By Henry Stark
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Additional resources for Application of Optical Fourier Transforms
OUTPUT f(x,y)»h(x,y) LASER Ί M FIG. 2-7. Optical correlator using a holographic filter. 3 PATTERN RECOGNITION VIA MATCHED FILTERING A. 3-1) 2 where S(v) is the signal spectrum, |iV(v)| is the noise spectral density, and k is a constant. For the optical counterpart of this matched filter, one can simply replace the temporal variables t and v by their spatial equivalents (x, y) and (M, V), respectively. 3-2) 54 SILVERIO P. ALMEIDA AND GUY INDEBETOUW where H(u, υ) = & [h(x9 y)~] and G*(u, v) = & [g*( - x, - y)~].
2-6). This is possible, of course, as long as the complex-valued filter transmittance T(xf,yf) can be constructed. Complex spatial filters have been found useful in many applications. Various names have been given to these filters according to the context in which they are used: The terms holographic filters and Fourier holograms refer to the technique usually involved in filter production. In image enhancement, they might be called inverse filters or deblurring filters, while in pattern recognition, their most common names are Vander Lugt filters (after their originator) or matched filters.
2-19) where d is the adjustable distance between input plane and Fourier plane. SILVERIO P. ALMEIDA AND GUY INDEBETOUW HOLOGRAPHIC PLATE REFERENCE BEAM FIG. 2-4. Recording arrangement allowing scale changes. ) The arrangement of Fig. 2-5 might be of interest if the size of the input is small or if the recording medium has limited resolution. In this case, the reference offset angle must be as small as possible. The setup in Fig. 2-6 serves the same purpose and allows an even smaller reference angle.
Application of Optical Fourier Transforms by Henry Stark