Abstract

Partially coherent light provides attractive benefits in imaging, beam shaping, free-space communications, random medium monitoring, among other applications. However, the experimental characterization of the spatial coherence is a difficult problem involving second-order statistics represented by four-dimensional functions that cannot be directly measured and analyzed. In addition, real-world applications usually require quantitative characterization of the local spatial coherence of a beam in the absence of a priori information, together with fast acquisition and processing of the experimental data. Here we propose and experimentally demonstrate a technique that solves this problem. It comprises an optical setup developed for automatized video-rate measurement and a method –phase-space tomographic coherenscopy– allowing parallel data acquisition, processing, and analysis. This technique significantly simplifies the spatial coherence analysis and opens up new perspectives for the development of tools exploiting the degrees of freedom hidden into light coherence.

© 2013 OSA

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2012

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon.6, 474–479 (2012).
[CrossRef]

2011

2010

2009

2008

2006

2005

Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E71, 056607 (2005).
[CrossRef]

2004

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

2003

X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun.225, 19–30 (2003).
[CrossRef]

T. Shirai, A. Dogariu, and E. Wolf, “Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence,” J. Opt. Soc. Am. A20, 1094–1102 (2003).
[CrossRef]

2002

2000

Z. Zalevsky, D. Medlovic, and H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. A2, 83–87 (2000).
[CrossRef]

1999

1998

1996

1995

T. Alieva and F. Agullo-Lopez, “Reconstruction of the optical correlation function in a quadratic refractive index medium,” Opt. Commun.114, 161–169 (1995).
[CrossRef]

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A12, 1942–1946 (1995).
[CrossRef]

1994

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett.72, 1137–1140 (1994).
[CrossRef] [PubMed]

1991

1989

E. Tervonen, J. Turunen, and A. T. Friberg, “Transverse laser-mode structure determination from spatial coherence measurements: Experimental results,” Appl. Phys. B49, 409–414 (1989).
[CrossRef]

1986

J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Med. Imag.5, 170–176 (1986).
[CrossRef]

1982

1981

M. J. Bastiaans, “The Wigner distribution function of partially coherent light,” Opt. Acta28, 1215–1224 (1981).
[CrossRef]

1979

M. Bastiaans, “Transport equations for the Wigner distribution function in an inhomogeneous and dispersive medium,” Opt. Acta26, 1333–1344 (1979).
[CrossRef]

1921

A. A. Michelson and F. G. Pease, “Measurement of the diameter of Alpha-Orionis by the interferometer,” Astrophys. J.53, 249–259 (1921).
[CrossRef]

Agarwal, G. S.

Agullo-Lopez, F.

T. Alieva and F. Agullo-Lopez, “Reconstruction of the optical correlation function in a quadratic refractive index medium,” Opt. Commun.114, 161–169 (1995).
[CrossRef]

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Alieva, T.

Alonso, M.

Arce, G.

X. Ma and G. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics (Wiley, 2011).

Arce, G. R.

Baldis, H. A.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Bandulet, H. C.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Bastiaans, M.

M. Bastiaans, “Transport equations for the Wigner distribution function in an inhomogeneous and dispersive medium,” Opt. Acta26, 1333–1344 (1979).
[CrossRef]

Bastiaans, M. J.

M. J. Bastiaans, “The Wigner distribution function of partially coherent light,” Opt. Acta28, 1215–1224 (1981).
[CrossRef]

J. A. Rodrigo, T. Alieva, and M. J. Bastiaans, Optical and Digital Image Processing (Wiley-VCH Verlag, 2011), chap. 12.

Baykal, Y.

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett.72, 1137–1140 (1994).
[CrossRef] [PubMed]

Bonnaud, G.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Borghi, R.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2006).

Brenner, K. H.

X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun.225, 19–30 (2003).
[CrossRef]

Cai, Y.

Calvo, M. L.

Cámara, A.

Cheben, P.

Chmelík, R.

Davidson, F. M.

Depierreux, S.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Dogariu, A.

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Dong, B.-Z.

Dorsch, R. G.

Dubois, F.

Erkmen, B. I.

Eyyuboglu, H. T.

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Ferreira, C.

Fleischer, J. W.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon.6, 474–479 (2012).
[CrossRef]

Friberg, A. T.

E. Tervonen, J. Turunen, and A. T. Friberg, “Transverse laser-mode structure determination from spatial coherence measurements: Experimental results,” Appl. Phys. B49, 409–414 (1989).
[CrossRef]

Gbur, G.

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” in Progress in Optics (Elsevier, 2010), 55, 285–341.

González, A. I.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, Colorado, USA, 2005).

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

Gori, F.

Gu, B.-Y.

Guattari, G.

Gureyev, T. E.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Hulin, S.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Joannes, L.

Kolman, P.

Korotkova, O.

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Labaune, C.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Legros, J.-C.

Lewis, K.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Liu, X.

X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun.225, 19–30 (2003).
[CrossRef]

Lohmann, A. W.

Ma, X.

Martínez-Matos, Ó.

McAlister, D. F.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett.72, 1137–1140 (1994).
[CrossRef] [PubMed]

Medlovic, D.

Z. Zalevsky, D. Medlovic, and H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. A2, 83–87 (2000).
[CrossRef]

Mejía, Y.

Mendlovic, D.

Michard, A.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Michel, P.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Michelson, A. A.

A. A. Michelson and F. G. Pease, “Measurement of the diameter of Alpha-Orionis by the interferometer,” Astrophys. J.53, 249–259 (1921).
[CrossRef]

Nugent, K. A.

Ozaktas, H. M.

Z. Zalevsky, D. Medlovic, and H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. A2, 83–87 (2000).
[CrossRef]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Pease, F. G.

A. A. Michelson and F. G. Pease, “Measurement of the diameter of Alpha-Orionis by the interferometer,” Astrophys. J.53, 249–259 (1921).
[CrossRef]

Qu, J.

Radon, J.

J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Med. Imag.5, 170–176 (1986).
[CrossRef]

Raymer, M. G.

M. G. Raymer, M. Beck, and D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett.72, 1137–1140 (1994).
[CrossRef] [PubMed]

Ren, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Riazuelo, G.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Ricklin, J. C.

Roberts, A.

Rodrigo, J. A.

Santarsiero, M.

Shapiro, J. H.

Shirai, T.

Simon, R.

Situ, G.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon.6, 474–479 (2012).
[CrossRef]

Tervonen, E.

E. Tervonen, J. Turunen, and A. T. Friberg, “Transverse laser-mode structure determination from spatial coherence measurements: Experimental results,” Appl. Phys. B49, 409–414 (1989).
[CrossRef]

Tikhonchuk, V. T.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Tran, C. Q.

Tur, M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Turunen, J.

E. Tervonen, J. Turunen, and A. T. Friberg, “Transverse laser-mode structure determination from spatial coherence measurements: Experimental results,” Appl. Phys. B49, 409–414 (1989).
[CrossRef]

Visser, T. D.

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” in Progress in Optics (Elsevier, 2010), 55, 285–341.

Waller, L.

L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon.6, 474–479 (2012).
[CrossRef]

Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Weber, S.

P. Michel, C. Labaune, H. C. Bandulet, K. Lewis, S. Depierreux, S. Hulin, G. Bonnaud, V. T. Tikhonchuk, S. Weber, G. Riazuelo, H. A. Baldis, and A. Michard, “Strong reduction of the degree of spatial coherence of a laser beam propagating through a preformed plasma,” Phys. Rev. Lett.92, 175001 (2004).
[CrossRef] [PubMed]

Willner, A. E.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Wolf, E.

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

Yang, G.-Z.

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nature Photon.6, 488–496 (2012).
[CrossRef]

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