Abstract

Diffraction of quasimonochromatic partially space-coherent light by annular apertures, which are of fundamental importance when reflecting components are used, has been examined theoretically. The work on slit and circular apertures by previous workers has been briefly reviewed. Use has been made of Schell’s theorem which gives the relationship between the far-field intensity and the Fourier transform of the product of the source autocorrelation function and the correlation function across the diffracting aperture. Exponential, besinc, and sinc forms of the degree of coherence have been assumed and the results are presented for three typical values of the central obstruction of the circular aperture.

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), Ch. 10, p. 491.
  2. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).
  3. M. Françon, Optical Interferometry (Academic Press Inc., New York, 1966), Chs. 1, 8, pp. 1, 162.
  4. M. Françon, Diffraction; Coherence in Optics (Pergamon Press, Inc., New York, 1966).
  5. W. H. Steel, Interferometry (Cambridge University Press, 1967).
  6. H. H. Hopkins, in Advances in Optical Techniques, A. C. S. van Heel, Ed. (North-Holland Publ. Co., Amsterdam, 1967), Ch. 6, p. 190.
  7. M. Françon and S. Mallick, in Progress in Optics VI, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1967), Ch. 3, p. 73.
  8. E. Wolf, Proc. Roy. Soc. (London) A230, 246 (1955).
  9. A. C. Schell, Ph.D. thesis, Massachusetts Institute of Technology (1961).
  10. G. B. Parrent, J. Opt. Soc. Am. 49, 787 (1959); also Ref. 2, p. 40.
  11. J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).
  12. G. B. Parrent and T. J. Skinner, Opt. Acta. 8, 93 (1961).
  13. W. T. Cathey, J. Opt. Soc. Am. 55, 1035 (1965).
  14. K. D. Mielenz, J. Opt. Soc. Am. 57, 66 (1967).
  15. A. Röseler, Optik 27, 179 (1968).
  16. R. A. Shore, Air Force Cambridge Research Laboratories Unclassified Research Report 62–715, August, 1962. Also in Proceedings of Symposium on Electro-magnelic Theory and Aldennas, Copenhagen, Denmark, June, 1962, E. C. Jordan, Ed. (Pergamon Press (Ltd.) London, 1963), p. 787.
  17. J. G. Meadors, Opt. Acta. 12, 379 (1965); and dissertation submitted to Ohio State University, Columbus, Ohio (1964).
  18. J. L. Poirier, W. Rotman, and R. A. Shore, Appl. Opt. 4, 1321 (1965).
  19. R. A. Shore, B. J. Thompson, and R. E. Whitney, J. Opt. Soc. Am. 56, 733 (1966).
  20. J. V. Cornacchio and R. P. Soni, Nuovo Cimento 38, 1169 (1965).
  21. J. V. Cornacchio and K. A. Farnham, Nuovo Cimento 42, 108 (1966).
  22. A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Alta Frequenza 32, 178E (1963).
  23. A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Radio Science 1, 523 (1966).
  24. P. Burlamacchi and A. Consortini, Opt. Acta. 14, 17 (1967).
  25. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
  26. D. L. Fried, Proc. IEEE 55, 57 (1967).
  27. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
  28. W. H. Steel, Rev. Opt. 32, 4, 143, 269 (1953). Also thesis, University of Paris (1953).
  29. E. L. O'Neill, J. Opt. Soc. Am. 46, 285 (1956). Also see Introduction to Statistical Optics (Addison-Wesley Pub. Co., Reading, Mass., 1963), p. 99, and E. B. Brown, Modern Optics (Reinhold Puth. Corn., New York, 1965), p. 496.
  30. R. Barakat and T. Asakura, Oyo Buturi 30, 728 (1961).
  31. R. Barakat and A. Houston, J. Opt. Soc. Am. 55, 538 (1965).
  32. J. V. Cornacchio, J. Opt. Soc. Am. 57, 1325 (1967).
  33. E. H. Linfoot and B. Wolf, Proc. Phys. Soc. (London) B66, 145 (1953). See also E. H. Linfoot, Recent Advances in Optics (Oxford at the Clarendon Press, 1955), p. 41.
  34. J. R. Izatt, J. Opt. Soc. Am. 55, 106 (1965).
  35. C. A. Taylor and B. J. Thompson, J. Opt. Soc. Am. 48, 844 (1958).
  36. B. J. Thompson, J. Opt. Soc. Am. 55, 145 (1965).
  37. W. T. Welford, J. Opt. Soc. Am. 50, 749 (1960).
  38. G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
  39. G. Lansraux, Rev. Opt. 32, 475 (1953).
  40. B. Roizen-Dossier, Rev. Opt. 33, 57, 147, 267 (1954).

Asakura, T.

R. Barakat and T. Asakura, Oyo Buturi 30, 728 (1961).

Bakos, J.

J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).

Barakat, R.

R. Barakat and A. Houston, J. Opt. Soc. Am. 55, 538 (1965).

R. Barakat and T. Asakura, Oyo Buturi 30, 728 (1961).

Beran, M. J.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), Ch. 10, p. 491.

Burlamacchi, P.

P. Burlamacchi and A. Consortini, Opt. Acta. 14, 17 (1967).

Cathey, W. T.

W. T. Cathey, J. Opt. Soc. Am. 55, 1035 (1965).

Consortini, A.

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Alta Frequenza 32, 178E (1963).

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Radio Science 1, 523 (1966).

P. Burlamacchi and A. Consortini, Opt. Acta. 14, 17 (1967).

Cornacchio, J. V.

J. V. Cornacchio, J. Opt. Soc. Am. 57, 1325 (1967).

J. V. Cornacchio and K. A. Farnham, Nuovo Cimento 42, 108 (1966).

J. V. Cornacchio and R. P. Soni, Nuovo Cimento 38, 1169 (1965).

Farnham, K. A.

J. V. Cornacchio and K. A. Farnham, Nuovo Cimento 42, 108 (1966).

Francia, G. Toraldo di

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Alta Frequenza 32, 178E (1963).

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Radio Science 1, 523 (1966).

Françon, M.

M. Françon, Optical Interferometry (Academic Press Inc., New York, 1966), Chs. 1, 8, pp. 1, 162.

M. Françon, Diffraction; Coherence in Optics (Pergamon Press, Inc., New York, 1966).

M. Françon and S. Mallick, in Progress in Optics VI, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1967), Ch. 3, p. 73.

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).

D. L. Fried, Proc. IEEE 55, 57 (1967).

D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).

Hopkins, H. H.

H. H. Hopkins, in Advances in Optical Techniques, A. C. S. van Heel, Ed. (North-Holland Publ. Co., Amsterdam, 1967), Ch. 6, p. 190.

Houston, A.

R. Barakat and A. Houston, J. Opt. Soc. Am. 55, 538 (1965).

Izatt, J. R.

J. R. Izatt, J. Opt. Soc. Am. 55, 106 (1965).

Kantor, K.

J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).

Lansraux, G.

G. Lansraux, Rev. Opt. 32, 475 (1953).

Linfoot, E. H.

E. H. Linfoot and B. Wolf, Proc. Phys. Soc. (London) B66, 145 (1953). See also E. H. Linfoot, Recent Advances in Optics (Oxford at the Clarendon Press, 1955), p. 41.

Mallick, S.

M. Françon and S. Mallick, in Progress in Optics VI, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1967), Ch. 3, p. 73.

Meadors, J. G.

J. G. Meadors, Opt. Acta. 12, 379 (1965); and dissertation submitted to Ohio State University, Columbus, Ohio (1964).

Mielenz, K. D.

K. D. Mielenz, J. Opt. Soc. Am. 57, 66 (1967).

O’Neill, E. L.

E. L. O'Neill, J. Opt. Soc. Am. 46, 285 (1956). Also see Introduction to Statistical Optics (Addison-Wesley Pub. Co., Reading, Mass., 1963), p. 99, and E. B. Brown, Modern Optics (Reinhold Puth. Corn., New York, 1965), p. 496.

Parrent, G. B.

G. B. Parrent and T. J. Skinner, Opt. Acta. 8, 93 (1961).

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).

G. B. Parrent, J. Opt. Soc. Am. 49, 787 (1959); also Ref. 2, p. 40.

Poirier, J. L.

J. L. Poirier, W. Rotman, and R. A. Shore, Appl. Opt. 4, 1321 (1965).

Roizen-Dossier, B.

B. Roizen-Dossier, Rev. Opt. 33, 57, 147, 267 (1954).

Ronchi, L.

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Radio Science 1, 523 (1966).

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Alta Frequenza 32, 178E (1963).

Röseler, A.

A. Röseler, Optik 27, 179 (1968).

Rotman, W.

J. L. Poirier, W. Rotman, and R. A. Shore, Appl. Opt. 4, 1321 (1965).

Scheggi, A. M.

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Alta Frequenza 32, 178E (1963).

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Radio Science 1, 523 (1966).

Schell, A. C.

A. C. Schell, Ph.D. thesis, Massachusetts Institute of Technology (1961).

Shore, R. A.

J. L. Poirier, W. Rotman, and R. A. Shore, Appl. Opt. 4, 1321 (1965).

R. A. Shore, B. J. Thompson, and R. E. Whitney, J. Opt. Soc. Am. 56, 733 (1966).

R. A. Shore, Air Force Cambridge Research Laboratories Unclassified Research Report 62–715, August, 1962. Also in Proceedings of Symposium on Electro-magnelic Theory and Aldennas, Copenhagen, Denmark, June, 1962, E. C. Jordan, Ed. (Pergamon Press (Ltd.) London, 1963), p. 787.

Skinner, T. J.

G. B. Parrent and T. J. Skinner, Opt. Acta. 8, 93 (1961).

Soni, R. P.

J. V. Cornacchio and R. P. Soni, Nuovo Cimento 38, 1169 (1965).

Steel, W. H.

W. H. Steel, Interferometry (Cambridge University Press, 1967).

W. H. Steel, Rev. Opt. 32, 4, 143, 269 (1953). Also thesis, University of Paris (1953).

Taylor, C. A.

C. A. Taylor and B. J. Thompson, J. Opt. Soc. Am. 48, 844 (1958).

Thompson, B. J.

C. A. Taylor and B. J. Thompson, J. Opt. Soc. Am. 48, 844 (1958).

B. J. Thompson, J. Opt. Soc. Am. 55, 145 (1965).

R. A. Shore, B. J. Thompson, and R. E. Whitney, J. Opt. Soc. Am. 56, 733 (1966).

Welford, W. T.

W. T. Welford, J. Opt. Soc. Am. 50, 749 (1960).

Whitney, R. E.

R. A. Shore, B. J. Thompson, and R. E. Whitney, J. Opt. Soc. Am. 56, 733 (1966).

Wolf, E.

E. Wolf, Proc. Roy. Soc. (London) A230, 246 (1955).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), Ch. 10, p. 491.

E. H. Linfoot and B. Wolf, Proc. Phys. Soc. (London) B66, 145 (1953). See also E. H. Linfoot, Recent Advances in Optics (Oxford at the Clarendon Press, 1955), p. 41.

Other (40)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1964), Ch. 10, p. 491.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964).

M. Françon, Optical Interferometry (Academic Press Inc., New York, 1966), Chs. 1, 8, pp. 1, 162.

M. Françon, Diffraction; Coherence in Optics (Pergamon Press, Inc., New York, 1966).

W. H. Steel, Interferometry (Cambridge University Press, 1967).

H. H. Hopkins, in Advances in Optical Techniques, A. C. S. van Heel, Ed. (North-Holland Publ. Co., Amsterdam, 1967), Ch. 6, p. 190.

M. Françon and S. Mallick, in Progress in Optics VI, E. Wolf, Ed. (North-Holland Publ. Co., Amsterdam, 1967), Ch. 3, p. 73.

E. Wolf, Proc. Roy. Soc. (London) A230, 246 (1955).

A. C. Schell, Ph.D. thesis, Massachusetts Institute of Technology (1961).

G. B. Parrent, J. Opt. Soc. Am. 49, 787 (1959); also Ref. 2, p. 40.

J. Bakos and K. Kantor, Nuovo Cimento 22, 519 (1961).

G. B. Parrent and T. J. Skinner, Opt. Acta. 8, 93 (1961).

W. T. Cathey, J. Opt. Soc. Am. 55, 1035 (1965).

K. D. Mielenz, J. Opt. Soc. Am. 57, 66 (1967).

A. Röseler, Optik 27, 179 (1968).

R. A. Shore, Air Force Cambridge Research Laboratories Unclassified Research Report 62–715, August, 1962. Also in Proceedings of Symposium on Electro-magnelic Theory and Aldennas, Copenhagen, Denmark, June, 1962, E. C. Jordan, Ed. (Pergamon Press (Ltd.) London, 1963), p. 787.

J. G. Meadors, Opt. Acta. 12, 379 (1965); and dissertation submitted to Ohio State University, Columbus, Ohio (1964).

J. L. Poirier, W. Rotman, and R. A. Shore, Appl. Opt. 4, 1321 (1965).

R. A. Shore, B. J. Thompson, and R. E. Whitney, J. Opt. Soc. Am. 56, 733 (1966).

J. V. Cornacchio and R. P. Soni, Nuovo Cimento 38, 1169 (1965).

J. V. Cornacchio and K. A. Farnham, Nuovo Cimento 42, 108 (1966).

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Alta Frequenza 32, 178E (1963).

A. Consortini, L. Ronchi, A. M. Scheggi, and G. Toraldo di Francia, Radio Science 1, 523 (1966).

P. Burlamacchi and A. Consortini, Opt. Acta. 14, 17 (1967).

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).

D. L. Fried, Proc. IEEE 55, 57 (1967).

D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).

W. H. Steel, Rev. Opt. 32, 4, 143, 269 (1953). Also thesis, University of Paris (1953).

E. L. O'Neill, J. Opt. Soc. Am. 46, 285 (1956). Also see Introduction to Statistical Optics (Addison-Wesley Pub. Co., Reading, Mass., 1963), p. 99, and E. B. Brown, Modern Optics (Reinhold Puth. Corn., New York, 1965), p. 496.

R. Barakat and T. Asakura, Oyo Buturi 30, 728 (1961).

R. Barakat and A. Houston, J. Opt. Soc. Am. 55, 538 (1965).

J. V. Cornacchio, J. Opt. Soc. Am. 57, 1325 (1967).

E. H. Linfoot and B. Wolf, Proc. Phys. Soc. (London) B66, 145 (1953). See also E. H. Linfoot, Recent Advances in Optics (Oxford at the Clarendon Press, 1955), p. 41.

J. R. Izatt, J. Opt. Soc. Am. 55, 106 (1965).

C. A. Taylor and B. J. Thompson, J. Opt. Soc. Am. 48, 844 (1958).

B. J. Thompson, J. Opt. Soc. Am. 55, 145 (1965).

W. T. Welford, J. Opt. Soc. Am. 50, 749 (1960).

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).

G. Lansraux, Rev. Opt. 32, 475 (1953).

B. Roizen-Dossier, Rev. Opt. 33, 57, 147, 267 (1954).

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