18 June 1998 Paraxial diffractive elements for space-variant linear transforms
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Abstract
Optical linear transform architectures bear good potential for future developments of very powerful hybrid vision systems and neural network classifiers. The optical modules of such systems could be used as pre-processors to solve complex linear operations at very high speed in order to simplify an electronic data post-processing. However, the applicability of linear optical architectures is strongly connected with the fundamental question of how to implement a specific linear transform by optical means and physical imitations. The large majority of publications on this topic focusses on the optical implementation of space-invariant transforms by the well-known 4f-setup. Only few papers deal with approaches to implement selected space-variant transforms. In this paper, we propose a simple algebraic method to design diffractive elements for an optical architecture in order to realize arbitrary space-variant transforms. The design procedure is based on a digital model of scalar, paraxial wave theory and leads to optimal element transmission functions within the model. Its computational and physical limitations are discussed in terms of complexity measures. Finally, the design procedure is demonstrated by some examples. Firstly, diffractive elements for the realization of different rotation operations are computed and, secondly, a Hough transform element is presented. The correct optical functions of the elements are proved in computer simulation experiments.
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Stephan Teiwes, Heiko Schwarzer, Ben-Yuan Gu, "Paraxial diffractive elements for space-variant linear transforms", Proc. SPIE 3291, Diffractive and Holographic Device Technologies and Applications V, (18 June 1998); doi: 10.1117/12.310593; https://doi.org/10.1117/12.310593
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