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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 57, Iss. 4 — Apr. 1, 1967
  • pp: 546–547

Application of the Convolution Theorem to Rayleigh’s Integral Formulas

GEORGE C. SHERMAN  »View Author Affiliations


JOSA, Vol. 57, Issue 4, pp. 546-547 (1967)
http://dx.doi.org/10.1364/JOSA.57.000546


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Citation
GEORGE C. SHERMAN, "Application of the Convolution Theorem to Rayleigh’s Integral Formulas," J. Opt. Soc. Am. 57, 546-547 (1967)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-57-4-546


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References

  1. J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 56, 588 (1966).
  2. C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964), pp. 311–313 for list of requirements.
  4. Kirchhoff's boundary conditions are sometimes used with Rayleigh's integral formulas to solve diffraction problems. The resulting theory is called the Rayleigh-Sommerfeld diffraction theory. Wolf and Marchand give a thorough comparison between the Rayleigh-Sommerfeld and Fresnel-Kirchhoff theories: E. Wolf and E. W. Marchand, J. Opt. Soc. Am. 54, 587 (1964). E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712
  5. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1965), 3rd ed., Sec. 11.7, Eq. 27.
  6. J. A. Stratton, Electromaagnetic Theory (McGraw-Hill Book Company, New York, 1941), p. 363.
  7. H. G. Booker and P. C. Clemmow, Proc. Inst. Elec. Engrs (London) Pt. III, 97, 11 (1950).
  8. J. A. Ratcliffe, Rept. Progr. Phys. 19, 188 (1956).
  9. E. Wolf, Proc. Phys. Soc. (London) 74, 280 (1959).
  10. D. Gabor in Progress in Optics Vol. 1, E. Wolf, editor (North-Holland Publishing Co., Amsterdam, 1961), p. 136.
  11. C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954). Eq. 2.18.
  12. H. Osterberg, J. Opt. Soc. Am. 55, 1467 (1965).
  13. A referee has indicated that John T. Winthrop has a derivation similar to that of this paper in his Ph.D. thesis, August 1966, written at the University of Michigan, Ann Arbor, Mich.

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