This paper addresses a method to implement ternary filters with binary phase spatial light modulators (SLMs) for realtime optical pattern recognition applications using a filtering-based optical processor. A complex ternary filter can be considered as a binary phase function multiplied by a binary amplitude filter, which selects information by blocking or letting pass spatial frequencies. The main problem is that commercially available SLMs cannot provide amplitude and phase modulation at the same time and at high filtering rates. The method presented here involves coding the binary amplitude in phase only, by adding a linear phase to the frequencies representing undesired information. This information will be rejected outside the correlation plane, whereas useful information will pass without alteration. Computer simulations and experimental results have been obtained for different applications. These results show that the pure phase filters obtained are absolutely equivalent to the desired ternary filters and, furthermore, that any ternary filtering function can be easily implemented in a VanderLugt correlator that uses a binary phase SLM, thanks to this technique.
A new formulation of a multiplex filter for filtering-based optical processors, based on the VanderLugt architecture, is presented. The multireference binary phase-only filter (MBPOF), optimized by regions of support (ROS), constitutes a formal rewriting of some multiplex or composite filters including optimization functions, such as the distribution function and the selection function. The first function optimizes the multiplexing of references into the multireference filter. The second function defines the ROS of an object's Fourier spectrum and can be independently used to optimize the conventional binary phase-only filter. Both functions result from a segmentation of the Fourier plane. The MBPOF with ROS can be optically implemented in a filtering-based optical processor owing to a binary-phase spatial light modulator. Simulation and optical results are given for different examples of the BPOF and the MBPOF, both with ROS optimizing different criteria of performance, such as peak-to-correlation energy, discrimination capability, and distortion sensitivity.
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