Abstract

A new method for automatic lens design is described. Instead of finding the approximate solution to the system of simultaneous nonlinear equations, the solution is found to the system of simultaneous nonlinear inequalities. Thus, the aberrations are driven into the domains which have been set up around target values. The bandwidth of the domain is the allowable tolerance associated with each aberration. A relaxation method is used to solve the system of linearized inequalities and iterative cycles are used to find the solution to the system of nonlinear ones. This method allows a high degree of control of individual performance functions. Mechanical conditions can be treated in the same way as aberrations. The program was written for the IBM 7090 computer and satisfactory designs were obtained in general within a few minutes for gauss-type photographic lenses.

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  1. D. P. Feder, J. Opt. Soc. Am. 52, 177 (1962).
  2. J. Merion and H. M. Loebenstein, J. Opt. Soc. Am. 47, 1104 (1957).
  3. B. Brixner, Appl. Opt. 2, 1281 (1963).
  4. C. G. Wynne and P. M. J. H. Wormell, Appl. Opt. 2, 1233 (1963).
  5. R. E. Hopkins and D. P. Feder, Appl. Opt. 2, 1227 (1963).
  6. G. H. Spencer, Appl. Opt. 2, 1257 (1963).
  7. R. E. Hopkins and G. Spencer, J. Opt. Soc. Am. 52, 172 (1962).
  8. A. V. Fiacco, Operations. Res. 9, 184 (1961).
  9. T. Suzuki et al., Proceedings of the Conference on Photographic and Spectroscopic Optics (Tokyo and Kyoto, 1964), [J. Appl. Phys. (Japan) Suppl. 4, 74 (1965)].
  10. S. Agmon, Can. J. Math. 6, 382 (1954).
  11. Yu. I. Merzlyakov, USSR Computational Math. Math. Phys. 3, 504 (1964).
  12. D. P. Feder, Appl. Opt. 2, 1209 (1963).
  13. J. B. Crockett and H. Chernoff, Pacific J. Math. 5, 33 (1955).
  14. D. P. Feder, J. Opt. Soc. Am. 47, 902 (1957).
  15. H. W. Kuhn and A. W. Tucker, Annals of Mathematical Studies (Princeton University Press, Princeton, New Jersey, 1956), No. 38, p. 99.

Agmon, S.

S. Agmon, Can. J. Math. 6, 382 (1954).

Brixner, B.

B. Brixner, Appl. Opt. 2, 1281 (1963).

Chernoff, H.

J. B. Crockett and H. Chernoff, Pacific J. Math. 5, 33 (1955).

Crockett, J. B.

J. B. Crockett and H. Chernoff, Pacific J. Math. 5, 33 (1955).

Feder, D. P.

D. P. Feder, J. Opt. Soc. Am. 52, 177 (1962).

D. P. Feder, J. Opt. Soc. Am. 47, 902 (1957).

R. E. Hopkins and D. P. Feder, Appl. Opt. 2, 1227 (1963).

D. P. Feder, Appl. Opt. 2, 1209 (1963).

Fiacco, A. V.

A. V. Fiacco, Operations. Res. 9, 184 (1961).

Hopkins, R. E.

R. E. Hopkins and D. P. Feder, Appl. Opt. 2, 1227 (1963).

R. E. Hopkins and G. Spencer, J. Opt. Soc. Am. 52, 172 (1962).

Kuhn, H. W.

H. W. Kuhn and A. W. Tucker, Annals of Mathematical Studies (Princeton University Press, Princeton, New Jersey, 1956), No. 38, p. 99.

Loebenstein, H. M.

J. Merion and H. M. Loebenstein, J. Opt. Soc. Am. 47, 1104 (1957).

Merion, J.

J. Merion and H. M. Loebenstein, J. Opt. Soc. Am. 47, 1104 (1957).

Merzlyakov, Yu. I.

Yu. I. Merzlyakov, USSR Computational Math. Math. Phys. 3, 504 (1964).

Spencer, G.

R. E. Hopkins and G. Spencer, J. Opt. Soc. Am. 52, 172 (1962).

Spencer, G. H.

G. H. Spencer, Appl. Opt. 2, 1257 (1963).

Suzuki, T.

T. Suzuki et al., Proceedings of the Conference on Photographic and Spectroscopic Optics (Tokyo and Kyoto, 1964), [J. Appl. Phys. (Japan) Suppl. 4, 74 (1965)].

Tucker, A. W.

H. W. Kuhn and A. W. Tucker, Annals of Mathematical Studies (Princeton University Press, Princeton, New Jersey, 1956), No. 38, p. 99.

Wormell, P. M. J. H.

C. G. Wynne and P. M. J. H. Wormell, Appl. Opt. 2, 1233 (1963).

Wynne, C. G.

C. G. Wynne and P. M. J. H. Wormell, Appl. Opt. 2, 1233 (1963).

Other

D. P. Feder, J. Opt. Soc. Am. 52, 177 (1962).

J. Merion and H. M. Loebenstein, J. Opt. Soc. Am. 47, 1104 (1957).

B. Brixner, Appl. Opt. 2, 1281 (1963).

C. G. Wynne and P. M. J. H. Wormell, Appl. Opt. 2, 1233 (1963).

R. E. Hopkins and D. P. Feder, Appl. Opt. 2, 1227 (1963).

G. H. Spencer, Appl. Opt. 2, 1257 (1963).

R. E. Hopkins and G. Spencer, J. Opt. Soc. Am. 52, 172 (1962).

A. V. Fiacco, Operations. Res. 9, 184 (1961).

T. Suzuki et al., Proceedings of the Conference on Photographic and Spectroscopic Optics (Tokyo and Kyoto, 1964), [J. Appl. Phys. (Japan) Suppl. 4, 74 (1965)].

S. Agmon, Can. J. Math. 6, 382 (1954).

Yu. I. Merzlyakov, USSR Computational Math. Math. Phys. 3, 504 (1964).

D. P. Feder, Appl. Opt. 2, 1209 (1963).

J. B. Crockett and H. Chernoff, Pacific J. Math. 5, 33 (1955).

D. P. Feder, J. Opt. Soc. Am. 47, 902 (1957).

H. W. Kuhn and A. W. Tucker, Annals of Mathematical Studies (Princeton University Press, Princeton, New Jersey, 1956), No. 38, p. 99.

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