## Abstract

A technique to reduce the influence of the dc and the
complex-conjugate correlation signals that are inherent in a joint
transform correlator is proposed. The key part of this technique is
the use of a phase mask. The mask contributes only extraneous
signals, so the influence of the signals is reduced. The desirable
correlation signal is not affected, and its shape is
retained. Computer simulations confirm the performance of the
proposed phase-encoded joint transform correlator.

© 1998 Optical Society of America

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### Equations (11)

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(1)
$$h\left(x\right)=f\left(x\right)+g\left(x\right).$$
(2)
$$|H\left(\mathrm{\nu}\right){|}^{2}=|F\left(\mathrm{\nu}\right)+G\left(\mathrm{\nu}\right){|}^{2}=F\left(\mathrm{\nu}\right)F*\left(\mathrm{\nu}\right)+G\left(\mathrm{\nu}\right)G*\left(\mathrm{\nu}\right)+F*\left(\mathrm{\nu}\right)G\left(\mathrm{\nu}\right)+F\left(\mathrm{\nu}\right)G*\left(\mathrm{\nu}\right),$$
(3)
$$c\left(x\right)={\mathrm{FT}}^{-1}\left[|H\left(\mathrm{\nu}\right){|}^{2}\right]=f\left(x\right)\u2605f\left(x\right)+g\left(x\right)\u2605g\left(x\right)+f\left(-x\right)\u2605g\left(-x\right)+f\left(x\right)\u2605g\left(x\right),$$
(4)
$$h\prime \left(x\right)=f\left(x\right)+g\left(x\right)*\mathrm{\varphi}\left(x\right),$$
(5)
$$|H\prime \left(\mathrm{\nu}\right){|}^{2}=|F\left(\mathrm{\nu}\right)+G\left(\mathrm{\nu}\right)\mathrm{\Phi}\left(\mathrm{\nu}\right){|}^{2}=F\left(\mathrm{\nu}\right)F*\left(\mathrm{\nu}\right)+G\left(\mathrm{\nu}\right)G*\left(\mathrm{\nu}\right)+F*\left(\mathrm{\nu}\right)G\left(\mathrm{\nu}\right)\mathrm{\Phi}\left(\mathrm{\nu}\right)+F\left(\mathrm{\nu}\right)G*\left(\mathrm{\nu}\right)\mathrm{\Phi}*\left(\mathrm{\nu}\right).$$
(6)
$$c\prime \left(x\right)={\mathrm{FT}}^{-1}\left[|H\prime \left(\mathrm{\nu}\right){|}^{2}\mathrm{\Phi}\left(\mathrm{\nu}\right)\right]={\mathrm{FT}}^{-1}\left[F\left(\mathrm{\nu}\right)F*\left(\mathrm{\nu}\right)\mathrm{\Phi}\left(\mathrm{\nu}\right)+G\left(\mathrm{\nu}\right)G*\left(\mathrm{\nu}\right)\mathrm{\Phi}\left(\mathrm{\nu}\right)+F*\left(\mathrm{\nu}\right)G\left(\mathrm{\nu}\right)\mathrm{\Phi}\left(\mathrm{\nu}\right)\mathrm{\Phi}\left(\mathrm{\nu}\right)+F\left(\mathrm{\nu}\right)G*\left(\mathrm{\nu}\right)\right]=f\left(x\right)\u2605f\left(x\right)*\mathrm{\varphi}\left(x\right)+g\left(x\right)\u2605g\left(x\right)*\mathrm{\varphi}\left(x\right)+f\left(-x\right)\u2605g\left(-x\right)*\mathrm{\varphi}\left(x\right)*\mathrm{\varphi}\left(x\right)+f\left(x\right)\u2605g\left(x\right).$$
(7)
$$\mathrm{\Phi}\left(\mathrm{\nu}\right)=exp\left[j\mathrm{\psi}\left(\mathrm{\nu}\right)\right],$$
(8)
$$\mathrm{\Phi}\left(\mathrm{\nu}\right)=\mathrm{\Phi}\left(\mathrm{\nu}-\mathrm{\alpha}\right)$$
(9)
$$\mathrm{\Phi}\left(\mathrm{\nu}\right)=exp\left[j\left(a\mathrm{\nu}+b\right)\right],$$
(10)
$$\mathrm{SNR}=\frac{{\mathrm{CS}}^{2}}{\mathrm{Var}\left[c\left(x\right)\right]},$$
(11)
$$\mathrm{SCR}=\frac{{\mathrm{CS}}^{2}}{{\mathrm{EC}}^{2}},$$