Accuracy in optical information processing
Low computational accuracy is an important obstacle for optical processors which blocks their way to becoming a practical reality and a serious chaUenger for classical computing paradigms. This research presents a comprehensive solution approach to the problem of accuracy enhancement in discrete analog optical information processing systems. Statistical analysis of a generic three-plane optical processor is carried out first, taking into account the effects of diffraction, interchannel crosstalk, and background radiation. Noise sources included in the analysis are photon, excitation, and emission fluctuations in the source array, transmission and polarization fluctuations in the modulator, and photoelectron, gain, dark, shot, and thermal noise in the detector array. Means and mutual coherence and probability density functions are derived for both optical and electrical output signals. Next, statistical models for a number of popular optoelectronic devices are studied. Specific devices considered here are light-emitting and laser diode sources, an ideal noiseless modulator and a Gaussian random-amplitudetransmittance modulator, p-f-n and avalanche photodiode detectors foUowed by electronic post-processing, and ideal free-space geometrical-optics propagation and single-lens imaging systems. Output signal statistics are determined for various interesting device combinations by inserting these models into the general formalism. Finally, based on these special-case output statistics, results on accuracy Hmitations and enhancement in optical processors are presented. Here, starting with the formulation of the accuracy enhancement problem as (1) an optimal detection problem, and (2) as a parameter estimation problem, the potential accuracy improvements achievable via the classical multiple-hypothesis testing and maximum likelihood and Bayesian parameter estimation methods are demonstrated. Merits of using proper normalizing transforms which can potentially stabilize high-order signal moments are also discussed in connection with the signal dependence of the noise at the processor output. A formal framework for complete statistical characterization and performance evaluation of a wide class of optical processors is thus provided.