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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. 19, Iss. 11 — Nov. 1, 2002
  • pp: 2313–2321

Criteria for correction of quadratic field-dependent aberrations

Chunyu Zhao and James H. Burge  »View Author Affiliations


JOSA A, Vol. 19, Issue 11, pp. 2313-2321 (2002)
http://dx.doi.org/10.1364/JOSAA.19.002313


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Abstract

Aberrations of imaging systems can be described by using a polynomial expansion of the dependence on field position, or the off-axis distance of a point object. On-axis, or zero-order, aberrations can be calculated directly. It is well-known that aberrations with linear field dependence can be calculated and controlled by using the Abbe sine condition, which evaluates only on-axis behavior. We present a new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations is derived by using Hamilton’s characteristic functions and simplified by evaluating astigmatism in the pupil. The equations, which we call the pupil astigmatism criteria, use on-axis behavior to evaluate and control all aberrations with quadratic dependence on the field and arbitrary dependence on the pupil. These relations are explained and are validated by using several specific optical designs.

© 2002 Optical Society of America

OCIS Codes
(220.1010) Optical design and fabrication : Aberrations (global)
(220.3620) Optical design and fabrication : Lens system design
(220.4830) Optical design and fabrication : Systems design

History
Original Manuscript: December 8, 2001
Revised Manuscript: May 28, 2002
Manuscript Accepted: May 28, 2002
Published: November 1, 2002

Citation
Chunyu Zhao and James H. Burge, "Criteria for correction of quadratic field-dependent aberrations," J. Opt. Soc. Am. A 19, 2313-2321 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-11-2313


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References

  1. M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964).
  2. R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, Berkeley, Calif., 1966).
  3. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).
  4. J. Dyson, “Unit magnification optical system without Seidel aberrations,” J. Opt. Soc. Am. 49, 713–716 (1959). [CrossRef]
  5. A. Offner, “New concepts in projection mask aligners,” Opt. Eng. 14, 130–132 (1975). [CrossRef]
  6. ZEMAX is an optical design code from Focus Software, Inc., Tucson, Arizona.
  7. L. Mertz, Excursions in Astronomical Optics (Springer, New York, 1996), Chap. 5, pp. 99–100.
  8. C. Zhao, J. H. Burge, “Application of the pupil astigmatism criteria in optical design,” Appl. Opt. (to be published).
  9. M. Herzberger, Strahlenoptik (Springer-Verlag, Berlin, 1931), pp. 157–161.  

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