noise ratio) but mustn't be exceeded. Increasing the modulating signal beyond that point, known as overmodulation, causes a standard AM modulator (see below) to fail, as the negative excursions of the wave envelope cannot become less than zero, resulting in distortion ("clipping") of the received modulation. Transmitters typically incorporate a limiter circuit to avoid overmodulation, and/or a compressor circuit (especially for voice communications) in order to still approach 100% modulation for maximum intelligibility above the noise. Such circuits are sometimes referred to as a vogad.
However it is possible to talk about a modulation index exceeding 100%, without introducing distortion, in the case of double-sideband reduced-carrier transmission. In that case, negative excursions beyond zero entail a reversal of the carrier phase, as shown in the third waveform below. This cannot be produced using the efficient high-level (output stage) modulation techniques (see below) which are widely used especially in high power broadcast transmitters. Rather, a special modulator produces such a waveform at a low level followed by a linear amplifier. What's more, a standard AM receiver using an envelope detector is incapable of properly demodulating such a signal. Rather, synchronous detection is required. Thus double-sideband transmission is generally not referred to as "AM" even though it generates an identical RF waveform as standard AM as long as the modulation index is below 100%. Such systems more often attempt a radical reduction of the carrier level compared to the sidebands (where the useful information is present) to the point of double-sideband suppressed-carrier transmission where the carrier is (ideally) reduced to zero. In all such cases the term "modulation index" loses its value as it refers to the ratio of the modulation amplitude to a rather small (or zero) remaining carrier amplitude.
thumb|400px|center|Figure 4: Modulation depth. In the diagram, the unmodulated carrier has an amplitude of 1.|alt=Graphs illustrating how signal intelligibility increases with modulation index, but only up to 100% using standard AM. |
Amplitude modulation | {{anchor | Modulation methods
300px|right|thumb|Anode (plate) modulation. A tetrode's plate and screen grid voltage is modulated via an audio transformer. The resistor R1 sets the grid bias; both the input and output are tuned circuits with inductive coupling.
Modulation circuit designs may be classified as low- or high-level (depending on whether they modulate in a low-power domain—followed by amplification for transmission—or in the high-power domain of the transmitted signal). |
Amplitude modulation | Low-level generation | Low-level generation
In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many types of AM are possible with software control (including DSB with carrier, SSB suppressed-carrier and independent sideband, or ISB). Calculated digital samples are converted to voltages with a digital-to-analog converter, typically at a frequency less than the desired RF-output frequency. The analog signal must then be shifted in frequency and linearly amplified to the desired frequency and power level (linear amplification must be used to prevent modulation distortion).
This low-level method for AM is used in many Amateur Radio transceivers.
AM may also be generated at a low level, using analog methods described in the next section. |
Amplitude modulation | High-level generation | High-level generation
High-power AM transmitters (such as those used for AM broadcasting) are based on high-efficiency class-D and class-E power amplifier stages, modulated by varying the supply voltage.
Older designs (for broadcast and amateur radio) also generate AM by controlling the gain of the transmitter's final amplifier (generally class-C, for efficiency). The following types are for vacuum tube transmitters (but similar options are available with transistors):
Plate modulation In plate modulation, the plate voltage of the RF amplifier is modulated with the audio signal. The audio power requirement is 50 percent of the RF-carrier power.
Heising (constant-current) modulation RF amplifier plate voltage is fed through a choke (high-value inductor). The AM modulation tube plate is fed through the same inductor, so the modulator tube diverts current from the RF amplifier. The choke acts as a constant current source in the audio range. This system has a low power efficiency.
Control grid modulation The operating bias and gain of the final RF amplifier can be controlled by varying the voltage of the control grid. This method requires little audio power, but care must be taken to reduce distortion.
Clamp tube (screen grid) modulation The screen-grid bias may be controlled through a clamp tube, which reduces voltage according to the modulation signal. It is difficult to approach 100-percent modulation while maintaining low distortion with this system.
Doherty modulation One tube provides the power under carrier conditions and another operates only for positive modulation peaks. Overall efficiency is good, and distortion is low.
Outphasing modulation Two tubes are operated in parallel, but partially out of phase with each other. As they are differentially phase modulated their combined amplitude is greater or smaller. Efficiency is good and distortion low when properly adjusted.
Pulse-width modulation (PWM) or pulse-duration modulation (PDM) A highly efficient high voltage power supply is applied to the tube plate. The output voltage of this supply is varied at an audio rate to follow the program. This system was pioneered by Hilmer Swanson and has a number of variations, all of which achieve high efficiency and sound quality.
Digital methods The Harris Corporation obtained a patent for synthesizing a modulated high-power carrier wave from a set of digitally selected low-power amplifiers, running in phase at the same carrier frequency. The input signal is sampled by a conventional audio analog-to-digital converter (ADC), and fed to a digital exciter, which modulates overall transmitter output power by switching a series of low-power solid-state RF amplifiers on and off. The combined output drives the antenna system. |
Amplitude modulation | {{anchor | Demodulation methods
The simplest form of AM demodulator consists of a diode which is configured to act as envelope detector. Another type of demodulator, the product detector, can provide better-quality demodulation with additional circuit complexity. |
Amplitude modulation | See also | See also
Airband
AM stereo
Amplitude modulation signalling system (AMSS)
Double-sideband suppressed-carrier transmission (DSB-SC)
Modulation sphere
Shortwave radio
Types of radio emissions |
Amplitude modulation | References | References |
Amplitude modulation | Bibliography | Bibliography
Newkirk, David and Karlquist, Rick (2004). Mixers, modulators and demodulators. In D. G. Reed (ed.), The ARRL Handbook for Radio Communications (81st ed.), pp. 15.1–15.36. Newington: ARRL. . |
Amplitude modulation | External links | External links
Amplitude Modulation by Jakub Serych, Wolfram Demonstrations Project.
Amplitude Modulation, by S Sastry.
Amplitude Modulation, an introduction by Federation of American Scientists.
Amplitude Modulation tutorial including related topics of modulators, demodulators, etc...
Analog Modulation online interactive demonstration using Python in Google Colab Platform, by C Foh.
Category:Radio modulation modes |
Amplitude modulation | Table of Content | short description, Foundation, Shift keying, Analog telephony, Amplitude reference, ITU type designations, History, Continuous waves, Early technologies, Vacuum tubes, Single-sideband, Analysis, Spectrum, Power and spectrum efficiency, Modulation index, {{anchor, Low-level generation, High-level generation, {{anchor, See also, References, Bibliography, External links |
Augustin-Jean Fresnel | Short description | Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830sDarrigol, 2012, pp. 220–223. until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric (purely refractive) stepped lens, first proposed by Count Buffon and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.
By expressing Huygens's principle of secondary waves and Young's principle of interference in quantitative terms, and supposing that simple colors consist of sinusoidal waves, Fresnel gave the first satisfactory explanation of diffraction by straight edges, including the first satisfactory wave-based explanation of rectilinear propagation.Darrigol, 2012, p. 205. Part of his argument was a proof that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. By further supposing that light waves are purely transverse, Fresnel explained the nature of polarization, the mechanism of chromatic polarization, and the transmission and reflection coefficients at the interface between two transparent isotropic media. Then, by generalizing the direction-speed-polarization relation for calcite, he accounted for the directions and polarizations of the refracted rays in doubly-refractive crystals of the biaxial class (those for which Huygens's secondary wavefronts are not axisymmetric). The period between the first publication of his pure-transverse-wave hypothesis, and the submission of his first correct solution to the biaxial problem, was less than a year.
Later, he coined the terms linear polarization, circular polarization, and elliptical polarization, explained how optical rotation could be understood as a difference in propagation speeds for the two directions of circular polarization, and (by allowing the reflection coefficient to be complex) accounted for the change in polarization due to total internal reflection, as exploited in the Fresnel rhomb. Defenders of the established corpuscular theory could not match his quantitative explanations of so many phenomena on so few assumptions.
Fresnel had a lifelong battle with tuberculosis, to which he succumbed at the age of 39. Although he did not become a public celebrity in his lifetime, he lived just long enough to receive due recognition from his peers, including (on his deathbed) the Rumford Medal of the Royal Society of London, and his name is ubiquitous in the modern terminology of optics and waves. After the wave theory of light was subsumed by Maxwell's electromagnetic theory in the 1860s, some attention was diverted from the magnitude of Fresnel's contribution. In the period between Fresnel's unification of physical optics and Maxwell's wider unification, a contemporary authority, Humphrey Lloyd, described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the domain of physical science, Newton's system of the universe alone excepted." |
Augustin-Jean Fresnel | Early life | Early life
thumb|Monument to Augustin Fresnel on the facade of his birthplace at 2 Rue Augustin Fresnel, Broglie (facing Rue Jean François Mérimée), inaugurated on 14 September 1884. The inscription, when translated, says:"Augustin Fresnel, engineer of Bridges and Roads, member of the Academy of Sciences, creator of lenticular lighthouses, was born in this house on 10 May 1788. The theory of light owes to this emulator of Newton the highest concepts and the most useful applications." |
Augustin-Jean Fresnel | Family | Family
Augustin-Jean Fresnel (also called Augustin Jean or simply Augustin), born in Broglie, Normandy, on 10 May 1788, was the second of four sons of the architect Jacques Fresnel and his wife Augustine, née Mérimée. The family moved twice—in 1789/90 to Cherbourg,Levitt (2013, p. 23) says "in 1790". Silliman (1967, p. 7) says "by 1790". Boutry (1948, p. 590) says the family left Broglie in 1789. and in 1794Silliman, 2008, p. 166. to Jacques's home town of Mathieu, where Augustine would spend 25 years as a widow,Boutry, 1948, p. 590. outliving two of her sons.
The first son, Louis, was admitted to the École Polytechnique, became a lieutenant in the artillery, and was killed in action at Jaca, Spain. The third, Léonor, followed Augustin into civil engineering, succeeded him as secretary of the Lighthouse Commission,Levitt, 2013, p. 99. and helped to edit his collected works.Fresnel, 1866–70. The fourth, Fulgence Fresnel, became a linguist, diplomat, and orientalist, and occasionally assisted Augustin with negotiations.Levitt, 2013, p. 72. Fulgence died in Bagdad in 1855 having led a mission to explore Babylon.
Madame Fresnel's younger brother, Jean François "Léonor" Mérimée, father of the writer Prosper Mérimée, was a painter who turned his attention to the chemistry of painting. He became the Permanent Secretary of the École des Beaux-Arts and (until 1814) a professor at the École Polytechnique,Levitt, 2009, p. 49. and was the initial point of contact between Augustin and the leading optical physicists of the day . |
Augustin-Jean Fresnel | Education | Education
The Fresnel brothers were initially home-schooled by their mother. The sickly Augustin was considered the slow one, not inclined to memorization;Levitt, 2013, pp. 24–25; Buchwald, 1989, p. 111. but the popular story that he hardly began to read until the age of eight is disputed.That age was given by Arago in his elegy (Arago, 1857, p. 402) and widely propagated (Encyclopædia Britannica, 1911; Buchwald, 1989, p. 111; Levitt, 2013, p. 24; etc.). But the reprint of the elegy at the end of Fresnel's collected works bears a footnote, presumably by Léonor Fresnel, saying that "eight" should be "five or six", and regretting "the haste with which we had to collect the notes that were belatedly requested for the biographical part of this speech" (Fresnel, 1866–70, vol. 3, p. 477n). Silliman (1967, p. 9n) accepts the correction. At the age of nine or ten he was undistinguished except for his ability to turn tree-branches into toy bows and guns that worked far too well, earning himself the title l'homme de génie (the man of genius) from his accomplices, and a united crackdown from their elders.Levitt, 2013, p. 25; Arago, 1857, p. 402; Boutry, 1948, pp. 590–591.
In 1801, Augustin was sent to the École Centrale at Caen, as company for Louis. But Augustin lifted his performance: in late 1804 he was accepted into the École Polytechnique, being placed 17th in the entrance examination.Levitt, 2013, pp. 25–26; Silliman, 1967, pp. 9–11. As the detailed records of the École Polytechnique begin in 1808, we know little of Augustin's time there, except that he made few if any friends and—in spite of continuing poor health—excelled in drawing and geometry:Boutry, 1948, p. 592. in his first year he took a prize for his solution to a geometry problem posed by Adrien-Marie Legendre.Silliman, 1967, p. 14; Arago, 1857, p. 403. Fresnel's solution was printed in the Correspondance sur l'École polytechnique, No. 4 (June–July 1805), pp. 78–80, and reprinted in Fresnel, 1866–70, vol. 2, pp. 681–684. Boutry (1948, p. 591) takes this story as referring to the entrance examination. Graduating in 1806, he then enrolled at the École Nationale des Ponts et Chaussées (National School of Bridges and Roads, also known as "ENPC" or "École des Ponts"), from which he graduated in 1809, entering the service of the Corps des Ponts et Chaussées as an ingénieur ordinaire aspirant (ordinary engineer in training). Directly or indirectly, he was to remain in the employment of the "Corps des Ponts" for the rest of his life.Levitt, 2013, pp. 26–27; Silliman, 2008, p. 166; Boutry, 1948, pp. 592,601. |
Augustin-Jean Fresnel | Religious formation | Religious formation
Fresnel's parents were Roman Catholics of the Jansenist sect, characterized by an extreme Augustinian view of original sin. Religion took first place in the boys' home-schooling. In 1802, his mother said:
Augustin remained a Jansenist.Levitt, 2013, p. 24. He regarded his intellectual talents as gifts from God, and considered it his duty to use them for the benefit of others.Kneller, 1911, p. 148. According to his fellow engineer Alphonse Duleau, who helped to nurse him through his final illness, Fresnel saw the study of nature as part of the study of the power and goodness of God. He placed virtue above science and genius. In his last days he prayed for "strength of soul," not against death alone, but against "the interruption of discoveries… of which he hoped to derive useful applications."Kneller, 1911, pp. 148–149n; cf. Arago, 1857, p. 470.
Jansenism is considered heretical by the Roman Catholic Church, and Grattan-Guinness suggests this is why Fresnel never gained a permanent academic teaching post;Grattan-Guinness, 1990, pp. 914–915. his only teaching appointment was at the Athénée in the winter of 1819–20.Fresnel, 1866–70, vol. 1, p. xcvii. The article on Fresnel in the Catholic Encyclopedia does not mention his Jansenism, but describes him as "a deeply religious man and remarkable for his keen sense of duty." |
Augustin-Jean Fresnel | Engineering assignments | Engineering assignments
Fresnel was initially posted to the western département of Vendée. There, in 1811, he anticipated what became known as the Solvay process for producing soda ash, except that recycling of the ammonia was not considered. That difference may explain why leading chemists, who learned of his discovery through his uncle Léonor, eventually thought it uneconomic.Cf. Silliman, 1967, pp. 28–33; Levitt, 2013, p. 29; Buchwald, 1989, pp. 113–114. The surviving correspondence on soda ash extends from August 1811 to April 1812; see Fresnel, 1866–70, vol. 2, pp. 810–817.
thumb|left|Nyons, France, 19th century, drawn by Alexandre Debelle (1805–1897)
About 1812, Fresnel was sent to Nyons, in the southern département of Drôme, to assist with the imperial highway that was to connect Spain and Italy. It is from Nyons that we have the first evidence of his interest in optics. On 15 May 1814, while work was slack due to Napoleon's defeat,Boutry, 1948, pp. 593–594. Fresnel wrote a "P.S." to his brother Léonor, saying in part:
As late as 28 December he was still waiting for information, but by 10 February 1815 he had received Biot's memoir.Boutry, 1948, p. 593; Arago, 1857, pp. 407–408; Fresnel, 1815a. (The Institut de France had taken over the functions of the French Académie des Sciences and other académies in 1795. In 1816 the Académie des Sciences regained its name and autonomy, but remained part of the institute.)
In March 1815, perceiving Napoleon's return from Elba as "an attack on civilization",Arago, 1857, p. 405; Silliman, 2008, p. 166. Arago does not use quotation marks. Fresnel departed without leave, hastened to Toulouse and offered his services to the royalist resistance, but soon found himself on the sick list. Returning to Nyons in defeat, he was threatened and had his windows broken. During the Hundred Days he was placed on suspension, which he was eventually allowed to spend at his mother's house in Mathieu. There he used his enforced leisure to begin his optical experiments.Levitt, 2013, pp. 38–39; Boutry, 1948, p. 594; Arago, 1857, pp. 405–406; Kipnis, 1991, p. 167. |
Augustin-Jean Fresnel | Contributions to physical optics | Contributions to physical optics |
Augustin-Jean Fresnel | Historical context: From Newton to Biot | Historical context: From Newton to Biot
The appreciation of Fresnel's reconstruction of physical optics might be assisted by an overview of the fragmented state in which he found the subject. In this subsection, optical phenomena that were unexplained or whose explanations were disputed are named in bold type.
thumb|Ordinary refraction from a medium of higher wave velocity to a medium of lower wave velocity, as understood by Huygens. Successive positions of the wavefront are shown in blue before refraction, and in green after refraction. For ordinary refraction, the secondary wavefronts (gray curves) are spherical, so that the rays (straight gray lines) are perpendicular to the wavefronts.
The corpuscular theory of light, favored by Isaac Newton and accepted by nearly all of Fresnel's seniors, easily explained rectilinear propagation: the corpuscles obviously moved very fast, so that their paths were very nearly straight. The wave theory, as developed by Christiaan Huygens in his Treatise on Light (1690), explained rectilinear propagation on the assumption that each point crossed by a traveling wavefront becomes the source of a secondary wavefront. Given the initial position of a traveling wavefront, any later position (according to Huygens) was the common tangent surface (envelope) of the secondary wavefronts emitted from the earlier position.Huygens, 1690, tr. Thompson, pp. 20–21. As the extent of the common tangent was limited by the extent of the initial wavefront, the repeated application of Huygens's construction to a plane wavefront of limited extent (in a uniform medium) gave a straight, parallel beam. While this construction indeed predicted rectilinear propagation, it was difficult to reconcile with the common observation that wavefronts on the surface of water can bend around obstructions, and with the similar behavior of sound waves—causing Newton to maintain, to the end of his life, that if light consisted of waves it would "bend and spread every way" into the shadows.Newton, 1730, p. 362.
Huygens's theory neatly explained the law of ordinary reflection and the law of ordinary refraction ("Snell's law"), provided that the secondary waves traveled slower in denser media (those of higher refractive index).Huygens, 1690, tr. Thompson, pp. 22–38. The corpuscular theory, with the hypothesis that the corpuscles were subject to forces acting perpendicular to surfaces, explained the same laws equally well,Darrigol, 2012, pp. 93–94,103. albeit with the implication that light traveled faster in denser media; that implication was wrong, but could not be directly disproven with the technology of Newton's time or even Fresnel's time .
Similarly inconclusive was stellar aberration—that is, the apparent change in the position of a star due to the velocity of the earth across the line of sight (not to be confused with stellar parallax, which is due to the displacement of the earth across the line of sight). Identified by James Bradley in 1728, stellar aberration was widely taken as confirmation of the corpuscular theory. But it was equally compatible with the wave theory, as Euler noted in 1746—tacitly assuming that the aether (the supposed wave-bearing medium) near the earth was not disturbed by the motion of the earth.Darrigol, 2012, pp. 129–130,258.
The outstanding strength of Huygens's theory was his explanation of the birefringence (double refraction) of "Iceland crystal" (transparent calcite), on the assumption that the secondary waves are spherical for the ordinary refraction (which satisfies Snell's law) and spheroidal for the extraordinary refraction (which does not).Huygens, 1690, tr. Thompson, pp. 52–105. In general, Huygens's common-tangent construction implies that rays are paths of least time between successive positions of the wavefront, in accordance with Fermat's principle.Young, 1855, pp. 225–226,229. In the special case of isotropic media, the secondary wavefronts must be spherical, and Huygens's construction then implies that the rays are perpendicular to the wavefront; indeed, the law of ordinary refraction can be separately derived from that premise, as Ignace-Gaston Pardies did before Huygens.Darrigol, 2012, pp. 62–64.
thumb|left|Altered colors of skylight reflected in a soap bubble, due to thin-film interference (formerly called "thin-plate" interference)
Although Newton rejected the wave theory, he noticed its potential to explain colors, including the colors of "thin plates" (e.g., "Newton's rings", and the colors of skylight reflected in soap bubbles), on the assumption that light consists of periodic waves, with the lowest frequencies (longest wavelengths) at the red end of the spectrum, and the highest frequencies (shortest wavelengths) at the violet end. In 1672 he published a heavy hint to that effect,Darrigol, 2012, p. 87. but contemporary supporters of the wave theory failed to act on it: Robert Hooke treated light as a periodic sequence of pulses but did not use frequency as the criterion of color,Darrigol, 2012, pp. 53–56. while Huygens treated the waves as individual pulses without any periodicity;Huygens, 1690, tr. Thompson, p. 17. and Pardies died young in 1673. Newton himself tried to explain colors of thin plates using the corpuscular theory, by supposing that his corpuscles had the wavelike property of alternating between "fits of easy transmission" and "fits of easy reflection",Darrigol, 2012, pp. 98–100; Newton, 1730, p. 281. the distance between like "fits" depending on the color and the mediumNewton, 1730, p. 284. and, awkwardly, on the angle of refraction or reflection into that medium.Newton, 1730, pp. 283,287. More awkwardly still, this theory required thin plates to reflect only at the back surface, although thick plates manifestly reflected also at the front surface.Newton, 1730, pp. 279,281–282. It was not until 1801 that Thomas Young, in the Bakerian Lecture for that year, cited Newton's hint, and accounted for the colors of a thin plate as the combined effect of the front and back reflections, which reinforce or cancel each other according to the wavelength and the thickness. Young similarly explained the colors of "striated surfaces" (e.g., gratings) as the wavelength-dependent reinforcement or cancellation of reflections from adjacent lines. He described this reinforcement or cancellation as interference.
thumb|Thomas Young (1773–1829)
Neither Newton nor Huygens satisfactorily explained diffraction—the blurring and fringing of shadows where, according to rectilinear propagation, they ought to be sharp. Newton, who called diffraction "inflexion", supposed that rays of light passing close to obstacles were bent ("inflected"); but his explanation was only qualitative.Darrigol, 2012, pp. 101–102; Newton, 1730, Book , Part . Huygens's common-tangent construction, without modifications, could not accommodate diffraction at all. Two such modifications were proposed by Young in the same 1801 Bakerian Lecture: first, that the secondary waves near the edge of an obstacle could diverge into the shadow, but only weakly, due to limited reinforcement from other secondary waves; and second, that diffraction by an edge was caused by interference between two rays: one reflected off the edge, and the other inflected while passing near the edge. The latter ray would be undeviated if sufficiently far from the edge, but Young did not elaborate on that case. These were the earliest suggestions that the degree of diffraction depends on wavelength.Darrigol, 2012, pp. 177–179. Later, in the 1803 Bakerian Lecture, Young ceased to regard inflection as a separate phenomenon,Young, 1855, p. 188. and produced evidence that diffraction fringes inside the shadow of a narrow obstacle were due to interference: when the light from one side was blocked, the internal fringes disappeared.Young, 1855, pp. 179–181. But Young was alone in such efforts until Fresnel entered the field.Darrigol, 2012, p. 187.
Huygens, in his investigation of double refraction, noticed something that he could not explain: when light passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second; but when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa.Huygens, 1690, tr. Thompson, pp. 92–94. For simplicity, the above text describes a special case; Huygens's description has greater generality. This discovery gave Newton another reason to reject the wave theory: rays of light evidently had "sides".Newton, 1730, pp. 358–361. Corpuscles could have sidesNewton, 1730, pp. 373–374. (or poles, as they would later be called); but waves of light could not,Newton, 1730, p. 363. because (so it seemed) any such waves would need to be longitudinal (with vibrations in the direction of propagation). Newton offered an alternative "Rule" for the extraordinary refraction,Newton, 1730, p. 356. which rode on his authority through the 18th century, although he made "no known attempt to deduce it from any principles of optics, corpuscular or otherwise."
thumb|left|Étienne-Louis Malus (1775–1812)
In 1808, the extraordinary refraction of calcite was investigated experimentally, with unprecedented accuracy, by Étienne-Louis Malus, and found to be consistent with Huygens's spheroid construction, not Newton's "Rule". Malus, encouraged by Pierre-Simon Laplace, then sought to explain this law in corpuscular terms: from the known relation between the incident and refracted ray directions, Malus derived the corpuscular velocity (as a function of direction) that would satisfy Maupertuis's "least action" principle. But, as Young pointed out, the existence of such a velocity law was guaranteed by Huygens's spheroid, because Huygens's construction leads to Fermat's principle, which becomes Maupertuis's principle if the ray speed is replaced by the reciprocal of the particle speed! The corpuscularists had not found a force law that would yield the alleged velocity law, except by a circular argument in which a force acting at the surface of the crystal inexplicably depended on the direction of the (possibly subsequent) velocity within the crystal. Worse, it was doubtful that any such force would satisfy the conditions of Maupertuis's principle.Frankel (1974) and Young (1855, pp. 225–228) debunk Laplace's claim to have established the existence of such a force. Fresnel (1827, tr. Hobson, pp. 239–241) more comprehensively addresses the mechanical difficulties of this claim. Admittedly, the particular statement that he attributes to Laplace is not found in the relevant passage from Laplace's writings (appended to Fresnel's memoir by the translator), which is similar to the passage previously demolished by Young; however, an equivalent statement is found in the works of Malus (Mémoires de Physique et de Chimie, de la Société d'Arcueil, vol. 2, 1809, p. 266, quoted in translation by Silliman, 1967, p. 131). In contrast, Young proceeded to show that "a medium more easily compressible in one direction than in any direction perpendicular to it, as if it consisted of an infinite number of parallel plates connected by a substance somewhat less elastic" admits spheroidal longitudinal wavefronts, as Huygens supposed.Young, 1855, pp. 228–232; cf. Whewell, 1857, p. 329.
thumb|300px|Printed label seen through a doubly-refracting calcite crystal and a modern polarizing filter (rotated to show the different polarizations of the two images)
But Malus, in the midst of his experiments on double refraction, noticed something else: when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like one of the two rays emerging from a calcite crystal.Darrigol, 2012, pp. 191–192; Silliman, 1967, pp. 125–127. It was Malus who coined the term polarization to describe this behavior, although the polarizing angle became known as Brewster's angle after its dependence on the refractive index was determined experimentally by David Brewster in 1815. Malus also introduced the term plane of polarization. In the case of polarization by reflection, his "plane of polarization" was the plane of the incident and reflected rays; in modern terms, this is the plane normal to the electric vibration. In 1809, Malus further discovered that the intensity of light passing through two polarizers is proportional to the squared cosine of the angle between their planes of polarization (Malus's law),Darrigol, 2012, p. 192; Silliman, 1967, p. 128. whether the polarizers work by reflection or double refraction, and that all birefringent crystals produce both extraordinary refraction and polarization.Young, 1855, pp. 249–250. As the corpuscularists started trying to explain these things in terms of polar "molecules" of light, the wave-theorists had no working hypothesis on the nature of polarization, prompting Young to remark that Malus's observations "present greater difficulties to the advocates of the undulatory theory than any other facts with which we are acquainted."Young, 1855, p. 233.
Malus died in February 1812, at the age of 36, shortly after receiving the Rumford Medal for his work on polarization.
In August 1811, François Arago reported that if a thin plate of mica was viewed against a white polarized backlight through a calcite crystal, the two images of the mica were of complementary colors (the overlap having the same color as the background). The light emerging from the mica was "depolarized" in the sense that there was no orientation of the calcite that made one image disappear; yet it was not ordinary ("unpolarized") light, for which the two images would be of the same color. Rotating the calcite around the line of sight changed the colors, though they remained complementary. Rotating the mica changed the saturation (not the hue) of the colors. This phenomenon became known as chromatic polarization. Replacing the mica with a much thicker plate of quartz, with its faces perpendicular to the optic axis (the axis of Huygens's spheroid or Malus's velocity function), produced a similar effect, except that rotating the quartz made no difference. Arago tried to explain his observations in corpuscular terms.Levitt, 2009, p. 37; Darrigol, 2012, pp. 193–194,290.
thumb|left|François Arago (1786–1853)
In 1812, as Arago pursued further qualitative experiments and other commitments, Jean-Baptiste Biot reworked the same ground using a gypsum lamina in place of the mica, and found empirical formulae for the intensities of the ordinary and extraordinary images. The formulae contained two coefficients, supposedly representing colors of rays "affected" and "unaffected" by the plate—the "affected" rays being of the same color mix as those reflected by amorphous thin plates of proportional, but lesser, thickness.Darrigol, 2012, pp. 194–195 (ordinary intensity); Frankel, 1976, p. 148 (both intensities).
thumb|Jean-Baptiste Biot (1774–1862)
Arago protested, declaring that he had made some of the same discoveries but had not had time to write them up. In fact the overlap between Arago's work and Biot's was minimal, Arago's being only qualitative and wider in scope (attempting to include polarization by reflection). But the dispute triggered a notorious falling-out between the two men.Buchwald, 1989, pp. 79–88; Levitt, 2009, pp. 33–54.
Later that year, Biot tried to explain the observations as an oscillation of the alignment of the "affected" corpuscles at a frequency proportional to that of Newton's "fits", due to forces depending on the alignment. This theory became known as mobile polarization. To reconcile his results with a sinusoidal oscillation, Biot had to suppose that the corpuscles emerged with one of two permitted orientations, namely the extremes of the oscillation, with probabilities depending on the phase of the oscillation.Frankel, 1976, pp. 149–150; Buchwald, 1989, pp. 99–103; Darrigol, 2012, pp. 195–196. Corpuscular optics was becoming expensive on assumptions. But in 1813, Biot reported that the case of quartz was simpler: the observable phenomenon (now called optical rotation or optical activity or sometimes rotary polarization) was a gradual rotation of the polarization direction with distance, and could be explained by a corresponding rotation (not oscillation) of the corpuscles.Frankel, 1976, pp. 151–152; Darrigol, 2012, p. 196.
Early in 1814, reviewing Biot's work on chromatic polarization, Young noted that the periodicity of the color as a function of the plate thickness—including the factor by which the period exceeded that for a reflective thin plate, and even the effect of obliquity of the plate (but not the role of polarization)—could be explained by the wave theory in terms of the different propagation times of the ordinary and extraordinary waves through the plate.Young, 1855, pp. 269–272. But Young was then the only public defender of the wave theory.Frankel, 1976, p. 176; cf. Silliman, 1967, pp. 142–143.
In summary, in the spring of 1814, as Fresnel tried in vain to guess what polarization was, the corpuscularists thought that they knew, while the wave-theorists (if we may use the plural) literally had no idea. Both theories claimed to explain rectilinear propagation, but the wave explanation was overwhelmingly regarded as unconvincing. The corpuscular theory could not rigorously link double refraction to surface forces; the wave theory could not yet link it to polarization. The corpuscular theory was weak on thin plates and silent on gratings;Newton (1730) observed feathers acting as reflection gratings and as a transmission gratings, but classified the former case under thin plates (p. 252), and the latter, more vaguely, under inflection (p. 322). In retrospect, the latter experiment (p. 322, end of Obs. 2) is dangerous to eyesight and should not be repeated as written. the wave theory was strong on both, but under-appreciated. Concerning diffraction, the corpuscular theory did not yield quantitative predictions, while the wave theory had begun to do so by considering diffraction as a manifestation of interference, but had only considered two rays at a time. Only the corpuscular theory gave even a vague insight into Brewster's angle, Malus's law, or optical rotation. Concerning chromatic polarization, the wave theory explained the periodicity far better than the corpuscular theory, but had nothing to say about the role of polarization; and its explanation of the periodicity was largely ignored.Frankel, 1976, p. 155. And Arago had founded the study of chromatic polarization, only to lose the lead, controversially, to Biot. Such were the circumstances in which Arago first heard of Fresnel's interest in optics. |
Augustin-Jean Fresnel | Rêveries | Rêveries
thumb|Bas-relief of Fresnel's uncle Léonor Mérimée (1757–1836), on the same wall as the Fresnel monument in Broglie
Fresnel's letters from later in 1814 reveal his interest in the wave theory, including his awareness that it explained the constancy of the speed of light and was at least compatible with stellar aberration. Eventually he compiled what he called his rêveries (musings) into an essay and submitted it via Léonor Mérimée to André-Marie Ampère, who did not respond directly. But on 19 December, Mérimée dined with Ampère and Arago, with whom he was acquainted through the École Polytechnique; and Arago promised to look at Fresnel's essay.Buchwald, 1989, pp. 116–117; Silliman, 1967, pp. 40–45; Fresnel, 1866–70, vol. 2, p. 831; Levitt, 2009, p. 49.The story that Ampère lost the essay (propagated from Boutry, 1948, p. 593?) is implicitly contradicted by Darrigol (2012, p. 198), Buchwald (1989, p. 117), Mérimée's letter to Fresnel dated 20 December 1814 (in Fresnel, 1866–70, vol. 2, pp. 830–831), and two footnotes in Fresnel's collected works (Fresnel, 1866–70, vol. 1, pp. xxix–xxx, note 4, and p. 6n).
In mid 1815, on his way home to Mathieu to serve his suspension, Fresnel met Arago in Paris and spoke of the wave theory and stellar aberration. He was informed that he was trying to break down open doors ("il enfonçait des portes ouvertes"), and directed to classical works on optics.Boutry, 1948, pp. 594–595. |
Augustin-Jean Fresnel | Diffraction | Diffraction |
Augustin-Jean Fresnel | First attempt (1815) | First attempt (1815)
On 12 July 1815, as Fresnel was about to leave Paris, Arago left him a note on a new topic:
Fresnel would not have ready access to these works outside Paris, and could not read English.Fresnel, 1866–70, vol. 1, pp. 6–7. But, in Mathieu—with a point-source of light made by focusing sunlight with a drop of honey, a crude micrometer of his own construction, and supporting apparatus made by a local locksmith—he began his own experiments.Fresnel, 1866–70, vol. 1, pp. xxxi (micrometer, locksmith , supports), 6n (locksmith); Buchwald, 1989, pp. 122 (honey drop), 125–126 (micrometer, with diagram); Boutry 1948, p. 595 and Levitt, 2013, p. 40 (locksmith, honey drop, micrometer); Darrigol 2012, pp. 198–199 (locksmith, honey drop). His technique was novel: whereas earlier investigators had projected the fringes onto a screen, Fresnel soon abandoned the screen and observed the fringes in space, through a lens with the micrometer at its focus, allowing more accurate measurements while requiring less light.Buchwald, 1989, pp. 122,126; Silliman, 1967, pp. 147–149.
Later in July, after Napoleon's final defeat, Fresnel was reinstated with the advantage of having backed the winning side. He requested a two-month leave of absence, which was readily granted because roadworks were in abeyance.Levitt, 2013, pp. 39,239.
On 23 September he wrote to Arago, beginning "I think I have found the explanation and the law of colored fringes which one notices in the shadows of bodies illuminated by a luminous point." In the same paragraph, however, Fresnel implicitly acknowledged doubt about the novelty of his work: noting that he would need to incur some expense in order to improve his measurements, he wanted to know "whether this is not useless, and whether the law of diffraction has not already been established by sufficiently exact experiments."Kipnis, 1991, p. 167; Fresnel, 1866–70, vol. 1, pp. 5–6. He explained that he had not yet had a chance to acquire the items on his reading lists, with the apparent exception of "Young's book", which he could not understand without his brother's help.Darrigol, 2012, p. 198. Silliman (1967, p. 146) identifies the brother as Fulgence, then in Paris; cf. Fresnel, 1866–70, vol. 1, p. 7n."Young's book", which Fresnel distinguished from the Philosophical Transactions, is presumably A Course of Lectures on Natural Philosophy and the Mechanical Arts (2 volumes, 1807). In vol. 1, the relevant illustrations are Plate (facing p. 777), including the famous two-source interference pattern (Fig. 267), and Plate (facing p. 787), including the hyperbolic paths of the fringes in that pattern (Fig. 442) followed by sketches of other diffraction patterns and thin-plate patterns, with no visual hints on their physical causes. In vol. 2, which includes the Bakerian lectures from the Philosophical Transactions, Fig. 108 (p. 632) shows just one case of an undeviated direct ray intersecting a reflected ray. Not surprisingly, he had retraced many of Young's steps.
In a memoir sent to the institute on 15 October 1815, Fresnel mapped the external and internal fringes in the shadow of a wire. He noticed, like Young before him, that the internal fringes disappeared when the light from one side was blocked, and concluded that "the vibrations of two rays that cross each other under a very small angle can contradict each other…"Darrigol, 2012, p. 199. But, whereas Young took the disappearance of the internal fringes as confirmation of the principle of interference, Fresnel reported that it was the internal fringes that first drew his attention to the principle. To explain the diffraction pattern, Fresnel constructed the internal fringes by considering the intersections of circular wavefronts emitted from the two edges of the obstruction, and the external fringes by considering the intersections between direct waves and waves reflected off the nearer edge. For the external fringes, to obtain tolerable agreement with observation, he had to suppose that the reflected wave was inverted; and he noted that the predicted paths of the fringes were hyperbolic. In the part of the memoir that most clearly surpassed Young, Fresnel explained the ordinary laws of reflection and refraction in terms of interference, noting that if two parallel rays were reflected or refracted at other than the prescribed angle, they would no longer have the same phase in a common perpendicular plane, and every vibration would be cancelled by a nearby vibration. He noted that his explanation was valid provided that the surface irregularities were much smaller than the wavelength.Buchwald, 1989, pp. 119,131–132; Darrigol, 2012, pp. 199–201; Kipnis, 1991, pp. 175–176.
On 10 November, Fresnel sent a supplementary note dealing with Newton's rings and with gratings,Darrigol, 2012, p. 201. including, for the first time, transmission gratings—although in that case the interfering rays were still assumed to be "inflected", and the experimental verification was inadequate because it used only two threads.Fresnel, 1866–70, vol. 1, pp. 48–49; Kipnis, 1991, pp. 176–178.
As Fresnel was not a member of the institute, the fate of his memoir depended heavily on the report of a single member. The reporter for Fresnel's memoir turned out to be Arago (with Poinsot as the other reviewer).Frankel, 1976, p. 158; Fresnel, 1866–70, vol. 1, p. 9n. On 8 November, Arago wrote to Fresnel:
Fresnel was troubled, wanting to know more precisely where he had collided with Young.Buchwald, 1989, pp. 137–139. Concerning the curved paths of the "colored bands", Young had noted the hyperbolic paths of the fringes in the two-source interference pattern, corresponding roughly to Fresnel's internal fringes, and had described the hyperbolic fringes that appear on the screen within rectangular shadows.Young, 1807, vol. 1, p. 787 & Figs. 442,445; Young, 1855, pp. 180–181,184. He had not mentioned the curved paths of the external fringes of a shadow; but, as he later explained,Young to Arago (in English), 12 January 1817, in Young, 1855, pp. 380–384, at p. 381; quoted in Silliman, 1967, p. 171. that was because Newton had already done so.Newton, 1730, p. 321, Fig. 1, where the straight rays contribute to the curved path of a fringe, so that the same fringe is made by different rays at different distances from the obstacle (cf. Darrigol, 2012, p. 101, Fig. 3.11 – where, in the caption, "1904" should be "1704" and "" should be ""). Newton evidently thought the fringes were caustics. Thus Arago erred in his belief that the curved paths of the fringes were fundamentally incompatible with the corpuscular theory.Kipnis, 1991, pp. 204–205.
Arago's letter went on to request more data on the external fringes. Fresnel complied, until he exhausted his leave and was assigned to Rennes in the département of Ille-et-Vilaine. At this point Arago interceded with Gaspard de Prony, head of the École des Ponts, who wrote to Louis-Mathieu Molé, head of the Corps des Ponts, suggesting that the progress of science and the prestige of the Corps would be enhanced if Fresnel could come to Paris for a time. He arrived in March 1816, and his leave was subsequently extended through the middle of the year.Silliman, 1967, pp. 163–164; Frankel, 1976, p. 158; Boutry, 1948, p. 597; Levitt, 2013, pp. 41–43,239.
Meanwhile, in an experiment reported on 26 February 1816, Arago verified Fresnel's prediction that the internal fringes were shifted if the rays on one side of the obstacle passed through a thin glass lamina. Fresnel correctly attributed this phenomenon to the lower wave velocity in the glass.Silliman, 1967, pp. 165–166; Buchwald, 1989, p. 137; Kipnis, 1991, pp. 178,207,213. Arago later used a similar argument to explain the colors in the scintillation of stars.Silliman (1967, p. 163) and Frankel (1976, p. 156) give the date of Arago's note on scintillation as 1814; but the sequence of events implies 1816, in agreement with Darrigol (2012, pp. 201,290). Kipnis (1991, pp. 202–203,206) proves the later date and explains the origin and propagation of the incorrect earlier date.
Fresnel's updated memoirFresnel, 1816. was eventually published in the March 1816 issue of Annales de Chimie et de Physique, of which Arago had recently become co-editor.Darrigol, 2012, p. 201; Frankel, 1976, p. 159. That issue did not actually appear until May.Kipnis, 1991, pp. 166n,214n. In March, Fresnel already had competition: Biot read a memoir on diffraction by himself and his student Claude Pouillet, containing copious data and arguing that the regularity of diffraction fringes, like the regularity of Newton's rings, must be linked to Newton's "fits". But the new link was not rigorous, and Pouillet himself would become a distinguished early adopter of the wave theory.Kipnis, 1991, pp. 212–214; Frankel, 1976, pp. 159–160,173. |
Augustin-Jean Fresnel | "Efficacious ray", double-mirror experiment (1816) | "Efficacious ray", double-mirror experiment (1816)
thumb|307px|Replica of Young's two-source interference diagram (1807), with sources A and B producing minima at C, D, E, and FCf. Young, 1807, vol. 1, p. 777 & Fig. 267.
thumb|307px|Fresnel's double mirror (1816). The mirror segments M1 and M2 produce virtual images S1 and S2 of the slit S. In the shaded region, the beams from the two virtual images overlap and interfere in the manner of Young (above).
On 24 May 1816, Fresnel wrote to Young (in French), acknowledging how little of his own memoir was new.Darrigol, 2012, p. 201; the letter is printed in Young, 1855, pp. 376–378, and its conclusion is translated by Silliman (1967, p. 170). But in a "supplement" signed on 14 July and read the next day,Fresnel, 1866–70, vol. 1, pp. 129–170. Fresnel noted that the internal fringes were more accurately predicted by supposing that the two interfering rays came from some distance outside the edges of the obstacle. To explain this, he divided the incident wavefront at the obstacle into what we now call Fresnel zones, such that the secondary waves from each zone were spread over half a cycle when they arrived at the observation point. The zones on one side of the obstacle largely canceled out in pairs, except the first zone, which was represented by an "efficacious ray". This approach worked for the internal fringes, but the superposition of the efficacious ray and the direct ray did not work for the external fringes.Silliman, 1967, pp. 177–179; Darrigol, 2012, pp. 201–203.
The contribution from the "efficacious ray" was thought to be only partly canceled, for reasons involving the dynamics of the medium: where the wavefront was continuous, symmetry forbade oblique vibrations; but near the obstacle that truncated the wavefront, the asymmetry allowed some sideways vibration towards the geometric shadow. This argument showed that Fresnel had not (yet) fully accepted Huygens's principle, which would have permitted oblique radiation from all portions of the front.Buchwald, 1989, pp. 134–135,144–145; Silliman, 1967, pp. 176–177.
In the same supplement, Fresnel described his well-known double mirror, comprising two flat mirrors joined at an angle of slightly less than 180°, with which he produced a two-slit interference pattern from two virtual images of the same slit. A conventional double-slit experiment required a preliminary single slit to ensure that the light falling on the double slit was coherent (synchronized). In Fresnel's version, the preliminary single slit was retained, and the double slit was replaced by the double mirror—which bore no physical resemblance to the double slit and yet performed the same function. This result (which had been announced by Arago in the March issue of the Annales) made it hard to believe that the two-slit pattern had anything to do with corpuscles being deflected as they passed near the edges of the slits.Silliman, 1967, pp. 173–175; Buchwald, 1989, pp. 137–138; Darrigol, 2012, pp. 201–2; Boutry, 1948, p. 597; Fresnel, 1866–70, vol. 1, pp. 123–128 (Arago's announcement).
But 1816 was the "Year Without a Summer": crops failed; hungry farming families lined the streets of Rennes; the central government organized "charity workhouses" for the needy; and in October, Fresnel was sent back to Ille-et-Vilaine to supervise charity workers in addition to his regular road crew.Levitt, 2013, p. 43; Boutry, 1948, p. 599. According to Arago,
Fresnel's letters from December 1816 reveal his consequent anxiety. To Arago he complained of being "tormented by the worries of surveillance, and the need to reprimand…" And to Mérimée he wrote: "I find nothing more tiresome than having to manage other men, and I admit that I have no idea what I'm doing."Levitt, 2013, pp. 28,237. |
Augustin-Jean Fresnel | Prize memoir (1818) and sequel | Prize memoir (1818) and sequel
On 17 March 1817, the Académie des Sciences announced that diffraction would be the topic for the biannual physics Grand Prix to be awarded in 1819.Kipnis, 1991, p. 218; Buchwald, 2013, p. 453; Levitt, 2013, p. 44. Frankel (1976, pp. 160–161) and Grattan-Guinness (1990, p. 867) note that the topic was first proposed on 10 February 1817. Darrigol alone (2012, p. 203) says that the competition was "opened" on 17 March 1818. Prizes were offered in odd-numbered years for physics and in even-numbered years for mathematics (Frankel, 1974, p. 224n). The deadline for entries was set at 1 August 1818 to allow time for replication of experiments. Although the wording of the problem referred to rays and inflection and did not invite wave-based solutions, Arago and Ampère encouraged Fresnel to enter.Buchwald, 1989, pp. 169–171; Frankel, 1976, p. 161; Silliman, 1967, pp. 183–184; Fresnel, 1866–70, vol. 1, pp. xxxvi–xxxvii.
In the fall of 1817, Fresnel, supported by de Prony, obtained a leave of absence from the new head of the Corp des Ponts, Louis Becquey, and returned to Paris.Fresnel, 1866–70, vol. 1, p. xxxv; Levitt, 2013, p. 44. He resumed his engineering duties in the spring of 1818; but from then on he was based in Paris,Silliman, 2008, p. 166; Frankel, 1976, p. 159. first on the Canal de l'Ourcq,Fresnel, 1866–70, vol. 1, pp. xxxv,xcvi; Boutry, 1948, pp. 599,601. Silliman (1967, p. 180) gives the starting date as 1 May 1818. and then (from May 1819) with the cadastre of the pavements.Fresnel, 1866–70, vol. 1, p. xcvi; Arago, 1857, p. 466.
On 15 January 1818, in a different context (revisited below), Fresnel showed that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. His method was similar to the phasor representation, except that the "forces" were plane vectors rather than complex numbers; they could be added, and multiplied by scalars, but not (yet) multiplied and divided by each other. The explanation was algebraic rather than geometric.
Knowledge of this method was assumed in a preliminary note on diffraction,Printed in Fresnel, 1866–70, vol. 1, pp. 171–181. dated 19 April 1818 and deposited on 20 April, in which Fresnel outlined the elementary theory of diffraction as found in modern textbooks. He restated Huygens's principle in combination with the superposition principle, saying that the vibration at each point on a wavefront is the sum of the vibrations that would be sent to it at that moment by all the elements of the wavefront in any of its previous positions, all elements acting separately . For a wavefront partly obstructed in a previous position, the summation was to be carried out over the unobstructed portion. In directions other than the normal to the primary wavefront, the secondary waves were weakened due to obliquity, but weakened much more by destructive interference, so that the effect of obliquity alone could be ignored.Cf. Fresnel, 1866–70, vol. 1, pp. 174–175; Buchwald, 1989, pp. 157–158. For diffraction by a straight edge, the intensity as a function of distance from the geometric shadow could then be expressed with sufficient accuracy in terms of what are now called the normalized Fresnel integrals:
307px|thumb|Normalized Fresnel integrals C(x),S(x)
307px|thumb|Diffraction fringes near the limit of the geometric shadow of a straight edge. Light intensities were calculated from the values of the normalized integrals C(x),S(x)
The same note included a table of the integrals, for an upper limit ranging from 0 to 5.1 in steps of 0.1, computed with a mean error of 0.0003,Buchwald, 1989, p. 167; 2013, p. 454. plus a smaller table of maxima and minima of the resulting intensity.
In his final "Memoir on the diffraction of light",Fresnel, 1818b. deposited on 29 JulySee Fresnel, 1818b, in Mémoires de l'Académie Royale des Sciences…, vol. , p. 339n, and in Fresnel, 1866–70, vol. 1, p. 247, note1. and bearing the Latin epigraph "Natura simplex et fecunda" ("Nature simple and fertile"),Fresnel, 1866–70, vol. 1, p. 247; Crew, 1900, p. 79; Levitt, 2013, p. 46. Fresnel slightly expanded the two tables without changing the existing figures, except for a correction to the first minimum of intensity. For completeness, he repeated his solution to "the problem of interference", whereby sinusoidal functions are added like vectors. He acknowledged the directionality of the secondary sources and the variation in their distances from the observation point, chiefly to explain why these things make negligible difference in the context, provided of course that the secondary sources do not radiate in the retrograde direction. Then, applying his theory of interference to the secondary waves, he expressed the intensity of light diffracted by a single straight edge (half-plane) in terms of integrals which involved the dimensions of the problem, but which could be converted to the normalized forms above. With reference to the integrals, he explained the calculation of the maxima and minima of the intensity (external fringes), and noted that the calculated intensity falls very rapidly as one moves into the geometric shadow.Crew, 1900, pp. 101–108 (vector-like representation), 109 (no retrograde radiation), 110–111 (directionality and distance), 118–122 (derivation of integrals), 124–125 (maxima & minima), 129–131 (geometric shadow). The last result, as Olivier Darrigol says, "amounts to a proof of the rectilinear propagation of light in the wave theory, indeed the first proof that a modern physicist would still accept."Darrigol, 2012, pp. 204–205.
For the experimental testing of his calculations, Fresnel used red light with a wavelength of 638nm, which he deduced from the diffraction pattern in the simple case in which light incident on a single slit was focused by a cylindrical lens. For a variety of distances from the source to the obstacle and from the obstacle to the field point, he compared the calculated and observed positions of the fringes for diffraction by a half-plane, a slit, and a narrow strip—concentrating on the minima, which were visually sharper than the maxima. For the slit and the strip, he could not use the previously computed table of maxima and minima; for each combination of dimensions, the intensity had to be expressed in terms of sums or differences of Fresnel integrals and calculated from the table of integrals, and the extrema had to be calculated anew.Crew, 1900, pp. 127–128 (wavelength), 129–131 (half-plane), 132–135 (extrema, slit); Fresnel, 1866–70, vol. 1, pp. 350–355 (narrow strip). The agreement between calculation and measurement was better than 1.5% in almost every case.Buchwald, 1989, pp. 179–182.
Near the end of the memoir, Fresnel summed up the difference between Huygens's use of secondary waves and his own: whereas Huygens says there is light only where the secondary waves exactly agree, Fresnel says there is complete darkness only where the secondary waves exactly cancel out.Crew, 1900, p. 144.
thumb|left|Siméon Denis Poisson (1781–1840)
The judging committee comprised Laplace, Biot, and Poisson (all corpuscularists), Gay-Lussac (uncommitted), and Arago, who eventually wrote the committee's report.Fresnel, 1866–70, vol. 1, p. xlii; Worrall, 1989, p. 136; Buchwald, 1989, pp. 171,183; Levitt, 2013, pp. 45–46. Although entries in the competition were supposed to be anonymous to the judges, Fresnel's must have been recognizable by the content.Levitt, 2013, p. 46. There was only one other entry, of which neither the manuscript nor any record of the author has survived.Frankel, 1976, p. 162. However, Kipnis (1991, pp. 222–224) offers evidence that the unsuccessful entrant was Honoré Flaugergues (1755–1830?) and that the essence of his entry is contained in a "supplement" published in Journal de Physique, vol. 89 (September 1819), pp. 161–186. That entry (identified as "no.1") was mentioned only in the last paragraph of the judges' report,Fresnel, 1866–70, vol. 1, pp. 236–237. noting that the author had shown ignorance of the relevant earlier works of Young and Fresnel, used insufficiently precise methods of observation, overlooked known phenomena, and made obvious errors. In the words of John Worrall, "The competition facing Fresnel could hardly have been less stiff."Worrall, 1989, pp. 139–140. We may infer that the committee had only two options: award the prize to Fresnel ("no. 2"), or withhold it.Cf. Worrall, 1989, p. 141.
thumb|Shadow cast by a 5.8mm-diameter obstacle on a screen 183cm behind, in sunlight passing through a pinhole 153cm in front. The faint colors of the fringes show the wavelength-dependence of the diffraction pattern. In the center is Poisson's/Arago's spot.
The committee deliberated into the new year. Then Poisson, exploiting a case in which Fresnel's theory gave easy integrals, predicted that if a circular obstacle were illuminated by a point-source, there should be (according to the theory) a bright spot in the center of the shadow, illuminated as brightly as the exterior. This seems to have been intended as a reductio ad absurdum. Arago, undeterred, assembled an experiment with an obstacle 2mm in diameter—and there, in the center of the shadow, was Poisson's spot.Darrigol, 2012, p. 205; Fresnel, 1866–70, vol. 1, p. xlii.
The unanimousFresnel, 1866–70, vol. 1, p. xlii; Worrall, 1989, p. 141. report of the committee,Fresnel, 1866–70, vol. 1, pp. 229–246. read at the meeting of the Académie on 15 March 1819,Fresnel, 1866–70, vol. 1, p. 229, note1; Grattan-Guinness, 1990, p. 867; Levitt, 2013, p. 47. awarded the prize to "the memoir marked no. 2, and bearing as epigraph: Natura simplex et fecunda."Fresnel, 1866–70, vol. 1, p. 237; Worrall, 1989, p. 140. At the same meeting, after the judgment was delivered, the president of the Académie opened a sealed note accompanying the memoir, revealing the author as Fresnel.Fresnel, 1866–70, vol. 1, p. 230n. The award was announced at the public meeting of the Académie a week later, on 22 March.
Arago's verification of Poisson's counter-intuitive prediction passed into folklore as if it had decided the prize.Worrall, 1989, pp. 135–138; Kipnis, 1991, p. 220. That view, however, is not supported by the judges' report, which gave the matter only two sentences in the penultimate paragraph.Worrall, 1989, pp. 143–145. The printed version of the report also refers to a note (E), but this note concerns further investigations that took place after the prize was decided (Worrall, 1989, pp. 145–146; Fresnel, 1866–70, vol. 1, pp. 236,245–246). According to Kipnis (1991, pp. 221–222), the real significance of Poisson's spot and its complement (at the center of the disk of light cast by a circular aperture) was that they concerned the intensities of fringes, whereas Fresnel's measurements had concerned only the positions of fringes; but, as Kipnis also notes, this issue was pursued only after the prize was decided. Neither did Fresnel's triumph immediately convert Laplace, Biot, and Poisson to the wave theory,Concerning their later views, see §Reception. for at least four reasons. First, although the professionalization of science in France had established common standards, it was one thing to acknowledge a piece of research as meeting those standards, and another thing to regard it as conclusive. Second, it was possible to interpret Fresnel's integrals as rules for combining rays. Arago even encouraged that interpretation, presumably in order to minimize resistance to Fresnel's ideas.Buchwald, 1989, pp. 183–184; Darrigol, 2012, p. 205. Even Biot began teaching the Huygens-Fresnel principle without committing himself to a wave basis.Kipnis, 1991, pp. 219–220,224,232–233; Grattan-Guinness, 1990, p. 870. Third, Fresnel's theory did not adequately explain the mechanism of generation of secondary waves or why they had any significant angular spread; this issue particularly bothered Poisson.Buchwald, 1989, pp. 186–198; Darrigol, 2012, pp. 205–206; Kipnis, 1991, p. 220. Fourth, the question that most exercised optical physicists at that time was not diffraction, but polarization—on which Fresnel had been working, but was yet to make his critical breakthrough. |
Augustin-Jean Fresnel | Polarization | Polarization |
Augustin-Jean Fresnel | Background: Emissionism and selectionism | Background: Emissionism and selectionism
An emission theory of light was one that regarded the propagation of light as the transport of some kind of matter. While the corpuscular theory was obviously an emission theory, the converse did not follow: in principle, one could be an emissionist without being a corpuscularist. This was convenient because, beyond the ordinary laws of reflection and refraction, emissionists never managed to make testable quantitative predictions from a theory of forces acting on corpuscles of light. But they did make quantitative predictions from the premises that rays were countable objects, which were conserved in their interactions with matter (except absorbent media), and which had particular orientations with respect to their directions of propagation. According to this framework, polarization and the related phenomena of double refraction and partial reflection involved altering the orientations of the rays and/or selecting them according to orientation, and the state of polarization of a beam (a bundle of rays) was a question of how many rays were in what orientations: in a fully polarized beam, the orientations were all the same. This approach, which Jed Buchwald has called selectionism, was pioneered by Malus and diligently pursued by Biot.Buchwald, 1989, pp. 50–51,63–5,103–104; 2013, pp. 448–449.
Fresnel, in contrast, decided to introduce polarization into interference experiments. |
Augustin-Jean Fresnel | Interference of polarized light, chromatic polarization (1816–21) | Interference of polarized light, chromatic polarization (1816–21)
In July or August 1816, Fresnel discovered that when a birefringent crystal produced two images of a single slit, he could not obtain the usual two-slit interference pattern, even if he compensated for the different propagation times. A more general experiment, suggested by Arago, found that if the two beams of a double-slit device were separately polarized, the interference pattern appeared and disappeared as the polarization of one beam was rotated, giving full interference for parallel polarizations, but no interference for perpendicular polarizations .Buchwald, 1989, pp. 203,205; Darrigol, 2012, p. 206; Silliman, 1967, pp. 203–205. These experiments, among others, were eventually reported in a brief memoir published in 1819 and later translated into English.Arago & Fresnel, 1819.
In a memoir drafted on 30 August 1816 and revised on 6 October, Fresnel reported an experiment in which he placed two matching thin laminae in a double-slit apparatus—one over each slit, with their optic axes perpendicular—and obtained two interference patterns offset in opposite directions, with perpendicular polarizations. This, in combination with the previous findings, meant that each lamina split the incident light into perpendicularly polarized components with different velocities—just like a normal (thick) birefringent crystal, and contrary to Biot's "mobile polarization" hypothesis.Darrigol, 2012, p. 207; Frankel, 1976, pp. 163–164,182.
Accordingly, in the same memoir, Fresnel offered his first attempt at a wave theory of chromatic polarization. When polarized light passed through a crystal lamina, it was split into ordinary and extraordinary waves (with intensities described by Malus's law), and these were perpendicularly polarized and therefore did not interfere, so that no colors were produced (yet). But if they then passed through an analyzer (second polarizer), their polarizations were brought into alignment (with intensities again modified according to Malus's law), and they would interfere.Darrigol, 2012, p. 206. This explanation, by itself, predicts that if the analyzer is rotated 90°, the ordinary and extraordinary waves simply switch roles, so that if the analyzer takes the form of a calcite crystal, the two images of the lamina should be of the same hue (this issue is revisited below). But in fact, as Arago and Biot had found, they are of complementary colors. To correct the prediction, Fresnel proposed a phase-inversion rule whereby one of the constituent waves of one of the two images suffered an additional 180° phase shift on its way through the lamina. This inversion was a weakness in the theory relative to Biot's, as Fresnel acknowledged,Frankel, 1976, p. 164. although the rule specified which of the two images had the inverted wave.Buchwald, 1989, p. 386. Moreover, Fresnel could deal only with special cases, because he had not yet solved the problem of superposing sinusoidal functions with arbitrary phase differences due to propagation at different velocities through the lamina.Buchwald, 1989, pp. 216,384.
He solved that problem in a "supplement" signed on 15 January 1818 (mentioned above). In the same document, he accommodated Malus's law by proposing an underlying law: that if polarized light is incident on a birefringent crystal with its optic axis at an angle θ to the "plane of polarization", the ordinary and extraordinary vibrations (as functions of time) are scaled by the factors cosθ and sinθ, respectively. Although modern readers easily interpret these factors in terms of perpendicular components of a transverse oscillation, Fresnel did not (yet) explain them that way. Hence he still needed the phase-inversion rule. He applied all these principles to a case of chromatic polarization not covered by Biot's formulae, involving two successive laminae with axes separated by 45°, and obtained predictions that disagreed with Biot's experiments (except in special cases) but agreed with his own.Buchwald, 1989, pp. 333–336; Darrigol, 2012, pp. 207–208. (Darrigol gives the date as 1817, but the page numbers in his footnote 95 fit his reference "1818b", not "1817".)
Fresnel applied the same principles to the standard case of chromatic polarization, in which one birefringent lamina was sliced parallel to its axis and placed between a polarizer and an analyzer. If the analyzer took the form of a thick calcite crystal with its axis in the plane of polarization, Fresnel predicted that the intensities of the ordinary and extraordinary images of the lamina were respectively proportional to
where is the angle from the initial plane of polarization to the optic axis of the lamina, is the angle from the initial plane of polarization to the plane of polarization of the final ordinary image, and is the phase lag of the extraordinary wave relative to the ordinary wave due to the difference in propagation times through the lamina. The terms in are the frequency-dependent terms and explain why the lamina must be thin in order to produce discernible colors: if the lamina is too thick, will pass through too many cycles as the frequency varies through the visible range, and the eye (which divides the visible spectrum into only three bands) will not be able to resolve the cycles.
From these equations it is easily verified that for all so that the colors are complementary. Without the phase-inversion rule, there would be a plus sign in front of the last term in the second equation, so that the -dependent term would be the same in both equations, implying (incorrectly) that the colors were of the same hue.
These equations were included in an undated note that Fresnel gave to Biot,Fresnel, 1866–70, vol. 1, pp. 533–537. On the provenance of the note, see p. 523. In the above text, φ is an abbreviation for Fresnel's , where e and o are the numbers of cycles taken by the extraordinary and ordinary waves to travel through the lamina. to which Biot added a few lines of his own. If we substitute
and
then Fresnel's formulae can be rewritten as
which are none other than Biot's empirical formulae of 1812,Buchwald, 1989, p. 97; Frankel, 1976, p. 148. except that Biot interpreted and as the "unaffected" and "affected" selections of the rays incident on the lamina. If Biot's substitutions were accurate, they would imply that his experimental results were more fully explained by Fresnel's theory than by his own.
Arago delayed reporting on Fresnel's works on chromatic polarization until June 1821, when he used them in a broad attack on Biot's theory. In his written response, Biot protested that Arago's attack went beyond the proper scope of a report on the nominated works of Fresnel. But Biot also claimed that the substitutions for and and therefore Fresnel's expressions for and were empirically wrong because when Fresnel's intensities of spectral colors were mixed according to Newton's rules, the squared cosine and sine functions varied too smoothly to account for the observed sequence of colors. That claim drew a written reply from Fresnel,Fresnel, 1821b. who disputed whether the colors changed as abruptly as Biot claimed,Fresnel, 1821b, §3. and whether the human eye could judge color with sufficient objectivity for the purpose. On the latter question, Fresnel pointed out that different observers may give different names to the same color. Furthermore, he said, a single observer can only compare colors side by side; and even if they are judged to be the same, the identity is of sensation, not necessarily of composition.Fresnel, 1821b, §1 & footnotes. Fresnel's oldest and strongest point—that thin crystals were subject to the same laws as thick ones and did not need or allow a separate theory—Biot left unanswered. Arago and Fresnel were seen to have won the debate.Buchwald, 1989, pp. 237–251; Frankel, 1976, pp. 165–168; Darrigol, 2012, pp. 208–209.
Moreover, by this time Fresnel had a new, simpler explanation of his equations on chromatic polarization. |
Augustin-Jean Fresnel | Breakthrough: Pure transverse waves (1821) | Breakthrough: Pure transverse waves (1821)
thumb|André-Marie Ampère (1775–1836)
In the draft memoir of 30 August 1816, Fresnel mentioned two hypotheses—one of which he attributed to Ampère—by which the non-interference of orthogonally-polarized beams could be explained if polarized light waves were partly transverse. But Fresnel could not develop either of these ideas into a comprehensive theory. As early as September 1816, according to his later account,Fresnel, 1821a, §10. he realized that the non-interference of orthogonally-polarized beams, together with the phase-inversion rule in chromatic polarization, would be most easily explained if the waves were purely transverse, and Ampère "had the same thought" on the phase-inversion rule. But that would raise a new difficulty: as natural light seemed to be unpolarized and its waves were therefore presumed to be longitudinal, one would need to explain how the longitudinal component of vibration disappeared on polarization, and why it did not reappear when polarized light was reflected or refracted obliquely by a glass plate.Fresnel, 1866–70, vol. 1, p. 394n; Fresnel, 1821a, §10; Silliman, 1967, pp. 209–210; Buchwald, 1989, pp. 205–206,208,212,218–219.
Independently, on 12 January 1817, Young wrote to Arago (in English) noting that a transverse vibration would constitute a polarization, and that if two longitudinal waves crossed at a significant angle, they could not cancel without leaving a residual transverse vibration.Young, 1855, p. 383. Young repeated this idea in an article published in a supplement to the Encyclopædia Britannica in February 1818, in which he added that Malus's law would be explained if polarization consisted in a transverse motion.
Thus Fresnel, by his own testimony, may not have been the first person to suspect that light waves could have a transverse component, or that polarized waves were exclusively transverse. And it was Young, not Fresnel, who first published the idea that polarization depends on the orientation of a transverse vibration. But these incomplete theories had not reconciled the nature of polarization with the apparent existence of unpolarized light; that achievement was to be Fresnel's alone.
In a note that Buchwald dates in the summer of 1818, Fresnel entertained the idea that unpolarized waves could have vibrations of the same energy and obliquity, with their orientations distributed uniformly about the wave-normal, and that the degree of polarization was the degree of non-uniformity in the distribution. Two pages later he noted, apparently for the first time in writing, that his phase-inversion rule and the non-interference of orthogonally-polarized beams would be easily explained if the vibrations of fully polarized waves were "perpendicular to the normal to the wave"—that is, purely transverse.Buchwald, 1989, pp. 225–226; Fresnel, 1866–70, vol. 1, pp. 526–527,529.
But if he could account for lack of polarization by averaging out the transverse component, he did not also need to assume a longitudinal component. It was enough to suppose that light waves are purely transverse, hence always polarized in the sense of having a particular transverse orientation, and that the "unpolarized" state of natural or "direct" light is due to rapid and random variations in that orientation, in which case two coherent portions of "unpolarized" light will still interfere because their orientations will be synchronized.
It is not known exactly when Fresnel made this last step, because there is no relevant documentation from 1820 or early 1821Buchwald, 1989, p. 226. (perhaps because he was too busy working on lighthouse-lens prototypes; see below). But he first published the idea in a paper on "Calcul des teintes…" ("calculation of the tints…"), serialized in Arago's Annales for May, June, and July 1821.Fresnel, 1821a. In the first installment, Fresnel described "direct" (unpolarized) light as "the rapid succession of systems of waves polarized in all directions",Buchwald, 1989, p. 227; Fresnel, 1821a, §1. and gave what is essentially the modern explanation of chromatic polarization, albeit in terms of the analogy between polarization and the resolution of forces in a plane, mentioning transverse waves only in a footnote. The introduction of transverse waves into the main argument was delayed to the second installment, in which he revealed the suspicion that he and Ampère had harbored since 1816, and the difficulty it raised.Buchwald, 1989, p. 212; Fresnel, 1821a, §10. He continued:
According to this new view, he wrote, "the act of polarization consists not in creating these transverse movements, but in decomposing them into two fixed perpendicular directions and in separating the two components".Fresnel, 1821a, §13; cf. Buchwald, 1989, p. 228.
While selectionists could insist on interpreting Fresnel's diffraction integrals in terms of discrete, countable rays, they could not do the same with his theory of polarization. For a selectionist, the state of polarization of a beam concerned the distribution of orientations over the population of rays, and that distribution was presumed to be static. For Fresnel, the state of polarization of a beam concerned the variation of a displacement over time. That displacement might be constrained but was not static, and rays were geometric constructions, not countable objects. The conceptual gap between the wave theory and selectionism had become unbridgeable.Cf. Buchwald, 1989, p. 230.
The other difficulty posed by pure transverse waves, of course, was the apparent implication that the aether was an elastic solid, except that, unlike other elastic solids, it was incapable of transmitting longitudinal waves.Fresnel, in an effort to show that transverse waves were not absurd, suggested that the aether was a fluid comprising a lattice of molecules, adjacent layers of which would resist a sliding displacement up to a certain point, beyond which they would gravitate towards a new equilibrium. Such a medium, he thought, would behave as a solid for sufficiently small deformations, but as a perfect liquid for larger deformations. Concerning the lack of longitudinal waves, he further suggested that the layers offered incomparably greater resistance to a change of spacing than to a sliding motion (Silliman, 1967, pp. 216–218; Fresnel, 1821a, §§ 11–12; cf. Fresnel, 1827, tr. Hobson, pp. 258–262). The wave theory was cheap on assumptions, but its latest assumption was expensive on credulity."This hypothesis of Mr.Fresnel is at least very ingenious, and may lead us to some satisfactory computations: but it is attended by one circumstance which is perfectly appalling in its consequences. The substances on which Mr.Savart made his experiments were solids only; and it is only to solids that such a lateral resistance has ever been attributed: so that if we adopted the distinctions laid down by the reviver of the undulatory system himself, in his Lectures, it might be inferred that the luminiferous ether, pervading all space, and penetrating almost all substances, is not only highly elastic, but absolutely solid!!!" — Thomas Young (written January 1823), Sect. in "Refraction, double, and polarisation of light", Supplement to the Fourth, Fifth, and Sixth Editions of the Encyclopædia Britannica, vol.6 (1824), at p.862, reprinted in Young, 1855, at p.415 (italics and exclamation marks in the original). The "Lectures" that Young quotes next are his own (Young, 1807, vol.1, p.627). If that assumption was to be widely entertained, its explanatory power would need to be impressive. |
Augustin-Jean Fresnel | Partial reflection (1821) | Partial reflection (1821)
In the second installment of "Calcul des teintes" (June 1821), Fresnel supposed, by analogy with sound waves, that the density of the aether in a refractive medium was inversely proportional to the square of the wave velocity, and therefore directly proportional to the square of the refractive index. For reflection and refraction at the surface between two isotropic media of different indices, Fresnel decomposed the transverse vibrations into two perpendicular components, now known as the s and p components, which are parallel to the surface and the plane of incidence, respectively; in other words, the s and p components are respectively square and parallel to the plane of incidence.The s originally comes from the German senkrecht, meaning perpendicular (to the plane of incidence). For the s component, Fresnel supposed that the interaction between the two media was analogous to an elastic collision, and obtained a formula for what we now call the reflectivity: the ratio of the reflected intensity to the incident intensity. The predicted reflectivity was non-zero at all angles.Buchwald, 1989, pp. 388–390; Fresnel, 1821a, §18.
The third installment (July 1821) was a short "postscript" in which Fresnel announced that he had found, by a "mechanical solution", a formula for the reflectivity of the p component, which predicted that the reflectivity was zero at the Brewster angle. So polarization by reflection had been accounted for—but with the proviso that the direction of vibration in Fresnel's model was perpendicular to the plane of polarization as defined by Malus. (On the ensuing controversy, see Plane of polarization.) The technology of the time did not allow the s and p reflectivities to be measured accurately enough to test Fresnel's formulae at arbitrary angles of incidence. But the formulae could be rewritten in terms of what we now call the reflection coefficient: the signed ratio of the reflected amplitude to the incident amplitude. Then, if the plane of polarization of the incident ray was at 45° to the plane of incidence, the tangent of the corresponding angle for the reflected ray was obtainable from the ratio of the two reflection coefficients, and this angle could be measured. Fresnel had measured it for a range of angles of incidence, for glass and water, and the agreement between the calculated and measured angles was better than 1.5° in all cases.Buchwald, 1989, pp. 390–391; Fresnel, 1821a, §§ 20–22.
Fresnel gave details of the "mechanical solution" in a memoir read to the Académie des Sciences on 7 January 1823. Conservation of energy was combined with continuity of the tangential vibration at the interface.Buchwald, 1989, pp. 391–393; Whittaker, 1910, pp. 133–135. The resulting formulae for the reflection coefficients and reflectivities became known as the Fresnel equations. The reflection coefficients for the s and p polarizations are most succinctly expressed as
and
where and are the angles of incidence and refraction; these equations are known respectively as Fresnel's sine law and Fresnel's tangent law.Whittaker, 1910, p. 134; Darrigol, 2012, p. 213; Fresnel, 1866–70, vol. 1, pp. 773,757. By allowing the coefficients to be complex, Fresnel even accounted for the different phase shifts of the s and p components due to total internal reflection.Buchwald, 1989, pp. 393–394; Whittaker, 1910, pp. 135–136; Fresnel, 1866–70, vol. 1, pp. 760–761,792–796.
This success inspired James MacCullagh and Augustin-Louis Cauchy, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a complex refractive index.Whittaker, 1910, pp. 177–179; Buchwald, 2013, p. 467. The same technique is applicable to non-metallic opaque media. With these generalizations, the Fresnel equations can predict the appearance of a wide variety of objects under illumination—for example, in computer graphics . |
Augustin-Jean Fresnel | Circular and elliptical polarization, optical rotation (1822) | Circular and elliptical polarization, optical rotation (1822)
thumb|305px|A right-handed/clockwise circularly polarized wave as defined from the point of view of the source. It would be considered left-handed/anti-clockwise circularly polarized if defined from the point of view of the receiver. If the rotating vector is resolved into horizontal and vertical components (not shown), these are a quarter-cycle out of phase with each other.
In a memoir dated 9 December 1822, Fresnel coined the terms linear polarization (French: polarisation rectiligne) for the simple case in which the perpendicular components of vibration are in phase or 180° out of phase, circular polarization for the case in which they are of equal magnitude and a quarter-cycle (±90°) out of phase, and elliptical polarization for other cases in which the two components have a fixed amplitude ratio and a fixed phase difference. He then explained how optical rotation could be understood as a species of birefringence. Linearly-polarized light could be resolved into two circularly-polarized components rotating in opposite directions. If these components propagated at slightly different speeds, the phase difference between them—and therefore the direction of their linearly-polarized resultant—would vary continuously with distance.Buchwald, 1989, pp. 230–232,442.
These concepts called for a redefinition of the distinction between polarized and unpolarized light. Before Fresnel, it was thought that polarization could vary in direction, and in degree (e.g., due to variation in the angle of reflection off a transparent body), and that it could be a function of color (chromatic polarization), but not that it could vary in kind. Hence it was thought that the degree of polarization was the degree to which the light could be suppressed by an analyzer with the appropriate orientation. Light that had been converted from linear to elliptical or circular polarization (e.g., by passage through a crystal lamina, or by total internal reflection) was described as partly or fully "depolarized" because of its behavior in an analyzer. After Fresnel, the defining feature of polarized light was that the perpendicular components of vibration had a fixed ratio of amplitudes and a fixed difference in phase. By that definition, elliptically or circularly polarized light is fully polarized although it cannot be fully suppressed by an analyzer alone.Cf. Buchwald, 1989, p. 232. The conceptual gap between the wave theory and selectionism had widened again. |
Augustin-Jean Fresnel | Total internal reflection (1817–23) | Total internal reflection (1817–23)
thumb|305px|Cross-section of a Fresnel rhomb (blue) with graphs showing the p component of vibration (parallel to the plane of incidence) on the vertical axis, vs. the s component (square to the plane of incidence and parallel to the surface) on the horizontal axis. If the incoming light is linearly polarized, the two components are in phase (top graph). After one reflection at the appropriate angle, the p component is advanced by 1/8 of a cycle relative to the s component (middle graph). After two such reflections, the phase difference is 1/4 of a cycle (bottom graph), so that the polarization is elliptical with axes in the s and p directions. If the s and p components were initially of equal magnitude, the initial polarization (top graph) would be at 45° to the plane of incidence, and the final polarization (bottom graph) would be circular.
By 1817 it had been discovered by Brewster, but not adequately reported,Lloyd, 1834, p. 368. that plane-polarized light was partly depolarized by total internal reflection if initially polarized at an acute angle to the plane of incidence. Fresnel rediscovered this effect and investigated it by including total internal reflection in a chromatic-polarization experiment. With the aid of his first theory of chromatic polarization, he found that the apparently depolarized light was a mixture of components polarized parallel and perpendicular to the plane of incidence, and that the total reflection introduced a phase difference between them.Darrigol, 2012, p. 207. Choosing an appropriate angle of incidence (not yet exactly specified) gave a phase difference of 1/8 of a cycle (45°). Two such reflections from the "parallel faces" of "two coupled prisms" gave a phase difference of 1/4 of a cycle (90°). These findings were contained in a memoir submitted to the Académie on 10 November 1817 and read a fortnight later. An undated marginal note indicates that the two coupled prisms were later replaced by a single "parallelepiped in glass"—now known as a Fresnel rhomb.
This was the memoir whose "supplement", dated January 1818, contained the method of superposing sinusoidal functions and the restatement of Malus's law in terms of amplitudes. In the same supplement, Fresnel reported his discovery that optical rotation could be emulated by passing the polarized light through a Fresnel rhomb (still in the form of "coupled prisms"), followed by an ordinary birefringent lamina sliced parallel to its axis, with the axis at 45° to the plane of reflection of the Fresnel rhomb, followed by a second Fresnel rhomb at 90° to the first.Buchwald, 1989, pp. 223,336; on the latter page, a "prism" means a Fresnel rhomb or equivalent. A footnote in the 1817 memoir (Fresnel, 1866–70, vol. 1, p. 460, note 2) described the emulator more briefly, and not in a self-contained manner. In a further memoir read on 30 March,Fresnel, 1818a, especially pp. 47–49. Fresnel reported that if polarized light was fully "depolarized" by a Fresnel rhomb—now described as a parallelepiped—its properties were not further modified by a subsequent passage through an optically rotating medium or device.
The connection between optical rotation and birefringence was further explained in 1822, in the memoir on elliptical and circular polarization. This was followed by the memoir on reflection, read in January 1823, in which Fresnel quantified the phase shifts in total internal reflection, and thence calculated the precise angle at which a Fresnel rhomb should be cut in order to convert linear polarization to circular polarization. For a refractive index of 1.51, there were two solutions: about 48.6° and 54.6°. |
Augustin-Jean Fresnel | Double refraction | Double refraction |
Augustin-Jean Fresnel | Background: Uniaxial and biaxial crystals; Biot's laws | Background: Uniaxial and biaxial crystals; Biot's laws
When light passes through a slice of calcite cut perpendicular to its optic axis, the difference between the propagation times of the ordinary and extraordinary waves has a second-order dependence on the angle of incidence. If the slice is observed in a highly convergent cone of light, that dependence becomes significant, so that a chromatic-polarization experiment will show a pattern of concentric rings. But most minerals, when observed in this manner, show a more complicated pattern of rings involving two foci and a lemniscate curve, as if they had two optic axes.Jenkins & White, 1976, pp. 576–579 (§27.9, esp. Fig. 27M). The two classes of minerals naturally become known as uniaxal and biaxal—or, in later literature, uniaxial and biaxial.
In 1813, Brewster observed the simple concentric pattern in "beryl, emerald, ruby &c." The same pattern was later observed in calcite by Wollaston, Biot, and Seebeck. Biot, assuming that the concentric pattern was the general case, tried to calculate the colors with his theory of chromatic polarization, and succeeded better for some minerals than for others. In 1818, Brewster belatedly explained why: seven of the twelve minerals employed by Biot had the lemniscate pattern, which Brewster had observed as early as 1812; and the minerals with the more complicated rings also had a more complicated law of refraction.Buchwald, 1989, pp. 254–255,402.
In a uniform crystal, according to Huygens's theory, the secondary wavefront that expands from the origin in unit time is the ray-velocity surface—that is, the surface whose "distance" from the origin in any direction is the ray velocity in that direction. In calcite, this surface is two-sheeted, consisting of a sphere (for the ordinary wave) and an oblate spheroid (for the extraordinary wave) touching each other at opposite points of a common axis—touching at the north and south poles, if we may use a geographic analogy. But according to Malus's corpuscular theory of double refraction, the ray velocity was proportional to the reciprocal of that given by Huygens's theory, in which case the velocity law was of the form
where and were the ordinary and extraordinary ray velocities according to the corpuscular theory, and was the angle between the ray and the optic axis.Cf. Buchwald, 1989, p. 269. By Malus's definition, the plane of polarization of a ray was the plane of the ray and the optic axis if the ray was ordinary, or the perpendicular plane (containing the ray) if the ray was extraordinary. In Fresnel's model, the direction of vibration was normal to the plane of polarization. Hence, for the sphere (the ordinary wave), the vibration was along the lines of latitude (continuing the geographic analogy); and for the spheroid (the extraordinary wave), the vibration was along the lines of longitude.
On 29 March 1819,Grattan-Guinness, 1990, p. 885. Biot presented a memoir in which he proposed simple generalizations of Malus's rules for a crystal with two axes, and reported that both generalizations seemed to be confirmed by experiment. For the velocity law, the squared sine was replaced by the product of the sines of the angles from the ray to the two axes (Biot's sine law). And for the polarization of the ordinary ray, the plane of the ray and the axis was replaced by the plane bisecting the dihedral angle between the two planes each of which contained the ray and one axis (Biot's dihedral law).Buchwald, 1989, pp. 269,418. Biot's laws meant that a biaxial crystal with axes at a small angle, cleaved in the plane of those axes, behaved nearly like a uniaxial crystal at near-normal incidence; this was fortunate because gypsum, which had been used in chromatic-polarization experiments, is biaxial.Cf. Fresnel, 1822a, tr. Young, in Quarterly Journal of Science, Literature, and Art, Jul.–Dec.1828, at pp. 178–179. |
Augustin-Jean Fresnel | First memoir and supplements (1821–22) | First memoir and supplements (1821–22)
Until Fresnel turned his attention to biaxial birefringence, it was assumed that one of the two refractions was ordinary, even in biaxial crystals.Buchwald, 1989, p. 260. But, in a memoir submittedIn Fresnel's collected works (1866–70), a paper is said to have been "presented" ("présenté") if it was merely delivered to the Permanent Secretary of the Académie for witnessing or processing (cf. vol. 1, p. 487; vol. 2, pp. 261,308). In such cases this article prefers the generic word "submitted", to avoid the impression that the paper had a formal reading. on 19 November 1821,Printed in Fresnel, 1866–70, vol. 2, pp. 261–308. Fresnel reported two experiments on topaz showing that neither refraction was ordinary in the sense of satisfying Snell's law; that is, neither ray was the product of spherical secondary waves.Silliman, 1967, pp. 243–246 (first experiment); Buchwald, 1989, pp. 261–267 (both experiments). The first experiment was briefly reported earlier in Fresnel, 1821c.
The same memoir contained Fresnel's first attempt at the biaxial velocity law. For calcite, if we interchange the equatorial and polar radii of Huygens's oblate spheroid while preserving the polar direction, we obtain a prolate spheroid touching the sphere at the equator. A plane through the center/origin cuts this prolate spheroid in an ellipse whose major and minor semi-axes give the magnitudes of the extraordinary and ordinary ray velocities in the direction normal to the plane, and (said Fresnel) the directions of their respective vibrations. The direction of the optic axis is the normal to the plane for which the ellipse of intersection reduces to a circle. So, for the biaxial case, Fresnel simply replaced the prolate spheroid with a triaxial ellipsoid,Buchwald (1989, pp. 267–272) and Grattan-Guinness (1990, pp. 893–894 call it the "ellipsoid of elasticity". which was to be sectioned by a plane in the same way. In general there would be two planes passing through the center of the ellipsoid and cutting it in a circle, and the normals to these planes would give two optic axes. From the geometry, Fresnel deduced Biot's sine law (with the ray velocities replaced by their reciprocals).Buchwald, 1989, pp. 267–272; Grattan-Guinness, 1990, pp. 885–887.
The ellipsoid indeed gave the correct ray velocities (although the initial experimental verification was only approximate). But it did not give the correct directions of vibration, for the biaxial case or even for the uniaxial case, because the vibrations in Fresnel's model were tangential to the wavefront—which, for an extraordinary ray, is not generally normal to the ray. This error (which is small if, as in most cases, the birefringence is weak) was corrected in an "extract" that Fresnel read to the Académie a week later, on 26 November. Starting with Huygens's spheroid, Fresnel obtained a 4th-degree surface which, when sectioned by a plane as above, would yield the wave-normal velocities for a wavefront in that plane, together with their vibration directions. For the biaxial case, he generalized the equation to obtain a surface with three unequal principal dimensions; this he subsequently called the "surface of elasticity". But he retained the earlier ellipsoid as an approximation, from which he deduced Biot's dihedral law.Buchwald, 1989, pp. 274–279.
Fresnel's initial derivation of the surface of elasticity had been purely geometric, and not deductively rigorous. His first attempt at a mechanical derivation, contained in a "supplement" dated 13 January 1822, assumed that (i) there were three mutually perpendicular directions in which a displacement produced a reaction in the same direction, (ii) the reaction was otherwise a linear function of the displacement, and (iii) the radius of the surface in any direction was the square root of the component, in that direction, of the reaction to a unit displacement in that direction. The last assumption recognized the requirement that if a wave was to maintain a fixed direction of propagation and a fixed direction of vibration, the reaction must not be outside the plane of those two directions.Buchwald, 1989, pp. 279–280.
In the same supplement, Fresnel considered how he might find, for the biaxial case, the secondary wavefront that expands from the origin in unit time—that is, the surface that reduces to Huygens's sphere and spheroid in the uniaxial case. He noted that this "wave surface" (surface de l'onde)Literally "surface of the wave"—as in Hobson's translation of Fresnel 1827. is tangential to all possible plane wavefronts that could have crossed the origin one unit of time ago, and he listed the mathematical conditions that it must satisfy. But he doubted the feasibility of deriving the surface from those conditions.Fresnel, 1866–70, vol. 2, pp. 340,361–363; Buchwald, 1989, pp. 281–283. The derivation of the "wave surface" from its tangent planes was eventually accomplished by Ampère in 1828 (Lloyd, 1834, pp. 386–387; Darrigol, 2012, p. 218; Buchwald, 1989, pp. 281,457).
In a "second supplement",Fresnel, 1866–70, vol. 2, pp. 369–442. Fresnel eventually exploited two related facts: (i) the "wave surface" was also the ray-velocity surface, which could be obtained by sectioning the ellipsoid that he had initially mistaken for the surface of elasticity, and (ii) the "wave surface" intersected each plane of symmetry of the ellipsoid in two curves: a circle and an ellipse. Thus he found that the "wave surface" is described by the 4th-degree equation
where and are the propagation speeds in directions normal to the coordinate axes for vibrations along the axes (the ray and wave-normal speeds being the same in those special cases).Buchwald, 1989, pp. 283–285; Darrigol, 2012, pp. 217–218; Fresnel, 1866–70, vol. 2, pp. 386–388. Later commentators put the equation in the more compact and memorable form
Earlier in the "second supplement", Fresnel modeled the medium as an array of point-masses and found that the force-displacement relation was described by a symmetric matrix, confirming the existence of three mutually perpendicular axes on which the displacement produced a parallel force.Grattan-Guinness, 1990, pp. 891–892; Fresnel, 1866–70, vol. 2, pp. 371–379. Later in the document, he noted that in a biaxial crystal, unlike a uniaxial crystal, the directions in which there is only one wave-normal velocity are not the same as those in which there is only one ray velocity.Buchwald, 1989, pp. 285–286; Fresnel, 1866–70, vol. 2, p. 396. Nowadays we refer to the former directions as the optic axes or binormal axes, and the latter as the ray axes or biradial axes .
Fresnel's "second supplement" was signed on 31 March 1822 and submitted the next day—less than a year after the publication of his pure-transverse-wave hypothesis, and just less than a year after the demonstration of his prototype eight-panel lighthouse lens . |
Augustin-Jean Fresnel | Second memoir (1822–26) | Second memoir (1822–26)
Having presented the pieces of his theory in roughly the order of discovery, Fresnel needed to rearrange the material so as to emphasize the mechanical foundations;Grattan-Guinness, 1990, pp. 896–897. Silliman, 1967, pp. 262–263; 2008, p.170 and he still needed a rigorous treatment of Biot's dihedral law.Buchwald, 1989, pp. 286–287,447. He attended to these matters in his "second memoir" on double refraction,Fresnel, 1827. published in the Recueils of the Académie des Sciences for 1824; this was not actually printed until late 1827, a few months after his death.Fresnel, 1866–70, vol. 2, p. 800n. Although the original publication (Fresnel, 1827) shows the year "1824" in selected page footers, it is known that Fresnel, slowed down by illness, did not finish the memoir until 1826 (Buchwald, 1989, pp. 289,447, citing Fresnel, 1866–70, vol. 2, p. 776n). In this work, having established the three perpendicular axes on which a displacement produces a parallel reaction,Fresnel, 1827, tr. Hobson, pp. 266–273. and thence constructed the surface of elasticity,Fresnel, 1827, tr. Hobson, pp. 281–285. he showed that Biot's dihedral law is exact provided that the binormals are taken as the optic axes, and the wave-normal direction as the direction of propagation.Fresnel, 1827, tr. Hobson, pp. 320–322; Buchwald, 1989, p. 447.
As early as 1822, Fresnel discussed his perpendicular axes with Cauchy. Acknowledging Fresnel's influence, Cauchy went on to develop the first rigorous theory of elasticity of non-isotropic solids (1827), hence the first rigorous theory of transverse waves therein (1830)—which he promptly tried to apply to optics.Grattan-Guinness, 1990, pp. 1003–1009,1034–1040,1043; Whittaker, 1910, pp. 143–145; Darrigol, 2012, p. 228. Grattan-Guinness offers evidence against any earlier dating of Cauchy's theories. The ensuing difficulties drove a long competitive effort to find an accurate mechanical model of the aether.Whittaker, 1910, chapter ; Darrigol, 2012, chapter 6; Buchwald, 2013, pp. 460–464. Fresnel's own model was not dynamically rigorous; for example, it deduced the reaction to a shear strain by considering the displacement of one particle while all others were fixed, and it assumed that the stiffness determined the wave velocity as in a stretched string, whatever the direction of the wave-normal. But it was enough to enable the wave theory to do what selectionist theory could not: generate testable formulae covering a comprehensive range of optical phenomena, from mechanical assumptions.Fresnel, 1827, tr. Hobson, pp. 273–281; Silliman, 1967, p. 268n; Buchwald, 1989, p. 288. |
Augustin-Jean Fresnel | Photoelasticity, multiple-prism experiments (1822) | Photoelasticity, multiple-prism experiments (1822)
thumb|Chromatic polarization in a plastic protractor, caused by stress-induced birefringence.
In 1815, Brewster reported that colors appear when a slice of isotropic material, placed between crossed polarizers, is mechanically stressed. Brewster himself immediately and correctly attributed this phenomenon to stress-induced birefringence—now known as photoelasticity.
In a memoir read in September 1822, Fresnel announced that he had verified Brewster's diagnosis more directly, by compressing a combination of glass prisms so severely that one could actually see a double image through it. In his experiment, Fresnel lined up seven 45°–90°–45° prisms, short side to short side, with their 90° angles pointing in alternating directions. Two half-prisms were added at the ends to make the whole assembly rectangular. The prisms were separated by thin films of turpentine (térébenthine) to suppress internal reflections, allowing a clear line of sight along the row. When the four prisms with similar orientations were compressed in a vise across the line of sight, an object viewed through the assembly produced two images with perpendicular polarizations, with an apparent spacing of 1.5mm at one metre.Whewell, 1857, pp. 355–356.
At the end of that memoir, Fresnel predicted that if the compressed prisms were replaced by (unstressed) monocrystalline quartz prisms with matching directions of optical rotation, and with their optic axes aligned along the row, an object seen by looking along the common optic axis would give two images, which would seem unpolarized when viewed through an analyzer but, when viewed through a Fresnel rhomb, would be polarized at ±45° to the plane of reflection of the rhomb (indicating that they were initially circularly polarized in opposite directions). This would show directly that optical rotation is a form of birefringence. In the memoir of December 1822, in which he introduced the term circular polarization, he reported that he had confirmed this prediction using only one 14°–152°–14° prism and two glass half-prisms. But he obtained a wider separation of the images by replacing the glass half-prism with quartz half-prisms whose rotation was opposite to that of the 14°–152°–14° prism. He added in passing that one could further increase the separation by increasing the number of prisms.Fresnel, 1866–70, vol. 1, pp. 737–739 (§4). Cf. Whewell, 1857, p. 356–358; Jenkins & White, 1976, pp. 589–590. |
Augustin-Jean Fresnel | Reception | Reception
For the supplement to Riffault's translation of Thomson's System of Chemistry, Fresnel was chosen to contribute the article on light. The resulting 137-page essay, titled De la Lumière (On Light),Fresnel, 1822a. was apparently finished in June 1821 and published by February 1822.Grattan-Guinness, 1990, p. 884. With sections covering the nature of light, diffraction, thin-film interference, reflection and refraction, double refraction and polarization, chromatic polarization, and modification of polarization by reflection, it made a comprehensive case for the wave theory to a readership that was not restricted to physicists.Cf. Frankel, 1976, p. 169.
To examine Fresnel's first memoir and supplements on double refraction, the Académie des Sciences appointed Ampère, Arago, Fourier, and Poisson.Fresnel, 1866–70, vol. 2, pp. 261n,369n. Their report,Printed in Fresnel, 1866–70, vol. 2, pp. 459–464. of which Arago was clearly the main author,Buchwald, 1989, p. 288. was delivered at the meeting of 19 August 1822. Then, in the words of Émile Verdet, as translated by Ivor Grattan-Guinness:
Whether Laplace was announcing his conversion to the wave theory—at the age of 73—is uncertain. Grattan-Guinness entertained the idea.Grattan-Guinness, 1990, p. 898. Buchwald, noting that Arago failed to explain that the "ellipsoid of elasticity" did not give the correct planes of polarization, suggests that Laplace may have merely regarded Fresnel's theory as a successful generalization of Malus's ray-velocity law, embracing Biot's laws.Buchwald, 1989, pp. 289–390.
thumb|Airy diffraction pattern 65mm from a 0.09mm circular aperture illuminated by red laser light. Image size: 17.3mm×13mm
In the following year, Poisson, who did not sign Arago's report, disputed the possibility of transverse waves in the aether. Starting from assumed equations of motion of a fluid medium, he noted that they did not give the correct results for partial reflection and double refraction—as if that were Fresnel's problem rather than his own—and that the predicted waves, even if they were initially transverse, became more longitudinal as they propagated. In reply Fresnel noted, inter alia, that the equations in which Poisson put so much faith did not even predict viscosity. The implication was clear: given that the behavior of light had not been satisfactorily explained except by transverse waves, it was not the responsibility of the wave-theorists to abandon transverse waves in deference to pre-conceived notions about the aether; rather, it was the responsibility of the aether modelers to produce a model that accommodated transverse waves.Frankel, 1976, pp. 170–171; cf. Fresnel, 1827, tr. Hobson, pp. 243–244,262. According to Robert H. Silliman, Poisson eventually accepted the wave theory shortly before his death in 1840.Silliman, 1967, pp. 284–285, citing Fresnel, 1866–70, vol. 1, p. lxxxix, note 2. Frankel (1976, p. 173) agrees. Worrall (1989, p. 140) is skeptical.
Among the French, Poisson's reluctance was an exception. According to Eugene Frankel, "in Paris no debate on the issue seems to have taken place after 1825. Indeed, almost the entire generation of physicists and mathematicians who came to maturity in the 1820s—Pouillet, Savart, Lamé, Navier, Liouville, Cauchy—seem to have adopted the theory immediately." Fresnel's other prominent French opponent, Biot, appeared to take a neutral position in 1830, and eventually accepted the wave theory—possibly by 1846 and certainly by 1858.Frankel, 1976, pp. 173–174.
In 1826, the British astronomer John Herschel, who was working on a book-length article on light for the Encyclopædia Metropolitana, addressed three questions to Fresnel concerning double refraction, partial reflection, and their relation to polarization. The resulting article, titled simply "Light", was highly sympathetic to the wave theory, although not entirely free of selectionist language. It was circulating privately by 1828 and was published in 1830.Buchwald, 1989, pp. 291–296; Darrigol, 2012, pp. 220–221,303. Meanwhile, Young's translation of Fresnel's De la Lumière was published in installments from 1827 to 1829.Fresnel, 1822a; Kipnis, 1991, pp. 227–228. George Biddell Airy, the former Lucasian Professor at Cambridge and future Astronomer Royal, unreservedly accepted the wave theory by 1831.Buchwald, 1989, p. 296. In 1834, he famously calculated the diffraction pattern of a circular aperture from the wave theory, thereby explaining the limited angular resolution of a perfect telescope . By the end of the 1830s, the only prominent British physicist who held out against the wave theory was Brewster, whose objections included the difficulty of explaining photochemical effects and (in his opinion) dispersion.Darrigol, 2012, pp. 222–223,248.
A German translation of De la Lumière was published in installments in 1825 and 1828. The wave theory was adopted by Fraunhofer in the early 1820s and by Franz Ernst Neumann in the 1830s, and then began to find favor in German textbooks.Kipnis, 1991, pp. 225,227; Darrigol, 2012, pp. 223,245.
The economy of assumptions under the wave theory was emphasized by William Whewell in his History of the Inductive Sciences, first published in 1837. In the corpuscular system, "every new class of facts requires a new supposition," whereas in the wave system, a hypothesis devised in order to explain one phenomenon is then found to explain or predict others. In the corpuscular system there is "no unexpected success, no happy coincidence, no convergence of principles from remote quarters"; but in the wave system, "all tends to unity and simplicity."Whewell, 1857, pp. 340–341; the quoted paragraphs date from the 1st Ed. (1837).
Hence, in 1850, when Foucault and Fizeau found by experiment that light travels more slowly in water than in air, in accordance with the wave explanation of refraction and contrary to the corpuscular explanation, the result came as no surprise.Whewell, 1857, pp. 482–483; Whittaker, 1910, p. 136; Darrigol, 2012, p. 223. |
Augustin-Jean Fresnel | Lighthouses and the Fresnel lens | Lighthouses and the Fresnel lens
Fresnel was not the first person to focus a lighthouse beam using a lens. That distinction apparently belongs to the London glass-cutter Thomas Rogers, whose first lenses, 53cm in diameter and 14cm thick at the center, were installed at the Old Lower Lighthouse at Portland Bill in 1789. Further samples were installed in about half a dozen other locations by 1804. But much of the light was wasted by absorption in the glass.Levitt, 2013, p.57.
thumb|upright|1: Cross-section of Buffon/Fresnel lens. 2: Cross-section of conventional plano-convex lens of equivalent power. (Buffon's version was biconvex.Levitt, 2013, p. 59.)
Nor was Fresnel the first to suggest replacing a convex lens with a series of concentric annular prisms, to reduce weight and absorption. In 1748, Count Buffon proposed grinding such prisms as steps in a single piece of glass. In 1790, the Marquis de Condorcet suggested that it would be easier to make the annular sections separately and assemble them on a frame; but even that was impractical at the time.Levitt, 2013, p. 71. These designs were intended not for lighthouses, but for burning glasses. Brewster, however, proposed a system similar to Condorcet's in 1811, and by 1820 was advocating its use in British lighthouses.
Meanwhile, on 21 June 1819, Fresnel was "temporarily" seconded by the Commission des Phares (Commission of Lighthouses) on the recommendation of Arago (a member of the Commission since 1813), to review possible improvements in lighthouse illumination.Levitt, 2013, pp. 51,53; Fresnel, 1866–70, vol. 1, p. xcvii, and vol. 3, p. xxiv. The commission had been established by Napoleon in 1811 and placed under the Corps des Ponts—Fresnel's employer.Levitt, 2013, pp. 49–50.
By the end of August 1819, unaware of the Buffon-Condorcet-Brewster proposal, Fresnel made his first presentation to the commission,Fresnel, 1866–70, vol. 3, pp. 5–14; on the date, see p. 6n. recommending what he called lentilles à échelons (lenses by steps) to replace the reflectors then in use, which reflected only about half of the incident light.Levitt, 2013, pp. 56,58.Another report by Fresnel, dated 29 August 1819 (Fresnel, 1866–70, vol. 3, pp. 15–21), concerns tests on reflectors, and does not mention stepped lenses except in an unrelated sketch on the last page of the manuscript. The minutes of the meetings of the Commission go back only to 1824, when Fresnel himself took over as Secretary (Fresnel, 1866–70, vol. 3, p. 6n). Thus, unfortunately, it is not possible to ascertain the exact date on which Fresnel formally recommended lentilles à échelons. One of the assembled commissioners, Jacques Charles, recalled Buffon's suggestion, leaving Fresnel embarrassed for having again "broken through an open door". But, whereas Buffon's version was biconvex and in one piece, Fresnel's was plano-convex and made of multiple prisms for easier construction. With an official budget of 500 francs, Fresnel approached three manufacturers. The third, François Soleil, produced the prototype. Finished in March 1820, it had a square lens panel 55cm on a side, containing 97 polygonal (not annular) prisms—and so impressed the Commission that Fresnel was asked for a full eight-panel version. This model, completed a year later in spite of insufficient funding, had panels 76cm square. In a public spectacle on the evening of 13 April 1821, it was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete.Levitt, 2013, pp. 59–66. On the dimensions see Elton, 2009, pp. 193–194; Fresnel, 1866–70, vol. 3, p. xxxiv; Fresnel, 1822b, tr. Tag, p. 7.
thumb|246px|Cross-section of a first-generation Fresnel lighthouse lens, with sloping mirrors m,n above and below the refractive panel RC (with central segment A). If the cross-section in every vertical plane through the lamp L is the same, the light is spread evenly around the horizon.
Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by Saint-Gobain, giving eight rotating beams—to be seen by mariners as a periodic flash. Above and behind each main panel was a smaller, sloping bull's-eye panel of trapezoidal outline with trapezoidal elements. This refracted the light to a sloping plane mirror, which then reflected it horizontally, 7 degrees ahead of the main beam, increasing the duration of the flash.Fresnel, 1822b, tr. Tag, pp. 13,25. Below the main panels were 128 small mirrors arranged in four rings, stacked like the slats of a louver or Venetian blind. Each ring, shaped as a frustum of a cone, reflected the light to the horizon, giving a fainter steady light between the flashes. The official test, conducted on the unfinished Arc de Triomphe on 20 August 1822, was witnessed by the commission—and by Louis XVIII and his entourage—from 32km away. The apparatus was stored at Bordeaux for the winter, and then reassembled at Cordouan Lighthouse under Fresnel's supervision. On 25 July 1823, the world's first lighthouse Fresnel lens was lit.Elton, 2009, p.195; Levitt, 2013, pp. 72–76. Soon afterwards, Fresnel started coughing up blood.Levitt, 2013, p. 97.
In May 1824, Fresnel was promoted to secretary of the Commission des Phares, becoming the first member of that body to draw a salary,Levitt, 2013, p. 82. albeit in the concurrent role of Engineer-in-Chief.Elton, 2009, p.190. He was also an examiner (not a teacher) at the École Polytechnique since 1821; but poor health, long hours during the examination season, and anxiety about judging others induced him to resign that post in late 1824, to save his energy for his lighthouse work.Grattan-Guinness, 1990, pp. 914–915, citing Young, 1855, p. 399; Arago, 1857, pp. 467,470; Boutry, 1948, pp. 601–602.
In the same year he designed the first fixed lens—for spreading light evenly around the horizon while minimizing waste above or below. Ideally the curved refracting surfaces would be segments of toroids about a common vertical axis, so that the dioptric panel would look like a cylindrical drum. If this was supplemented by reflecting (catoptric) rings above and below the refracting (dioptric) parts, the entire apparatus would look like a beehive.Cf. Elton, 2009, p. 198, Figure 12. The second Fresnel lens to enter service was indeed a fixed lens, of third order, installed at Dunkirk by 1 February 1825.Levitt, 2013, p. 84. However, due to the difficulty of fabricating large toroidal prisms, this apparatus had a 16-sided polygonal plan.Elton, 2009, pp. 197–198.
In 1825, Fresnel extended his fixed-lens design by adding a rotating array outside the fixed array. Each panel of the rotating array was to refract part of the fixed light from a horizontal fan into a narrow beam.Elton, 2009, pp. 198–199.
Also in 1825, Fresnel unveiled the Carte des Phares (Lighthouse Map), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes (called orders, the first order being the largest), with different characteristics to facilitate recognition: a constant light (from a fixed lens), one flash per minute (from a rotating lens with eight panels), and two per minute (sixteen panels).Levitt, 2013, pp. 82–84.
thumb|left|First-order rotating catadioptric Fresnel lens, dated 1870, displayed at the Musée national de la Marine, Paris. In this case the dioptric prisms (inside the bronze rings) and catadioptric prisms (outside) are arranged to give a purely flashing light with four flashes per rotation. The assembly stands 2.54 metres tall and weighs about 1.5 tonnes.
In late 1825,Elton, 2009, p. 200. to reduce the loss of light in the reflecting elements, Fresnel proposed to replace each mirror with a catadioptric prism, through which the light would travel by refraction through the first surface, then total internal reflection off the second surface, then refraction through the third surface.Levitt, 2013, pp. 79–80. The result was the lighthouse lens as we now know it. In 1826 he assembled a small model for use on the Canal Saint-Martin, but he did not live to see a full-sized version.
The first fixed lens with toroidal prisms was a first-order apparatus designed by the Scottish engineer Alan Stevenson under the guidance of Léonor Fresnel, and fabricated by Isaac Cookson & Co. from French glass; it entered service at the Isle of May in 1836.Elton, 2009, pp. 199,200,202; Levitt, 2013, pp. 104–105. The first large catadioptric lenses were fixed third-order lenses made in 1842 for the lighthouses at Gravelines and Île Vierge. The first fully catadioptric first-order lens, installed at Ailly in 1852, gave eight rotating beams assisted by eight catadioptric panels at the top (to lengthen the flashes), plus a fixed light from below. The first fully catadioptric lens with purely revolving beams—also of first order—was installed at Saint-Clément-des-Baleines in 1854, and marked the completion of Augustin Fresnel's original Carte des Phares.Levitt, 2013, pp. 108–110, 113–116, 122–123.
thumb|upright|Close-up view of a thin plastic Fresnel lens
Production of one-piece stepped dioptric lenses—roughly as envisaged by Buffon—became practical in 1852, when John L. Gilliland of the Brooklyn Flint-Glass Company patented a method of making such lenses from press-molded glass. By the 1950s, the substitution of plastic for glass made it economic to use fine-stepped Fresnel lenses as condensers in overhead projectors.A. Finstad, "New developments in audio-visual materials", Higher Education, vol. 8, no.15 (1 April 1952), pp. 176–178, at p.176. Still finer steps can be found in low-cost plastic "sheet" magnifiers. |
Augustin-Jean Fresnel | Honors | Honors
thumb|Bust of Augustin Fresnel by David d'Angers (1854), formerly at the lighthouse of Hourtin, Gironde, and now exhibited at the
Fresnel was elected to the Société Philomathique de Paris in April 1819,Kipnis, 1991, p. 217. and in 1822 became one of the editors of the Société's Bulletin des Sciences.Frankel, 1976, p. 172. As early as May 1817, at Arago's suggestion, Fresnel applied for membership of the Académie des Sciences, but received only one vote. The successful candidate on that occasion was Joseph Fourier. In November 1822, Fourier's elevation to Permanent Secretary of the Académie created a vacancy in the physics section, which was filled in February 1823 by Pierre Louis Dulong, with 36 votes to Fresnel's 20. But in May 1823, after another vacancy was left by the death of Jacques Charles, Fresnel's election was unanimous.Grattan-Guinness, 1990, pp. 861,913–914; Arago, 1857, p. 408. Silliman (1967, p. 262n) gives the dates of the respective elections as 27 January and 12 May 1823. In 1824,Levitt, 2013, p. 77. Fresnel was made a chevalier de la Légion d'honneur (Knight of the Legion of Honour).
Meanwhile, in Britain, the wave theory was yet to take hold; Fresnel wrote to Thomas Young in November 1824, saying in part:
But "the praise of English scholars" soon followed. On 9 June 1825, Fresnel was made a Foreign Member of the Royal Society of London. In 1827 he was awarded the society's Rumford Medal for the year 1824, "For his Development of the Undulatory Theory as applied to the Phenomena of Polarized Light, and for his various important discoveries in Physical Optics."
A monument to Fresnel at his birthplace was dedicated on 14 September 1884 with a speech by , Permanent Secretary of the Académie des Sciences. "" is among the 72 names embossed on the Eiffel Tower (on the south-east side, fourth from the left). In the 19th century, as every lighthouse in France acquired a Fresnel lens, every one acquired a bust of Fresnel, seemingly watching over the coastline that he had made safer.Levitt, 2013, p. 233. The lunar features Promontorium Fresnel and Rimae Fresnel were later named after him. |
Augustin-Jean Fresnel | Decline and death | Decline and death
thumb|upright|Fresnel's grave at Père Lachaise Cemetery, Paris, photographed in 2018
Fresnel's health, which had always been poor, deteriorated in the winter of 1822–1823, increasing the urgency of his original research, and (in part) preventing him from contributing an article on polarization and double refraction for the Encyclopædia Britannica.Levitt, 2013, pp. 75–76; Silliman, 1967, pp. 276–277. The memoirs on circular and elliptical polarization and optical rotation, and on the detailed derivation of the Fresnel equations and their application to total internal reflection, date from this period. In the spring he recovered enough, in his own view, to supervise the lens installation at Cordouan. Soon afterwards, it became clear that his condition was tuberculosis.
In 1824, he was advised that if he wanted to live longer, he needed to scale back his activities. Perceiving his lighthouse work to be his most important duty, he resigned as an examiner at the École Polytechnique, and closed his scientific notebooks. His last note to the Académie, read on 13 June 1825, described the first radiometer and attributed the observed repulsive force to a temperature difference.Boutry, 1948, pp. 601–602; Silliman, 1967, p. 278; Fresnel, 1866–70, vol. 2, pp. 667–672. Although his fundamental research ceased, his advocacy did not; as late as August or September 1826, he found the time to answer Herschel's queries on the wave theory.Fresnel, 1866–70, vol. 2, pp. 647–660. It was Herschel who recommended Fresnel for the Royal Society's Rumford Medal.Boutry, 1948, p. 603.
Fresnel's cough worsened in the winter of 1826–1827, leaving him too ill to return to Mathieu in the spring. The Académie meeting of 30 April 1827 was the last that he attended. In early June he was carried to Ville-d'Avray, west of Paris. There his mother joined him. On 6 July, Arago arrived to deliver the Rumford Medal. Sensing Arago's distress, Fresnel whispered that "the most beautiful crown means little, when it is laid on the grave of a friend." Fresnel did not have the strength to reply to the Royal Society. He died eight days later, on Bastille Day.Levitt, 2013, p. 98; Silliman, 1967, p. 279; Arago, 1857, p. 470; Boutry, 1948, .
He is buried at Père Lachaise Cemetery, Paris. The inscription on his headstone is partly eroded away; the legible part says, when translated, "To the memory of Augustin Jean Fresnel, member of the Institute of France". |
Augustin-Jean Fresnel | Posthumous publications | Posthumous publications
thumb|upright|Émile Verdet (1824–1866)
Fresnel's "second memoir" on double refraction was not printed until late 1827, a few months after his death.Fresnel, 1866–70, vol. 2, p. 800n. Until then, the best published source on his work on double refraction was an extract of that memoir, printed in 1822.Buchwald, 1989, p. 289. His final treatment of partial reflection and total internal reflection, read to the Académie in January 1823, was thought to be lost until it was rediscovered among the papers of the deceased Joseph Fourier (1768–1830), and was printed in 1831. Until then, it was known chiefly through an extract printed in 1823 and 1825. The memoir introducing the parallelepiped form of the Fresnel rhomb,Fresnel, 1818a. read in March 1818, was mislaid until 1846,Kipnis, 1991, pp. 207n,217n; Buchwald, 1989, p. 461, ref.1818d; Fresnel, 1866–70, vol. 1, p. 655n. and then attracted such interest that it was soon republished in English.In Taylor, 1852, pp. 44–65. Most of Fresnel's writings on polarized light before 1821—including his first theory of chromatic polarization (submitted 7 October 1816) and the crucial "supplement" of January 1818—were not published in full until his Oeuvres complètes ("complete works") began to appear in 1866.Buchwald, 1989, pp. 222,238,461–462. The "supplement" of July 1816, proposing the "efficacious ray" and reporting the famous double-mirror experiment, met the same fate,Grattan-Guinness, 1990, p. 861. as did the "first memoir" on double refraction.Whittaker, 1910, p. 125n.
Publication of Fresnel's collected works was itself delayed by the deaths of successive editors. The task was initially entrusted to Félix Savary, who died in 1841. It was restarted twenty years later by the Ministry of Public Instruction. Of the three editors eventually named in the Oeuvres, Sénarmont died in 1862, Verdet in 1866, and Léonor Fresnel in 1869, by which time only two of the three volumes had appeared.Boutry, 1948, pp. 603–604; Fresnel, 1866–70, vol. 1, pp. i–vii. At the beginning of vol. 3 (1870), the completion of the project is described in a long footnote by "J. Lissajous."
Not included in the OeuvresSilliman, 2008, p. 171. are two short notes by Fresnel on magnetism, which were discovered among Ampère's manuscripts. In response to Ørsted's discovery of electromagnetism in 1820, Ampère initially supposed that the field of a permanent magnet was due to a macroscopic circulating current. Fresnel suggested instead that there was a microscopic current circulating around each particle of the magnet. In his first note, he argued that microscopic currents, unlike macroscopic currents, would explain why a hollow cylindrical magnet does not lose its magnetism when cut longitudinally. In his second note, dated 5 July 1821, he further argued that a macroscopic current had the counterfactual implication that a permanent magnet should be hot, whereas microscopic currents circulating around the molecules might avoid the heating mechanism. He was not to know that the fundamental units of permanent magnetism are even smaller than molecules . The two notes, together with Ampère's acknowledgment, were eventually published in 1885. |
Augustin-Jean Fresnel | Lost works | Lost works
Fresnel's essay Rêveries of 1814 has not survived.Buchwald, 1989, p. 116. The article "Sur les Différents Systèmes relatifs à la Théorie de la Lumière" ("On the Different Systems relating to the Theory of Light"), which Fresnel wrote for the newly launched English journal European Review,Fresnel, 1866–70, vol. 2, pp. 768n,802. was received by the publisher's agent in Paris in September 1824. The journal failed before Fresnel's contribution could be published. Fresnel tried unsuccessfully to recover the manuscript. The editors of his collected works were unable to find it, and concluded that it was probably lost.Fresnel, 1866–70, vol. 2, p. 803n. Grattan-Guinness (1990, p. 884n) gives the year of composition as 1825, but this does not match the primary sources. |
Augustin-Jean Fresnel | Unfinished work | Unfinished work |
Augustin-Jean Fresnel | Aether drag and aether density | Aether drag and aether density
In 1810, Arago found experimentally that the degree of refraction of starlight does not depend on the direction of the earth's motion relative to the line of sight. In 1818, Fresnel showed that this result could be explained by the wave theory,Cf. Darrigol, 2012, pp. 258–260. on the hypothesis that if an object with refractive index moved at velocity relative to the external aether (taken as stationary), then the velocity of light inside the object gained the additional component . He supported that hypothesis by supposing that if the density of the external aether was taken as unity, the density of the internal aether was , of which the excess, namely , was dragged along at velocity , whence the average velocity of the internal aether was . The factor in parentheses, which Fresnel originally expressed in terms of wavelengths,Fresnel, 1818c. became known as the Fresnel drag coefficient.
In his analysis of double refraction, Fresnel supposed that the different refractive indices in different directions within the same medium were due to a directional variation in elasticity, not density (because the concept of mass per unit volume is not directional). But in his treatment of partial reflection, he supposed that the different refractive indices of different media were due to different aether densities, not different elasticities.Darrigol, 2012, p. 212; Fresnel, 1821a, §§ 14,18. |
Augustin-Jean Fresnel | Dispersion | Dispersion
The analogy between light waves and transverse waves in elastic solids does not predict dispersion—that is, the frequency-dependence of the speed of propagation, which enables prisms to produce spectra and causes lenses to suffer from chromatic aberration. Fresnel, in De la Lumière and in the second supplement to his first memoir on double refraction, suggested that dispersion could be accounted for if the particles of the medium exerted forces on each other over distances that were significant fractions of a wavelength.Darrigol, 2012, p. 246; Buchwald, 1989, pp. 307–308; Fresnel, 1822a, tr. Young, in Quarterly Journal of Science, Literature, and Art, Jan.–Jun.1828, at pp. 213–215. Whittaker, 1910, p. 132; Fresnel, 1866–70, vol. 2, p. 438. Later, more than once, Fresnel referred to the demonstration of this result as being contained in a note appended to his "second memoir" on double refraction.Fresnel, 1827, tr. Hobson, pp. 277n,331n; Lloyd, 1834, p. 316. No such note appeared in print, and the relevant manuscripts found after his death showed only that, around 1824, he was comparing refractive indices (measured by Fraunhofer) with a theoretical formula, the meaning of which was not fully explained.Fresnel, 1866–70, vol. 1, p. xcvi.
In the 1830s, Fresnel's suggestion was taken up by Cauchy, Baden Powell, and Philip Kelland, and it was found to be tolerably consistent with the variation of refractive indices with wavelength over the visible spectrum for a variety of transparent media .Whittaker, 1910, pp. 182–183; Whewell, 1857, pp. 365–367; Darrigol, 2012, pp. 246–249. These investigations were enough to show that the wave theory was at least compatible with dispersion; if the model of dispersion was to be accurate over a wider range of frequencies, it needed to be modified so as to take account of resonances within the medium .Darrigol, 2012, p. 252. |
Augustin-Jean Fresnel | Conical refraction | Conical refraction
The analytical complexity of Fresnel's derivation of the ray-velocity surface was an implicit challenge to find a shorter path to the result. This was answered by MacCullagh in 1830, and by William Rowan Hamilton in 1832.Lloyd, 1834, pp. 387–388. |
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