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Proceedings Paper

Imaging limitations related to the skew invariant
Author(s): Douglas S. Goodman
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Paper Abstract

It is the aim of this paper to call attention to and to suggest practical applications in imaging of the long known but neglected skeew invariant. For a ray passing through a rotationally symmetric optical system whose axis is the z- axis of a Cartesian coordinate system, the quantity S=n((beta) x-ay) where n is the refractive index and ((alpha) ,(beta) ) are direction cosines, is constant. Despite the generality of this result and the strength of the constrain that it expresses, this result is little used by optical designers, except with non-imaging systems. The skew invariant precludes perfect imaging of more than one object plane (except for the well-known special case of afocal system). With one perfect imaging plane, the skew invariant limits the quality possible on another plane. For a lens that images one plane the upper limits of imaging at another are restrained by the invariant. Similar restraints exist with two imperfectly images planes. Additional applications are speculated upon.

Paper Details

Date Published: 10 December 2001
PDF: 11 pages
Proc. SPIE 4442, Novel Optical Systems Design and Optimization IV, (10 December 2001); doi: 10.1117/12.449960
Show Author Affiliations
Douglas S. Goodman, Polaroid Corp. (United States)

Published in SPIE Proceedings Vol. 4442:
Novel Optical Systems Design and Optimization IV
Jose M. Sasian; Paul K. Manhart, Editor(s)

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