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Conventional techniques of designing distortion-invariant filters for optical correlators presuppose the use of complex-valued filters. Synthetic-discriminant-functions (SDFs)," lock-and-tumble filters," and circular harmonic filters5 are examples of these methods. However, since programmable, complex-valued spatial-light-modulators (SLMs) do not exist and appear difficult to fabricate, the utility of these techniques for actual implementation are severely limited. On the other hand, programmable SLMs limited to quantized levels of amplitude and/or phase are presently available. Jared and Ennis6 recently proposed a modification to the conventional SDF approach which includes the filter modulation in the filter synthesis called filter-SDF (fSDF). They demonstrated that it is possible to construct a filter limited to binary modulation or phase modulation that will achieve a specified peak-correlation for a set of training images. The development of the fSDF approach was driven by the practical concern to make present-day SLMs with limited modulation capabilities functional for distortion-invariant pattern recognition. However, initial work on fSDFs did not examine the peak-correlation response for images in the distortion-range that were not members of the training set. This paper considers the performance of fSDF binary-phase-only-filters (BPOFs) for images in the distortion-range that were not members of the training set. This evaluation is essential towards understanding the number of training images necessary to span a distortion-range. As the extent of the distortion-range increases, the number of training images necessary to effectively cover the distortion-range increases. Since filters of limited modulation have an implicit information capacity, a trade-off occurs between the extent of the distortion-range and the performance of the correlator. This paper considers the nature of this trade-off for fSDF-BPOFs, and the likely constraints this trade-off will impose on a realized optical correlator. A brief review of the fSDF method is presented in Section 2. Aspects of the simulation are discussed in Section 3. The results of correlating fSDF-BPOFs with images not in the training set and the effect of increasing the distortion-range are presented in Section 4 for in-plane-rotation and out-of-plane-rotation. A discussion of these results and the conclusions reached are found in Sections 5 and 6, respectively.
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