One obstacle to optimizing performance of large-scale coded aperture systems operating in the diffractive regime has
been the lack of a robust, rapid, and efficient method for generating diffraction patterns that are projected by the system
onto the focal plane. We report on the use of the 'Shrekenhamer Transform' for a systematic investigation of various
types of coded aperture designs operating in the diffractive mode. Each design is evaluated in terms of its
autocorrelation function for potential use in future imaging applications. The motivation of our study is to gain insight
into more efficient optimization methods of image reconstruction algorithms.
A novel and memory efficient method for computing diffraction patterns produced on large-scale focal planes by largescale
Coded Apertures at wavelengths where diffraction effects are significant has been developed and tested. The
scheme, readily implementable on portable computers, overcomes the memory limitations of present state-of-the-art
simulation codes such as Zemax. The method consists of first calculating a set of reference complex field (amplitude
and phase) patterns on the focal plane produced by a single (reference) central hole, extending to twice the focal plane
array size, with one such pattern for each Line-of-Sight (LOS) direction and wavelength in the scene, and with the
pattern amplitude corresponding to the square-root of the spectral irradiance from each such LOS direction in the scene
at selected wavelengths. Next the set of reference patterns is transformed to generate pattern sets for other holes. The
transformation consists of a translational pattern shift corresponding to each hole’s position offset and an electrical phase
shift corresponding to each hole’s position offset and incoming radiance’s direction and wavelength. The set of
complex patterns for each direction and wavelength is then summed coherently and squared for each detector to yield a
set of power patterns unique for each direction and wavelength. Finally the set of power patterns is summed to produce
the full waveband diffraction pattern from the scene. With this tool researchers can now efficiently simulate diffraction
patterns produced from scenes by large-scale Coded Apertures onto large-scale focal plane arrays to support the
development and optimization of coded aperture masks and image reconstruction algorithms.
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