Application of Optical Fourier Transforms by Henry Stark

By Henry Stark

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56, 575-578. [17] R. W. Gerchberg (1974). Opt. Acta 21, 709-720. [18] A. Papoulis (1975). IEEE Trans. Circuits Syst. CAS-22, 735-742. [19] J. A. Cadzow (1979). IEEE Trans. , Speech, Signal Process. ASS-27, 4-11. [20] M. S. Sabri and W. Steenaart (1978). IEEE Trans. Circuits Syst. CAS-25, 74-78. [21] D. C. Youla (1978). IEEE Trans. Circuits Syst. CAS-25, 694-701. [22] H. Stark and G. Shao (1977). Appl. Opt. 10, 1670-1674. APPLICATIONS OF OPTICAL FOURIER TRANSFORMS Chapter 2 Pattern Recognition via Complex Spatial Filtering SILVERIO P.

The Minimum-Bias Window Pair The solution to the bias minimization theorem is obtained with the help of the Fejer-Riesz theorem [8, p. 152]. We note that the one-dimensioned form of this problem has been considered in the literature by Papoulis [9] and that the solution to the two-dimensioned problem has been treated by Stark and Dimitriadis [10]. Hence we shall give the solution here and refer the reader to the listed references for details. 5l· z = 2 wp c FIG. 6-1. The minimum-bias spectral window W0(p) of Eq.

Analog smoothing with a uniform window is demonstrated in Figs. 7-2. 7-1 is an estimate of the spectrum offilmgrain 6 X 10 E S D 3h cr \- o UJ Q. CO 32 64 96 128 160 CYCLES / m m FIG. 7-1. Inadequate smoothing of the spectral estimate with a uniform frequency plane window that is too narrow. The window diameter here is 50 μιη. 1. 25 THEORY OF THE OPTICAL FOURIER TRANSFORM 6 X 10 E D I- o ÜJ £L 160 CYCLES / m m FIG. 7-2. The same spectral estimate as in Fig. 7-1 smoothed with a uniform 120-/midiameter window.

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