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Applied Optics

Applied Optics


  • Vol. 17, Iss. 2 — Jan. 15, 1978
  • pp: 181–186

Phase image differentiation with linear intensity output

Bruce A. Horwitz  »View Author Affiliations

Applied Optics, Vol. 17, Issue 2, pp. 181-186 (1978)

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A heuristic development of the operation of a square root filter (one whose amplitude transmittance is proportional to the square root of position in frequency space) is presented. The output of a coherent optical processor utilizing this filter for phase image inputs is shown to be an intensity which is directly proportional to the derivative of the input phase function. The results of a digital filtering experiment which confirms this linear relationship are presented. The use of this filter in phase image visualization systems is also discussed.

© 1978 Optical Society of America

Original Manuscript: March 25, 1977
Published: January 15, 1978

Bruce A. Horwitz, "Phase image differentiation with linear intensity output," Appl. Opt. 17, 181-186 (1978)

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  1. R. A. Sprague, B. J. Thompson, Appl. Opt. 11, 1469 (1972). [CrossRef] [PubMed]
  2. B. A. Horwitz, Dissertation, University of Rochester (1976).
  3. R. Hoffman, L. Gross, Appl. Opt. 14, 1169 (1975). [CrossRef] [PubMed]
  4. P. DeSantis, F. Gori, G. Guattari, C. Palma, Appl. Opt. 15, 2385 (1976). [CrossRef]
  5. B. A. Horwitz, Opt. Commun. 17, 231 (1976). [CrossRef]
  6. K. B. Oldham, J. Spanier, The Fractional Calculus (Academic, New York, 1974).
  7. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), p. 113.
  8. See, for example, bandwidth calculations for FM signals in M. Schwartz, Information Transmission, Modulation, and Noise, (McGraw-Hill, New York, 1970), pp. 238–246.
  9. G. E. Sommargren, B. J. Thompson, Appl. Opt. 12, 2130 (1973). [CrossRef] [PubMed]
  10. M. Abramowitz, I. A. Stegun, Eds. Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1970), pp. 300, 301.

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