Abstract

An appropriate Green’s function is constructed by use of the eigenfunctions of the Helmholtz equation for spherical geometry such that it vanishes on the sphere. The diffracted amplitude is expressed as an integral on the surface of the sphere that involves only the amplitude distribution in the aperture. In terms of the Laplace coefficients, the integral reduces to a product relation that allows us to define the transfer function of free space. The normal derivative of the Green’s function plays the role of the impulse response of the diffraction problem.

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  1. A. Sommerfeld, Optics (Academic, New York, 1972), Vol. IV, p. 199.
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 42.
  3. Reference 2, p. 39.
  4. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 377 and 378.
  5. Reference 2, p. 48.
  6. Éamon Lalor, Ph. D. thesis (University of Rochester, 1970).
  7. E. Byckling, J. Phys. A 7, 505 (1974); 7, 519 (1974).
  8. Reference 2, p. 40.
  9. Reference 1, p. 207.
  10. A. Sommerfeld, Partial Differential Equations in Physics, Vol. VI (Academic, New York, 1972), p. 135.
  11. M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964), p. 39.
  12. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1963), p. 541, Eq. (16–17).
  13. Reference 10, p. 142.
  14. Reference 12, p. 541.
  15. G. Arfken, Mathematical Methods for Physics (Academic, New York, 1970), p. 768.
  16. Reference 15, p. 571.
  17. Reference 15, p. 522.
  18. Reference 2, p. 37.
  19. Reference 2, p. 39.
  20. Reference 12, p. 14.
  21. Reference 12, p. 85.
  22. Reference 12, p. 541.
  23. Reference 15, p. 572.
  24. Reference 2, p. 54.

Arfken, G.

G. Arfken, Mathematical Methods for Physics (Academic, New York, 1970), p. 768.

Beran, M. J.

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964), p. 39.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 377 and 378.

Byckling, E.

E. Byckling, J. Phys. A 7, 505 (1974); 7, 519 (1974).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 42.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1963), p. 541, Eq. (16–17).

Lalor, Éamon

Éamon Lalor, Ph. D. thesis (University of Rochester, 1970).

Parrent, Jr., G. B.

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964), p. 39.

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, New York, 1972), Vol. IV, p. 199.

A. Sommerfeld, Partial Differential Equations in Physics, Vol. VI (Academic, New York, 1972), p. 135.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 377 and 378.

Other (24)

A. Sommerfeld, Optics (Academic, New York, 1972), Vol. IV, p. 199.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 42.

Reference 2, p. 39.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1959), pp. 377 and 378.

Reference 2, p. 48.

Éamon Lalor, Ph. D. thesis (University of Rochester, 1970).

E. Byckling, J. Phys. A 7, 505 (1974); 7, 519 (1974).

Reference 2, p. 40.

Reference 1, p. 207.

A. Sommerfeld, Partial Differential Equations in Physics, Vol. VI (Academic, New York, 1972), p. 135.

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N. J., 1964), p. 39.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1963), p. 541, Eq. (16–17).

Reference 10, p. 142.

Reference 12, p. 541.

G. Arfken, Mathematical Methods for Physics (Academic, New York, 1970), p. 768.

Reference 15, p. 571.

Reference 15, p. 522.

Reference 2, p. 37.

Reference 2, p. 39.

Reference 12, p. 14.

Reference 12, p. 85.

Reference 12, p. 541.

Reference 15, p. 572.

Reference 2, p. 54.

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