TY - GEN
T1 - On the computation of the coherent point-spread function using a low-complexity representation
AU - Bagheri, Saeed
AU - Pucci De Parias, Daniela
AU - Barbastathis, George
AU - Neifeld, Mark A.
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
KW - Diffraction
KW - Fourier transforms
KW - Numerical approximation and analysis
KW - Point-spread function
UR - http://www.scopus.com/inward/record.url?scp=33750685661&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33750685661&partnerID=8YFLogxK
U2 - 10.1117/12.680632
DO - 10.1117/12.680632
M3 - Conference contribution
AN - SCOPUS:33750685661
SN - 0819463906
SN - 9780819463906
T3 - Proceedings of SPIE - The International Society for Optical Engineering
BT - Optical Information Systems IV
T2 - Optical Information Systems IV
Y2 - 16 August 2006 through 17 August 2006
ER -