Optical correlation techniques have been used successfully in applications involving the detection of signals in noise, in multichannel processing, and in pattern and character recognition. The systems are advantageous in that signals having a large space-bandwidth product can be processed rapidly. In this chapter, we discuss some of the analog optical correlation techniques and give an example of the use of each type of system discussed. No attempt is made to discuss all correlator systems or applications as this would be well beyond the scope of this chapter. The subjects of correlation and convolution and their comparisons were treated previously in Chapter 28.
33.2 INCOHERENT LIGHT CORRELATION
If two transparencies, emulsion facing emulsion, are shifted with respect to each other, then the measurement of the total light output as a function of the shift variable is the autocorrelation function.
For purposes of demonstration, two negative transparencies of the distribution shown in Fig. 33.1 will exhibit an autocorrelation function when slid across each other in front of an incoherent light source and viewed with an unaided eye. This figure may be used to demonstrate that the autocorrelation length of the distribution is determined primarily by the larger sized particles.
33.3 COHERENT LIGHT CORRELATION
Optical correlation can also be accomplished using coherent light and the generalized system of Fig. 30.1 of Chapter 30. In this case, one of the functions f(Î¾, Î·) is imaged with unit magnification by an additional optical system onto the object plane in which the transparency of another function g(Î¾, Î·) is shifted to avoid scratching of the emulsion (this could also have been done in the incoherent light case). Thus, in the object plane we have constructed the function, f(Î¾, Î·)g(Î¾ â Î¾0, Î·) by shifting only in the positive Î¾ direction.