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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 7, Iss. 3 — Mar. 1, 1968
  • pp: 489–494

A Direct Approach to the Evaluation of the Variance of the Wave Aberration

W. B. King  »View Author Affiliations


Applied Optics, Vol. 7, Issue 3, pp. 489-494 (1968)
http://dx.doi.org/10.1364/AO.7.000489


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Abstract

Marechal’s treatment of tolerance theory shows that in designing high quality systems one should aim at minimizing the variance E of the wave aberration. Since the value of E is essentially positive, a useful criterion for the whole field is the sum of the suitably weighted values of E for a typical set of image points. It is shown here that the variance E (for both the axial and extraaxial images) may be calculated very simply by means of a set of universal coefficients [P(i,j), Q(i,j), and R(i,j)] once the wave aberrations of selected rays are known. The values of these coefficients are uniquely determined by the form of polynomial assumed for the wave aberration and by the pattern of rays traced. Tables of P(i,j), Q(i,j), and R(i,j) are presented for the different cases that can arise in practice.

© 1968 Optical Society of America

History
Original Manuscript: September 8, 1967
Published: March 1, 1968

Citation
W. B. King, "A Direct Approach to the Evaluation of the Variance of the Wave Aberration," Appl. Opt. 7, 489-494 (1968)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-7-3-489


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References

  1. A. Maréchal, Thesis, University of Paris (1948).
  2. H. H. Hopkins, Japan. J. Appl. Phys. 4, Suppl. 1, 31 (1965).
  3. H. H. Hopkins, Opt. Acta, 13, 343 (1966). [CrossRef]
  4. W. B. King, Appl. Opt. 7, 197 (1968). [CrossRef] [PubMed]

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