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Examples of Physical Optics Propagation

Free Space Propagation using the Angular Spectrum Method

The following figures show the computed intensity patterns at various distances from a circular aperture. The computations were carried out on a discrete 512 x 512 mesh using Fast Fourier Transform (FFT).

Circular aperture, illuminated by a uniform plane wave. Propagation distance z = 0.

Fresnel number = 18

Fresnel number = 4

Fresnel number = 1

Free Space Propagation using Fresnel Integral

The Fresnel propagator is used for computing the far field distribution. The images below are taken for Fresnel numbers 4 and 1. They are identical to the corresponding images obtained with the angular spectrum method as shown above, except that the Fresnel propagator has been used.

Fresnel number = 4

Fresnel number = 1

Talbot Effect

The Talbot imaging phenomenon is present for periodic structures. The figure to the left shows the self imaging effect of a transmissive periodic grating in the region of Fresnel diffraction. The structure is illuminated by a plane wave.

The side lobes are due to the finite extent of the grating structure.

Double Pinhole

In this example the input screen contains two very small apertures (pinholes): a Youngs interferometer. The results of interference are shown for two positions behind the screen.

Input field

Full overlap of beams. Note the slight ellipticity, which is due to the rectangular "pinholes", having a 4:5 aspect ratio.