OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 3 — Mar. 1, 1999
  • pp: 602–612

Generalized sine condition for image-forming systems with centering errors

S. A. Comastri, J. M. Simon, and R. Blendowske  »View Author Affiliations

JOSA A, Vol. 16, Issue 3, pp. 602-612 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (373 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The generalized sine condition for an image-forming system with centering errors but allowing for one symmetry plane is derived according to the Fourier optics approach. The variation of the wave-front-aberration function associated with a small displacement of field coordinates is given. The symmetry properties of aberrations are discussed.

© 1999 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1010) Optical design and fabrication : Aberrations (global)

Original Manuscript: March 31, 1998
Revised Manuscript: November 6, 1998
Manuscript Accepted: October 20, 1998
Published: March 1, 1999

S. A. Comastri, J. M. Simon, and R. Blendowske, "Generalized sine condition for image-forming systems with centering errors," J. Opt. Soc. Am. A 16, 602-612 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Cox, System of Optical Design (Focal, New York, 1964).
  2. S. A. Comastri, J. M. Simon, “Aberration function dependence on field, a way to obtain better profit from ray tracing,” Optik (Stuttgart) 69, 135–140 (1985).
  3. H. H. Hopkins, “Image formation by a general optical system. 1. General theory,” Appl. Opt. 24, 2491–2505 (1985). [CrossRef]
  4. S. A. Comastri, J. M. Simon, “Ray tracing, aberration function and spatial frequencies,” Optik (Stuttgart) 66, 175–190 (1984).
  5. S. A. Comastri, J. M. Simon, “Field derivative of the variance of wavefront aberration,” J. Mod. Opt. 36, 1073 (1989). [CrossRef]
  6. J. M. Simon, S. A. Comastri, “Image-forming systems: matrix formulation of the optical invariant via Fourier optics,” J. Mod. Opt. 43, 2533–2541 (1996). [CrossRef]
  7. M. Mansuripur, “Abbés sine condition,” Opt. Photonics News 9(2), 56–60 (1998). [CrossRef]
  8. R. Blendowske, “Fourier optical approach to the sine condition,” Opt. Photonics News 9(2), 6 (1998).
  9. R. Blendowske, W. Vollrath, “Strehl ratio split for production-limited optics,” Opt. Photonics News 8(5) (1997).
  10. R. Blendowske, U. Voigt, W. Vollrath, “Delta optics: theoretical aspects of design and production” Sci. Technol. Inf. 10, 147–155 (1993).
  11. S. A. Comastri, “Pupil exploration and calculation of vignetting,” Optik (Stuttgart) 85, 173–176 (1990).
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  13. S. A. Comastri, “Optical systems and spatial frequencies,” Optik (Stuttgart) 105, 129–133 (1997).
  14. R. S. Longhurst, Geometrical and Physical Optics (Longman, London, 1973).
  15. M. Born, B. Wolf, Principles of Optics (Pergamon, Oxford, 1987).
  16. M. Totzek, H. J. Tiziani, “Interference microscopy of sub λ structures: a rigorous computation method and measurements,” Opt. Commun. 136, 61–74 (1997). [CrossRef]
  17. J. Rey Pastor, P. Pi Calleja, C. Trejo, Analisis Matematico (Kapelusz, Argentina, 1957), Vol. II, p. 158.
  18. V. Mahajan, “Zernike circle polynomials and optical aberrations of systems with circular pupils,” Appl. Opt. , 8121–8124 (1994). [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited