An account is given of the self-pumped optical neural network (SPONN) fine-grained optical architecture, which features massive parallelism and much higher interconnectivity than either bus-oriented or hypercube electronic architectures. Connections among neurons are implemented by SPONN as sets of angularly and spatially multiplexed volume phase gratings. The mapping of neural-network models onto the SPONN architecture occurs without the need for neuron-multiplexing or dealing with electronic parallel computers'' bottlenecks, greatly simplifying programming.

We describe an optical disk based system for handwritten character recognition. The recognition scheme is based on a radial basis function approach to pattern classification. The optical system computes the Euclidean distance between an unknown input and 650 stored patterns at a demonstrated rate of26,000 pattern comparisons per second.

We review different categories of associative processors with attention to the properties of their key and recollection vectors, the test procedures to be used and the performance measures to be used to compare various associative processors. We review new pseudoinverse and Ho-Kashyap associative processors and robust versions of each. Q uantitative data is presented on the performance of these new pattern recognition associative processors. In all cases we show significant improvement over prior data with M >> N (M is the number of key/recollection vectors pairs stored and N is the dimensionality of the input key vector). Quantization of the number of analog levels and comparisons of various recollection vector encodings are considered.

This paper summarizes the results of an optical amplification test using 45-deg-cut BaTiO3 crystals. The effects of beam fanning on two-wave-coupling gain and image amplification are presented. Plots of output-pump and signal-beam powers show the temporal effects of beam fanning on two-wave-coupling gain. A linear relationship for the logarithm of the input-signal power is presented. Optical amplification of a resolution-chart image and the Fourier transform of the image are discussed. Recommendations for use in an optical feedback system are presented.

The present discussion of real-time laboratory test results for a hybrid, optical/digital multifunctional neural-network system gives attention to the system''s application to a general-memory associative processor and multitarget-tracking (MTT) optimization neural network. MTT optimization neural network data are presented in tabular form.

A heteroassociative memory is proposed that allows a key word in a dictionary of key words to be used to recall an associated holographic image in a database of images. Symbolic substitution search finds the word sought in a dictionary of key words and generates a beam that selects the corresponding holographic image from a directory of images. In this case, symbolic substitution is used to orthogonalize the key words. Spatial light rebroadcasters are proposed for the key word database. Experimental results demonstrate that symbolic substitution will enable a holographic image to be selected and reconstructed. In the case considered, a holographic image having over 40,000-bits is selected out of eight by using a key word from a dictionary of eight words.

A liquid-crystal TV spatial light modulator (LCTV SLM) input device and LCTV nonlinear thresholding element are presently used to accomplish an all-optical implementation of an inner-product neural associative memory. This architecture represents an alternative to the vector-matrix multiplication method of the Hopfield model, which is most often employed by neural network associative memory models. LCTV SLM experimental results are presented and discussed.

Error-diffusion computer-generated holograms (CGHs) are extended to allow the use of multilevels (rather than the conventional binary 0,1 values) and to phase modulation (to improve efficiency). These new CGHs allow high accuracy and reduced space-bandwidth-product transfer functions. CGHs for optical processing operations are described and laboratory data are included.

High data rates, low retrieval times, and simple implementation are presently shown to be obtainable by means of a motionless-head 2D parallel-readout system for optical disks. Since the optical disk obviates mechanical head motions for access, focusing, and tracking, addressing is performed exclusively through the disk''s rotation. Attention is given to a high-performance associative memory system configuration which employs a parallel readout disk.

This paper describes an application of recurrent neural networks with feedback to the restoration of gray scale images corrupted by Gaussian disturbances. The two dimensional autoregressive (discrete homogeneous random Gaussian-Markov field) model of gray scale images are considered and identified as a base for future restoration. For the image restoration the concept of 2-D Kalman filtering (with reduced update procedure) has been utilized. The 2-D Kalman filter for the image restoration has been implemented as a tandem of two recurrent neural networks trained according to the 2-D Kalman filtering algorithm.

SNR expressions are derived for four different correlators in which, respectively, (1) the input and template are gray-scale signals, (2) the template signal is binarized, (3) the input is binarized, and (4) both signals are binarized. These expressions can be used with any reference image to quantify the loss of SNR due to binarization. The present results indicate that SNR loss due to binarization is not severe, allowing a relaxation of linearity and dynamic range requirements.

The design and development of a compact acousto-optic image correlator capable of performing real-time correlations on grayscale imagery will be described. The system utilizes one-dimensional optical devices to perform the desired two-dimensional correlation. The two-dimensional correlation is performed as a series of multichannel time-integrating correlations between each input image line and a reference template that is stored in an electronic memory. The rows of the reference template are introduced into the processor in parallel using a one-dimensional laser diode array. The correlation in the vertical direction is performed using a modified charge-coupled device (CCD) operating in the shift-and-add mode. A laser diode array, as opposed to an LED array used in previous systems, provides more power so that full use can be made of the dynamic range capabilities of the acoustooptic device and CCD. Key features of the system will be presented, including the random access template memory, the custom laser diode array consisting of 64 individually addressed laser diodes, and the custom optical design to achieve nearly diffraction-limited image quality and compactness.

The ''bispectrum'' of a signal measures the degree of correlation between three interacting frequency components due to a quadratic nonlinearity. Attention is here given to an acoustooptic implementation of the bispectrum which can operate on relatively wide-bandwidth signals. The overall architecture employed is that of a modified Mach-Zehnder interferometer which contains three acoustooptic modulators in conjunction with appropriate transforming lenses. The cross-bispectrum of the input and output signals are computed for a quadratically nonlinear system; an accurate estimate of the time delay between the signals is derived from the cross-bispectrum information.

A new hybrid optical/digital method for scale- and rotation-invariant pattern recognition is presented using a rotating kernel mm-max transformation. In this method, the input object is convolved with a long, narrow 2-D kernel. As the kernel rotates, the convolution output is monitored and the maximum [=Maxl and minimum [=MinJ values, along with the angle °M at which Max is found, are stored. The processed object is given by some function f[ , I of Max and Mm values. From the description (f[ , , OM), the 9-projection is first calculated. To obtain scale invariance, this projection is normalized by its integral. The normalized 0-projection exhibits an approximate scale invariance, the recognition capability depending to a small degree on the kernel length used. Since the kernel rotates, rotation invariance is achieved. Results of numerical experiments are presented. Some effects that variations in the kernel length have on the discrimination of objects are discussed.

A real-time optical correlator based on GaAs and liquid-crystal TV (LCTV) is demonstrated. The demonstrated system has a video-frame rate limited by the speed of the LCTVs; if faster spatial-light modulators are used, the potential frame rate of a GaAs-based correlator can be as fast as 1000 frames/sec under experimental conditions. Comparisons are made between VanderLugt and joint transform and between degenerate and nondegenerate four-wave mixing. The edge-enhancement effect and the Bragg diffraction effect are discussed.

When we recognize a word JAS in a page of a text by an optical pattern recognition system with a matched spatial filter, we form the filter using the same pattern JAS as a reference object. In the conventional matched spatial filter theory, the word to be detected is regarded as one pattern, therefore, only one autocorrelation peak is given in one identification. In this paper, we propose a new theory for the analysis of an autocorrelation peak signal. On the basis of the multiplexed matched spatial filter theory, we show, in the paper, the analysis of the autocorrelation signal that it is composed of three autocorrelations from 'J', 'A' and '5' and it actually appears in the same position to be superposed.

The synthetic estimation filter (SEF) crafts an affine variation into its response to a changing parameter (e.g. scale or rotation). Sets of such filters are used in an estimation correlator to reduce the number of filters required for a given tracking accuracy. By over-specifying the system (one more SEF than parameters to be tracked), the ratio of correlation responses between filters forms a robust estimator into the spanned domain of the parameters. Previous results have dealt with a laboratory correlator which could track a single parameter. This paper explores the SEF and estimator's extension to more dimensions. A two dimensional example is given in which we show a reduction of ifiters from 25 to 3, minimally to span a 4 degree square portion of pose space.

A robust optical correlator that is a miniaturized version of the classic Vander-Lugt correlator is developed. The correlator consists of a simple diode laser for illumination and a CMOS photodetector to detect the correlation peak. A set of roof prisms is configured to fold the light path into a compact design. A holographic plate is used for storing the matched filter. This correlator is particularly applicable to docking autonomous vehicles near a predesignated landing mark. This miniature optical correlator is described in terms of its functional performance.

Discrete frequency domain design of Minimum Average Correlation Energy filters for optical pattern recognition introduces an implementational limitation of circular correlation. An alternative methodology which uses space domain computations to overcome this problem is presented. The technique is generalized to construct an improved synthetic discriminant function which satisfies the conflicting requirements of reduced noise variance and sharp correlation peaks to facilitate ease of detection. A quantitative evaluation of the performance characteristics of the new filter is conducted and is shown to compare favorably with the well known Minimum Variance Synthetic Discriminant Function and the space domain Minimum Average Correlation Energy filter, which are special cases of the present design.

Limitations associated with the binary phase-only filter often used in optical correlators are presently circumvented in the writing of complex-valued data on a gray-scale spatial light modulator through the use of a computer-generated hologram (CGH) algorithm. The CGH encodes complex-valued data into nonnegative real CGH data in such a way that it may be encoded in any of the available gray-scale spatial light modulators. A CdS liquid-crystal light valve is used for the complex-valued CGH encoding; computer simulations and experimental results are compared, and the use of such a CGH filter as the synapse hologram in a holographic optical neural net is discussed.

DNA, the molecule containing the genetic code of an organism, is a linear chain of subunits. It is the sequence of subunits, of which there are four kinds, that constitutes the unique blueprint of an individual. This sequence is the focus of a large number of analyses performed by an army of geneticists, biologists, and computer scientists. Most of these analyses entail searches for specific subsequences within the larger set of sequence data. Thus, most analyses are essentially pattern recognition or correlation tasks. Yet, there are special features to such analysis that influence the strategy and methods of an optical pattern recognition approach. While the serial processing employed in digital electronic computers remains the main engine of sequence analyses, there is no fundamental reason that more efficient parallel methods cannot be used. We describe an approach using optical pattern recognition (OPR) techniques based on matched spatial filtering. This allows parallel comparison of large blocks of sequence data. In this study we have simulated a Vander Lugt1 architecture implementing our approach. Searches for specific target sequence strings within a block of DNA sequence from the Co/El plasmid2 are performed.

The joint transform correlator (JTC) operation has been extended to include complex reference images. Such amplitude and phase images are common when using a single harmonic (circular, radial, logarithmic, etc.) in correlation setups or when implementing composite filters. The analysis of an aspect view (tilt) invariant pattern recognition system, using logarithmic harmonics decomposition, JTC principles and composite filter techniques, is described followed by experimental results that can be obtained in real time.

The inactive areas of certain pixellated SLMs are transmissive rather than opaque, while their active areas modulate the optical phase or amplitude. Computer simulations of optical correlators are made for a continuous-input SLM and a filter SLM implementing either a classical matched, phase-only, or binary phase-only filter. The correlation peak and signal-to-noise ratio are studied as a function of dead-zone area in both the input and filter SLMs. These results are compared with those obtained from correlators whose SLMs have only opaque dead zones.

The phase modulating capabilities of a commercially available liquid crystal television have been investigated and applied to the joint transform optical correlator architecture. Operating the LCTV in a phase modulating mode requires a much smaller coherent light source while still producing a good joint transform power spectrum and good correlation signals.

The speed at which one or more targets can be recognized in a time-sequencing rotation-invariant binary phase-only filter (BPOF) optical recognition system can be improved significantly by integrating sequential correlation responses and using the integrated peak responses as inputs to the same statistical correlation plane filter (CPF) used for individual sequential correlation responses. Since commercially available BPOFs can be written at very high frame rates (350 frames per second), more than 10 correlation responses can be integrated during the frame time of an output camera operating at video rates. Therefore, the use of of integrated rather than individual sequential correlation responses reduces the processing time by a factor of 10 or more if the same standard video rate camera is used at the correlation plane. This paper presents results obtained using a prototype time-integrating BPOF correlator to achieve near real-time rotation-invariant recognition of both single and multiple targets in a noisy and cluttered input scene.

The implementation of nonlinear procedures in optical inforraation processing systems is the recently studied proruising step in the optical correlators development . Optical correlators with phase-only filters and binary phase-only filters belong to the class of such a nonlinear systems with the nonlinearity in the Fourier transfornt plane. The generalization of nonlinear matched filtering such that both the filter transfer function and the Fourier transform of the input objec are processed nonlinearly are recently under investigation. Pattern recognition by using phase nomation only is the particular case of nonlinear matched filtering. As a result of the nonlinear procedure one keeps only phase information about both the target and the input scene, and the pure phase-only correlation is realized. The discrimination capability of the phase-only correlation method is enhanced, even in comparison with the results obtained in the case of the phase-only filtering, and the autocorrelation signal is the diffraction limited delta function.

Ternary phase-amplitude filters (encoding only -1, 0, and +1 modulation values) have been designed to respond to geometric features oftargetobjectsin scenes, forexample thewhecls on atruck. The filtersarebasedongenenc models involving only a few parameters, whose adjustment allows the model to be matched to different instances ofthe feature (e.g., different size wheels). The formulation ofthe model-based filtersand theircorrelation performance usingrealistic images ofvehicles in clutter backgrounds willbepresented. Candidatepost-processing approaches to exploitthe correlation results fortargetrecognition will be discussed.

Experimental results of an optical binary phase-only correlator using aerial imagery for ground exploitation is presented. The correlator uses magnetooptic spatial light modulators (SLMs) for dynamic operation. Input images to the correlator originate from actual aerial imagery containing aircraft and a variety of distortions. Digital image processing techniques are used on images before being input into the optical correlator to enhance the performance of the system. Filters or templates used as a database for the system are derived from models of aircraft. Rotation and scale invariance is achieved through an adaptive filtering technique in which filters are displayed sequentially against an input image. Experimental results are presented which show that the system performs well with different types of segmented images.

Computer-controlled miniature optical correlators employing pixelated input and filter transducers can serve as either powerful plug-in modules for larger target-recognition systems, or as specialized, stand-alone portable correlators for specific image-processing and recognition applications. Attention is presently given to such design considerations for these devices as filter design, overall correlator length minimization, and the effect of aberrations on system performance. Two prototype miniature binary phase-only filter correlators employing magnetooptic spatial light modulators at the output and filter planes are presented.

The transmission of quantum noise through the basic systems used in optical computing is discussed. Multipliers, linear algebra processors, nonlinear elements, and cascaded systems involving detection and regeneration of light are examined.

A 1 lens focal length binary joint transform correlator is described. This correlator uses a iuagneto-optic spatial light inodu lator, lens, and standard 8bit resolution CCD camera. Computer simulations and experimental results of the effects of changes in scale, in-plane rotation, and multiple targets are discussed.

Experimental results are presented from spatial light modulators, in the form of a liquid crystal light valve and a ferroelectric liquid crystal. The experiments gave attention to the modulated response of the read beam as a function of the write light intensity. Regions of nonlinear response of the modulated read beam are noted.

The performance of binary joint-transform correlation using realistic input scenes has been studied by simulations addressing the effects of variations in threshold level, low-frequency blocks, and spurious signals due to regularly spaced groups of multiple (identical) input targets. A design tradeoff between better correlation performance and easier implementation (higher thresholding levels) was observed for constant thresholding. A new adaptive thresholding technique is introduced which alleviates the problems encountered using constant thresholds and significantly improves performance. Results are given for input scenes consisting of challenging backgrounds with multiple targets.

The present spatial light modulator employs an amorphous silicon photoconductor and a nematic liquid crystal to yield 501 p/mm MTF. The resolution is found to be improved by thinning the photoconductor and liquid crystal, as well as through the optimization of the device''s driving condition. Device response is limited by liquid crystal response; it is anticipated that faster response will be possible through the use of a ferroelectric liquid crystal.

Many similarities exist between the class of nonlinear filters called stack filters and neural networks. In this chapter, we describe the relationships between these areas and how the theory of stack filters may be applied to the study of neural nets. The concept of a neural network represents one of the most original ideas ever to appear in the field of computing and artificial intelligence. However, many of the tools used to study these architectures are not innovative, but are the same tools used to analyze more conventional systems. Some of these tools are the mean squared error measure, orthogonality of functions, and optimization by minimizing energy, and correlation techniques. These are the same tools that have largely failed modern Al as well as the study of nonlinear systems. We believe these classical tools of linear theory will be of limited use in the study of neural systems.

We investigate the performance of the binary joint transform correlator(JTC) for three types of threshoicling used to binarize the joint power spectrum. The first method is the fixed thresholding which uses the median of the joint power spectrum of the reference image and it does not include the effect of input scene noise. The second method( called the variable thresholding) takes into account the effect of the input scene noise and is the median of the joint power spectrum of the input scene and the reference image. The third method is the segmented thresholding that takes into account the effect of the input scene noise and is computed for each segment of the joint power spectrum. The correlation performance of the binary JTC is determined for each thresholding method and is compared to the linear( conventional) JTC. Computer simulation is used to determine the correlation peak intensity, peak to sidelobe ratio, and correlation width for various thresholding techniques. The results indicate that the thresholding of the joint power spectrum using the methods that take into account the input scene noise produce reasonably good correlation performance for large input scene noise

A new optical Fourier domain filtering scheme that combines the conventional optical space-invariant linear filtering with a self-pumped nonlinear optical phase-conjugation technique is proposed. The new method is used for a real-time detection and channel evaluation of the multi-path information needed in radar, sonar, and communication signal processing applications. Preliminary experimental demonstrations are included.

An experimental investigation is conducted of joint-power spectrum nonlinear transformation effects on the performance of a joint transform correlator. Attention is given to correlation-peak intensity, SNR, peak/sidelobe value, and peak width, for various degrees of the nonlinearity employed at the Fourier plane. The results obtained indicate increases of peak intensity, SNR, and peak/sidelobe, in conjunction with a decrease of the correlation, as the severity of the joint power spectrum''s nonlinear transformation increases. Attention is given to the performance of the liquid crystal light-valve spatial light modulator employed.

In this presentation the topic surrounding NSF's role in the growing research area of optical communications & optical information processing is discussed. In particular, the interaction of university research and industrial participation is explored. Opportunities for joint projects, information exchange, sharing of equipment, expertise, and facilities among research partners is explored. The changing posture of NSF in terms of emphasis on education, cross-disciplinary activities, human resources and interaction with government labs and industry is introduced.

The spatially-scanning, 2D, time-integrating hybrid interferometric processors presented employ directly-modulated CW laser diodes as input sources and are applicable to complex SAR data processing in real time. Crossed acoustooptic cells scan the input signal over a virtual 2D input space, and an optical interference pattern is detected with a solid-state detector array camera. Continuous transfer of the frames of integrated interference from the camera to a digital image processor, overall dynamic range is increased over that of the camera alone. Envelope detection in the display circuitry generates a continuous real-time representation of image magnitude.

An account is given of a novel incoherent-image subtraction technique employing ET materials, which possess no coherent noise, high resolution, gray level, high space-bandwidth product, high speed, and cost-effectiveness. The present ET devices are based on thin films of Ca(x)Sr(1-x)S:Eu, Ce, Sm. Prospective applications of this ET device encompass IC manufacture/inspection, data compression, and high-definition TV. Experimental results are presented.

To obtain the averaged Fourier power spectrum of a time-varying stellar speckle images from a binary star a portable real-time Fourier-transform processor is developed for stellar speckle interferometry, in which the Fourier transform of the image is done optically by using a microchannel spatial light modulator. Several double star images are analyzed on the telescope sites by the real-time processor. The cycle time of 2-10 Hz is achieved in this instrument depending upon incoming light level.

A fast algorithm has been developed for the reconstruction of an arbitrary permutation array from its two-dimensional aperiodic autoconelation function. The method is simple to apply. It is based on a backtracking search of a difference triangle associated with the permutation array. The issue of homometric arrays is also addressed. These are inequivalent arrays under the group ofEuclidean motions which share the same autocorrelation function. It is shown that the developed algorithm determines all homometric permutation arrays corresponding to a given autocorrelation function.

In this paper we discuss the potential for application of x-ray holographic imaging techniques to the sequencing of DNA. We formulate an approximate model for the scattering of partially coherent x-rays from an oriented DNA fiber and show the feasibility of reconstruction of heavy atom label positions from the x-ray scattering data. A series of simulations has been done to demonstrate the required reconstruction algorithms. An x-ray experiment is currently in progress to demonstrate the real feasibility of the technique. The potential of x-ray imaging techniques for the sequencing of DNA is attractive because of their inherently parallel nature. Hundreds or thousands of base pairs could be sequenced in a single set of x-ray images. The fundamental idea is to attach heavy atom labels to a selected base type on the DNA fragment to be sequenced. A large number (> 1012) of identical fragments can be constructed as an oriented fiber and illuminated with partially coherent x-rays. The heavy label positions can then be determined from the recorded pattern of scattered x-rays. If this operation is repeated for each of the four bases, the sequence can be reconstructed. The phase determination problem is solved by attaching to each DNA fragment a reference label in a known position. The scattered field then forms a Fourier transform hologram of the averaged DNA fragment. Because of the high photoelectric absorption of DNA relative to its coherent scattering cross-section, a single molecule would be damaged before an image could be formed. We solve this problem by distributing the damage over a large number of identical copies of the DNA fragment. In this paper we model a relatively simple experiment whose objective is to form a Fourier transform hologram of a labelled DNA fiber using 1 .54 A x-rays. We will first describe the hologram formation process and then the method for reconstructing the label positions.

Holospectral Imaging (HI), unlike the conventional technique, acquires data over a wide energy range. The new data is then used to form a series of frames corresponding to the object's spatial distribution at different energies. The multidimensional information is examined using the principal component analysis in order to characterize the different energy-dependent processes, namely: the primary photon information, the Compton scattering, the camera distorsions and the quantum noise. Each one of these factors has a typical location in the energy space RN (N is the number of energy frames). The primary photon is the main source of variance and has the most important contribution to the "principal" axis. In theory, without interference from other processes, the primaiy photon distribution defines a straight line in RN. Quantum noise will be distributed "around" this principal axis. However, scattering and camera distorsions will tend to pull the distribution toward a definite direction in the energy space. HI then finds, for each set of data, a transformation optimizing the "principal" information, the quality of this information being limited by the level of the statistical noise. Resulting images show an improvement in contrast to noise ratio and in quantitative analysis. We conclude that HI is a useful tool to describe the different contributions of scatter, camera non-uniformity and quantum noise to image variance. Therefore, energy variable should be included in the generalized transfer function of future nuclear medicine imaging systems.

The Fourier transforming properties of coherent imaging systems are well known and thoroughly developed. Optical spatial filtering techniques for coherent imaging systems are also a well developed field of study. Most of the advances in spatial filtering techniques were developed for systems with a known set of input characteristics. Once these filters were developed, they were static and unable to change wih a new set of inputs exhibiting a different set of characteristics. This paper will present the theoretical basis and desiy of an adaptive coherent imaging system using a two-dimensional spatial light modulator (5124) in the frequency plane. A computer controller is used as a feedback loop from the output plane back to the 5124. The filter implemented by the SLM is developed by simulated annealing. This iterative process enables the filter to adapt to a variety of inputs and automatically optimize given sufficient iterations. This paper will also present feasible applications of this technique in image processing and pattern recognition.

A year''s worth of developmental accomplishment in optical computing hardware materials and interconnection array configurations is evaluated. Attention is given to an optically interconnected 3D computer architecture, the features of programmable and reconfigurable interconnections, and the accomplishment of interconnect reconfiguration via the photorefractive effect and optical disks. Lead lanthanum zirconate titanate material has been used due to its comparative developmental maturity, producibility, and dynamic range.

The most plausible possible uses of nonlinear optics as the bases for interconnections among complex optical modules are evaluated, with a view to such applications as neural networks that entail large numbers of interconnections and numerous stages. Optical interconnection allows such a system to be composed of many modules as well as to incorporate switching- and amplification-function optical nonlinearities. While it is possible to achieve a pixel-by-pixel, diffraction-limited flat-field relay with nonlinearity, where the interconnect allows for cascadability, the wave-particle duality is destroyed between stages.

Realization of direct forms infinite-impulse response digital filters using various radiatively-tappered fiber optic delay lines is discussed. Such filters are attractive because they can provide better magnitude characteristics in their frequency response for a smaller number of taps than finite-impulse response filters can. These realizations use spatial light modulators and thus can be incorporated into optical adaptive filters for processing lightwave signals. Models of error sources in the fiber optical realization and their effects on both time and frequency response characteristics are explained. Cascading of lower order subsystems to obtain higher order filters is discussed. A possible way of improving the insertion loss using Erbium doped fiber optic amplifiers is derived.

The design of a high-speed, parallel arithmetic unit using the redundant binary representation is presented. The arithmetic unit consists of an adder and multiplier. The adder performs the addition/subtraction of two numbers in a single stage independent of the length of the numbers and the multiplier performs the multiplication in a computation time of O(log n) with O(n squared) computational elements.

A practical, special purpose digital optical computer architecture is proposed which exploits the energetic advantages of a Wave Particle Duality computer. A specific, practical algorithm is proposed which contains operations that proceed at an energy cost per operation ofless than kT.

A new improved version of the arithmetic Fourier transform algorithm is presented. This algorithm computes the Fourier coefficients of continuous -time signals using the number-theoretic technique ofMobius inversion. The major advantage of this algorithm is that it needs mostly addition operations, except for a few real multiplications. The improved version can be realized efficiently on integrated circuit chips and optical parallel processors using tapped delay lines.

A five-channel wavelength-division demultiplexer (WDDM) is demonstrated that is fabricated in polymer microstructure waveguides and operates over a 100-nm bandwidth centered at 750 nm in the near-IR. The device has a maximum diffraction efficiency of about 50 percent at 730 nm, a spectral bandwidth of about 15 nm, and effectively utilizes the large optical transparency of the photolime gelatin polymer material at laser diode wavelengths.

Given certain simple and well defined operations and complexity measures, the product of spatial complexity with temporal complexity must exceed a certain minimum problem complexity if that processor is to solve that problem. Some optical processors violate that condition in a favorable direction (anomalously small temporal complexity). We next extend the requirement to embrace those optical processors. In its final form, the theorem requires that the product of spatial, temporal, and fanin complexities equal or exceed the problem complexity.

An optical parallel adder based on polarization-coded symbolic substitution is presented. This adder eliminates the carry propagation chain associated with binary addition, thereby performing the addition of two numbers in a single stage regardless of the length of the two numbers.

Fundamental design issues are discussed relevant to the free-space optical interconnection of silicon-integrated circuits. Such systems require spatial light modulators integrated onto the surface of very large scale integrated devices, and detection circuits which allow recovery of the optically transmitted signal. Transmitter and receiver designs are discussed for free-space optical interconnects, and the design of a differential detection circuit is examined which allows recovery of binary data from a transmitter under condition of low modulation efficiency. Results from a custom fabricated CMOS differential receiving circuit are given which demonstrate the feasibility of low modulation differential detection.