George Eichmann

Conditional symbolic modified signed-digit arithmetic using optical content-addressable memory logic elements

A new conditional symbolic substitution rule for modified signed-digit arithmetic computation is introduced. Using this substitution rule, the numbers to be added or subtracted are first replaced by a pair of new equivalent strings, which in a second step are then subject to another substitution to generate both the addition or subtraction result and its complement. For an optical implementation, a holographic contentaddressable memory is used. Correspondingly, the input encoding, the logic reduction, and the optical processing techniques are described.

Content-addressable-memory-based single-stage optical modified-signed-digit arithmetic

Using a novel nonholographic optoelectronic content-addressable memory in a free-space angular multiplexing geometry, a single-optical-stage compact parallel optical modified-signed-digit arithmetic processing architecture is proposed. Some spatial light modulator based experimental results are also presented.

Topologically invariant texture descriptors

Abstract Texture is one of the important image characteristics and is used to identify objects or regions of interest. The problem of texture classification has been widely studied. Texture classification techniques are either statistical or structural. Some statistical texture classification approaches use Fourier power-spectrum features, while others are based on first- and second-order statistics of gray level differences. Periodic textures that consist of mostly straight lines are of particular interest. In this paper, a new structural approach based on the Hough method of line detection is introduced. This classification is based on the relative orientation and location of the lines within the texture. With proper normalization, the classification is independent of geometrical transformations such as rotation, translation, and/or scaling. Experimental results will also be presented.

Coherent optical production of the Hough transform.

The Hough transform (HT) is an efficient shape detector that maps straight lines into a two-parameter feature space. Recently it has been pointed out that the forward Radon transform (FRT), well known from the theory of computed tomography, and the HT are equivalent for binary images. In this paper, analog coherent optical implementation of the FRT is discussed. The FRT will not only be of use in implementing the HT shape descriptors but also act as a coherent optical preprocessor for the implementation of multidimensional convolution, correlation, and spectral analysis using 1-D acoustooptical signal processing devices. Several different coherent optical FRT architectures are presented. Experimental results using conventional coherent Fourier transform configuration are given. The relationship between the coherent optical implementation of the FRT and the inverse Radon transform, an important tool in computed tomography, is also detailed.

Optical binary coded ternary arithmetic and logic.

Two ternary, an ordinary ternary (OT) and a binary balance ternary (BT), number representations to be used for optical computing are discussed. An unsigned OT number is represented by a string of symbols (0, 1, 2), while for the BT, the three logic symbols take on the set (−1, 0, +1). The BT symbols can represent a signed number. Using a particular binary encoding method, the three ternary symbols are converted to a pair of binary symbols. The binary coded ternary (BCT) representation has two advantages. First, it allows use of the well-developed binary optical components. Second, compared with other optical multiple-valued number encoding schemes, it reduces the number of input–output channels and thus is able to conserve the optical space–bandwidth product. As an example for arithmetic operations, BCT full addition algorithms are given. As examples for multiple-valued logic computing, BCT Post, Webb, and residue logic elements are discussed. Using the two-port Sagnac interferometric switches, optical implementations of various BCT arithmetic and logic operations are described.

Propagation of Plane Waves in Biaxially Anisotropic Layered Media

This paper is concerned with the general theory of wave propagation in layered biaxially anisotropic media. Details are presented for the calculation of the induced waves that are due to an arbitrarily polarized and obliquely incident wave impinging on a three-layer structure. The total numbers of partial waves with their respective phase velocities, direction of phase propagation, and polarization are determined by the use of the Fresnel equation and Snell’s law applied to each layer. The vector amplitudes of the partial waves are found by proper matching of the field components at the interfaces. The expressions thus found are shown to reduce to known results for a uniaxial three-layer structure. An extension of this theory to an arbitrary number of layers is also presented.

Optical learning (inference) machines

Two different approaches to decision aids are explored. In one, forced binary decisions are made. In the other, a set of a posteriori probabilities is calculated. In both cases fast inferences can be calculated by optical matrix operations.

Two-dimensional optical filtering of 1-D signals

One-dimensional signals have complementary attributes, their space and spatial frequency properties. Recently, another signal representation was introduced in optics, the Wigner distribution (WD) function, which allows the simultaneous display of the two attributes of a 1-D signal. In this paper optical implementation of a generalized space-spatial frequency (GSF) function is discussed. Special cases of the GSF representations are the WD, the radar ambiguity function (AF), the energy distribution function, the various pseudo-WD functions, the spectrogram, the local frequency and the local Doppler frequency spectrum. The GSF representation allows the simultaneous filtering of both the spatial and the spatial frequency content of a 1-D signal. The 2-D filtering of a 1-D signal allows sidelobe reduction of the WD and AF of quasi-periodic 1-D signals, display of the instantaneous spatial frequency content of a 1-D signal, space-spatial frequency excision of a desired portion of a 1-D signal as well as the usual matched filter detection. Experimental results using coherent space-integrating techniques for the realization of different GSF are presented.

Coherent optical generation of Hartley transform of real images

Abstract A new method to generate optical Hartley transform (OHT) for 2D real images is proposed. The method is based on polarization encoding of the coherent optical beam. Different coherent optical image processing techniques are discussed.

Shape representation by Gabor expansion

De8cription of boundary curves (shapes) is an important problem in image processing and pattern recognition. During the last two decades there have been a variety of approaches to the problem. Among these approaches the Fourier description (FD) techniques seem to be the most promising in extracting the features of an object. But the problem of the FD techniques that have been practised is the difficulty in describing local information. A modified FD technique is suggested in this paper which use a combined I requencyposition space as the shape descriptor domain. This new set of position-dependent Fourier descriptors provides the best spectral information along the boundary curve. Experimental results are presented in this paper. 1.