Filters of the type exp(in theta)sgn J(n)(z(o)r) with theta the azimuthal angle and r the radial coordinate in the filter plane, are shown to maximize the energy content in a narrow annular image of radius z(o) with respect to incident energy. The simplest optimal filter, sgnJ(o)(z(o)r), is well approximated by the binary circular phase grating sgn cos(z(o)r - pi/4). The single lobe of the first order image of this filter contains 46% of the incident energy within the half-width 0.4lambdaf/a, centered around the image radins Nlambdaf/(2a), where N approximately z(o)/pi is the number of filter sections.
An inversion method which reproduces the radial variation of dielectric constant in a dielectric target from its microwave scattering pattern is presented. Inversion criteria are developed showing what part of the target can be reconstructed. The technique is applied to experimentally measured scattering patterns.
The fine structure of the annular images of circular gratings is analyzed in terms of diffraction patterns of axicon pairs. Each image arises substantially from only one converging and one diverging axicon of equal deflection angle. Single main lobe, symmetric double main lobe, and various intermediate asymmetric double lobe structures are obtained depending on the phase relationship and strengths of the two axicon beams, which in turn depend on the design of the circular grating. Approximate expressions are derived for the intensity distribution and energy content of the symmetric single and double lobe images.
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