<title>Rapid Unbiased Bipolar Incoherent Calculator Cube</title>

Abstract

Rapid unbiased bipolar incoherent calculator cubeR. P. BockerSignal Processing Technology Branch, Naval Ocean Systems Center271 Catalina Boulevard, San Diego, California 92152H. J. CaulfieldAerodyne Research, Inc.45 Manning Road, Billerica, Massachusetts 01821K. BromleySignal Processing Technology Branch, Naval Ocean Systems Center271 Catalina Boulevard, San Diego, California 92152AbstractAn electrooptical engagement array architecture for performing matrix -matrix multiplication using incoherent light is presented. Keycomponents of this newly proposed processing device include a single pulsed incoherent light source, two dynamic light valves, and atwo -dimensional photodetector array.IntroductionIn this paper we present a new concept for performing the algebraic operation of matrix -matrix multiplication using electroopticaltechnology. This concept is based on the pioneering work of H. T. Kung (ref. 1) for performing matrix -matrix multiplication using an allelectronic systolic array architecture as well as subsequent work by J. M. Speiser and H. J. Whitehouse (ref. 2) on electronic engagementarray architectures. Before describing the electrooptical approach, a brief review of prior work for performing both matrix -vector andmatrix -matrix multiplication using optical techniques will be presented.BackgroundThe use of optical correlation techniques involving coherent light for performing both matrix - vector and matrix -matrix multiplicationhas been studied analytically (ref. 3) and verified experimentally for matrices of order two (ref. 4). This technique has the undesirablefeature that as the matrix order increases, the number of unwanted circular distributions of light appearing in the output plane of theprocessor rapidly escalates, thus reducing the light available at those positions corresponding to product matrix element information. Therehave been a number of other techniques, particularly those using incoherent light, for performing matrix -vector multiplication. For example,preliminary studies in this area describe the computation of one -dimensional discrete Fourier transforms (ref. 5), sine, cosine, Walsh -Hadamardtransforms, as well as a variety of linear filtering operations (ref. 6). The technical feasibility of this approach was demonstrated for matricesof order 32 using an earlier developed (ref. 7) optical correlation device. In the original version of this optical correlator, a single light emit-ting diode, mechanical scanning mirror, photographic film transparency, and a vidicon detector were employed. More recently (ref. 8,9), thescanning mirror and vidicon detector were replaced by a solid -state area -array charge -coupled device, thus greatly reducing the size of theprocessor. Matrix -vector multiply operations involving matrices of order 128 are presently performed using this approach.A second technique for computing matrix -vector products using incoherent light involves the use of a linear array of light emittingdiodes, an optical transparency, and a linear array of photodetectors (ref. 10). This architecture has the advantage that the data vectorinformation may be entered in parallel, thus allowing for higher throughput rates. The feasibility of this approach has been demonstratedfor matrices of order 10. Combining this architecture with a one -dimensional adder in a feedback loop gives rise to an iterative electroopticalprocessor (ref. 11). With this capability it is possible to perform other higher level matrix operations such as the solution of simultaneousalgebraic equations, least squares approximate solution of linear systems, matrix inversion, and eigensystem determination (ref. 12,13), justto mention a few.Most recently, much attention has been focused on implementing parallel processing architectures for performing a variety of matrixoperations using exclusively electronic components. Most noteworthy is the work of H. T. Kung on systolic array architectures (ref. 1,14,15).Combining VLSI /VHSIC technology with systolic array processing techniques should give rise to increased signal- processing capabilities byat least a factor of one hundred (ref. 16). Already a two -dimensional systolic array testbed has been designed and fabricated for validatingmany of the proposed architectures and algorithms envisioned (ref. 17). A similar all electronics parallel approach has been proposed (ref. 2)using an engagement array architecture. As it turns out, these new systolic /engagement type of architectures are not restricted to solely allelectronic implementations. For example, an acoustooptic approach using incoherent light for performing matrix -vector multiplicationemploying the systolic /engagement array architecture has recently been described (ref. 18). This acoustooptic processor uses a linear arrayof light emitting diodes for inputing the matrix information, an acoustooptic traveling wave modulator for inputing the vector information,and a linear array charge -coupled device for computing the desired output vector information. This approach has the advantage that theinput vector and matrix information may be entered in real -time.