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30 August 2006 On the computation of the coherent point-spread function using a low-complexity representation
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Abstract
Computation of the coherent point-spread function (PSF) involves evaluation of the diffraction integral, which is an integration of a highly oscillating function. This oscillation becomes severe as the value of defocus increases and thus makes PSF computation a costly task. We present a novel algorithm for computing the PSF, which works efficiently for any arbitrarily large value of defocus. It is theoretically proved that the complexity of our new algorithm does not depend on the value of defocus. We also develop an implementation scheme for the new algorithm. Using this implementation we experimentally demonstrate the low complexity of our method. We quantify the rapid convergence and numerical stability of this method over all ranges of defocus. Finally, we compare the computational cost of this method, in terms of time and memory, with other numerical methods such as direct numerical integration and the Fast Fourier Transform.
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Saeed Bagheri, Daniela Pucci de Farias, George Barbastathis, and Mark A. Neifeld "On the computation of the coherent point-spread function using a low-complexity representation", Proc. SPIE 6311, Optical Information Systems IV, 631108 (30 August 2006); doi: 10.1117/12.680632; https://doi.org/10.1117/12.680632
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