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A digital processor has been designed and built to implement Lockheed's Phase Correlation technique at a rate of 30 correlations per second on 128 x 128 element images digitized to eight bits. Phase Correlation involves taking the inverse Fourier transform of the appropriately filtered phase of the Fourier crosspower spectrum of a pair of images to extract their relative displacement vector.It achieves sub -pixel accuracy with relative insensitivity to scene content, illumination differences and narrow -band noise. The processor, which is designed to accept inputs from a variety of sensors, is built with conventional TTL and MOS components and employs only a moderate amount of parallelism. It uses floating point arithmetic with equal exponents for real and imaginary parts. Multiplications are performed by table lookup. Application areas for the correlator include'image velocity sensing, correlation guidance and scene tracking.

noise-free image. This attribute was demonstrated by computer simulations using imagery with seasonal, illumination, and atmospheric differences, as well as differences in spectral band. A parametric study has verified that, by the use of appropriate phase filters, the technique can be made to accommodate moderate amounts of geometric distortion at the price of reduced accuracy. If higher precision is required, an image rectification step must be carried out prior to the correlation computation. This procedure has been shown to significantly increase phase correlation accuracy. The possibility of correctly positioning a small sensed image within a larger reference image, as required for target acquisition, has been demonstrated using phase correlation. A compact implementation, based upon the FFT and using a novel phase quantization procedure, can provide high data rates using available components.

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We have developed a method for determining the band structure of crystals which combines the best features of a first-principles approach with the best features of an empirical approach. The first step in our method is a first-principles OPW band calculation based on the free-electron exchange approximation. In the second step, we depart from a purely first-principles approach, and introduce a small empirical correction which brings key features of the calculated energy level scheme into exact (or close) agreement with the most reliably established features of the experimental level scheme. In addition to obtaining reliable energy band models valid over a wide energy range, we obtain the electronic wave functions for a large number of levels, the core and valence electronic charge distributions, and many other "first-principles" quantities. Following a summary of the shortcomings of purely first-principles and purely empirical band calculations, we sketch the essential features of our intermediate treatment. Recent studies of the band structure of diamond, cubic silicon carbide, silicon, and germanium-carried out both by our method and other methods-are then discussed and compared. It is shown how improved band models for these crystals can be generated with the aid of some crucial information about the band structure derived from experiment. Finally, we observe that although the use of a universal exchange potential is an important simplification, and one that has greatly accelerated recent progress in energy band calculations, this approximation is to some extent an oversimplification. I t appears likely that some of the empirical corrections that we now have to introduce in order to bring theory and experiment closer together could be reduced substantially if we could define one exchange potential for s-like electrons, another for p-like electrons, and still another for d-like electrons. This idea of I-dependent exchange potentials represents a middle ground between the Hartree-Fock extreme of different exchange potentials for different orbitals, and the Slater extreme of the same exchange potential for all orbitals.