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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 8 — Aug. 1, 2007
  • pp: 2274–2279

Differential operator approach for Fourier image processing

Ismael Núñez and José A. Ferrari  »View Author Affiliations


JOSA A, Vol. 24, Issue 8, pp. 2274-2279 (2007)
http://dx.doi.org/10.1364/JOSAA.24.002274


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Abstract

We present a differential operator approach for Fourier image processing. We demonstrate that when the mask in the processor Fourier plane is an analytical function, it can be described by means of a differential operator that acts directly on the input field to give the processed output image. In many cases (e.g., Schlieren imaging) this approach simplifies the calculations, which usually involve the evaluation of convolution integrals, and gives a new insight into the image-processing procedure.

© 2007 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.6110) Fourier optics and signal processing : Spatial filtering

ToC Category:
Fourier Optics and Optical Signal Processing

History
Original Manuscript: November 29, 2006
Revised Manuscript: March 5, 2007
Manuscript Accepted: March 17, 2007
Published: July 11, 2007

Citation
Ismael Núñez and José A. Ferrari, "Differential operator approach for Fourier image processing," J. Opt. Soc. Am. A 24, 2274-2279 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-8-2274


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References

  1. K. Iizuka, Engineering Optics (Springer-Verlag, 1985).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988).
  3. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, 1989). [CrossRef]
  4. A. Papoulis, Systems and Transform with Applications in Optics (McGraw-Hill, 1968), Chap. 2.
  5. B. Zakharin and J. Stricker, "Schlieren systems with coherent illumination for quantitative measurements," Appl. Opt. 43, 4786-4795 (2004). [CrossRef] [PubMed]
  6. E. W. Weisstein, "Heaviside step function," MathWorld--A Wolfram Web Resource, http://mathworld.wolfram.com/HeavisideStepFunction.html.
  7. J. Glückstad and P. C. Mogensen, "Optimal phase contrast in common-path interferometry," Appl. Opt. 40, 268-282 (2001). [CrossRef]
  8. I. Núñez and J. A. Ferrari, "Bright versus dark Schlieren imaging: quantitative analysis of quasisinusoidal phase objects," Appl. Opt. 46, 725-729 (2007). [CrossRef] [PubMed]
  9. R. L. White, Basic Quantum Mechanics (McGraw-Hill, 1966), Chaps. 3 and 7.

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