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]

“Adaptive optics kits, tabletop deformable mirrors and more,” Nature Photon.5, 27–27 (2011).

J. A. Rodrigo, T. Alieva, A. Cámara, Ó. Martínez-Matos, P. Cheben, and M. L. Calvo, “Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections,” Opt. Express19, 6064–6077 (2011).

[CrossRef]
[PubMed]

A. I. González and Y. Mejía, “Nonredundant array of apertures to measure the spatial coherence in two dimensions with only one interferogram,” J. Opt. Soc. Am. A28, 1107–1113 (2011).

[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase-space tomography with a programmable Radon–Wigner display,” Opt. Lett.36, 2441–2443 (2011).

[CrossRef]

M. Alonso, “Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles,” Adv. Opt. Photon.3, 272–365 (2011).

[CrossRef]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon.2, 405–450 (2010).

[CrossRef]

P. Kolman and R. Chmelík, “Coherence-controlled holographic microscope,” Opt. Express18, 21990–22003 (2010).

[CrossRef]
[PubMed]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Tomographic reconstruction of the Wigner distribution of non-separable beams,” in PIERS Proceedings (2010), 526–530.

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express17, 4976–4983 (2009).

[CrossRef]
[PubMed]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates,” J. Opt. Soc. Am. A26, 1301–1306 (2009).

[CrossRef]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express17, 17344–17356 (2009).

[CrossRef]
[PubMed]

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

[CrossRef]

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]

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

[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “Intensity-based modal analysis of partially coherent beams with Hermite–Gaussian modes,” Opt. Lett.23, 989–991 (1998).

[CrossRef]

Y. Zhang, B.-Y. Gu, B.-Z. Dong, and G.-Z. Yang, “Optical implementations of the Radon–Wigner display for one-dimensional signals,” Opt. Lett.23, 1126–1128 (1998).

[CrossRef]

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]

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]

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]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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]

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]

J. A. Rodrigo, T. Alieva, A. Cámara, Ó. Martínez-Matos, P. Cheben, and M. L. Calvo, “Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections,” Opt. Express19, 6064–6077 (2011).

[CrossRef]
[PubMed]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase-space tomography with a programmable Radon–Wigner display,” Opt. Lett.36, 2441–2443 (2011).

[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Tomographic reconstruction of the Wigner distribution of non-separable beams,” in PIERS Proceedings (2010), 526–530.

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates,” J. Opt. Soc. Am. A26, 1301–1306 (2009).

[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express17, 4976–4983 (2009).

[CrossRef]
[PubMed]

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]

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

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

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]

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]

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

[CrossRef]

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.

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]

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]

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

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

[CrossRef]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express17, 17344–17356 (2009).

[CrossRef]
[PubMed]

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

[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase-space tomography with a programmable Radon–Wigner display,” Opt. Lett.36, 2441–2443 (2011).

[CrossRef]

J. A. Rodrigo, T. Alieva, A. Cámara, Ó. Martínez-Matos, P. Cheben, and M. L. Calvo, “Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections,” Opt. Express19, 6064–6077 (2011).

[CrossRef]
[PubMed]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Tomographic reconstruction of the Wigner distribution of non-separable beams,” in PIERS Proceedings (2010), 526–530.

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates,” J. Opt. Soc. Am. A26, 1301–1306 (2009).

[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express17, 4976–4983 (2009).

[CrossRef]
[PubMed]

J. A. Rodrigo, T. Alieva, A. Cámara, Ó. Martínez-Matos, P. Cheben, and M. L. Calvo, “Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections,” Opt. Express19, 6064–6077 (2011).

[CrossRef]
[PubMed]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase-space tomography with a programmable Radon–Wigner display,” Opt. Lett.36, 2441–2443 (2011).

[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Tomographic reconstruction of the Wigner distribution of non-separable beams,” in PIERS Proceedings (2010), 526–530.

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates,” J. Opt. Soc. Am. A26, 1301–1306 (2009).

[CrossRef]

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]

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]

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]

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]

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

[CrossRef]

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

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

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]

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]

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

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]

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]

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

[CrossRef]

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]

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

[CrossRef]

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]

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]

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

[CrossRef]

C. Q. Tran and K. A. Nugent, “Recovering the complete coherence function of a generalized Schell model field,” Opt. Lett.31, 3226–3227 (2006).

[CrossRef]
[PubMed]

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]

K. A. Nugent, “Partially coherent diffraction patterns and coherence measurement,” J. Opt. Soc. Am. A8, 1574–1579 (1991).

[CrossRef]

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).

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

[CrossRef]

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

[CrossRef]

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]

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]

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]

J. A. Rodrigo, T. Alieva, A. Cámara, Ó. Martínez-Matos, P. Cheben, and M. L. Calvo, “Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections,” Opt. Express19, 6064–6077 (2011).

[CrossRef]
[PubMed]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase-space tomography with a programmable Radon–Wigner display,” Opt. Lett.36, 2441–2443 (2011).

[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Tomographic reconstruction of the Wigner distribution of non-separable beams,” in PIERS Proceedings (2010), 526–530.

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates,” J. Opt. Soc. Am. A26, 1301–1306 (2009).

[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express17, 4976–4983 (2009).

[CrossRef]
[PubMed]

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

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

[CrossRef]

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]

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]

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]

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]

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

[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]

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]

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]

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]

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]

E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am.72, 343–351 (1982).

[CrossRef]

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

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]

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]

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]

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

[CrossRef]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, “Optical illustration of a varied fractional Fourier-transform order and the Radon—Wigner display,” Appl. Opt.35, 3925–3929 (1996).

[CrossRef]
[PubMed]

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

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

[CrossRef]

F. Dubois, L. Joannes, and J.-C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt.38, 7085–7094 (1999).

[CrossRef]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, “Optical illustration of a varied fractional Fourier-transform order and the Radon—Wigner display,” Appl. Opt.35, 3925–3929 (1996).

[CrossRef]
[PubMed]

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]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

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. A19, 1794–1802 (2002).

[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]

K. A. Nugent, “Partially coherent diffraction patterns and coherence measurement,” J. Opt. Soc. Am. A8, 1574–1579 (1991).

[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]

A. I. González and Y. Mejía, “Nonredundant array of apertures to measure the spatial coherence in two dimensions with only one interferogram,” J. Opt. Soc. Am. A28, 1107–1113 (2011).

[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates,” J. Opt. Soc. Am. A26, 1301–1306 (2009).

[CrossRef]

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]

“Adaptive optics kits, tabletop deformable mirrors and more,” Nature Photon.5, 27–27 (2011).

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

[CrossRef]

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

[CrossRef]

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]

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

[CrossRef]

Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express17, 17344–17356 (2009).

[CrossRef]
[PubMed]

X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express16, 20126–20141 (2008).

[CrossRef]
[PubMed]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express17, 4976–4983 (2009).

[CrossRef]
[PubMed]

P. Kolman and R. Chmelík, “Coherence-controlled holographic microscope,” Opt. Express18, 21990–22003 (2010).

[CrossRef]
[PubMed]

J. A. Rodrigo, T. Alieva, A. Cámara, Ó. Martínez-Matos, P. Cheben, and M. L. Calvo, “Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections,” Opt. Express19, 6064–6077 (2011).

[CrossRef]
[PubMed]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Phase-space tomography with a programmable Radon–Wigner display,” Opt. Lett.36, 2441–2443 (2011).

[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “Intensity-based modal analysis of partially coherent beams with Hermite–Gaussian modes,” Opt. Lett.23, 989–991 (1998).

[CrossRef]

Y. Zhang, B.-Y. Gu, B.-Z. Dong, and G.-Z. Yang, “Optical implementations of the Radon–Wigner display for one-dimensional signals,” Opt. Lett.23, 1126–1128 (1998).

[CrossRef]

G. S. Agarwal and R. Simon, “Reconstruction of the Wigner transform of a rotationally symmetric two-dimensional beam from the Wigner transform of the beam’s one-dimensional sample,” Opt. Lett.17 [17], 1379–1381.

M. Santarsiero and R. Borghi, “Measuring spatial coherence by using a reversed-wavefront Young interferometer,” Opt. Lett.31, 861–863 (2006).

[CrossRef]
[PubMed]

C. Q. Tran and K. A. Nugent, “Recovering the complete coherence function of a generalized Schell model field,” Opt. Lett.31, 3226–3227 (2006).

[CrossRef]
[PubMed]

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

[CrossRef]

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]

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]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, “Tomographic reconstruction of the Wigner distribution of non-separable beams,” in PIERS Proceedings (2010), 526–530.

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

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

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

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

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

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

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

[CrossRef]