Abstract

The optical properties of an aberration-free defocused optical system used to image incoherently illuminated objects are analyzed. The exact diffraction optical transfer function (OTF) and point spread function (PSF) are compared to the geometrical OTF and PSF, respectively, for both small and large amounts of defocusing. It follows that geometrical optics does not describe diffraction optics very well for any reasonable amount of defocusing. Calculation of the diffraction OTF is complicated and time consuming, even with a large computer. An empirically derived analytic approximation to the diffraction OTF which is much easier to calculate, is formulated. It is also shown, and examples are presented to demonstrate, that the exact OTF and PSF are different in planes at equal distances on the two sides of the in-focus plane.

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  1. H. H. Hopkins, Proc. Roy. Soc. (London) A231, 91 (1955).
  2. H. H. Hopkins, Proc. Phys. Soc. (London) B70, 1002 (1957).
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., New York, 1968), p. 115.
  4. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 485.
  5. This transfer function is obtained by combining Eqs. (10) and (15) in Ref. 1.
  6. A nice example of this is given in Ref. 3, p. 126.
  7. R. E. Stephens and L. E. Sutton, J. Opt. Soc. Am. 58 1001 (1968).
  8. Reference 4, p. 490.
  9. Reference 3, p. 85.
  10. H. H. Hopkins, Wave Theory of Aberrations (Clarendon Press, Oxford, 1950), p. 14.
  11. R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Book Co., New York, 1965), p. 249.
  12. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill Book Co., New York, 1957), 3rd ed., p. 303.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 485.

Bracewell, R.

R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Book Co., New York, 1965), p. 249.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., New York, 1968), p. 115.

Hopkins, H. H.

H. H. Hopkins, Proc. Roy. Soc. (London) A231, 91 (1955).

H. H. Hopkins, Wave Theory of Aberrations (Clarendon Press, Oxford, 1950), p. 14.

H. H. Hopkins, Proc. Phys. Soc. (London) B70, 1002 (1957).

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill Book Co., New York, 1957), 3rd ed., p. 303.

Stephens, R. E.

R. E. Stephens and L. E. Sutton, J. Opt. Soc. Am. 58 1001 (1968).

Sutton, L. E.

R. E. Stephens and L. E. Sutton, J. Opt. Soc. Am. 58 1001 (1968).

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill Book Co., New York, 1957), 3rd ed., p. 303.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 485.

Other (12)

H. H. Hopkins, Proc. Roy. Soc. (London) A231, 91 (1955).

H. H. Hopkins, Proc. Phys. Soc. (London) B70, 1002 (1957).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., New York, 1968), p. 115.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), 2nd ed., p. 485.

This transfer function is obtained by combining Eqs. (10) and (15) in Ref. 1.

A nice example of this is given in Ref. 3, p. 126.

R. E. Stephens and L. E. Sutton, J. Opt. Soc. Am. 58 1001 (1968).

Reference 4, p. 490.

Reference 3, p. 85.

H. H. Hopkins, Wave Theory of Aberrations (Clarendon Press, Oxford, 1950), p. 14.

R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill Book Co., New York, 1965), p. 249.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill Book Co., New York, 1957), 3rd ed., p. 303.

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