Application of Optical Fourier Transforms by Henry Stark

By Henry Stark

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13-15]) and gives the user precise control over the bandwidth of the window. Reducing the bandwidth of the window ("window closing") enables the user to look for finer detail in the spectrum. Of course, narrowing the window eventually leads to instability, and the question of when to stop the process of narrowing the width of W(p) is not governed by rigid rules. However, the user should always recall that the spectrum has to make sense physically, otherwise the results can be of little value. Smoothing in the frequency plane can be done by analog or digital techniques.

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. As stated in the beginning of this chapter, an interferometric technique widely used to record any complex filter for which the point spread function is known was introduced in 1963 by Vander Lugt [49].

5-2) using the window of Eq. 6-14). Of course, once the data are in the computer, we have considerable flexibility with respect to realizing a large number of processing operations. To emphasize that the smoothing operations are being performed in the focal plane, we shall use xf and yf to denote Cartesian displacements co­ ordinates in the focal plane. , Eq. , F(u, v) = F{xfJkf9 yfJkf) = F(xf9 yf). If smoothing is done directly in the focal plane of the lens, a shaded scanning aperture must be used to realize the smoothing associated with the optimum window.

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