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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 6 — Jun. 1, 2009
  • pp: 1503–1517

Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry

Kevin P. Thompson, Tobias Schmid, Ozan Cakmakci, and Jannick P. Rolland  »View Author Affiliations

JOSA A, Vol. 26, Issue 6, pp. 1503-1517 (2009)

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It has been found that the field dependence of the aberrations of misaligned optical systems made of otherwise rotationally symmetric optical surfaces are often multinodal, including low-order astigmatism and distortion and higher-order coma, astigmatism, oblique spherical, elliptical coma (trifoil), and distortion. The exact location of the nodes in the image is a weighted sum of individual surface contributions. The location of the center of rotational symmetry for the field dependence for all aberrations contributed by a particular rotationally symmetric surface is along the line that connects the center of curvature of the surface with the center of the pupil. Previously, a paraxial ray-trace method was developed to locate the aberration field center for a series of rotationally symmetric surfaces with small tilt and decenter perturbations. The method is based on rotating the coordinate system into the local coordinate system of the surface and then advancing using the conventional paraxial ray-trace equations. This method, developed by Buchroeder [Ph.D. dissertation (University of Arizona, 1976)] , heavily constrains how tilts and decenters were implemented in the optical system model, which prevented integration of these equations into an optical design environment. In this paper, a method for locating the aberration field centers using real-ray-trace data that is entirely model independent and, significantly, that is not restricted to small tilts and decenters, is presented. With this new insight, it is now possible to extend any optical design and analysis environment to include multinodal aberration analysis.

© 2009 Optical Society of America

OCIS Codes
(080.2740) Geometric optics : Geometric optical design
(080.2468) Geometric optics : First-order optics

Original Manuscript: November 6, 2008
Revised Manuscript: March 3, 2009
Manuscript Accepted: March 9, 2009
Published: May 29, 2009

Kevin P. Thompson, Tobias Schmid, Ozan Cakmakci, and Jannick P. Rolland, "Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry," J. Opt. Soc. Am. A 26, 1503-1517 (2009)

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  1. R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, 1976).
  2. K. P. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry,” J. Opt. Soc. Am. A 22, 1389-1401 (2005). [CrossRef]
  3. K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry; spherical aberration,” J. Opt. Soc. Am. A 26, 1090-1100 (2009). [CrossRef]
  4. H. H. Hopkins, The Wave Theory of Aberrations (Oxford on Clarendon Press, 1950).
  5. C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc. 103, 159-165 (1942).
  6. R. V. Shack, Optical Sciences Center, University of Arizona, Tucson, Arizona 85721. Phone, 520-621-1356. (Personal communication, 1977).

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