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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 55, Iss. 8 — Aug. 1, 1965
  • pp: 1014–1019

Method for Obtaining the Transfer Function from the Edge Response Function

BERGE TATIAN  »View Author Affiliations


JOSA, Vol. 55, Issue 8, pp. 1014-1019 (1965)
http://dx.doi.org/10.1364/JOSA.55.001014


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Abstract

The transfer function is expressed as a trigonometric series whose coefficients are proportional to the sampled values of the edge response function. The series may be modified by means of added terms to take into account the known asymptotic behavior of the edge response function. Numerical results are given for pure defocusing.

Citation
BERGE TATIAN, "Method for Obtaining the Transfer Function from the Edge Response Function," J. Opt. Soc. Am. 55, 1014-1019 (1965)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-55-8-1014


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References

  1. R. Barakat, J. Opt. Soc. Am. 54, 920 (1964).
  2. The area under τ(x), which is the total energy, equals unity.
  3. M. Born and E. Wolf, Princi ples of Optics (Pergamon Press, Inc., London 1959), pp. 369, 484.
  4. G. Toraldo di Francia, J. Opt. Soc. Am. 45, 497 (1955).
  5. See Ref. 1.
  6. M. Born and E. Wolf, Ref. 3, p. 483.
  7. M. Born and E. Wolf, Ref. 3, p. 752.
  8. This formula is due to R. Barakat (private communication).
  9. E. C. Titchmarsh, The Theory of Functions (Oxford University Press, New York, 1939) 2nd ed., p. 434.
  10. G. H. Hardy, Divergent Series (Oxford University Press, New York, 1949).
  11. G. H. Hardy, Ref. 10, p. 101.
  12. R. Barakat and A. Houston, J. Opt. Soc. Am. 53, 1244 (1963).
  13. The first two expressions in (26) are obtained by summing the complex exponential, einu, according to the (C,1) definition. The remaining relationships in (26) can be found in R. Courant, Differential and Integral Calculus (Blackie & Son, Ltd., London and Glasgow, 1958), Vol. I, p. 446.
  14. R. Barakat and A. Houston, J. Opt. Soc. Am. 54, 768 (1964).
  15. It is easily seen that (28) gives the values T1 (0) =, and T1 (½∊) =0.

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