A graph of the Airy pattern on the interval <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ka\sin \theta =[-10,10]}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>k</mi><mi>a</mi><mi>sin</mi><mo>⁡<!-- ⁡ --></mo><mi>θ<!-- θ --></mi><mo>=</mo><mo stretchy="false">[</mo><mo>−<!-- − --></mo><mn>10</mn><mo>,</mo><mn>10</mn><mo stretchy="false">]</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle ka\sin \theta =[-10,10]}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc1aa3532bac299bd347370ee8c48fad37334b91" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:19.045ex; height:2.843ex;" alt="ka\sin \theta =[-10,10]"></span>:
<dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I(\theta )=I_{0}\left({\frac {2J_{1}(ka\sin \theta }{ka\sin \theta }}\right)^{2}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>I</mi><mo stretchy="false">(</mo><mi>θ<!-- θ --></mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow><mn>2</mn><msub><mi>J</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mi>k</mi><mi>a</mi><mi>sin</mi><mo>⁡<!-- ⁡ --></mo><mi>θ<!-- θ --></mi></mrow><mrow><mi>k</mi><mi>a</mi><mi>sin</mi><mo>⁡<!-- ⁡ --></mo><mi>θ<!-- θ --></mi></mrow></mfrac></mrow><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle I(\theta )=I_{0}\left({\frac {2J_{1}(ka\sin \theta }{ka\sin \theta }}\right)^{2}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e564d1f6757b5bfec987a1ffc8dc3981e05c78f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:26.132ex; height:6.676ex;" alt="I(\theta )=I_{0}\left({\frac  {2J_{1}(ka\sin \theta }{ka\sin \theta }}\right)^{2}"></span></dd></dl></dd></dl><ul><li><i>k</i> is the wavenumber, in m <sup>−1</sup></li>
<li><i>a</i> is the radius of the aperture</li>
<li><i>θ</i> is the angle of observation.</li>
<li><i>I</i><sub>0</sub> is the maximum intensity.</li>
<li><i>J</i><sub>1</sub> is the order one <a href="https://en.wikipedia.org/wiki/Bessel_function" class="extiw" title="w:Bessel function">Bessel function</a> of the first kind.</li></ul>
<a href="//commons.wikimedia.org/wiki/User:Inductiveload" title="User:Inductiveload">Inductiveload</a>
2009-03-04
<span class="int-own-work" lang="en">Own work</span>