The Specification Of Optical Systems By Paraxial Transfer Matrices

Douglas C. Sinclair

doi:10.1117/12.953780

1 March 1974 The Specification Of Optical Systems By Paraxial Transfer Matrices

Douglas C. Sinclair

Proceedings Volume 0039, Applications of Geometrical Optics II; (1974) https://doi.org/10.1117/12.953780
Event: Annual Technical Symposium, 1973, San Diego, United States

Abstract

Matrix optics is currently enjoying great popularity as a pedagogical tool, but the technique has not been widely accepted by optical designers, probably because it offers no advantage for numerical computation over ynv ray tracing. The essence of matrix optics, however, is not that it provides a tool for numerical computation, but that it provides an abstract formulation of first-order optics which is at the same time easy to work with and penetrating in its analysis of paraxial optics as a linear system. Numerical values of the matrix elements, if required, can be determined by ynv ray tracing. Such a formulation leads naturally to the introduction of abstract ray coordinates analogous to Buchdahl's paracanonical coordinates, s and t. This, however, often leads to theories which are elegant, but which are very difficult to understand. Our present study suggests that a useful compromise between this, and the straightforward method described in elementary textbooks, can be achieved by a judicious choice of reference planes used for the definition of the system transfer matrix. In particular, if the transfer matrix is taken between the entrance pupil and the last refracting surface, then the matrix elements yield the focal length, the back focus, the pupil mag-nification, and the exit pupil location directly.

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Douglas C. Sinclair "The Specification Of Optical Systems By Paraxial Transfer Matrices", Proc. SPIE 0039, Applications of Geometrical Optics II, (1 March 1974); https://doi.org/10.1117/12.953780

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KEYWORDS

Ray tracing

Matrices

Geometrical optics

Optical design

Optical components

Optical matrix switches

Refractive index

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