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In this work, a three-step modified signed-digit (MSD) addition by using binary logic operations is proposed. Each input digit is encoded with two binary bits. Through binary logic operations, all of the weight and transfer digits and the final sum digits represented with the same encoding scheme will be generated. The operations can be performed at each digit position in parallel. In our suggested optical arithmetic and logic unit (ALU), a single electron trapping (ET) device is employed to serve as the binary logic device. This technique based on ET logic possesses the advantage of high signal-to-noise ratio (SNR). The optoelectronic system can be constructed in a simple, compact and general-purpose form.

Conventional algorithms process addition and subtraction in different ways. In this paper, by introducing bipolar carries, a unified negabinary symbolic arithmetic for the two operations can be derived, using only the same six substitution rules. Based on the polarization-encoded optical shadow-casting technique, the encoding and decoding patterns for half-addition, half-subtraction and unified arithmetic are designed, with the fixed LED pattern and separate and simultaneous generation of the multi-outputs. The architecture is simple, programmable, cost-efficient, and the addition and subtraction of multiple pairs of bipolar numbers can be handled in parallel in the same manner.

Instead of using the truth look-up table residue arithmetic, a technique for multiplying two N -bit negabinary numbers, modulo (−2) N −1 with digital partitioning, is introduced for optical computing. Both numbers are decomposed into k -bit bytes, and the product is obtained by the cyclic convolution of the sequences of the bytes. The operation with respect to other moduli can be performed similarly. The algorithm has such features as smaller computational complexity, ease of implementation, the ability to handle bipolar numbers without signs, and simple pre- and post-processing. As a proof-of-principle experiment, an optical correlator is used to perform the multiplication in parallel. The experimental results are given.

Optical higher-order negabinary addition is investigated for fast operation. A new method for recognizing multiple reference patterns in a channel is presented, and thus the substitution rules are logically minimized, resulting in fewer channels for processing. A content-addressable-memory based incoherent optoelectronic symbolic substitution architecture is proposed. The system is simple and flexible, and the multi-channel operations for all the modules are performed in parallel. An experiment is demonstrated.

Based on the quadratic residue number system (QRNS), a novel optical matrix-vector multiplication is proposed. Complex number multiplication has higher parallelism than other algorithms. If the residue number is binary encoded, this multiplication can be easily implemented with a multichannel incoherent optical correlator. © 1996 John Wiley & Sons, Inc.

The CC-banyan network represents a large class of nonequivalent multistage interconnection networks. The optical implementation of a regular rectangular CC-banyan network, which is based on polarizing beam splitters and 1D liquid crystal spatial light modulators, is proposed and demonstrated, and its corresponding routing control for a path between any (S, D) pair is given. It possesses a low energy loss, a high signal-to-noise ratio and an available large number of optical channels.

The bi-imaginary number system is exploited for complex operation, in which a complex number is represented by a single digit string. Complex multiplication is realized by two real-like multiplications with no signs and carriers, simple preprocessing and postprocessing. No subtraction is included. Furthermore, the proposed architecture is cascadable. On this basis, complex matrix-vector multiplication is demonstrated in parallel using a multichannel incoherent optical correlator.

Based on negabinary number representation, complex matrix-vector multiplication is performed using an optical multichannel shadow-casting incoherent correlator. The architecture resolves the difficulties presented in the systems using other number encodings. In multiplication, bipolar data are processed without signs and extensional digits, and the mixed negabinary product can be summed directly. Through negative 2's complement operation, subtraction is converted to addition. By the decomposition of complex numbers, the complex matrix-vector operation is executed in parallel. The experiment is demonstrated, too.

A compact integrating module technique for packaging a optical multistage Cantor network with a polarization multiplex technique is suggested. The modules have a unique configuration, which is the solid-state combination of a polarization rotator, double birefringent slabs, and a 2 × 2 switch array. The design and the fabrication of an eight-channel optical nonblocking Cantor network are demonstrated, and a fast-setup control algorithm is developed. The network systems are easy to assemble and insensitive to environment disturbance.

We describe a modified engagement method for matrix operation based on a two-dimensional crossed-ring interconnection network. Our method incorporates fewer steps than that reported by Bocker et al. [Appl. Opt. 22, 804 (1983)], and its performance is found to be the most efficient (minimum steps) in comparison with other systolic and/or engagement methods for matrix operation. Thus, it may be helpful for other optical and electronic implementations of matrix operations. One compact optoelectronic integrity approach for implementing the modified engagement method is briefly described.

A programmable shifter that uses birefringent crystal plates and programmable half-wave plates is described. It can accomplish right, left, right-cyclic, and left-cyclic shifting on the fly.

Based on the dual-rail encoding concept, beam splitting, and beam combining, an optical logic gate capable of performing all 256 logic functions of three input binary patterns is proposed. The gate is programmed by polarization customizing. The full adder and the full subtractor are thus suggested, and the experimental results are presented.

Based on the mixed negative binary number system, we propose an inner-product algorithm for digital complex-valued matrix-vector multiplication. The features are no carries, no signs, no indications for decimal points, and simple preprocessing and postprocessing. Correspondingly, an optical architecture of incoherent optical correlation with spatial digital coding of data is suggested. Negative binary complex matrix-vector multiplication can be realized optically in parallel with a high accuracy. The experimental result is also given.

A novel orthogonal shadow-casting and imaging optical system is proposed for performing multiple matrix multiplication. An analysis is given for describing the construction of a matrix processor. Preliminary experiments of matrix multiplication are demonstrated.

A more powerful tool for binary image processing, i.e., logic-operated mathematical morphology (LOMM), is proposed. With LOMM the image and the structuring element (SE) are treated as binary logical variables, and the multiply between the image and the SE in correlation is replaced with 16 logical operations. A total of 12 LOMM operations are obtained. The optical implementation of LOMM is described. The application of LOMM and its experimental results are also presented.

A novel, to our knowledge, two-step digit-set-restricted modified signed-digit (MSD) addition-subtraction algorithm is proposed. With the introduction of the reference digits, the operand words are mapped into an intermediate carry word with all digits restricted to the set {1, 0} and an intermediate sum word with all digits restricted to the set {0, 1}, which can be summed to form the final result without carry generation. The operation can be performed in parallel by use of binary logic. An optical system that utilizes an electron-trapping device is suggested for accomplishing the required binary logic operations. By programming of the illumination of data arrays, any complex logic operations of multiple variables can be realized without additional temporal latency of the intermediate results. This technique has a high space-bandwidth product and signal-to-noise ratio. The main structure can be stacked to construct a compact optoelectronic MSD adder-subtracter.

A compact two-step modified-signed-digit arithmetic-logic array processor is proposed. When the reference digits are programmed, both addition and subtraction can be performed by the same binary logic operations regardless of the sign of the input digits. The optical implementation and experimental demonstration with an electron-trapping device are shown. Each digit is encoded by a single pixel, and no polarization is included. Any combinational logic can be easily performed without optoelectronic and electro-optic conversions of the intermediate results. The system is compact, general purpose, simple to align, and has a high signal-to-noise ratio.

A new binary-encoded matrix-matrix multiplication architecture based on correlation by shadow casting is presented. It can perform a binary-encoded matrix-matrix multiplication in a fully parallel manner to gel the mixed-binary output matrix in the focal plane of the lens. Both the advantages and the disadvantages of the proposed architecture are carefully discussed. The proof-of-principle experiments demonstrate the effectiveness of the proposed architecture. © 1994 John Wiley & Sons, Inc.

Hexagonal array devices are widely used in optical communication and optical computing. Near field Talbot array illuminator is an ideal method for the illumination of these devices. Ultrafast pulse provides high transmission bit-rate and high peak energy, thus it is favorable for optical communication, diffractive optics, and other applications. In this paper we studied the hexagonal array Talbot effect under ultrafast pulse illumination. Ultrafast pulse has wide wavelength spectra range, and each spectral component corresponds to a unique wavelength that is directly relating to the Talbot distance. Thus the Talbot effect of hexagonal array is different from those of continuous wave in a whole. From the experimental result we can see that, comparing with that of the monochromic illumination, the efficiency and contrast of ultrafast pulse illumination are decreased. The result should be highly interesting for ultrafast fiber communication as well as other optical devices.

An imaging system with the use of a liquid crystal device for two-dimensional optical Hopfield associative memory is described. Experimental operations for 7 × 7–pixel patterns are demonstrated. © 1992 John Wiley & Sons, Inc.

A compact two-step modified-signed-digit arithmetic-logic array processor is proposed. When the reference digits are programmed, both addition and subtraction can be performed by the same binary operations regardless of the sign of the input digits. The optical implementation and experimental demonstration using an electron-trapping device are shown. Each digit is encoded by a single pixel, and no polarization is included. Any combinatorial logic can be easily performed without optoelectronic and electro-optic conversions of the intermediate results. The system is compact, general- purpose, simple to align and has a high signal-to-noise ratio.

The modified signed-digit (MSD) number system offers parallel arithmetic operations because of its redundancy property. For exploiting the high parallelism of the MSD representation, MSD form and 2's complement binary form have to be converted to and from each other. In this paper, an efficient lookahead-mode conversion algorithm is introduced. The operation can be performed in parallel by binary logic and is thus suitable for optical implementation. The optical system utilizing a single electronic trapping device is suggested to realize the required operations. By programming the illumination of data arrays, any complex logic operations of multiple variables can be performed easily. The main hardware can be stacked to construct a compact optoelectronic processor of versatile functions. A proof-of- the-principle experiment is demonstrated.

This paper summarized our developments on the integration of miniaturized optical 3D systems using crystal substrates, which include a birefringence-customized stacking technique with the building blocks of double refraction and a photorefractive integration technique with the photorefractive local holograms thermally fixed by CO2 laser heating. The principles are introduced and the corresponding configurations are given, and the examples of various integrated digital optical computing systems such as logic processor, morphological image processor, and interconnection networks are shown.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, we presented a scheme for complex-valued modular multiplication based on digital partitioning technique. The module (-2)N-1 is introduced for its simple arithmetic. Both of the operands joining in the complex number multiplication are treated as two N-bit real numbers. Because of its advantage in expressing number, the negabinary number system is adopted. The subtraction in complex number multiplication is converted to addition operation by weighting shifting. Although the direct result takes the looks of a serial of residues, we proposed an algorithm for reconstructing the complex-valued multiplication produce by studying the product decomposing rules. The algorithm can be implemented in parallel manner, we studied the optical implementation based on an incoherent optical correlator and some electronic devices as auxiliary for reconstructing the product. Both the advantage and the disadvantage are analyzed. And the comparison with other optical complex-valued multiplication algorithms is also presented.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A optical perfect shuffle interconnection and array of exchange boxes are given. The optical perfect shuffle network is implemented using repeated stages of PS together with arrays of exchange boxes.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Negabinary is a component of the positional number system. A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/subtraction algorithm based on negabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normal negabinary in the carry-look-ahead mode. All the arithmetic operations can be performed with binary logic. By programming the binary reference bits, addition and subtraction can be realized in parallel with the same binary logic functions. This offers a technique to perform space-variant arithmetic-logic functions with space-invariant instructions. Multiplication can be performed in the tree structure and it is simpler than the modified signed-digit (MSD) counterpart. The parallelism of the algorithms is very suitable for optical implementation. Correspondingly, a general-purpose optical logic system using an electron trapping device is suggested. Various complex logic functions can be performed by programming the illumination of the data arrays without additional temporal latency of the intermediate results. The system can be compact. These properties make the proposed negabinary arithmetic-logic system a strong candidate for future applications in digital optical computing with the development of smart pixel arrays. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)00803-X].

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

A parallel architecture for gray-tone image processing is proposed that utilizes the concept of threshold sum-superposition into a cellular two-layer logic binary-image processor. Various processing functions constituted by gray-tone dilation, erosion, fuzzy-logic operations, and arithmetic operations are obtained. The optoelectronic implementation is illustrated.

An optical crossbar element that uses birefringent crystal plates and programmable half-wave plates is proposed. It is compact, cascadable, and well suited for realizing an array of switching elements employed in multistage interconnection networks. Arrays of two-input/two-output and four-input/fourputput crossbar switching elements and a Clos (4, 4, 4) network are also presented.

One-dimensional perfect-shuffle networks are extended to two-dimensional perfect-shuffle networks, and this extension is analyzed by means of the finite-state model. The routing algorithm presented is based on quaternary numbers for 4 × 4 switches, and its extension to k × k switches is briefly discussed. In order to take full advantage of the three-dimensional interconnection capability and two-dimensional space-bandwidth product of free-space optics, we map one-dimensional perfect-shuffle networks into two-dimensional perfect-shuffle networks, with both having 4 × 4 switching elements. Finally we compare the permutation capability of two-dimensional perfect-shuffle networks with one-dimensional perfect-shuffle networks.

A birefringence phenomenon is used to construct Boolean logic gates that output three logic functions. Logic gate modules are proposed that consist of Bi12SiO20 opto-optical birefringence switches, LiNbO3 electro-optical half-wave plates, and calcite plates. The gate can be driven by optical inputs and can also be electrically programmed for different logic operations. An array-packed solid-state module is described.

A cyclic matrix representation for complex numbers is proposed for sequential multiplication of complex matrices. The related optical implementation is discussed.

An optical parallel architecture is suggested to implement a basic programmable cellular logic array for image processing. Interconnection of the neighboring cells is achieved by using an optical correlator. The required parallel logic gates are executed with spatial coding and electronic thresholding methods. Another optical correlator is used to spatially code the outputs from the 2-bit decoder array of shadowgrams. The optical method for the directional interconnection is also discussed. An image processing example is simulated and verified experimentally.

The optical implementations of a 2-D neural net with a third-order interconnection for image quadratic associative memory are reported. Two types of incoherent optical systems, based on multiple imaging and correlation, are used. In particular, a compact-encoding method, which can greatly reduce the size of the interconnection tensor, is also proposed. The experimental results are given.