## Self-affinity in phase space

JOSA A, Vol. 17, Issue 4, pp. 756-761 (2000)

http://dx.doi.org/10.1364/JOSAA.17.000756

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### Abstract

The expression for the Wigner distribution (WD) in polar coordinates was derived, based on the decomposition of coherent and partially coherent fields on the orthogonal sets of Hermite–Gauss modes. This representation allows one to analyze easily the structure of the WD and to describe the field propagation through first-order optical systems, including the self-imaging phenomenon.

© 2000 Optical Society of America

**OCIS Codes**

(070.1170) Fourier optics and signal processing : Analog optical signal processing

(110.1650) Imaging systems : Coherence imaging

(110.6980) Imaging systems : Transforms

**Citation**

Tatiana Alieva and Martin J. Bastiaans, "Self-affinity in phase space," J. Opt. Soc. Am. A **17**, 756-761 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-4-756

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### References

- R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, Calif., 1966).
- K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979).
- M. Nazarathy and J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982).
- C. Gomez-Reino, “GRIN optics and its application in optical connections,” Int. J. Optoelectron. 7, 607–680 (1992).
- V. Namias, “The fractional order Fourier transform and its application to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).
- D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).
- D. F. V. James and G. S. Agarwal, “The generalised Fresnel transform and its application to optics,” Opt. Commun. 126, 207–212 (1996).
- G. Cincotti, F. Gori, and M. Santarsiero, “Generalized self-Fourier functions,” J. Phys. A 25, L1191–L1194 (1992).
- T. Alieva and A. Barbé, “Self-fractional Fourier functions and selection of modes,” J. Phys. A 30, L211–L215 (1997).
- T. Alieva and A. Barbé, “Self-imaging in fractional Fourier transform systems,” Opt. Commun. 152, 11–15 (1998).
- T. Alieva and M. J. Bastiaans, “Self-imaging in first-order optical systems,” in Optics and Optoelectronics: Theory, Devices and Applications, O. P. Nijhawan, A. K. Gupta, A. K. Musla, and K. Singh, eds. (Narosa, New Delhi, 1998), Vol. 1, pp. 126–131.
- T. Alieva and M. J. Bastiaans, “Powers of transfer matrices determined by means of eigenfunctions,” J. Opt. Soc. Am. A 16, 2413–2418 (1999).
- T. Alieva and A. Barbé, “Self-fractional Fourier images,” J. Mod. Opt. 46, 83–99 (1999).
- M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979).
- M. J. Bastiaans, “Application of the Wigner distribution function in optics,” in The Wigner Distribution, W. Mecklenbräuker and F. Hlawatsch, eds. (Elsevier, Amsterdam, 1997).
- T. Alieva and F. Agullo-Lopez, “Diffraction analysis of random fractal fields,” J. Opt. Soc. Am. A 15, 669–674 (1998).
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 838.
- S. Y. Lee and H. H. Szu, “Fractional Fourier transforms, wavelet transforms, and adaptive neural networks,” Opt. Eng. 33, 2326–2329 (1994).

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