An Axial Form of the Sampling Theorem and its Application to Optical Diffraction

Abstract

The sampling theorem is used to obtain expressions for the diffracted amplitude G(y, z) at any point in space, once the distribution along the axis G(y, 0) is known at the sampling points. In the case of a circular symmetrical pupil, G(y, 0) is simply the Fourier transform of the pupil function. The real or imaginary parts of G(y, z) may be obtained either from the real or from the imaginary part of G(y, 0). By suitable oversampling, the real part of G(y, z) may be found from its imaginary part, and vice versa. A technique for the synthesis of antenna patterns is suggested.

A New Series Representation of the Fresnel Diffraction Field of Axially Symmetrical Filters

“…The total energy transmitted through the filter g(t), By means of the Fourier series (2) the diffraction integral (1) may be expressed as the sum [3,4] G(u, v)= I g.0 (u., v), ( 8 ) n where un…”

“…In contrast to the general character of considerations in the previous paper [3] inspired by the Arsenault-Boivin representation [4], we shall study the behaviour of the focal diffraction patterns in more detail . The representation from [4] can be transformed to the series expansion in which the number of periods M directly control the rapidity of the series convergence ( §3) .…”

“…The representation from [4] can be transformed to the series expansion in which the number of periods M directly control the rapidity of the series convergence ( §3) . This property of the new series representation facilitates considerably the discussion and calculation of the diffraction patterns due to the filter transmissivities with different number of periods M-cf.…”

Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: comment

“…To our knowledge Arsenault and Boivin originally published the AST in 1967. 3 The authors of Refs. 2 and 3 dealt with coherently illuminated optical systems in which axially symmetric spherical converging light waves were diffracted (Fig.…”

Tunable hyperbolic apodizer

“…Some experts may not be aware of the following analogy; which exploits McCutchen theorem [2][3][4][5][6].…”