Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 24, Issue 7, 2007, Pages 1937-1944

  Wang, Fei ^a   Cai, Yangjian ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER TRANSFORMS; OPTICAL PROPERTIES; OPTICAL SYSTEMS; STATISTICS;

COHERENT OPTICAL BEAM; FRACTIONAL FOURIER TRANSFORM; GAUSSIAN STATISTICS;

COHERENT LIGHT;

EID: 34548321521     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.24.001937     Document Type: Article

References (39)

1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
2. Q. S. He, J. Turunen, and A. T. Friberg, "Propagation and imaging experiments with Gaussian Schell-model beams," Opt. Commun. 67, 245-250 (1988).
3. E. Tervonen, A. T. Friberg, and J. Turunen, "Gaussian Schell-model beams generated with synthetic acousto-optic holograms," J. Opt. Soc. Am. A 9, 796-803 (1992).
4. A. Belendez, L. Carretero, and A. Fimia, "The use of partially coherent light to reduce the efficiency of silver-halide noise gratings," Opt. Commun. 98, 236-240 (1993).
5. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, "Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression," Phys. Rev. Lett. 53, 1057-1060 (1984).
6. J. C. Ricklin and F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication," J. Opt. Soc. Am. A 19, 1794-1802 (2002).
7. E. Wolf, "Non-cosmological redshifts of spectral lines," Nature 326, 363-366 (1987).
8. J. Pu, H. Zhang, and S. Nemoto, "Spectral shifts and spectral switches of partially coherent light passing through an aperture," Opt. Commun. 162, 57-63 (1999).
9. S. Anand, B. K. Yadav, and H. C. Kandpal, "Experimental study of the phenomenon of 1 X N spectral switch due to diffraction of partially coherent light," J. Opt. Soc. Am. A 19, 2223-2228 (2002).
10. Y. Cai and S. Zhu, "Ghost interference with partially coherent radiation," Opt. Lett. 29, 2716-2718 (2004).
11. Y. Cai and S. Zhu, "Ghost imaging with incoherent and partially coherent light radiation," Phys. Rev. E 71, 056607 (2005).
12. R. Simon, E. C. G. Sudarshan, and N. Mukunda, "Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants," Phys. Rev. A 31, 2419-2434 (1985).
13. R. Simon and N. Mukunda, "Twisted Gaussian Schell-model beams," J. Opt. Soc. Am. A 10, 95-109 (1993).
14. M. J. Bastiaans, "Application of the Wigner distribution function to partially coherent light," J. Opt. Soc. Am. A 3, 1227-1238 (1986).
15. Q. Lin and Y. Cai, "Tensor ABCD law for partially coherent twisted anisotropic Gaussian Schell-model beams," Opt. Lett. 27, 216-218 (2002).
16. Y. Cai and Q. Lin, "Spectral shift of partially coherent twisted anisotropic Gaussian Schell-model beams in free space," Opt. Commun. 204, 17-23 (2002).
17. Y. Cai and Q. Lin, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media," J. Opt. Soc. Am. A 19, 2036-2042 (2002).
18. Y. Cai and L. Hu, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system," Opt. Lett. 31, 685-687 (2006).
19. Y. Cai and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere," Appl. Phys. Lett. 89, 041117 (2006).
20. A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).
21. D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation: I," J. Opt. Soc. Am. A 10, 1875-1881 (1993).
22. H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transforms and their optical implementation: II," J. Opt. Soc. Am. A 10, 2522-2531 (1993).
23. A. W. Lohmann, D. Medlovic, and Z. Zalevsky, "Fractional transformations in optics," in Progress in Optics, Vol. XXXVIII, E. Wolf, ed. (Elsevier, 1998).
24. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
25. A. Tbrre, "The fractional Fourier transform and some of its applications to optics," in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), Vol. 43.
26. D. Mendlovic, Z. Zalevsky, R. G. Dorsch, Y. Bitran, A. W. Lohmann, and H. Ozaktas, "New signal representation based on the fractional Fourier transform: definitions," J. Opt. Soc. Am. A 12, 2424-2431 (1995).
27. S. C. Pei, M. H. Yeh, and T. L. Luo, "Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform," IEEE Mrans. Signal Process. 47, 2883-2888 (1999).
28. B. Zhu, S. Liu, and Q. Ran, "Optical image encryption based on multi-fractional Fourier transforms," Opt. Lett. 25, 1159-1161 (2000).
29. Y. Zhang, B. Dong, B. Gu, and G. Yang, "Beam shaping in the fractional Fourier transform domain," J. Opt. Soc. Am. A 15, 1114-1120 (1998).
30. X. Xue, H. Q. Wei, and A. G. Kirk, "Beam analysis by fractional Fourier transform," Opt. Lett. 26, 1746-1748 (2001).
31. Q. Lin and Y Cai, "Fractional Fourier transform for partially coherent Gaussian-Schell model beams," Opt. Lett. 27, 1672-1674 (2002).
32. Y. Cai and Q. Lin, "Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane," J. Opt. Soc. Am. A 20, 1528-1536 (2003).
33. C. Zheng, "Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam," J. Opt. Soc. Am. A 23, 2161-2165 (2006).
34. Y. Cai, Q. Lin, and S. Zhu, "Coincidence fractional Fourier transform with entangled photon pairs and incoherent light," Appl. Phys. Lett. 86, 021112 (2005).
35. Y. Cai and S. Zhu, "Coincidence fractional Fourier transform with partially coherent light radiation," J. Opt. Soc. Am. A 22, 1798-1804 (2005).
36. Y. Cai, Q. Lin, and S. Zhu, "Coincidence subwavelength fractional Fourier transform," J. Opt. Soc. Am. A 23, 835-841 (2006).
37. Y. Cai and F. Wang, "Lensless optical implementation of the coincidence fractional Fourier transform," Opt. Lett. 31, 2278-2280 (2006).
38. F. Wang, Y Cai, and S. He, "Experimental observation of coincidence fractional Fourier transform with a partially coherent beam," Opt. Express 14, 6999-7004 (2006).
39. R. Simon, E. C. G. Sudarshan, and N. Mukunda, "Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields," Phys. Rev. A 29, 3273-3279 (1984).