precise measurements of the optical properties of biological 
 tissues and fluids are   important for a large class of medical diagnostics as 
 well as therapeutic and surgical approaches that employ light .   often blood is present and therefore its 
 optical properties need to be considered in the design or deployment of these 
 optical methods [ 14 ] . given its complexity as a propagating environment for 
 light , a wide array of experimental investigations into the optical properties 
 of blood has been carried out .   there are 
 methods that directly estimate the light transmission and scattering properties 
 of blood but they can be applied only to thin blood samples , require 
 complicated optical setups , and are suitable only for ex - vivo situations 
 [ 5 , 6 ] . a number of studies have been 
 published about blood properties based on widely used indirect methods of 
 modeling light propagation in turbid environments : wave - scattering theory [ 7 , 8 ] , photon - diffusion theory [ 1 , 9 ] , and inverse monte - carlo simulations [ 10 , 11 ] . although extensive and rigorous in the mathematical sense , the results 
 depend on a precise model of the tissue structures as well as the optical 
 properties associated with these structures . often simplified tissue model geometries are employed in these cases to 
 render analytical or computationally tractable solutions and , when coupled with 
 imprecise knowledge of the various optical parameters , the accuracy of these 
 indirect methods can be questioned .   in 
 this paper , we demonstrate a simple and efficient method to directly determine 
 a number of clinically relevant optical parameters such as the index of 
 refraction , the attenuation coefficient , and the scattering anisotropy factor 
 of blood . these parameters are measured at 1300 nm , a promising wavelength to 
 be used in clinical devices for probing highly scattering biological samples 
 because it is scattered less than light at shorter wavelengths . the estimations 
 of the attenuation coefficient and of the anisotropy factor are based on a 
 numerical algorithm fit on the experimentally acquired optical coherence 
 tomography ( oct ) heterodyne efficiency curve . the connection between these 
 parameters characterizing blood and the dependence on the propagation distance 
 within blood of the detected oct signal is provided by the extended 
 huyghens - fresnel principle . previously , this optical method has been used successfully in 
 determining the scattering properties of various biological samples as well as 
 phantom probes of blood [ 1316 ] . the oct measurements presented here are 
 acquired in fresh blood that flows freely within a system of flow cells . the 
 results obtained in this configuration could be relevant in designing and using 
 intravascular oct catheters . also , the viability of the extended 
 huygens - fresnel principle is verified for oct probing beams at low powers . checking the viability of this principle at low intensities is necessary 
 because in clinical settings the investigating beam could be strongly quenched 
 while passing through other tissues before reaching the region of interest . oct images are recorded using radiation emitted 
 from a super - luminescent sld-571-hp diode with the central wavelength at 1300 nm 
 and a coherence length of 14 m 
 ( full width at half maximum ) measured in air . due to its 
 lower absorption and scattering losses in tissues when compared to visible and 
 shorter near - infrared wavelengths , the spectral region around 1300 nm has the 
 potential to become important for a number of biophotonics applications   [ 1719 ] . in both arms of the interferometer , sample and reference , light is 
 guided through single - mode fibers terminated with collimating lenses . in the 
 reference arm , a rapid scanning optical delay line with a constant velocity of 
 600 a weakly focusing lens with a 48-mm focal 
 distance and a focal depth of 1.6 mm is located near the exit of the sample 
 fiber for the purpose of focusing the collimated light onto the sample . such a small 
 value of the numerical aperture together with the proper positioning of the 
 probed region within the depth of focus provides a beam that could be 
 approximated as collimated along the axial section of the scanned volume . this 
 configuration ensures that the beam divergence does not influence the intensity 
 of the oct signal along the depth of interest . the fiber - lens assembly is mounted on a computer - controlled horizontal 
 translation stage that can scan the focused spot of the illuminating beam along 
 the surface of interest with a maximum spatial resolution of 1 m . the power of the beam exiting the sample arm of the interferometer is 2 mw . fresh porcine blood is acquired from an 
 abattoir immediately after sacrifice . 
 using a masterflex pump , blood is continuously circulated in a 
 closed - loop circuit through two consecutive 48/q/2 starna flow cells at a 
 constant flow rate of 1 ml / min . one cell has the thickness of its flowing 
 channel of 2 mm while the other flow channel in the other cell is 0.2 mm wide . blood is flowing normal to the propagation direction of light exiting the 
 focusing lens that terminates the sample arm of the oct system . the measured 
 haematocrit , that is , the ratio of the volume of red blood cells to the entire 
 volume of blood , stayed constant at 44% for the duration of the experiment . in 
 order to avoid coagulation , 2 ml / l of heparin heparin was added at 
 a rate of 1 ml / l at 1-hour intervals for the remainder of the protocol . the oct image presented in figure 1(a ) is 
 obtained by acquiring a set of 1600 consecutive depth scans ( also known as line 
 scans or a - scans ) . this image shows the detected signal backscattered by blood 
 cells that are flowing through the 0.2-mm cell during its acquisition time . to 
 eliminate the random thermal , mechanical , and electronic noise , each depth scan the image presents itself as a speckled pattern that is 
 generated by the portion of the light flux that reaches the oct detection 
 system after it is scattered at the interfaces of blood cells with the 
 surrounding plasma . this image shows the entire cross - section of the flow 
 channel crossing through the 0.2-mm cell . in this case , both blood and glass 
 interfaces are distinguishable and the optical distance between them can be 
 assessed directly from the oct image . knowing the width of the flow channel , 
 the value of the optical refraction index of blood is readily obtained by 
 dividing the optical distance between the upper and lower blood / glass 
 interfaces determined when the channel is filled with blood with the width of 
 the flow channel . the value obtained for the optical index of refraction for 
 blood at 1300 nm by this method is nblood = 1.39  0.05 . the 
 uncertainty in the measured optical refractive index arises from both the 
 specified tolerance in the width of the flow cell channel , 0.01 mm ( starna inc . catalog ) , and the imprecision introduced by the finite coherence length of the 
 oct source , ~0.014 mm . another two - dimensional oct image , this time of 
 blood flowing through the 2-mm flow cell , is presented in 
 figure 1(b ) . as light penetrates deeper inside blood , it is reflected , scattered , 
 and absorbed by various cellular aggregates and fluidic blood components . due 
 to the strong light scattering environment that is flowing blood , there is no 
 recorded oct signal that comes from the second glass / interface , that is , the 
 interface located at a 2-mm distance from the interface through which light enters blood . it is known that while light 
 propagates through blood , it undergoes diffuse reflection from the blood cell membranes and therefore 
 the backscattered oct signal is weak . also , according to 
  [ 11 , 20 ] , the scattering anisotropy factor for 
 blood measured at various wavelengths is reported to be between 0.94 and 0.995 . such values of the anisotropy factor are characteristic to a strong forward 
 scattering of light in blood and translate into a reduced probability for its 
 backscattering toward the oct detection system . the cumulative effect of 
 multiple scattering events is another factor reducing the detected signal . by 
 undergoing multiple interactions within the turbid environment , part of the 
 probing light flux is pushed out from the field of view of the objective lens 
 or beyond the spatial detection gate imposed by the optical delay line in the 
 reference arm . these factors , plus the low power of the interrogating beam , 
 contribute to an oct signal that is detected after probing a maximum distance 
 of only 0.25 mm within blood . an example of a demodulated a - scan 
 interferogram is indicated   in figure 2 by the dotted line . it shows the signal 
 generated into the oct detection system through backscattering of light by 
 blood cells during the 600th a - scan . the position of this particular a - scan is 
 marked with a white interrupted line in the two - dimensional oct 
 image from figure 1(b ) . in figure 2 , the specular reflection peak corresponding to the glass / blood 
 interface is eliminated in order to better emphasize the signal generated only 
 by the diffuse reflections occurring within the blood environment . the noisy 
 profile of the single a - scan is common for oct scans of highly scattering media 
 and can be attributed to the random positions of scattering centers and to the 
 speckle noise generated by 
 multiple scattering . speckle noise 
 occurs in oct imaging applied to turbid media because of multiple scattered light that experiences 
 changes in the travel distance relative to its initial ballistic path 
 reaching the detection 
 system [ 17 , 21 ] . in order to accurately estimate the propagation properties of 
 light in a highly scattering medium , speckle noise can 
 be suppressed by adding spatially independent scans [ 2224 ] . in the presented 
 case , because of the blood flow , there is a dynamic distribution of cellular 
 aggregates that act as scattering centers , which in turn induces variations of 
 the speckle pattern from one a - scan to another . adding ( compounding ) 
 independent individual a - scans with uncorrelated speckle patterns results into 
 a smoothed depth profile where some of the speckle noise as well as the noise 
 generated by random electronic and thermal variations in the oct detection 
 system are eliminated . such a compounded profile is exemplified by the 
 continuous curve from figure 2 , which is obtained by compounding 1000 
 individual a - scans . to account for the scaling difference between profiles , the 
 single scan as well as the compounded one is normalized to unity in 
 figure 2 . as light penetrates deeper inside blood , the 
 recorded oct signal decreases due to both optical absorption and scattering . 
 within the depths probed in our experiment , scattering is predominantly 
 responsible for dissipation of the near - infrared signal while absorption is 
 responsible for less than 0.5% of the total radiation loss . therefore , in 
 the following we will consider that the profiles of individual and compounded 
 depth scans are exclusively shaped by the scattering properties of blood . the aggregate recorded oct signal power , i(z) , 
 corresponding to the oct signal received from a given depth , z , inside 
 the blood environment can be expressed as the product between the mean square 
 heterodyne signal in the absence of scattering , i0 , 
 and the heterodyne efficiency , presented as the sum of three terms that account 
 for the scattering losses : 
 ( 1)i2(z)  =  i20  [ exp(2z )  +  4exp(z)[1    exp(z)]1  +  r2(z )  +  [ 1    exp(z)]2r2(z ) ] . in 
 ( 1 ) ,  represents the scattering coefficient and r is the halo parameter , that is , the ratio between the squares of the 1/e irradiance radii in the z - plane in the presence and absence of 
 scattering . the halo coefficient is a measure of the lateral coherence length 
 including its dependence on the penetration distance , that is , the shower 
 curtain effect . as shown by the compounded profile in figure 2 , the 
 light penetration in blood for which a readable oct signal is obtained for this 
 particular experimental configuration is approximately 0.25 mm , which is small 
 when compared to the focal distance ( 48 mm ) of the objective lens used in the 
 sample arm . besides the single - backscattered component , there is also 
 multiple - scattered signal that is recorded in our oct measurements despite the 
 low depth of penetration into the turbid environment [ 2628 ] . the following 
 fact has to be considered in our analysis : blood cells are not point - like 
 scattering centers but disk - like entities with diameters around 8 m and thicknesses of approximately 3 m that occupy a certain volume in space 
 to the extent that light spends an amount of time propagating through the cell 
 ensemble comparable to the time spent propagating into the blood plasma . 
 therefore , because of intra- and intercell multiple light reflections occurring 
 at the cell / plasma interfaces , oct signal that experienced multiple scattering 
 events is recorded even after short distances ( tens of m ) of propagation through blood . the 
 early onset of a multiple - scattered component in the recorded signal generated 
 when light propagates in blood phantoms or blood / saline mixtures has been 
 documented in previous publications [ 2628 ] . 
 also , the amount of multiple scattered signal increases as the oct 
 signal is recorded from deeper within the scattering environment [ 2628 ] . in our experimental configuration , the depth within 
 blood that is probed is centered at the waist of the weakly focused probe beam . therefore , the lens - induced axial variation in its intensity has a minimal 
 impact on the recorded oct profile . avoiding the influence of the beam 
 divergence on the intensity of the compounded profile is helped also by the 
 small value of the numerical aperture of the optical system from the oct sample 
 arm , that is 0.025 . within these experimental conditions and taking into 
 account the configuration of the oct system sample arm , the halo factor can be 
 expressed as 
 ( 2)r2(z )  =  1  +  cz3 . in ( 2 ) , c is a constant depending on 
 sample parameters like the blood refraction index and the scattering anisotropy 
 parameter , g , as well as on instrumental constants : the effective 
 numerical aperture , n.a . , of the objective lens used to focus the probing beam 
 onto the sample and the free - space wavelength of the source ,  : 
 ( 3)c  =  823(n.a.)2(1    g)nblood2 . the 
 term contained in the brackets in relation ( 1 ) , that is , the heterodyne 
 efficiency which can be also expressed as the i(z)/i0 ratio , is fit with the experimentally measured 
 and normalized compounded oct signal power shown in figures 3(a ) 
 and 3(b ) . having previously measured the index of refraction of blood and knowing the 
 wavelength as well as the effective numerical aperture , the latter precisely 
 measured using the technique described in 
  [ 29 , 30 ] , only the 
 scattering coefficient and the anisotropy parameter are used as fitting 
 parameters . the numerical fit with the experimental heterodyne efficiency curve 
 is performed up to the point where the signal is 1.5 times higher than the 
 detection shot noise . values of 12.15 mm and 0.95 are obtained for 
 the total attenuation coefficient and for the scattering anisotropy factor . these values are consistent with the values obtained in . when compared to 
 results determined at visible and shorter near - infrared wavelengths , the trend 
 of decreasing scattering coefficients for longer wavelengths in the 
 near - infrared region is also confirmed . this trend has been both experimentally observed and theoretically predicted 
 in several publications [ 11 , 20 , 31 ] . the anisotropy factor estimated in this work by 
 applying the extended huygens - fresnel principle to the compounded oct profile has a value that is approximately 4% smaller than values theoretically 
 calculated or measured from transmission - type experimental arrangements . in 
 such experimental setups , the amount of scattered flux is measured or 
 calculated at detection points located at distances much greater than the 
 dimensions of the volume where the scattering takes place . therefore , the 
 signatures of individual scattering centers , blood cells in the case under 
 study , are lost because only the far - field flux is measured . the far - field flux 
 is a quantity that is an averaged result of the overall scattering events 
 occurring in the entire probed volume . meanwhile , due to the interference - based 
 axial sectioning capabilities and due to the coherence - imposed limitations on 
 the detected signal , only the scattering properties of blood constituents from 
 specific locations confined within a small volume are assessed with an 
 oct - based configuration . more clearly , in an oct configuration the detected 
 signal can be envisioned as portioned into units that are the result of light 
 interacting only with a small number of cells located within a sample volume 
 defined by the coherence length of the oct source and the area of the probing 
 beam . therefore , the detected oct signal is sensitive to the optical and 
 geometrical characteristics of the individual blood cell and the morphological 
 discontinuities occurring on microscopic scales can affect its outcome . figures 3(a ) and 3(b ) help in determining the 
 sensitivity of the fitting procedure to small variations of the attenuation 
 coefficient and anisotropy scattering parameter . for comparison , curves 
 corresponding to attenuation coefficients of 11.35 mm and 12.85 mm are calculated and shown 
 in figure 3(a ) with the anisotropy parameter kept at 
 0.95 , the value obtained from the numerical fit . similarly , curves with two 
 different anisotropy scattering factors , 0.97 and 0.93 , are plotted 
 in figure 3(b ) using the attenuation coefficient numerically obtained from fitting the 
 compounded oct profile . differences between the curves obtained with these 
 values of the attenuation coefficient and anisotropy factor and the curve that 
 provides the best numerical fit to the experimental data are obvious from the 
 figure . the values used to derive the unfit curves are used to estimate the 
 precision of the procedure . the root - mean - squared error ( rmse ) provides a 
 quantitative measurement of the deviation of the numerical models from the 
 experimental data . the smallest rmse is of course obtained for the numerical 
 fit . as a comparison among the other four cases , that rmse value is still 35% greater than the one corresponding to 
 the numerical fit . a method based on the extended huygens - fresnel 
 principle applied   to time - domain oct measurements is demonstrated to directly 
 estimate optical parameters of blood .   by 
 employing this procedure , the use of phantom samples prepared under 
 predetermined physiological conditions as well as complicated reconstruction 
 algorithms could be avoided . the research presented here fills a knowledge gap 
 regarding the optical interaction between blood constituents and light at 1300 nm . 
 knowing the refractive index of blood and the attenuation induced in the 
 signal by light scattering enables a more precise estimation of the effective 
 propagation distance of oct signal into blood for a system configuration 
 similar to an oct - based intravascular catheter design . the effective depth that 
 can be probed within blood before the signal becomes imbedded into the shot 
 noise is a useful parameter to be known when designing and using oct - based 
 intravascular catheters . values of 12.15 mm , 1.39 , and 0.95 are 
 estimated for the total attenuation , the refraction index , and the scattering 
 anisotropy factor , respectively . both the attenuation coefficient and the 
 anisotropy factor are determined simultaneously by applying the extended huygens - fresnel 
 principle to the experimental heterodyne efficiency curve . the refraction index 
 of blood is determined to a second decimal precision while the total 
 attenuation coefficient and the scattering anisotropy parameter values are 
 within experimental error margins of 5% and 2% , respectively .
a direct method for the measurement of the optical attenuation coefficient and the scattering anisotropy parameter based on applying the extended huygens - fresnel principle to optical coherence tomography images of blood is demonstrated . 
 the images are acquired with a low - power probing beam at the wavelength of 1300 nm . 
 values of 12.15 mm1 and 0.95 are found for the total attenuation coefficient and the scattering anisotropy factor , respectively . also , as a preliminary step , the optical refraction index is determined with a precision of two decimal numbers directly from optical coherence images . 
 the total attenuation coefficient and the scattering anisotropy factor are determined with precisions within experimental error margins of 5% and 2% , respectively . 
 readable oct signal is obtained for a maximum propagation of light into blood of 0.25 mm . at the maximum 
 probed depth , the measured signal is almost 103 smaller than its initial intensity when entering the sample .