Optical computation using residue arithmetic

Huang, Alan; Tsunoda, Yoshito; Goodman, Joseph W.; Ishihara, Satoshi

doi:10.1364/ao.18.000149

Cited by 159 publications

(35 citation statements)

References 9 publications

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“…13 The first optical implementation was carried out by Psaltis et al,1 4 and schemes to incorporate it in optical linear algebra processors were forwarded by Guilfoyle1 5 and Collins et al1 6 In the last four years numerous modifications to the basic idea have been suggested with different predicted performances.1 7 -2 2 In this paper we will examine in detail the trade-offs involved in performing the digital calculations by linear analog optical systems. Section II contains a general trade-off analysis for a generic system.…”

Section: Introductionmentioning

confidence: 99%

High accuracy computation with linear analog optical systems: a critical study

Athale¹

1986

Appl. Opt.

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High accuracy optical processors based on the algorithm of digital multiplication by analog convolution (DMAC) are studied for ultimate performance limitations. Variations of optical processors that perform high accuracy vector-vector inner products are studied in abstract and with specific examples. It is concluded that the use of linear analog optical processors in performing digital computations with DMAC leads to impractical requirements for the accuracy of analog optical systems and the complexity of postprocessing electronics.

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Section: Introductionmentioning

confidence: 99%

High accuracy computation with linear analog optical systems: a critical study

Athale¹

1986

Appl. Opt.

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“…In this recent work, at least three distinguishable ways have been suggested for representing numbers in an optical residue system. 7 These include phase or polarization coding and pulse-position coding. Collins 6 has chosen the former method and Huang et al 7 the latter approach.…”

Section: Introductionmentioning

confidence: 99%

“…7 These include phase or polarization coding and pulse-position coding. Collins 6 has chosen the former method and Huang et al 7 the latter approach.…”

Section: Introductionmentioning

confidence: 99%

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Optical residue arithmetic: a correlation approach

Casasent

1979

Appl. Opt.

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A numerical optical processor is described that performs operations in residue arithmetic. The position coding used to represent decimal and residue numbers allows one to describe the various conversions and operations in a correlation formulation. This description of residue arithmetic leads directly to novel residue adder and decimal/residue/decimal converter designs, which are described and experimentally demonstrated. The accuracy, dynamic range also discussed.

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“…In this paper, we utilize a correlation formulation [2] of residue arithmetic operations. Rather than using spatial pulse-position coding [1 ] to represent decimal and residue numbers, we employ a variant we refer to as temporal pulse-position coding. We describe a time integrating correlator and demonstrate its use in decimal-to-residue conversion.…”

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confidence: 99%

Decimal/residue conversion by time-integrating correlation

Caimi

Casasent

Goutzoulis

1981

Optics Communications

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A time integrating acousto-optic correlator for residue arithmetic processing is described with experimental confirmation included. This system offers superior input and output space bandwidth product to space integrating systems described previously.Optical residue arithmetic processors have received considerable attention [1--4]. These systems are attractive because they enable arithmetic operations to be performed without carries (and hence in parallel at high rates) and at high accuracy (without the need for components with large dynamic range). Optical systems are attractive for these processors because of their large time or space-bandwidth product and parallel processing features. In this paper, we utilize a correlation formulation [2] of residue arithmetic operations. Rather than using spatial pulse-position coding [1 ] to represent decimal and residue numbers, we employ a variant we refer to as temporal pulse-position coding. We describe a time integrating correlator and demonstrate its use in decimal-to-residue conversion. This system differs considerably from prior space-integrating correlators for optical residue processing [2] and offers superior input and output space-bandwidth product performance plus allows realization with available acousto-optic transducers with high bandwidth.In residue arithmetic, an integer J is represented by the N-tuple set of remainders or residues (Rml, Rm2, ..., RmN ) with respect to the N integer moduli (M 1 , M 2 .... , MN). The maximum integer value that can be represented by the N moduli is M -1 where M = HN1 m i. It is useful background to review the correlation processing used to convert J into R m when spatial pulse position coding is used [2]. Consider a multichannel frequency plane correlator with input g(xo) = 8(x 0 -JAx), i.e. a delta function whose spatial location encodes J. Its Fourier transform G(u)is incident on the frequency plane where a square-wave grating with fundamental frequency Ug is placed. The separation between orders in the transform of the grating is chosen to satisfy max = Ug~,J'L, where fL is the focal length of the transform lens. In the output correlation plane, we obtain( 1) //Since RmdXX = U ~ nm)Zxx, we can aperture the region 0 ~

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Optical computation using residue arithmetic

Cited by 159 publications

References 9 publications

High accuracy computation with linear analog optical systems: a critical study

High accuracy computation with linear analog optical systems: a critical study

Optical residue arithmetic: a correlation approach

Decimal/residue conversion by time-integrating correlation

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