Analysis of a white-light processing system based on the cross-spectral density function

X. J. Lu; F. T. S. Yu

doi:10.1364/JOSAA.4.001419

Journal of the Optical Society of America A
Vol. 4,
Issue 8,
pp. 1419-1427
(1987)
•https://doi.org/10.1364/JOSAA.4.001419

Analysis of a white-light processing system based on the cross-spectral density function

X. J. Lu and F. T. S. Yu

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X. J. Lu and F. T. S. Yu, "Analysis of a white-light processing system based on the cross-spectral density function," J. Opt. Soc. Am. A 4, 1419-1427 (1987)

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Abstract

An analysis of a white-light optical-processing system is presented based on the cross-spectral density function. A plane-by-plane analysis of the cross-spectral density function is given, including the effects of source size and grating frequency. The degree of coherence in the Fourier plane is examined in detail, and an explanation of the fan-shaped deblurring filter based on this analysis is also given.

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Amplitude Sinusoidal Grating	Phase Sinusoidal Grating	Ronchi Grating

$g_{1} = \frac{1}{2} (1 + cos 2 π \frac{y}{h})$	$g_{2} = exp (\frac{A}{2} sin 2 π \frac{y}{h})$	$g_{3} = \sum_{n} sinc [\frac{n a}{l} exp (i 2 π n y / l)]$
$g_{1} {g_{1}}^{*} = \frac{1}{4} (1 + cos 2 π \frac{y + \frac{Δ y}{2}}{h}) \times (1 + cos 2 π \frac{y - \frac{Δ y}{2}}{h})$	$g_{2} {g_{2}}^{*} = \sum_{m, n} J_{m} (\frac{A}{2}) J_{n} (\frac{A}{2}) exp (- i 2 π \frac{m - n}{h} y) \times exp (i 2 π \frac{m + n}{2 h} Δ y)$	$g_{3} {g_{3}}^{*} = \sum_{m, n} sinc (\frac{m a}{l}) sinc (\frac{n a}{l}) \times exp (i 2 π \frac{m + n}{l} y) \times exp (i 2 π \frac{m - n}{2 l} Δ y)$
$\begin{array}{l} G_{1} = \frac{1}{4} (\frac{y}{λ f}, \frac{Δ y}{λ f}) + \frac{1}{16} [δ (\frac{y}{λ f} - \frac{1}{h}, \frac{Δ y}{λ f}) \\ + δ (\frac{y}{λ f} + \frac{1}{h}, \frac{Δ y}{λ f})] + \frac{1}{16} [δ (\frac{y}{λ f}, \frac{Δ y}{λ f} - \frac{2}{h}) \\ + δ (\frac{y}{λ f}, \frac{Δ y}{λ f} + \frac{2}{h}) \\ + \frac{1}{8} [δ (\frac{y}{λ f} - \frac{1}{2 h}, \frac{Δ y}{λ f} - \frac{1}{h}) \\ + δ (\frac{y}{λ f} + \frac{1}{2 h}, \frac{Δ y}{λ f} - \frac{1}{h}) \\ + δ (\frac{y}{λ f} - \frac{1}{2 h}, \frac{Δ y}{λ f} + \frac{1}{h}) \\ + δ (\frac{y}{λ f} + \frac{1}{2 h}, \frac{Δ y}{λ f} + \frac{1}{h})] \end{array}$	$G_{2} = \sum_{m, n} J_{m} (\frac{A}{2}) J_{n} (\frac{A}{2}) \times δ (\frac{y}{λ f} - \frac{m + n}{2 h}, \frac{Δ y}{λ f} + \frac{m - n}{h})$	$G_{3} = \sum_{m, n} sinc (\frac{m a}{l}) sinc (\frac{n a}{l}) \times δ (\frac{y}{λ f} - \frac{m - n}{2 l}, \frac{Δ y}{λ f} - \frac{m + n}{l})$

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Journal of the Optical Society of America A