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-IPI-880

“Real-Time Nonlinear Optical Information Processing”

by Ahmad Armand

June 1979

Existing methods for nonlinear optical processing involve an intermediate photographic step which prevents real-time operation. Although optical information processors have a large space-bandwidth product, the problem of real-time input has been a major limitation in taking advantage of this processing ability. In this research, the realization of nonlinear optical processing in real time is investigated. Several techniques for performing such operations are presented. One approach realizes the halftone method of nonlinear optical processing in real time by replacing the conventional photographic recording medium with a real-time image transducer. In the second approach halftoning is eliminated and the real-time device is used directly. In this case the nonlinearity is obtained by the inherent nonlinear characteristic of the real-time device. A third method uses the ability of certain real-time devices to perform an intensity-to-spatial frequency conversion.

Following a review of halftoning and real-time devices, a general analysis of the halftone process considering the nonideal characteristic of the recording medium is presented. From this analysis one can predict the amount of degradation of the output due to different parts of the recording medium characteristic curve for any nonlinear transformation. Specific results for logarithmic and level slice processes are obtained.

The problem of designing the halftone screen cell shape is considered for a piecewise linear recording medium by solving a nonlinear integral equation. It is shown that the solution can be achieved for certain monotonic functions including exponential and power transformations. To obtain the solution in general, an approximate method which considers a discrete halftone screen density profile is described. This gives the halftone screen density profile for any form of recording medium characteristic curve and any type of nonlinearity by minimizing in mean-square sense the difference between desired and degraded outputs. The results of computer simulation for logarithmic and level slice functions are shown. Experimental results are obtained for an optimized halftone screen which matches the characteristic of a liquid crystal light valve (LCLV). An overall logarithmic transfer function is produced in real time.

The procedure for obtaining nonlinearities without halftone preprocessing is explained. Experimental results using a special birefringent liquid crystal device which produces a 3-bit parallel A/D converter in real time are shown. The variable grating mode (VGM) of liquid crystal light valve system and its application in real-time nonlinear optical processing is discussed. A detailed analysis of the variable phase grating is made and from this the processing limitations of the VGM are determined. Experimental results showing real-time level-slicing with a VGM liquid crystal device are given. Possible extensions and limitations of this work are discussed.

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