On a vacation to the West of Ireland last summer, my wife and I took a ferry out to the Aran Isles that sit at the mouth of Galway Bay. We were going to visit a Stone Age fort, Dun Aenghus, that was built at the edge of a cliff on the island of Inishmore.

The interest in parallel binary and non-binary computer arithmetic in digital computing was initiated with the pioneering works of Avizienis.1 The parallel nature of such modified binary systems prompted researchers to adopt the modified signed-digit (MSD) algorithm for optical computing.2 Around the same time, non-binary systems such as multiple valued logic (MVL) (Ref.

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.

Carry-free parallel arithmetic computing using redundant binary number representation is exploited. Based on the original two-step algorithm, several improved algorithms including modified two-step, one- step, canonical, and three-input algorithms are proposed to increase processing speed and simplify the implementation system. The symbolic substitution rules for redundant binary addition are represented by binary logic operations and realized using optical space-variant binary logic gates. The proposed optical architecture is suitable for realizing both binary logic and arithmetic operations.

Novel fully parallel one-step adders that use the redundant signed-digit number representation are proposed for optical computing. A new method for spatially encoding the signed-digit is proposed based on digit grouping and pixel assignment. The scheme of digital grouping of the signed-digit numbers enables a huge reduction of the number of symbolic substitution computation rules involved in the arithmetic computations and consequently increases the speed of arithmetic operations. Furthermore, the proposed spatial encoding scheme effectively increases the space bandwidth product of the spatial light modulators and decreases the size of the matched spatial filters of the optical system.

Optical scalable parallel and high-speed 2D-data array computing based on modified signed-digit arithmetic and digit- decomposition-plane representation is presented. The digit- decomposition-plane coding uses m binary planes or m blocks of a binary plane to code an m-digit data array. Therefore, we can easily access each digit individually and can implement array addition with only 13 combinatorial logic formulas. A duplication-shifting-superimposition algorithm for digital array multiplication is proposed. The algorithm generates and records all the bitwise products in mn binary planes simultaneously, and then processes them based on a modified signed-digit (MSD) adder tree. Only five basic operations of bitwise product, duplication, shifting, masking and magnification are required for digital computing. The features of the proposed algorithm are that it requires no bistable devices, no decimal point, no sign, and no carry. The algorithm and its implementing scheme are scalable because they are independent to the sizes of data arrays. Therefore it has great promise for large- scale array computing. Optical implementation with classical optical elements, such as beamsplitters, parallel plates, and mirrors, is discussed. A preliminary demonstration experiment with an optoelectronic scheme is described.

The trinary signed-digit (TSD) number system has been found to be very useful for parallel addition and subtraction of any arbitrary length operands in constant time. Using the TSD addition and multiplication modules as the basic building blocks, we develop an efficient algorithm for performing parallel TSD division in constant time. The proposed division technique uses one TSD subtraction and two TSD multiplication steps. An optoelectronic correlator based architecture is suggested for implementation of the proposed TSD division algorithm, which fully exploits the parallelism and high processing speed of optics. An efficient spatial encoding scheme is used to ensure better utilization of space bandwidth product of the spatial light modulators used in the optoelectronic implementation.

An optical implementation using a correlation technique for modified signed-digit (MSD) trinary logic processing is presented. In particular, a synthetic matched filter (SMF) correlator model is used to demonstrate the realization of the carry-propagation-free trinary MSD addition. It is shown that proper encoding of the MSD numerals are of utmost importance for the correlator model to work. The developed method is expected to have far-reaching application in the optical higher radix numeric and logic processing.

A new binary logic based modified-signed-digit (MSD) adder is proposed. By encoding MSD digits in pairs of binary bits, each of the four MSD transforms can be represented by two cascaded binary logic operations. This leads to the design of a compact and integrated programmable MSD addition module. The three operation steps in the MSD addition can be realized using this same module simply by programming the decoding masks.

Multiple valued logic (MVL) is sought for designing high complexity, highly compact, parallel digital circuits. However, the practical realization of an MVL-based system is dependent on optimization of cost, which directly affects the optical setup. We propose a minimization technique for MVL logic optimization based on graphical visualization, such as a Karnaugh map. The proposed method is utilized to solve signed-digit binary and trinary logic minimization problems. The usefulness of the minimization technique is demonstrated for the optical implementation of MVL circuits.

Two novel full adder architectures are proposed that can be implemented with optical couplers using fiber optics or integrated optics. The first adder has the advantage over other proposed approaches by requiring only three different component devices: optical logical OR, optical logical NOT, and optical couplers. Configurations of the three components are described that are relatively simple to implement and are expected to function at greater than gigabit per second rates. The second adder requires fewer gates by using additional different gates: analog ADD and thresholding. Methods of implementing in fiber optics and with integrated optics are suggested including the synchronization of the lasers and methods for changing phase. The optical full adder can be used to provide high speed word addition by multiplexing independent additions. The pros and cons of fiber optics versus integrated optics for one architecture versus the other are discussed.

Today, most fuzzy logic operations are performed via software means, which is inevitably slow. While searching for long term hardware solutions to realize analog fuzzy logic operations, the use of the well-developed Boolean logic hardware with analog to digital (A/D) and digital to analog (D/A) converters to implement the digitized fuzzy logic could provide an efficient solution. Similar to Boolean logic, digitized fuzzy logic operations can be written as a minimized sum-of- productterm format, which can then be implemented based on programmable logic arrays. We address a fundamental issue of the computational complexity of this method. We derive the minimum number of the Boolean sum-of-product terms for some key fuzzy logic operations, such as Union, Intersection, and Complement operators. Our derivations provide ways to estimate the general computational complexity or memory capacity of using binary circuits, electronic or optoelectronic, to implement the digitized analog logic operations.

We experimentally implement a new method for high- accuracy optical computing using interval arithmetic and the fixed-point theorem. In the implementation, a fixed point of an affine transformation is calculated by a Tv feedback system. Employing interval arithmetic, the errors associated with an optical setup can be ignored. We evaluate two constraints on the optical system that seriously affect computing efficiency. The minimum value of computational accuracy achieved is 10-13, which is determined by the control accuracy of the required affine transformation coefficients.

In the bimodal optical computer, linear and nonlinear acts occur in rapid succession generating solutions to Ax=b. Both chaos and stochastic resonance can appear in some cases. This is the first observation of such complexity effects in optical processors. © 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)00903-4]

We show how multilayer optical-interconnect-based digital logic systems can be made fault-tolerant by distributed redundancy techniques implementable at the gate level, while incurring the expense of an increased number of gates with greater individual fan-in and fan-out. We demonstrate that braided logical interconnections between redundantly doubled, tripled, and quadrupled NOR gates enable the correction of device and interconnection errors. We present an extrapolated error analysis for the quadding, doubling, and tripling schemes, which shows the quadratic and cubic dependence of the system error on device error rates, in comparison with the linear relationship of a nonredundant system. Because the interconnections between the braided circuits are quite regular, they appear to be very amenable to optical implementations, and with the appropriate choice of device topology employing sparse device placement they are compatible with the regular, layered structure of conventional shift-invariant digital optical computer interconnects, without a penalty in circuit depth or latency. We show device topologies and interconnection architectures for the optical implementation of a fault-tolerant quadded programmable two-shuffle interconnection system that use holographic shift-invariant interconnects. Using these redundant optical logic schemes with only moderate device error probabilities, extremely low system error rates can be achieved.

Multivalued logic (MVL) is seriously being considered for optical implementation for its algorithmic parallelism. Practical implementation of an MVL algorithm using any technology demands engineering analysis of such implementations. Instead of concentrating on the algorithm and architectural aspects, we attempt to address the system issues such as logic levels, signal-to-noise ratio, and threshold value for intensity-coded MVL. Both computer simulation and experimental results are provided.

We develop a new method to separate touching handwritten numeral pairs using structural analysis. The string is preprocessed with an efficient algorithm for smoothing, linearization, and detection of structural points of image contours. The structural region of the string is determined. Some left- or right-side numerals of the string are recognized. The property of each hole contour in a string is detected. The touching model of a string is determined, whether single- or double-touching. For double-touching, the touching hole contour is determined. For the two touching models, the touching point is preselected, its position is corrected, and the corresponding match touching point is found. The string is separated based on all touching points. All processing procedures are based on morphological structural analyses. We have tested our method on image samples taken from the U.S. National Institute of Science and Technology (NIST) database. We used 500 sample images to design the required models. For 3287 test samples the correct-separation rate was 97.2% for single-touching strings, and 97% for double-touching strings.

This paper presents a computer vision algorithm that segregates spurious optical flow artifacts to detect a moving object. The algorithm consists of six steps. First, the pixels in each image are shifted to compensate for camera rotation. Second, the images are smoothed with a spatiotemporal Gaussian filter. Third, the optical flow is computed with a gradient-based technique. Fourth, optical flow vectors with small magnitudes are discarded. Fifth, vectors with similar locations, magnitudes, and directions are clustered together using a spatial consistency test. Sixth, similar optical flow vectors are extended temporally to make predictions about future optical flow locations, magnitudes, and directions in subsequent frames. The actual optical flow vectors that are consistent with those predictions are associated with a moving object. This algorithm was tested on images obtained with a video camera mounted below the nose of a Boeing 737. The camera recorded two sequences containing a second flying aircraft. The algorithm detected the aircraft in 82% of the frames from the first sequence and 78% of the frames from the second sequence. In each sequence, the false-alarm rate was zero. These results illustrate the effectiveness of using a comprehensive predictive technique when detecting moving objects.

We propose and analyze novel fully depleted optical thyristors (DOTs) using multiple quantum wells (MQWs) and quarter- wavelength reflector stacks (QWRSs). MQWs are employed to enhance the absorption, while a QWRS is employed as a bottom mirror to enhance the emission efficiency as well as the optical sensitivity. In order to analyze the switching characteristics, we simulate S-shaped nonlinear current-voltage curves using a coupled junction model associated with the current-oriented method. Furthermore, emission characteristics are obtained by using the scattering-matrix method and the van Roosbroeck-Shockley relation. According to our analysis, the novel DOTs significantly improve the switching and light emission characteristics. Compared to a conventional DOT, the optical switching energy and the bit rate of the novel DOT using both mQws and a QWRS are improved by a factor of 0.45 and 1.61, respectively, for a cascading operation. We also analyze the performances of free-space optical interconnects using the novel DOTs.

A method based on the Herzberger approach has been investigated for the selection of glasses for the apochromatic correction at near-infrared (NIR) wavelength. The method avoids the algebraic complexity and simplifies the glass selection processes. Doublet and triplet glass combinations can be chosen directly from the plot of partial dispersion versus V number. Good combinations of NIR doublets and triplets are given. Design examples show that the method is practical and efficient.

A new type of phase-locked laser diode interferometer that uses self-mixing interference in the optical system is described. The selfmixing interference (SMI) signal is obtained easily by optical feedback, i.e., feeding back the laser beam from the object to the laser diode (LD). The SMI signal can be detected by a photodiode in the package of the LD. Therefore, a beamsplitter, reference mirror, and external photodetector are not required, and an interference signal is obtained using a simple optical system. Although the mechanism of SMI is completely different from that of conventional interference, it is shown that the response of the SMI signal to phase changes is the same as that of conventional interference. We used the phase-locked technique to fix the phase change and demonstrated measurement of absolute distance and displacement.

The phenomenon that a birefringent He-Ne laser outputs two frequency differences of 43 and 77 MHz is reported. Theoretical analysis shows that the multiple transverse modes and mode competition give rise to this phenomenon. When TEM01q of o light and TEM00q of e light oscillate in the cavity, the frequency difference is 77 MHz, and when TEM00q of o light and TEM00q of e light oscillate, the frequency difference is 43 MHz.

This paper is devoted to rigorous electromagnetic diffraction analysis, in the near infrared, for micromechanical silicon interdigitated beam gratings with both lateral and vertical displacement of movable beams. In the wavelength-to-period ratio domain where the gratings support three diffraction orders, the specific designs of high-efficiency switches for polarized radiation, such as switches from a transmitter to a 1 x 3 transmission beamsplitter and from a retroreflector to an 1 x2 reflection beam divider, are presented. The possibility of light modulation, which follows from these designs, is discussed. The analysis with respect to wavelength, beam-width, beam-height, and incidence-angle variations shows a good tolerance of the devices' performance to spectral shifts and to fabrication and mounting errors. in addition, with the use of our software we simulated the diffraction efficiency versus displacement at a visible wavelength for a micromechanical grating reported in the literature. There is good agreement between theory and experiment.

An analog nonlinear optoelectronic image-processing system for detection of moving objects in an input image stream is proposed and analyzed. Its operation is based on the effect of self-suppression of a stationary-state image background, with enhancement of the contrast of a moving object. Analytical results obtained in the linear approximation are verified by direct numerical simulations.

This PDF file contains the errata for “OE Vol. 38 Issue 03 Paper 602041” for OE Vol. 38 Issue 03