Abstract

Maréchal’s treatment of tolerance theory shows that, in designing high-quality optical systems, we should aim at minimizing the variance <i>E</i> of the wave aberration. This suggests that the value of E may serve as a diffraction-based criterion of image quality in the fine-correction stage of automatic optical design. For this purpose, it would be desirable to know the range of states of poorer correction over which <i>E</i> may still be regarded as a useful criterion. In the present investigation, it is found that a necessary condition to be satisfied is that the Strehl ratio of the system should exceed 0.5.

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  1. K. Strehl, Z. Instrumentenk. 22, 213 (1902).
  2. A. Maréchal, Rev. Opt. 26, 257 (1947).
  3. 3 A. Maréchal, thesis, University of Paris (1948). See also: M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1965), 3rd ed., p. 468; E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Publ. Co., Reading, Mass., 1963), p. 62.
  4. The shape of the pupil periphery for an extra-axial pencil was first approximated by a best-fitting ellipse, and then scaled to correspond to a unit-circle. W. B. King, Appl. Opt. 7, 197 (1968).
  5. H. H. Hopkins, Proc. Phys. Soc. (London) B, 70, 1002 (1957).
  6. Here we intend to investigate the Strehl ratio under the condition that the secondary spherical aberration coefficient is fixed, while relative amounts of primary spherical and defocusing are variable. For the even-aberration case, the scaling parameter ƒ is numerically equal to W60.
  7. R. Richter, Z. Instrumentenk. 45, 1 (1925); E. H. Linfoot, Opt. Acta 10, 84 (1963).
  8. This special property also served to check the accuracy of the numerical-integration technique over the range of aberration values employed. Using M=1 and N=10, we have found that the numerical results for the Strehl ratio corresponding to these two cases agree to the seventh decimal place; the respective phases are, of course, different.
  9. W. B. King, Appl. Opt. 7, 489 (1968); R. Barakat and A. Houston, J. Opt. Soc. Am. 55, 1142 (1965).
  10. H. H. Hopkins, Optica Acta, 13, 343 (1966).

Hopkins, H. H.

H. H. Hopkins, Proc. Phys. Soc. (London) B, 70, 1002 (1957).

H. H. Hopkins, Optica Acta, 13, 343 (1966).

King, W. B.

W. B. King, Appl. Opt. 7, 489 (1968); R. Barakat and A. Houston, J. Opt. Soc. Am. 55, 1142 (1965).

The shape of the pupil periphery for an extra-axial pencil was first approximated by a best-fitting ellipse, and then scaled to correspond to a unit-circle. W. B. King, Appl. Opt. 7, 197 (1968).

Maréchal, A.

A. Maréchal, Rev. Opt. 26, 257 (1947).

3 A. Maréchal, thesis, University of Paris (1948). See also: M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1965), 3rd ed., p. 468; E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Publ. Co., Reading, Mass., 1963), p. 62.

Richter, R.

R. Richter, Z. Instrumentenk. 45, 1 (1925); E. H. Linfoot, Opt. Acta 10, 84 (1963).

Strehl, K.

K. Strehl, Z. Instrumentenk. 22, 213 (1902).

Other

K. Strehl, Z. Instrumentenk. 22, 213 (1902).

A. Maréchal, Rev. Opt. 26, 257 (1947).

3 A. Maréchal, thesis, University of Paris (1948). See also: M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1965), 3rd ed., p. 468; E. L. O'Neill, Introduction to Statistical Optics (Addison-Wesley, Publ. Co., Reading, Mass., 1963), p. 62.

The shape of the pupil periphery for an extra-axial pencil was first approximated by a best-fitting ellipse, and then scaled to correspond to a unit-circle. W. B. King, Appl. Opt. 7, 197 (1968).

H. H. Hopkins, Proc. Phys. Soc. (London) B, 70, 1002 (1957).

Here we intend to investigate the Strehl ratio under the condition that the secondary spherical aberration coefficient is fixed, while relative amounts of primary spherical and defocusing are variable. For the even-aberration case, the scaling parameter ƒ is numerically equal to W60.

R. Richter, Z. Instrumentenk. 45, 1 (1925); E. H. Linfoot, Opt. Acta 10, 84 (1963).

This special property also served to check the accuracy of the numerical-integration technique over the range of aberration values employed. Using M=1 and N=10, we have found that the numerical results for the Strehl ratio corresponding to these two cases agree to the seventh decimal place; the respective phases are, of course, different.

W. B. King, Appl. Opt. 7, 489 (1968); R. Barakat and A. Houston, J. Opt. Soc. Am. 55, 1142 (1965).

H. H. Hopkins, Optica Acta, 13, 343 (1966).

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