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On algebraic foundations of Fourier holography

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Fourier holography is considered as the physical basis of an algebraic model. A constructive interpretation of the formal axiomatics is presented. It is shown that the scheme of Fourier holography corresponds to an additive semigroup with convolution serving as abstract summation. The correlation operation plays the role of subtraction, and a diffraction-limited point source becomes an additive neutral element. The Fourier holography scheme sequentially constructs model elements in accordance with the Peano axioms. It realizes the axis of model elements correctly with respect to the summation and subtraction operations within the limits of angular invariance.

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Translated from Optika i Spektroskopiya, Vol. 90, No. 3, 2001, pp. 515–520.

Original Russian Text Copyright © 2001 by Pavlov.

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Pavlov, A.V. On algebraic foundations of Fourier holography. Opt. Spectrosc. 90, 452–457 (2001).

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