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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 33 — Nov. 20, 1998
  • pp: 7689–7697

Dispersion relation for real-plane zeros as a concept of wave-front measurement

Valeri A. Tartakovski and Nadežda N. Mayer  »View Author Affiliations


Applied Optics, Vol. 37, Issue 33, pp. 7689-7697 (1998)
http://dx.doi.org/10.1364/AO.37.007689


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Abstract

The functional relationship between the phase logarithm and the amplitude logarithm of a wave function near its real-plane zero point is found. This result takes the form of the dispersion relation that is deduced analytically and supported by the numerical simulation of the light-wave propagation in an inhomogeneous medium. The sufficient and necessary conditions of existence of this relationship are discussed, and their validity for infinite spectra is shown.

© 1998 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.5070) Image processing : Phase retrieval

History
Original Manuscript: January 5, 1998
Revised Manuscript: May 27, 1998
Published: November 20, 1998

Citation
Valeri A. Tartakovski and Nadežda N. Mayer, "Dispersion relation for real-plane zeros as a concept of wave-front measurement," Appl. Opt. 37, 7689-7697 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-33-7689


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References

  1. D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992). [CrossRef] [PubMed]
  2. N. N. Mayer, V. A. Tartakovski, “Phase dislocations and the minimum phase representation of wave function,” Atmos. Oceanic Opt. 8, 231–234 (1995).
  3. H. M. Nussenzweig, Causality and Dispersion Relations (Academic, New York, 1972).
  4. B. Ja. Levin, Distribution of Zeros of Entire Function (Gostekhizdat, Moscow, 1956), Translation of Vol. 5 of Mathematical Monographs (1964).
  5. J. Peřina, Coherence of Light, (Van Nostrand, London, 1972).
  6. R. E. Burge, M. A. Fiddy, F. H. Greenaway, G. Ross, “The application of dispersion relations (Hilbert transform) to the phase retrieval,” J. Phys. D 7, 165–168 (1974). [CrossRef]
  7. V. A. Tartakovski, “On the continuation of interferograms beyond the domain of definition,” Atmos. Oceanic Opt. 6, 898–901 (1993).
  8. N. I. Muschelishvili, Singular Integral Equations: Boundary Problems of the Function Theory and Some of Their Applications to Mathematical Physics (Nauka, Moscow, 1968) [Singulyarnye integralnye uravneniya. Granichnye zadachi teorii funktsyi i nekotorye ikh prilozheniya k matematicheskoi fizike (Nauka, Moskva, 1968), in Russian].
  9. R. C. Singleton, “An algorithm for computing the mixed radix fast Fourier transform,” IEEE Trans. Audio Electroacoust. AU-17, 93–103 (1969). [CrossRef]
  10. L. A. Weinstein, D. E. Wakmann, Frequency Separation in the Oscillation and Wave Theory (Nauka, Moscow, 1983) [Razdelenie chastot v teorii kolebanii i voln (Nauka, Moskva, 1983), in Russian].
  11. B. V. Fortes, V. P. Lukin, “Modeling of the image observed through turbulent atmosphere,” in Atmospheric Propagation and Remote Sensing, A. Kohnle, W. B. Miller, eds. Proc. SPIE1668, 477–488 (1992). [CrossRef]
  12. N. N. Mayer, V. A. Tartakovski, “Phase dislocations and focal spots,” Atmos. Oceanic Opt. 9, 1457–1461 (1996).

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