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Proceedings Paper

Imaging equations for spectroscopic systems using Lie transformations: I. Theoretical foundations
Author(s): Christopher A. Palmer; Wayne R. McKinney; Benjamin S. Wheeler
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Paper Abstract

The conceptual framework for the characterization of systems of gratings and mirrors is reviewed, based on the methods of Lie optics, which represents each optical element by a mapping that transforms a ray in object space into a ray in image space. The mathematical tools of Lie optics are presented, the complete transformation for a single grating is given in terms of its elementary transformations, and imaging equations are derived using this transformation that correspond with well-known expressions for aberration coefficients. Lie algebraic techniques have certain significant advantages over the more commonly used wavefront aberration theory, which will become apparent when the imaging properties of multi-element systems are considered in Part II of this work.

Paper Details

Date Published: 24 September 1998
PDF: 12 pages
Proc. SPIE 3450, Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, (24 September 1998); doi: 10.1117/12.323404
Show Author Affiliations
Christopher A. Palmer, Richardson Grating Lab. (United States)
Wayne R. McKinney, Lawrence Berkeley National Lab. (United States)
Benjamin S. Wheeler, Hewlett-Packard Co. (United States)


Published in SPIE Proceedings Vol. 3450:
Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications
Wayne R. McKinney; Christopher A. Palmer, Editor(s)

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