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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 8 — Aug. 1, 1988
  • pp: 1237–1243

Characteristic functions and the aberrations of symmetric optical systems. III. Calculation of eikonal coefficients

C. H. F. Velzel and J. L. F. de Meijere  »View Author Affiliations


JOSA A, Vol. 5, Issue 8, pp. 1237-1243 (1988)
http://dx.doi.org/10.1364/JOSAA.5.001237


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Abstract

We give a complete description of the calculation of the eikonal coefficients of symmetric optical systems. First, we show how to express the eikonal coefficients of each component as functions of the component data and the position of the object and the stop. We decompose each eikonal into meridional and sagittal subseries, and we give a proof of the uniqueness of this decomposition. Second, we give simple formulas to calculate system eikonal coefficients of the sixth order in the direction cosines and a fast algorithm to obtain a good estimate of coefficients of orders higher than the sixth. We conclude with a discussion on pseudoaberrations and their uses and also a generalization of the Seidel formulas for the addition of aberrations.

© 1988 Optical Society of America

History
Original Manuscript: January 13, 1988
Manuscript Accepted: April 5, 1988
Published: August 1, 1988

Citation
C. H. F. Velzel and J. L. F. de Meijere, "Characteristic functions and the aberrations of symmetric optical systems. III. Calculation of eikonal coefficients," J. Opt. Soc. Am. A 5, 1237-1243 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-8-1237


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References

  1. C. H. F. Velzel, J. L. F. de Meijere, “Characteristic functions and the aberrations of symmetric optical systems. I. Transverse aberrations when the eikonal is given,” J. Opt. Soc. Am. A 5, 246–250 (1988). [CrossRef]
  2. C. H. F. Velzel, J. L. F. de Meijere, “Characteristic functions and the aberrations of symmetric optical systems. II. Addition of aberrations,” J. Opt. Soc. Am. A 5, 251–256 (1988). [CrossRef]
  3. T. Smith, “The changes in aberrations when the object and stop are moved,” Trans. Opt. Soc. London 23, 311–322 (1921–1922).
  4. C. H. F. Velzel, “Image formation by a general optical system, using Hamilton’s method,” J. Opt. Soc. Am. A 4, 1342–1348 (1987). [CrossRef]
  5. G. C. Steward, The Symmetric Optical System (Cambridge U. Press, London, 1927).
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  9. D. Shafer, “Optical design methods: your head as a personal computer,” in Geometrical Optics: Critical Review of Technology, R. E. Fischer, W. H. Price, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.531, 49–58 (1985). [CrossRef]
  10. D. Shafer, “Optical design and relaxation response,” in Recent Trends in Optical Systems Design: Computer Lens Design Workshop, C. Londono, R. E. Fischer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.766, 2–8 (1987). [CrossRef]

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