Consequences of sampling an image and Fourier planes in a numerical light propagation model based on the Helmholtz-Kirchhoff approximation

Aleksander Sokołowski

doi:10.1364/JOSAA.23.002764

Journal of the Optical Society of America A
Vol. 23,
Issue 11,
pp. 2764-2767
(2006)
•https://doi.org/10.1364/JOSAA.23.002764

Consequences of sampling an image and Fourier planes in a numerical light propagation model based on the Helmholtz–Kirchhoff approximation

Aleksander Sokołowski

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Aleksander Sokołowski, "Consequences of sampling an image and Fourier planes in a numerical light propagation model based on the Helmholtz-Kirchhoff approximation," J. Opt. Soc. Am. A 23, 2764-2767 (2006)

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Abstract

The numerical model of the light propagation phenomenon based on the Helmholtz–Kirchhoff approximation has been analyzed. The model is based on the fast Fourier transform algorithm. It is proved that the fast Fourier transform algorithm limits the class of describing phenomena to the Talbot effects.

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Values of m, n	$n = 0$	$n = 1$	$n = 2$	$n = 3$	$n = 4$	$n = 5$
$m = 0$	1	$- 1 / 2 + i \sqrt{3} / 2$	$- 1 / 2 + i \sqrt{3} / 2$	1	$- 1 / 2 + i \sqrt{3} / 2$	$- 1 / 2 + i \sqrt{3} / 2$
$m = 1$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$
$m = 2$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$
$m = 3$	1	$- 1 / 2 + i \sqrt{3} / 2$	$- 1 / 2 + i \sqrt{3} / 2$	1	$- 1 / 2 + i \sqrt{3} / 2$	$- 1 / 2 + i \sqrt{3} / 2$
$m = 4$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$
$m = 5$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$	$- 1 / 2 + i \sqrt{3} / 2$	$- \sqrt{3} / 2 - i / 2$	$- \sqrt{3} / 2 - i / 2$

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Journal of the Optical Society of America A