Optical competitive learning with, VLSI/liquid-crystal winner-take-all modulators

Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor

We present a spatio-temporal operator formalism and beam propagation simulations that describe the broadband efficient adaptive method for a true-time-delay array processing (BEAMTAP) algorithm for an optical beamformer by use of a photorefractive crystal. The optical system consists of a tapped-delay line implemented with an acoustooptic Bragg cell, an accumulating scrolling time-delay detector achieved with a traveling-fringes detector, and a photorefractive crystal to store the adaptive spatio-temporal weights as volume holographic gratings. In this analysis, linear shift-invariant integral operators are used to describe the propagation, interference, grating accumulation, and volume holographic diffraction of the spatio-temporally modulated optical fields in the system to compute the adaptive array processing operation. In addition, it is shown that the random fluctuation in time and phase delays of the optically modulated and transmitted array signals produced by fiber perturbations (temperature fluctuations, vibrations, or bending) are dynamically compensated for through the process of holographic wavefront reconstruction as a byproduct of the adaptive beam-forming and jammer-excision operation. The complexity of the cascaded spatial-temporal integrals describing the holographic formation, and subsequent readout processes, is shown to collapse to a simple imaging condition through standard operator manipulation. We also present spatio-temporal beam propagation simulation results as an illustrative demonstration of our analysis and the operation of a BEAMTAP beamformer.

Optical finite impulse response neural networks

The finite impulse response neural network is described in detail. Different algorithms capable of temporal back-propagation are considered, including a novel modification to the conventional algorithm, called the delayed-feedback back-propagation algorithm. We present and analyze different optoelectronic processors making use of adaptive volume holograms and three-dimensional optical processing. Two single-layer architectures are presented: the input delay plane architecture and the output delay plane architecture. By combining them it is possible to implement both forward and backward propagation in two multi-layer architectures: the first making use of the conventional temporal back-propagation and the second making use of delayed-feedback back-propagation.

High-capacity photorefractive neural network implementing a kohonen topological map

We designed and built a high-capacity neural network based on volume holographic interconnections in a photorefractive crystal. We used this system to implement a Kohonen topological map. We describe and justify our optical setup and present some experimental results of self-organization in the learning database.

64-channel correlator implementing a Kohonen-like neural network for handwritten-digit recognition

We present an optical implementation of an improved version of the Kohonen map neural network applied to the recognition of handwritten digits taken from a postal code database. Improvements result from the introduction of supervision during the learning stage, a technique that also simplifies the map layer labeling. The experimental implementation is based on a frequency-multiplexed raster computer-generated hologram used to realize the required N(4) interconnection. The setup is shown to be equivalent to a 64-channel correlator. Computer simulations are used to study various detection and classification procedures. The results of the optical experiments, obtained with binary phase computer-generated holograms, are presented and shown to be in excellent agreement with the simulations.

Convergence of backward-error-propagation learning in photorefractive crystals

We analytically determine that the backward-error-propagation learning algorithm has a well-defined region of convergence in neural learning-parameter space for two classes of photorefractive-based optical neural-network architectures. The first class uses electric-field amplitude encoding of signals and weights in a fully coherent system, whereas the second class uses intensity encoding of signals and weights in an incoherent/coherent system. Under typical assumptions on the grating formation in photorefractive materials used in adaptive optical interconnections, we compute weight updates for both classes of architectures. Using these weight updates, we derive a set of conditions that are sufficient for such a network to operate within the region of convergence. The results are verified empirically by simulations of the xor sample problem. The computed weight updates for both classes of architectures contain two neural learning parameters: a learning-rate coefficient and a weight-decay coefficient. We show that these learning parameters are directly related to two important design parameters: system gain and exposure energy. The system gain determines the ratio of the learning-rate parameter to decay-rate parameter, and the exposure energy determines the size of the decay-rate parameter. We conclude that convergence is guaranteed (assuming no spurious local minima in the error function) by using a sufficiently high gain and a sufficiently low exposure energy per weight update.

All-optical implementation of a self-organizing map: Learning and taxonomy capability assessment

We present some experimental results obtained with an all-optical implementation of a self-organizing map. The system is based on two ferroelectric liquid-crystal, bistable optically addressed spatial light modulators (BOASLM's) used as parallel read/write optical memories and as thresholding devices. Modifications made to adapt the basic algorithm to the BOASLM's are studied in computer simulations that predict training-class loss due to the simplified decision stage as the principal drawback. Experimental results show good system behavior in recognition mode, demonstrating generalization properties and confirming the choice of a BOASLM memory. All-optical learning is shown in simple cases, and the elementary BOASLM decision function is confirmed as the major limiting factor. The ultimate possible system performance is discussed, and ways of overcoming present limits are suggested.

Holographic stars

Holographic stars fabricated on DuPont's holographic recording film HRF 600X010 by the use of He-Ne laser light are demonstrated. The stars operate with plane waves, the transmitted portions of the input beams are used at the corresponding outputs, and the gratings are in the volume regime of diffraction. Multiple exposure based on the Bragg degeneracy effect is employed, which drastically reduces the number of multiplexed gratings and requires a three-dimensional arrangement of the replay beams.The star operates at different wavelengths only by the readjustment of the Bragg angles.

Neural network that incorporates direct optical imaging

A compact neural network architecture is described that can be trained to sense and classify an optical image directly projected onto it. The system is based on the combination of a two-dimensional amorphous silicon photoconductor array and a liquid-crystal spatial light modulator. Appropriate filtering of the incident optical image on capture is incorporated into the network training rules through a modification of the standard backpropagation training algorithm. Training of the network on two image-classification problems is described: the recognition of handprinted digits and facial recognition. The network, once trained, is capable of stand-alone operation, sensing an incident image, and outputting a final classification signal in real time.

Real-time pattern recognition system based on a bipolar winner-take-all model with a threshold

A threshold is added to recognize an input pattern that has too few similarities to be one of the memory patterns. A real-time pattern recognition system based on the improved model is given. The unipolar optical pattern recognition system has all the characteristics of a fully bipolar winner-take-all model and has illumination invariance. A liquid-crystal spatial light modulator is used as a real-time input device, and a mask and a lens array perform the threshold and weighted sums of the input pattern. Some experimental results are also shown.