.. _sphx_glr_api_gallery_optics_diffraction:

Diffraction
-----------

Scalar wave optics from Huygens through Airy: Huygens' wavelet
construction as diffractive spreading of a pinhole, Young's double-slit
interference fringes (including an animated sweep of the near-to-far-field
wavefront propagation), Fresnel's near-field diffraction theory and the
Poisson/Arago spot, and Airy's circular-aperture pattern and the
diffraction limit it implies.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="George Biddell Airy worked out the exact Fraunhofer diffraction pattern of a circular aperture, finding a bright central disk surrounded by faint concentric rings rather than the sharp geometric image predicted by ray optics. Lord Rayleigh turned Airy&#x27;s pattern into a practical resolving-power criterion: two point sources are just resolvable when the central peak of one Airy pattern falls on the first dark ring of the other, giving the diffraction limit \theta_{\min} \approx 1.22\,\lambda/D that bounds every microscope, telescope, and camera lens. circular_aperture and fraunhofer_diffraction reproduce the Airy pattern directly from a numerical Fourier transform -- no closed-form Bessel function is needed -- and its first dark ring lands exactly at the Rayleigh angle computed independently.">

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  .. image:: /api/gallery/optics/diffraction/images/thumb/sphx_glr_plot_airy_diffraction_limit_thumb.png
    :alt:

  :doc:`/api/gallery/optics/diffraction/plot_airy_diffraction_limit`

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      <div class="sphx-glr-thumbnail-title">The Airy disk and the diffraction limit</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Augustin-Jean Fresnel combined Huygens&#x27; wavelet construction with Young&#x27;s principle of interference into a quantitative near-field diffraction theory. Simeon Poisson pointed out -- intending it as a reductio ad absurdum -- that Fresnel&#x27;s own theory predicted a bright spot at the center of the shadow of a circular obstacle; Francois Arago promptly observed the &quot;Poisson spot&quot; in the laboratory, turning a supposed refutation into the theory&#x27;s most dramatic confirmation.">

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  .. image:: /api/gallery/optics/diffraction/images/thumb/sphx_glr_plot_fresnel_poisson_spot_thumb.png
    :alt:

  :doc:`/api/gallery/optics/diffraction/plot_fresnel_poisson_spot`

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      <div class="sphx-glr-thumbnail-title">Fresnel diffraction and the Poisson/Arago spot</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Christiaan Huygens&#x27; 1690 construction treats every point of an advancing wavefront as the source of a new spherical secondary wavelet; the envelope of all those wavelets a moment later reconstructs the propagated wavefront. angular_spectrum_propagate realizes exactly this modern form of the picture. The scalar field U_0(x,y) right after the aperture is decomposed into its plane-wave (angular) spectrum by a 2D Fourier transform; each plane-wave component, labeled by transverse spatial frequency (f_x,f_y), is a secondary wavelet that advances rigidly along z picking up phase e^{ik_z z}; re-synthesizing (inverse Fourier transform) sums the interference of all these wavelets at the new plane:">

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  .. image:: /api/gallery/optics/diffraction/images/thumb/sphx_glr_plot_huygens_wavelets_thumb.png
    :alt:

  :doc:`/api/gallery/optics/diffraction/plot_huygens_wavelets`

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      <div class="sphx-glr-thumbnail-title">Huygens' wavelets: diffractive spreading of a pinhole</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Thomas Young argued in his 1801 Bakerian Lecture that light passing through two closely spaced slits produces alternating bright and dark fringes on a distant screen, explicable only if light is a wave capable of constructive and destructive interference. Where the two path lengths from the slits to an observation point differ by an integer number of wavelengths the waves reinforce; where they differ by a half-integer number, they cancel. double_slit_aperture builds exactly this two-slit transmission mask, and fraunhofer_diffraction propagates it to the far field, reproducing Young&#x27;s fringe pattern directly from a computed intensity distribution -- no \sin\theta fringe formula is used, only the wave field itself. Rather than jumping straight to that far-field limit, animate_diffraction_propagation animates the near-field wavefronts developing continuously into the far-field fringe pattern as the propagation distance grows.">

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  .. image:: /api/gallery/optics/diffraction/images/thumb/sphx_glr_plot_young_double_slit_thumb.png
    :alt:

  :doc:`/api/gallery/optics/diffraction/plot_young_double_slit`

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      <div class="sphx-glr-thumbnail-title">Young's double-slit fringes</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/optics/diffraction/plot_airy_diffraction_limit
   /api/gallery/optics/diffraction/plot_fresnel_poisson_spot
   /api/gallery/optics/diffraction/plot_huygens_wavelets
   /api/gallery/optics/diffraction/plot_young_double_slit