## Abstract

The optimality of correlation filters is an important issue in applications of pattern recognition. We consider here both binary phase-only filters (BPOFs) and amplitude encoded binary phase-only filters (AE BPOFs) and study the results of optimizing the filters for a real world object (the Space Shuttle). We find that while only small improvements result from optimizing a BPOF, optimization of the AE BPOF is quite important in obtaining a useful correlation function. In the case of an AE BPOF, both signal-to-noise and peak-to-sidelobe measures must be studied. Computer simulation and experimental correlation results are presented.

© 1990 Optical Society of America

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### Equations (6)

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(1)
$$\mid c(0,0){\mid}^{2}={\left|{\int}_{\infty}^{\infty}{\int}_{\infty}^{\infty}H(u,v)S(u,v)dudv\right|}^{2},$$
(2)
$$\gamma =\frac{\mid c(0,0){\mid}^{2}}{\int \int \mid c(x,y){\mid}^{2}dxdy\hspace{0.17em}-\mid c(0,0){\mid}^{2}},$$
(3)
$$\begin{array}{l}\text{denom}={\int}_{\infty}^{\infty}{\int}_{\infty}^{\infty}\mid c(x,y){\mid}^{2}dxdy\hspace{0.17em}-\mid c(0,0){\mid}^{2}\\ ={\int}_{\infty}^{\infty}{\int}_{\infty}^{\infty}\mid C(u,v){\mid}^{2}dudv\hspace{0.17em}-\mid c(0,0){\mid}^{2}\\ ={\int}_{\infty}^{\infty}{\int}_{\infty}^{\infty}\mid H(u,v){\mid}^{2}\mid S(u,v){\mid}^{2}dudv\hspace{0.17em}-\mid c(0,0){\mid}^{2},\end{array}$$
(4)
$$\gamma =\frac{\mid \int \int H(u,v)S(u,v)dudv{\mid}^{2}}{\int \int \mid H(u,v){\mid}^{2}\mid S(u,v){\mid}^{2}dudv\hspace{0.17em}-\mid \int \int H(u,v)S(u,v)dudv{\mid}^{2}}.$$
(5)
$$s(x,y)=\frac{\pi /4+{s}_{t}(x,y)}{\pi /2}\xb7\text{rect}\left(\frac{x}{2\pi}\right),$$
(6)
$${s}_{t}(x,y)=\sum _{m=0}^{\infty}\frac{\text{sin}[(2m+1)x]}{(2m+1)}.$$