Abstract

In viewing systems that employ critical, Kohler, or collimated illumination, the illumination may frequently be characterized by the complex degree of coherence in the form of a first-order Bessel function divided by its argument. The anomalies that occur in the image of a tri-bar target viewed in partially coherent illumination of this form are discussed for a two-dimensional circular diffraction-limited imaging system. The Sparrow criterion, which in this case correlates with experimental measurements of resolving power, is applied to determine the resolution limit. The computed resolution-limit curve for a tri-bar target is shown and compared to the previously published two-point resolution-limit curve for a one-dimensional system and to the limiting values obtained in a two-dimensional system for coherent and incoherent illumination. In the latter case, the full curve is shown as a special case of the application of the Sparrow criterion to the partially coherent imaging equations for a circular two-dimensional system. Experimental confirmation of the calculations is given.

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  1. D. H. Kelly, Appl. Opt. 4, 435 (1965).
  2. W. N. Charman, Phot. Sci. Eng. 8, 253 (1964).
  3. R. Becherer and G. B. Parrent, Jr., J. Opt. Soc. Am. 57, 1479 (1967).
  4. R. Swing and J. Clay, J. Opt. Soc. Am. 57, 1180 (1967).
  5. R. Barakat, Opt. Acta 17, 337 (1970).
  6. A. Offner and J. Meiron, Appl. Opt. 8, 183 (1969).
  7. Lord Rayleigh, Collected Papers (Cambridge U. P., Cambridge, England, 1902), Vol. 3 (also Dover, New York, 1964).
  8. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 524.
  9. H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. (London) B63, 737 (1950).
  10. C. Sparrow, Astrophys. J. 44, 76 (1916).
  11. F. Rojak, M. S. thesis, Lowell Technological Institute, Lowell, Massachusetts, 1961.
  12. M. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice–Hall, Englewood Cliffs, N. J., 1964), p. 123.
  13. R. Barakat, J. Opt. Soc. Am. 52, 276 (1962).
  14. R. Barakat, J. Opt. Soc. Am. 53, 415 (1963).
  15. D. N. Grimes and B. J. Thompson, J. Opt. Soc. Am. 57, 1330 (1967).
  16. B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957).
  17. On the surface, these values may not seem realistic. However, the ANSI preliminary draft of the standard on MTF of photographic emulsions specifies these values.

Barakat, R.

R. Barakat, Opt. Acta 17, 337 (1970).

R. Barakat, J. Opt. Soc. Am. 52, 276 (1962).

R. Barakat, J. Opt. Soc. Am. 53, 415 (1963).

Barham, P. M.

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. (London) B63, 737 (1950).

Becherer, R.

R. Becherer and G. B. Parrent, Jr., J. Opt. Soc. Am. 57, 1479 (1967).

Beran, M.

M. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice–Hall, Englewood Cliffs, N. J., 1964), p. 123.

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 524.

Charman, W. N.

W. N. Charman, Phot. Sci. Eng. 8, 253 (1964).

Clay, J.

R. Swing and J. Clay, J. Opt. Soc. Am. 57, 1180 (1967).

Grimes, D. N.

D. N. Grimes and B. J. Thompson, J. Opt. Soc. Am. 57, 1330 (1967).

Hopkins, H. H.

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. (London) B63, 737 (1950).

Kelly, D. H.

D. H. Kelly, Appl. Opt. 4, 435 (1965).

Meiron, J.

A. Offner and J. Meiron, Appl. Opt. 8, 183 (1969).

Offner, A.

A. Offner and J. Meiron, Appl. Opt. 8, 183 (1969).

Parrent, Jr., G. B.

R. Becherer and G. B. Parrent, Jr., J. Opt. Soc. Am. 57, 1479 (1967).

M. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice–Hall, Englewood Cliffs, N. J., 1964), p. 123.

Rayleigh, Lord

Lord Rayleigh, Collected Papers (Cambridge U. P., Cambridge, England, 1902), Vol. 3 (also Dover, New York, 1964).

Rojak, F.

F. Rojak, M. S. thesis, Lowell Technological Institute, Lowell, Massachusetts, 1961.

Sparrow, C.

C. Sparrow, Astrophys. J. 44, 76 (1916).

Swing, R.

R. Swing and J. Clay, J. Opt. Soc. Am. 57, 1180 (1967).

Thompson, B. J.

D. N. Grimes and B. J. Thompson, J. Opt. Soc. Am. 57, 1330 (1967).

B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957).

Wolf, E.

B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957).

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 524.

Other

D. H. Kelly, Appl. Opt. 4, 435 (1965).

W. N. Charman, Phot. Sci. Eng. 8, 253 (1964).

R. Becherer and G. B. Parrent, Jr., J. Opt. Soc. Am. 57, 1479 (1967).

R. Swing and J. Clay, J. Opt. Soc. Am. 57, 1180 (1967).

R. Barakat, Opt. Acta 17, 337 (1970).

A. Offner and J. Meiron, Appl. Opt. 8, 183 (1969).

Lord Rayleigh, Collected Papers (Cambridge U. P., Cambridge, England, 1902), Vol. 3 (also Dover, New York, 1964).

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), p. 524.

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. (London) B63, 737 (1950).

C. Sparrow, Astrophys. J. 44, 76 (1916).

F. Rojak, M. S. thesis, Lowell Technological Institute, Lowell, Massachusetts, 1961.

M. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice–Hall, Englewood Cliffs, N. J., 1964), p. 123.

R. Barakat, J. Opt. Soc. Am. 52, 276 (1962).

R. Barakat, J. Opt. Soc. Am. 53, 415 (1963).

D. N. Grimes and B. J. Thompson, J. Opt. Soc. Am. 57, 1330 (1967).

B. J. Thompson and E. Wolf, J. Opt. Soc. Am. 47, 895 (1957).

On the surface, these values may not seem realistic. However, the ANSI preliminary draft of the standard on MTF of photographic emulsions specifies these values.

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