Abstract

A general theory of optical-aberration tests, encompassing many well-known practical tests, is presented, utilizing the formalism of spatial filtering, employing coherent illumination. The basic diffraction integrals of the Ronchi-grating test, Foucault knife-edge test, phase Foucault knife-edge test, and the Zernike phase-contrast test are derived. Typical situations have been analyzed and numerical results are shown and discussed.

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  1. L. C. Martin, Technical Optics, Vol. 2 (Pitman and Sons, Ltd., London, 1960), 2nd ed.
  2. I. Adachi, Atti Fond. Ronchi 15, 461, 550 (1960).
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).
  4. M. Kline and I. Kay, Electromagnetic Theory and Geometrical Optics (Wiley—Interscience, Inc., New York, 1965).
  5. In the integrations in this and succeeding sections, numerical constants have often been omitted, because the final normalization can be performed at the end of the analysis.
  6. G. Toraldo di Francia, in Optical Image Evaluation Symposium, Natl. Bur. Std. (U.S.) Circ. 526 (U. S. Gov't Printing Office, Washington, D. C., 1954), p. 161.
  7. P. Erdös, J. Opt. Soc. Am. 49, 865 (1959).
  8. H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, Oxford, 1950).
  9. Adachi has previously solved the case of an aberration-free defocused system and performed some low-frequency grating experiments, I. Adachi, Atti Fond. G. Ronchi 18, 344 (1963).
  10. A. Papoulis, The Fourier Integral and Its Applications (McGraw—Hill Book Co., New York, 1962), p. 38.
  11. E. H. Linfoot, Recent Advances in Optics, 2 (Oxford University Press, Oxford, 1958), Ch. 2.
  12. H. Wolther in Handbuch der Physik 24, S. Flügge, Ed. (Springer-Verlag, Berlin, 1956), p. 258.
  13. E. H. Linfoot, Proc. Phys. Soc. (London) 58, 759 (1946).
  14. S. C. Gascoigne, Monthly Not. Roy. Astron. Soc. 104, 326 (1945). Gascoigne treats the two-dimensional model. The author has rederived all of his results, using the theory of prolate spheroidal functions.
  15. F. Zernike, Physica 1, 689 (1934).
  16. C. R. Burch, Monthly Not. Roy. Astron. Soc. 94, 384 (1934).

Adachi, I.

I. Adachi, Atti Fond. Ronchi 15, 461, 550 (1960).

Adachi has previously solved the case of an aberration-free defocused system and performed some low-frequency grating experiments, I. Adachi, Atti Fond. G. Ronchi 18, 344 (1963).

Burch, C. R.

C. R. Burch, Monthly Not. Roy. Astron. Soc. 94, 384 (1934).

di Francia, G. Toraldo

G. Toraldo di Francia, in Optical Image Evaluation Symposium, Natl. Bur. Std. (U.S.) Circ. 526 (U. S. Gov't Printing Office, Washington, D. C., 1954), p. 161.

Erdös, P.

P. Erdös, J. Opt. Soc. Am. 49, 865 (1959).

Gascoigne, S. C.

S. C. Gascoigne, Monthly Not. Roy. Astron. Soc. 104, 326 (1945). Gascoigne treats the two-dimensional model. The author has rederived all of his results, using the theory of prolate spheroidal functions.

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, Oxford, 1950).

Kay, I.

M. Kline and I. Kay, Electromagnetic Theory and Geometrical Optics (Wiley—Interscience, Inc., New York, 1965).

Kline, M.

M. Kline and I. Kay, Electromagnetic Theory and Geometrical Optics (Wiley—Interscience, Inc., New York, 1965).

Linfoot, E. H.

E. H. Linfoot, Proc. Phys. Soc. (London) 58, 759 (1946).

E. H. Linfoot, Recent Advances in Optics, 2 (Oxford University Press, Oxford, 1958), Ch. 2.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).

Martin, L. C.

L. C. Martin, Technical Optics, Vol. 2 (Pitman and Sons, Ltd., London, 1960), 2nd ed.

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw—Hill Book Co., New York, 1962), p. 38.

Wolther, H.

H. Wolther in Handbuch der Physik 24, S. Flügge, Ed. (Springer-Verlag, Berlin, 1956), p. 258.

Zernike, F.

F. Zernike, Physica 1, 689 (1934).

Other

L. C. Martin, Technical Optics, Vol. 2 (Pitman and Sons, Ltd., London, 1960), 2nd ed.

I. Adachi, Atti Fond. Ronchi 15, 461, 550 (1960).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).

M. Kline and I. Kay, Electromagnetic Theory and Geometrical Optics (Wiley—Interscience, Inc., New York, 1965).

In the integrations in this and succeeding sections, numerical constants have often been omitted, because the final normalization can be performed at the end of the analysis.

G. Toraldo di Francia, in Optical Image Evaluation Symposium, Natl. Bur. Std. (U.S.) Circ. 526 (U. S. Gov't Printing Office, Washington, D. C., 1954), p. 161.

P. Erdös, J. Opt. Soc. Am. 49, 865 (1959).

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, Oxford, 1950).

Adachi has previously solved the case of an aberration-free defocused system and performed some low-frequency grating experiments, I. Adachi, Atti Fond. G. Ronchi 18, 344 (1963).

A. Papoulis, The Fourier Integral and Its Applications (McGraw—Hill Book Co., New York, 1962), p. 38.

E. H. Linfoot, Recent Advances in Optics, 2 (Oxford University Press, Oxford, 1958), Ch. 2.

H. Wolther in Handbuch der Physik 24, S. Flügge, Ed. (Springer-Verlag, Berlin, 1956), p. 258.

E. H. Linfoot, Proc. Phys. Soc. (London) 58, 759 (1946).

S. C. Gascoigne, Monthly Not. Roy. Astron. Soc. 104, 326 (1945). Gascoigne treats the two-dimensional model. The author has rederived all of his results, using the theory of prolate spheroidal functions.

F. Zernike, Physica 1, 689 (1934).

C. R. Burch, Monthly Not. Roy. Astron. Soc. 94, 384 (1934).

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