By Henry Stark
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Additional resources for Application of Optical Fourier Transforms
2-1 is capable of performing a general linear-invariant transformation as expressed by Eqs. 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.
We briefly reviewed the problem of measuring the spec trum at low spatial frequencies and at the origin. Finally we considered the problem of space-limited or band-limited extrapolation. Space and time constraints forced our discussion in this area to be necessarily brief, but we felt that the interesting work going on in this area should be mentioned. In the subsequent chapters of this book, numerous applications of the Fourier properties of optical systems will be presented. 40 HENRY STARK REFERENCES  J.
10-lla) gn-A^y) = /η-Λχ,ν)™χ(χ/ί)π<ΛΜνν), Gn_Mv) = ^2lgn-i(x,y)l F (u v) = | F ^ ' ^ ' [Gn_1(u,v), ^' ^ G *' elsewhere. 10-12) J — oo J — oo and, analogously to Eq. 10-7), that convergence is ensured. Other extrapolation algorithms are discussed by Cadzow  and Sabri and Steenaart . , how well these algorithms work when noise is present, is discussed in an excellent and noteworthy paper by Youla . 11 CONCLUSION In this chapter we have explored the basic principles associated with obtaining and measuring Fourier spectra using optical systems.