OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 23 — Aug. 10, 1998
  • pp: 5472–5478

Phase-Change Visualization in Two-Dimensional Phase Objects With a Semiderivative Real Filter

Tomasz Szoplik, Vicent Climent, Enrique Tajahuerce, Jesús Lancis, and Mercedes Fernández-Alonso  »View Author Affiliations


Applied Optics, Vol. 37, Issue 23, pp. 5472-5478 (1998)
http://dx.doi.org/10.1364/AO.37.005472


View Full Text Article

Acrobat PDF (220 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A method of visualization of phase changes in two-dimensional pure-phase objects by use of two orthogonal Fourier plane filters that realize the half-order differentiation is presented. Real semiderivative filters used in two dimensions and in sequence yield output-image intensity signals proportional to the first derivatives of the input-object phase that appear on a constant background. This nonlinear filtration of spatial frequencies permits the alleviation of the consequences of square-law detection and makes phase changes visible. Phase changes in gradient-index phosphate glass are calculated experimentally. We discuss the accuracy of the proposed method.

© 1998 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.4560) Fourier optics and signal processing : Data processing by optical means
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Citation
Tomasz Szoplik, Vicent Climent, Enrique Tajahuerce, Jesús Lancis, and Mercedes Fernández-Alonso, "Phase-Change Visualization in Two-Dimensional Phase Objects With a Semiderivative Real Filter," Appl. Opt. 37, 5472-5478 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-23-5472


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. K. B. Oldham and J. Spanier, The Fractional Calculus (Academic, Orlando, Fla., 1974).
  2. S. G. Samko, A. A. Kilbas, and O. I. Maritchev, Fractional Integrals and Derivatives and their Applications (Science and Technique, Minsk, Russia, 1987) (in Russian).
  3. M. W. Michalski, “Derivatives of noninteger order and their applications,” Diss. Math. 328, 3–47 (1993).
  4. J. Lancis, T. Szoplik, E. Tajahuerce, V. Climent, and M. Fernández-Alonso, “Fractional derivative Fourier plane filter for phase-change visualization,” Appl. Opt. 36, 7461–7464 (1997).
  5. E. Tajahuerce, T. Szoplik, J. Lancis, V. Climent, and M. Fernández-Alonso, “Phase-objet fractional differentiation using Fourier plane filters,” Pure Appl. Opt. 6, 481–490 (1997).
  6. V. Climent, M. Fernández-Alonso, J. Lancis, E. Tajahuerce, and T. Szoplik, “Visualization of phase changes using semiderivative Fourier plane filter,” in Diffractive Optics, EOS Topical Meeting Digest Series Vol. 12 (European Optical Society, Orsay, France, 1997), pp. 272–273.
  7. G. O. Reynolds, J. B. DeVelis, G. B. Parrent, and B. J. Thompson, The New Physical Optics Notebook (SPIE Press, Bellingham, Wash., 1989), pp. 474–502.
  8. L. M. Soroko, Hilbert Optics (Science, Moscow, Russia, 1981), pp. 34–94 (in Russian).
  9. K. Gniadek, Optical Information Processing (Panstwowe Wydawnictwo Naukowe, Warsaw, Poland, 1992), pp. 257–269, 306–311 (in Polish).
  10. A. W. Lohmann and D. P. Paris, “Computer generated spatial filters for coherent optical data processing,” Appl. Opt. 7, 651–655 (1968).
  11. R. A. Sprague and B. J. Thompson, “Quantitative visualization of large variation phase objects,” Appl. Opt. 11, 1469–1479 (1972).
  12. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1986).
  13. H. Kasprzak, “Differentiation of a noninteger order and its optical implementation,” Appl. Opt. 21, 3287–3291 (1982).
  14. B. A. Horwitz, “Phase image differentiation with linear intensity output,” Appl. Opt. 17, 181–186 (1978).
  15. R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1990).
  16. M. Kowalczyk, T. Cichocki, M. Martinez-Corral, and V. Kober, “Binarization of continuous-tone pupil filters: a comparison of several digital halftoning procedures,” Pure Appl. Opt. 4, 553–570 (1995).
  17. I. Moreno, C. Gorecki, J. Campos, and M. J. Yzuel, “Comparison of computer-generated holograms produced by laser printers and lithography: application to pattern recognition,” Opt. Eng. 34, 3520–3525 (1995).
  18. M. Wychowaniec, “Phosphate glass for gradient-index lenses,” Opt. Eng. 36, 1622–1624 (1997).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited