## Abstract

An associative-memory model and its optical implementation with grating structures are presented. The transmission function of each pixel of the content-addressable memory is calculated by use of scalar diffraction theory. The filter of the calculated transmission function can be fabricated with computer-generated holography and a multiexposure holographic technique. The proposed approach is found useful in terms of storage and the simple thresholding at the number of on-state pixels in the input.

© 1994 Optical Society of America

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### Equations (7)

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(1)
$${V}_{i}^{\text{out}}=\sum _{p}{V}_{i}^{p}\sum _{j}{V}_{j}^{p}{V}_{j}^{\text{in}}.$$
(2)
$$\begin{array}{lll}{V}_{i}^{{p}_{0}}& =1& \text{for}\hspace{0.17em}{V}_{i}^{\text{out}}\ge n\\ \hspace{0.17em}& =0& \text{for}\hspace{0.17em}{V}_{i}^{\text{out}}<n.\end{array}$$
(3)
$$t(x,y)=1+m\hspace{0.17em}\text{cos}[(2\mathrm{\pi}/\mathrm{\lambda}z)Ly],$$
(4)
$$U({x}_{0},{y}_{0})=\frac{\text{exp}(j2\mathrm{\pi}z/\mathrm{\lambda})\text{exp}[j(\mathrm{\pi}/\mathrm{\lambda}z)({x}_{0}^{2}+{y}_{0}^{2})]}{j\mathrm{\lambda}z}\times \iint t(x,y)x\hspace{0.17em}\text{exp}[-j(2\mathrm{\pi}/\mathrm{\lambda}z)({x}_{0}x+{y}_{0}y)]\text{d}x\text{d}y.$$
(5)
$$I({x}_{0},{y}_{0})=(1/4{\mathrm{\pi}}^{2})\mathrm{\delta}({x}_{0},{y}_{0})+(m/8{\mathrm{\pi}}^{2})\times [\mathrm{\delta}({x}_{0},{y}_{0}+L)+\mathrm{\delta}({x}_{0},{y}_{0}-L)].$$
(6)
$${T}_{ij}(x,y)=1+\frac{1}{k}\sum _{p=1}^{p}\sum _{n=1}^{N}\sum _{m=1}^{M}{S}_{nm}^{p}{S}_{ij}^{p}\times \left(\text{cos}\frac{2\mathrm{\pi}}{\mathrm{\lambda}D}\{(m-j)ax+[L-(n+N-i)a]y\}\right),$$
(7)
$$k=\sum _{p=1}^{p}\sum _{n=1}^{N}\sum _{m=1}^{M}{S}_{nm}^{p}.$$