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Applied Optics

Applied Optics


  • Vol. 34, Iss. 17 — Jun. 10, 1995
  • pp: 3128–3135

Complex-valued Fresnel-transform sampling

Filippus Stefanus Roux  »View Author Affiliations

Applied Optics, Vol. 34, Issue 17, pp. 3128-3135 (1995)

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VanderLugt [Appl. Opt. 29, 3352 (1990)] presented sampling rates for the amplitude of Fresnel diffraction patterns. These apply to any plane in a coherent optical system. Although these sampling rates represent the amplitude of diffraction patterns accurately, they are not adequate for the retention of complete information in complex-valued Fresnel diffraction patterns. I show this by considering the ability to reconstruct the original input image through backward diffraction of the forward diffraction pattern of such an image. I then extend the VanderLugt sampling techniques such that reliable sampling of the phase of these Fresnel diffraction patterns can also be achieved. The analysis is restricted to lensless optical systems. The new sampling rates are tested with numerical computations of Fresnel diffraction patterns and rigorous scalar diffraction patterns in both forward and backward directions.

© 1995 Optical Society of America

Original Manuscript: November 14, 1994
Published: June 10, 1995

Filippus Stefanus Roux, "Complex-valued Fresnel-transform sampling," Appl. Opt. 34, 3128-3135 (1995)

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  1. F. G. Stremler, Introduction to Communication Systems, 3rd ed. (Addison-Wesley, Reading, Mass., 1990), Chap. 3, p. 129.
  2. A. VanderLugt, “Optimal sampling of Fresnel transforms,” Appl. Opt. 29, 3352–3361 (1990). [CrossRef] [PubMed]
  3. A. J. Devaney, G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973). [CrossRef]

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