or
 h(x,y) = s(-x,-y). (2.34)


Equation 2.34 shows that the impulse response of the matched filter

(with white noise) is simply the signal image in reverse order

(inverted and perverted). Thus, the filter is said to be matched to

the signal. Filtering with a matched filter is equivalent to cross-

correlating with the expected signal or pattern. That is,


 O(x,y) = Rhs(x,y)


 = ff s(xo,yo)h(xo-x,yo-y) dxo dy (2.35)


Also, it can be seen that the frequency response of the matched filter

is equivalent to that of the signal but with the phase negated so that

the output of the filter is real. That is, the matched filter removes

the phase variations and provides a real valued output.19

 Matched filters are used extensively in radar signal

processing, seismic data processing, and communications. These

filters are implemented using electronic circuitry and digital

computers. For image processing, the need to process large two-

dimensional arrays places a large burden on conventional filtering

techniques. For these applications, optical processing techniques

provide the highest throughput speeds for matched filtering. One such

optical processing technique was proposed by Vander Lugt7 in 1969.

 Vander Lugt Filtering

 If an image is placed on a transparent sheet and illuminated by a

plane wave of coherent light, its Fourier transform is formed using a

simple lens.19 Once the Fourier transform is formed, specific

frequency components in the image can be removed or attenuated. The