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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 67, Iss. 12 — Dec. 1, 1977
  • pp: 1666–1671

A generalized sampling theorem with application to computer-generated transparencies

Martin J. Bastiaans  »View Author Affiliations

JOSA, Vol. 67, Issue 12, pp. 1666-1671 (1977)

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A set of generalized Dirac functions (Δ functions) is introduced which resemble the Dirac function (δ function) in that their masses equal unity. Different members out of this set are determined by different values of a certain parameter. The sampling theorem—which tells us that a band-limited function can be synthesized by a proper low-pass filtering of a sequence of equidistant δ functions having variable masses, these masses being equal to the corresponding sample values of the band-limited function—no longer holds, if the practically unrealizable δ functions are replaced by realized Δ functions. It must be replaced by a generalized sampling theorem, which tells us what relationship exists between the parameters of the Δ functions and the sample values of the function to be generated at the ouput of the low-pass filter. Once a set of Δ functions has been chosen, this relationship can be determined explicitly. An application to the synthesis of coherent optical fields by means of computer-generated transparencies is given.

© 1978 Optical Society of America

Martin J. Bastiaans, "A generalized sampling theorem with application to computer-generated transparencies," J. Opt. Soc. Am. 67, 1666-1671 (1977)

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  1. A. Papoulis, Systems and transforms with applications in optics (McGraw-Hill, New York, 1968) pp. 119–128.
  2. B. R. Brown and A. W. Lohmann, "Complex spatial filtering with binary masks," Appl. Opt. 5, 967–969 (1966).
  3. J. J. Burch, "A computer algorithm for the synthesis of spatial frequency filters," Proc. IEEE 55, 599–601 (1967).
  4. A. W. Lohmann and D. P. Paris, "Binary Fraunhofer holograms, generated by computer," Appl. Opt. 6, 1739–1748 (1967).
  5. B. R. Brown and A. W. Lohmann, "Computer-generated binary holograms," IBM J. Res. Dev. 13, 160–168 (1969).
  6. W. H. Lee, "Sampled Fourier transform hologram generated by computer," Appl. Opt. 9, 639–643 (1970).
  7. C. B. Burckhardt, "A simplification of Lee's method of generating holograms by computer," Appl. Opt. 9, 1949 (1970).
  8. W. H. Lee, "Binary synthetic holograms," Appl. Opt. 13, 1677–1682 (1974).
  9. J. P. Hugonin and P. Chavel, "A complement to the theory of Lohmann-type computer holograms," Opt. Commun. 16, 342–346 (1976).
  10. P. Chavel and J. P. Hugonin, "High quality computer holograms: The problem of phase representation," J. Opt. Soc. Am. 66, 989–996 (1976).
  11. B. Braunecker and R. Hauck, "Grey level on axis computer holograms for incoherent image processing," Opt. Commun. 20, 234–238 (1977).
  12. A. W. Lohmann, "Incoherent optical processing of complex data," Appl. Opt. 16, 261–263 (1977).
  13. V. Volterra, Theory of functionals and of integrals and integro-differential equations (Dover, New York, 1959).
  14. J. F. Barrett, "The use of functionals in the analysis of nonlinear physical systems," J. Electron. Control 15, 567–615 (1963).
  15. A. Halme, "Polynomial operators for nonlinear systems analysis," Act. Polytech. Math. 24, 1–64 (1972).
  16. L. A. Pipes, "The reversion method for solving nonlinear differential equations," J. App. Phys. 23, 202–207 (1952).

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