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

Tadeusz Kryszczynski

doi:10.1117/12.353082

14 July 1999 First steps toward an algebraic method of optical design in the range of all aberration orders

Tadeusz Kryszczynski

Proceedings Volume 3820, 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics; (1999) https://doi.org/10.1117/12.353082
Event: Eleventh Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 1998, Stara Lesna, Slovakia

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.

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Tadeusz Kryszczynski "First steps toward an algebraic method of optical design in the range of all aberration orders", Proc. SPIE 3820, 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, (14 July 1999); https://doi.org/10.1117/12.353082

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KEYWORDS

Mirrors

Monochromatic aberrations

Geometrical optics

Optical design

Refraction

Complex systems

Spherical lenses

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