## Abstract

The technique of measuring the velocity of a moving image by means of a parallel-slit spatial filter is treated as continuous optical correlation processing. This technique is compared with other approaches to measuring image velocity by correlation and is shown to be a special case where the image displacement necessary for the correlation measurement is held constant and the time interval required to traverse this fixed distance is measured. The time measurement is accomplished inherently in terms of the frequency of the periodic signal generated by the image motion. Based on a derived mathematical model of the process and the characteristics of spatial filters, some conclusions are drawn about the way various parameters affect signal quality and continuity.

© 1966 Optical Society of America

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### Equations (8)

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(1)
$$\phi (\tau )=\underset{T\to \infty}{\text{lim}}\frac{1}{T}{\int}_{0}^{T}f(t)\times f(t+\tau )dt,$$
(2)
$$R(u,v)=\frac{1}{KL}{\int}_{x-K/2}^{x+K/2}{\int}_{y-L/2}^{y+L/2}{f}_{\text{FIL}}(x,y)\times {f}_{\text{FIL}}(x+u,\hspace{0.17em}y+v)dxdy.$$
(3)
$$\phi (u,v)=\frac{{\int}_{x-K/2}^{x+K/2}{\int}_{y-L/2}^{y+L/2}{f}_{\text{FIL}}(x,y){f}_{\text{FIL}}(x+u,\hspace{0.17em}y+v)dxdy}{{\int}_{x-K/2}^{x+K/2}{\int}_{y-L/2}^{y+L/2}\mid {f}_{\text{FIL}}(x,y){\mid}^{2}dxdy}.$$
(4)
$$\phi (u,v)=\frac{1}{KL}{\int}_{x-K/2}^{x+K/2}{\int}_{y-L/2}^{y+L/2}{f}_{\text{FIL}}(x,y){f}_{\text{IM}}(x+u,\hspace{0.17em}y+v)dxdy.$$
(5)
$$R(x)=\{\begin{array}{l}\frac{x-jd}{d/2},\hspace{0.17em}jd<x<(j+1/2)d\hfill \\ 1-\frac{x-(j+1/2)d}{d/2},\hspace{0.17em}(j+1/2)d<x<(j+1)d,\hfill \end{array}$$
(6)
$$\phi (x)=\frac{1}{K}{\int}_{x-K}^{x}[R(x)][{f}_{\text{A}}(x)]dx+\frac{1}{K}{\int}_{x-K}^{x}[R(x+d/2)][{f}_{\text{B}}(x)]dx.$$
(7)
$$\phi (x)=\frac{1}{K}{\int}_{x-K}^{x}[R(x)][{f}_{\text{A}}(x)]dx+\frac{1}{K}{\int}_{x-K}^{x}[1-R(x)][{f}_{\text{B}}(x)]dx,$$
(8)
$$\phi (x)=\frac{1}{K}{\int}_{x-K}^{x}[R(x)][{f}_{\text{A}}(x)-{f}_{\text{B}}(x)]dx+\frac{1}{K}{\int}_{x-K}^{x}{f}_{\text{B}}(x)dx.$$