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Matrix method for nonlinear transformation and its application to an optical lens system

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Abstract

The method formulated can be used to calculate multiple transformation of nonlinear systems that have many variables as a cascade product of matrices. In an optical lens system, for example, the focusing characteristics with aberrations are given as a product of matrices corresponding to the component lenses and spaces. In an axially symmetric system the matrix size is 8 for third-order and 20 for fifth-order approximation. The addition rule of primary aberrations for axisymmetric optical systems has been extended for nonaxisymmetric and nonoptical systems, and a simple method for deriving a practical aberration calculation formula is shown.

© 1996 Optical Society of America

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