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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 22 — Aug. 1, 2008
  • pp: E88–E98

Minimal optical decomposition of ray transfer matrices

Xiyuan Liu and Karl-Heinz Brenner  »View Author Affiliations

Applied Optics, Vol. 47, Issue 22, pp. E88-E98 (2008)

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The properties of first-order optical systems are described paraxially by a ray transfer matrix, also called the ABCD matrix. Here we consider the inverse problem: an ABCD matrix is given, and we look for the minimal optical system that consists of only lenses and pieces of free-space propagation. Similar decompositions have been studied before but without the restriction to these two element types or without an attempt at minimalization. As the main results of this paper, we found that general lossless one- dimensional optical systems can be synthesized with a maximum of four elements and two-dimensional optical systems can be synthesized with six elements at most.

© 2008 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.2740) Geometric optics : Geometric optical design
(220.2740) Optical design and fabrication : Geometric optical design

ToC Category:
Optical Design and Optical Synthesis

Original Manuscript: January 8, 2008
Manuscript Accepted: April 2, 2008
Published: June 23, 2008

Xiyuan Liu and Karl-Heinz Brenner, "Minimal optical decomposition of ray transfer matrices," Appl. Opt. 47, E88-E98 (2008)

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