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First steps toward an algebraic method of optical design in the range of all aberration orders
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Paper Abstract

Essence of this work is formulation of nonlinear dependencies, which allow to determine parameters of an optical system. Previous methods of the aberration correction have commonly used algebraic methods in a simple form for primary aberrations and thin lenses. Efficiency of those methods should be appreciated critically because they usually need a further aberration correction. Nowadays, progress in development professional mathematical software commercially available encourages to taking out works concerning algebraic correction methods. In this work aberration dependencies are investigated in their full complexity without simplification and approximation. Dependencies containing angles and ratios of dimensions have form of very complex trigonometric expressions. An optical system may be corrected by controlling these dependencies in the entire optical systems. Solution of the problem require the selection of number of unknowns, and expression of all residual relations as a function of these unknowns. Problem of the algebraic correction relies on solving of a non- linear equation system with separately described auxiliary functions which are nested up to certain depth. Radii of curvatures and eventual distances between surfaces are determined in the second final stage after solving the nonlinear equation system and taking account of the scale. Two simple numerical examples are presented.

Paper Details

Date Published: 14 July 1999
PDF: 7 pages
Proc. SPIE 3820, 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, (14 July 1999); doi: 10.1117/12.353082
Show Author Affiliations
Tadeusz Kryszczynski, Institute of Applied Optics (Poland)

Published in SPIE Proceedings Vol. 3820:
11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics
Miroslav Hrabovsky; Anton Strba; Waclaw Urbanczyk, Editor(s)

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