## Abstract

Here we study the optical phase errors introduced into an optical correlator by the input and filter plane magneto-optic spatial light modulators. We measure and characterize the magnitude of these phase errors, evaluate their effects on the correlation results, and present a means of correction by a design modification of the binary phase-only optical-filter function. The efficacy of the phase-correction technique is quantified and is found to restore the correlation characteristics to those obtained in the absence of errors, to a high degree. The phase errors of other correlator system elements are also discussed and treated in a similar fashion.

© 1992 Optical Society of America

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### Equations (10)

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(1)
$$c\left(x,y\right)={\mathcal{F}}^{-1}\left\{\mathcal{F}\left\{s\left(x,y\right){\varphi}_{i}\left(x,y\right)\right\}H*\left(u,\upsilon \right)\right\},$$
(2)
$${\varphi}_{i}\left(x,y\right)=\text{exp}\left[j\frac{2\pi}{\lambda}z\left(x,y\right)\right],$$
(3)
$$\begin{array}{cc}c\left(x,y\right)& ={\mathcal{F}}^{-1}\left\{\mathcal{F}\left\{s\left(x,y\right)\right\}H*\left(u,\upsilon \right){\Phi}_{f}\left(u,\upsilon \right)\right\}\\ & ={\mathcal{F}}^{-1}\left\{S\left(u,\upsilon \right)H*\left(u,\upsilon \right){\Phi}_{f}\left(u,\upsilon \right)\right\}\\ & ={c}_{0}\left(x,y\right)**{\mathcal{F}}^{-1}\left\{{\Phi}_{f}\left(u,\upsilon \right)\right\},\end{array}$$
(4)
$$H\left(u,\upsilon \right)=\mathcal{M}\left\{\mathcal{F}\left\{s\left(x,y\right)\right\}\right\}=\mathcal{M}\left\{S\left(u,\upsilon \right)\right\},$$
(5)
$$\mathcal{M}\left\{S\left(u,\upsilon \right)\right\}=\{\begin{array}{cc}+1& S\left(u,\upsilon \right)\in \text{Region}\phantom{\rule{0.2em}{0ex}}1\\ -1& S\left(u,\upsilon \right)\in \text{Region}\phantom{\rule{0.2em}{0ex}}2.\end{array}$$
(6)
$${s}^{\prime}\left(x,y\right)=s\left(x,y\right){\varphi}_{i}\left(x,y\right).$$
(7)
$${H}^{\prime}\left(u,\upsilon \right)=\mathcal{M}\left\{\mathcal{F}\left\{s\left(x,y\right){\Phi}_{i}\left(x,y\right)\right\}\right\}.$$
(8)
$${U}_{fp}=S\left(u,\upsilon \right)\Phi \left(u,\upsilon \right),$$
(9)
$${H}^{\prime}\left(u,\upsilon \right)=\mathcal{M}\left\{S\left(u,\upsilon \right)\Phi \left(u,\upsilon \right)\right\}.$$
(10)
$${H}^{\prime}\left(u,\upsilon \right)=\mathcal{M}\left\{\mathcal{F}\left\{s\left(x,y\right){\Phi}_{i}\left(x,y\right)\right\}{\varphi}_{f}\left(u,\upsilon \right){\Phi}_{p}\left(u,\upsilon \right)\right\}.$$