The estimation of the spectral density of a spatial random process by diffraction requires that the parameters of the diffraction system be compatible with the statistical properties of the process. Otherwise, the estimate of the spectrum can be unstable or unduly biased. The relation between the second-order statistics of the process and the parameters of a basic diffraction system that are required for reasonable spectral estimates is investigated. Such parameters include aperture dimensions, wavelength, focal length of the lens, and scanning slit size. With the typical diffraction system, it is difficult to estimate the power spectrum because of the presence of the zero-order aperture-diffracted light. A technique is furnished in this paper for spectral estimation at dc. Experimental results are furnished for film grain and total film noise. It is shown that the residual phase noise of film at dc even under so-called matched conditions is large enough to prevent the accurate estimation of the dc value of grain noise.

In conventional real-time electrooptical signal processors, the variation of the output intensity with time is directly detected with a photodetector. As a result of this, any information carried in the phase of the light is lost. However, if the light is detected coherently, i.e., it is heterodyned with another coherent local oscillator light source on the detector surface, the phase associated with the amplitude of the light may be preserved. This paper presents the results of a theoretical and experimental study of the properties of real-time electrooptical spectrum analyzers with coherent detection. Basic equations of operation are presented and discussed, and confirmed by experiment, and it is concluded that the construction of such devices is feasible.

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The operation of fused-silica Debye-Sears light modulators is investigated for normal light incidence over a range of conditions such that the effect of amplitude modulation of the light beam by the acoustic wave, as well as phase modulation, must be taken into account. Using the approximations of Raman and Nath, for which the ultrasonic wave can be treated as a phase grating, the relationships between input electrical excitation and the resulting spatial modulation are determined for shear and compression waves. The effect of the length of the light path on the operation of the light modulator is then considered for a range of values for which Raman and Nath's simplified approach is no longer valid. From the results of Bhatia and Noble it is shown theoretically and verified experimentally that, for single frequency excitation, a value of this dimension can be specified such that the effective spatial modulation of the light beam can be maximized. The case of electrical excitation over a finite frequency band is also considered, and a simple expression describing the frequency response of the light modulator, in terms of the total spatial modulation of the light beam, is derived. Measurements of light-modulator frequency response under conditions such that the amplitude-modulation effects are not signficant are presented. These measurements are found to agree with theoretical predictions.

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