The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-325

“Nonlinear Optical Processing and its Application to Invariant Pattern Recognition”

by Lev Sadovnik

December 1995

Coherent optical information processing systems have the ability to process large bandwidth data in parallel at high speed. Unfortunately, their range of operations has been restricted to linear operations, or fixed nonlinear operations achieved using an intermediate pulse width modulation (halftone) step. This research encompasses three issues related to nonlinear optical processing. Flexible dynamically variable nonlinear processing is accomplished by utilizing a halftoned input formed in projection geometry. The transfer characteristic of the halftone process which governs the nonlinear is determined by considering the diffraction pattern produced by a periodic structure is analyzed. Deviations of the specific diffraction patterns are performed using a Fresnel approximation whose validity for the halftone process is confirmed. Based on the diffraction pattern calculations, the inverse problem of dynamically variable halftoning is solved, i.e., the halftone process which will produce the desired nonlinear transformation is determined (in terms of its geometry and the transmission of the apodizing mask). Numerical solutions for the design of the two different nonlinear characteristics are presented. The next advance toward achieving flexible, high input dynamic range nonlinear optical processing is made by introducing a new type of input image representation- intensity-to-phase coding. Experimental results of a nonmonotonic nonlinear optical transformation achieved with a simple sinusoidal grating are demonstrated and the application of this coding to the instantaneous measurement of the characteristic curve of photosensitive phase-only materials is described. This novel type of optical encoding leads directly the design of a new optical processor capable of scale, translation, and rotation invariant automatic pattern recognition. Both the numerical simulations and the experimental results prove that this technique can provide invariant object identification.

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