Publication: Wigner distribution moments measured as intensity moments in separable first-order optical systems
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2005
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Hindawi Publishing Corporation
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Abstract
It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of separable first-order optical systems (generally anamorphic ones). The minimum number of such systems that are needed for the determination of these moments is derived.
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© 2005 M. J. Bastiaans and T. Alieva
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[1] E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Physical Review, vol. 40, no. 5, pp. 749–759, 1932.
[2] M. J. Bastiaans, “TheWigner distribution function applied to optical signals and systems,” Optics Communications, vol. 25, no. 1, pp. 26–30, 1978.
[3] M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” Journal of the Optical Society of America, vol. 69, no. 12, pp. 1710–1716, 1979.
[4] M. J. Bastiaans, “Application of theWigner distribution function to partially coherent light,” Journal of the Optical Society of America {A}, vol. 3, no. 8, pp. 1227–1238, 1986.
[5] W.Mecklenbräuker and F. Hlawatsch, Eds., TheWigner Distribution – Theory and Applications in Signal Processing, Elsevier, Amsterdam, The Netherlands, 1997.
[6] International Organization for Standardization, Technical Committee/Subcommittee 172/SC9, “Lasers and laser-related equipment—test methods for laser beam parameters—beam widths, divergence angle and beam propagation factor,” ISO Doc. 11146: 1999, International Organization for Standardization, Geneva, Switzerland, 1999.
[7] R. K. Luneburg, Mathematical Theory of Optics, University of California Press, Berkeley and Los Angeles, Calif, USA, 1966.
[8] G.Nemes and A. E. Siegman, “Measurement of all ten secondorder moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics,” Journal of the Optical Society of America {A}, vol. 11, no. 8, pp. 2257–2264, 1994.
[9] B. Eppich, C. Gao, and H. Weber, “Determination of the ten second order intensity moments,” Optics & Laser Technology, vol. 30, no. 5, pp. 337–340, 1998.
[10] R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Optics Communications, vol. 65, no. 5, pp. 322–328, 1988.
[11] C. Martínez, F. Encinas-Sanz, J. Serna, P. M. Mejías, and R. Martínez-Herrero, “On the parametric characterization of the transversal spatial structure of laser pulses,” Optics Communications,
vol. 139, no. 4–6, pp. 299–305, 1997.
[12] J. Serna, R. Martínez-Herrero, and P. M. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” Journal of the Optical Society of America {A}, vol. 8, no. 7, pp. 1094–1098, 1991.
[13] J. Serna, F. Encinas-Sanz, and G. Nemes, “Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens,” Journal of the Optical Society of America A, vol. 18, no. 7, pp. 1726–1733, 2001.
[14] E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources. I. Fields with a narrow spectral range,” Proceedings of the Royal Society of London. Series A, vol. 225, pp. 96–111, 1954.
[15] E.Wolf, “Amacroscopic theory of interference and diffraction of light from finite sources. II. Fields with a spectral range of arbitrary width,” Proceedings of the Royal Society of London. Series A, vol. 230, pp. 246–265, 1955.
[16] A. Papoulis, Systems and Transforms with Applications in Optics, McGraw-Hill, New York, NY, USA, 1968.
[17] M. J. Bastiaans, “A frequency-domain treatment of partial coherence,” Optica Acta, vol. 24, no. 3, pp. 261–274, 1977.
[18] L.Mandel and E.Wolf, “Spectral coherence and the concept of cross-spectral purity,” Journal of the Optical Society of America, vol. 66, no. 6, pp. 529–535, 1976.
[19] A. Walther, “Radiometry and coherence,” Journal of the Optical Society of America, vol. 58, no. 9, pp. 1256–1259, 1968.
[20] A.Walther, “Propagation of the generalized radiance throughlenses,” Journal of the Optical Society of America, vol. 68, no. 11, pp. 1606–1610, 1978.
[21] D. Dragoman, “Applications of theWigner distribution function in signal processing,” EURASIP Journal on Applied Signal Processing, vol. 2005, no. 10, pp. 1520–1534, 2005.
[22] K. B. Wolf, Integral Transforms in Science and Engineering, chapter 9, Plenum Press, New York, NY, USA, 1979.
[23] A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” Journal of the Optical Society of America {A}, vol. 10, no. 10, pp. 2181–2186, 1993.
[24] M. J. Bastiaans and T. Alieva, “Wigner distribution moments measured as fractional Fourier transformintensity moments,” in Proc. 19th Congress of the International Commission for Optics, Optics for the Quality of Life (ICO-19), A. Consortini and G. C. Righini, Eds., vol. 4829 of Proceedings of SPIE, pp. 245–246, Firenze, Italy, August 2002.
[25] M. J. Bastiaans and T. Alieva, “Wigner distribution moments in fractional Fourier transformsystems,” Journal of the Optical Society of America {A}, vol. 19, no. 9, pp. 1763–1773, 2002.