Binary logic based purely on Fresnel diffraction

H. Hamam; J. L. de Bougrenet de la Tocnaye

doi:10.1364/AO.34.005901

Applied Optics
Vol. 34,
Issue 26,
pp. 5901-5906
(1995)
•https://doi.org/10.1364/AO.34.005901

Binary logic based purely on Fresnel diffraction

H. Hamam and J. L. de Bougrenet de la Tocnaye

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H. Hamam and J. L. de Bougrenet de la Tocnaye, "Binary logic based purely on Fresnel diffraction," Appl. Opt. 34, 5901-5906 (1995)

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Abstract

Binary logic operations on two-dimensional data arrays are achieved by use of the self-imaging properties of Fresnel diffraction. The fields diffracted by periodic objects can be considered as the superimposition of weighted and shifted replicas of original objects. We show that a particular spatial organization of the input data can result in logical operations being performed on these data in the considered diffraction planes. Among various advantages, this approach is shown to allow the implementation of dual-track, nondissipative logical operators. Image algebra is presented as an experimental illustration of this principle.

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Equations (25)

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a	p

	1	1	3	1	3

	q

	4	8		16
0	$\frac{1}{\sqrt{2}} exp (i \frac{π}{4})$	$\frac{1}{2} exp (i \frac{3 π}{4})$	$\frac{1}{2} exp (- i \frac{3 π}{4})$	$\frac{1}{\sqrt{8}} exp (- i \frac{π}{4})$	$\frac{1}{\sqrt{8}} exp (i \frac{π}{4})$
1	$\frac{1}{\sqrt{2}} exp (- i \frac{π}{4})$	$\frac{1}{2}$	$\frac{1}{2}$	$\frac{1}{\sqrt{8}} exp (i \frac{7 π}{8})$	$\frac{1}{\sqrt{8}} exp (i \frac{5 π}{8})$
2		$\frac{1}{2} exp (- i \frac{π}{4})$	$\frac{1}{2} exp (i \frac{π}{4})$	$\frac{1}{\sqrt{8}} exp (i \frac{π}{4})$	$\frac{1}{\sqrt{8}} exp (- i \frac{π}{4})$
3		$\frac{1}{2}$	$\frac{1}{2}$	$\frac{1}{\sqrt{8}} exp (- i \frac{π}{8})$	$\frac{1}{\sqrt{8}} exp (- i \frac{3 π}{8})$

Abstract

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Applied Optics