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Applied Optics

Applied Optics


  • Vol. 7, Iss. 6 — Jun. 1, 1968
  • pp: 1193–1197

The Evaluation of the Variance of the Wave-Aberration Difference Function

W. B. King and J. Kitchen  »View Author Affiliations

Applied Optics, Vol. 7, Issue 6, pp. 1193-1197 (1968)

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Hopkins’ treatment of tolerance theory shows that, in designing quality optical systems, we should aim at minimizing the variance K of the wave-aberration difference function. Since the value of K is essentially positive, a useful criterion for the whole field is the sum of the suitably weighted values of K for a typical set of image points, corresponding to a range of selected values of spatial frequencies s and azimuths ψ. In this paper we show that the variance K (for both the axial and the extraaxial images) may be calculated by means of a set of universal coefficients P(i,j;s),Q(i,j;s,ψ) and R(i,j;s,ψ) once the wave-aberrations of certain rays are known. The values of these coefficients are uniquely determined by the function of the wave-aberration polynomial assumed and by the pattern of rays traced. Examples of the coefficients are presented.

© 1968 Optical Society of America

Original Manuscript: January 31, 1968
Published: June 1, 1968

W. B. King and J. Kitchen, "The Evaluation of the Variance of the Wave-Aberration Difference Function," Appl. Opt. 7, 1193-1197 (1968)

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  1. H. H. Hopkins, Opt. Acta 13, 343 (1966). [CrossRef]
  2. K. Strehl, Z. Instrumk. 22, 213 (1902).
  3. M. Maréchal, Thesis, U. of Paris (1948). See also M. Born, E. Wolf, Principles of Optics (Pergamon Press, Ltd., London, 1965), 3rd ed., p. 468; E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Company, Inc., Reading, Mass., 1963), p. 62.
  4. W. B. King, Appl. Opt. 7, 489 (1968). [CrossRef] [PubMed]
  5. H. H. Hopkins, Proc. Phys. Soc. 70, 5B, 449 (1957).
  6. W. B. King, Appl. Opt. 7, 197 (1968). [CrossRef] [PubMed]
  7. See, for example, H. H. Hopkins, Wave Theory of Aberration, (Clarendon Press, Oxford, 1950), Chap. 4.
  8. See, for example, K. Levenberg, Q. Appl. Math. 2, 164 (1944); C. G. Wynne, Proc. Phys. Soc. 73, 777 (1959); J. Meiron, J. Opt. Soc. Amer. 55, 1105 (1965). [CrossRef]

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