OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 11 — Jun. 3, 2013
  • pp: 13169–13183

Optical coherenscopy based on phase-space tomography

Alejandro Cámara, José A. Rodrigo, and Tatiana Alieva  »View Author Affiliations


Optics Express, Vol. 21, Issue 11, pp. 13169-13183 (2013)
http://dx.doi.org/10.1364/OE.21.013169


View Full Text Article

Enhanced HTML    Acrobat PDF (3110 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(100.5070) Image processing : Phase retrieval
(090.1995) Holography : Digital holography
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: April 17, 2013
Manuscript Accepted: May 16, 2013
Published: May 22, 2013

Citation
Alejandro Cámara, José A. Rodrigo, and Tatiana Alieva, "Optical coherenscopy based on phase-space tomography," Opt. Express 21, 13169-13183 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-11-13169


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).
  2. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2006).
  3. G. Gbur and T. D. Visser, “The structure of partially coherent fields,” in Progress in Optics (Elsevier, 2010), 55, 285–341. [CrossRef]
  4. A. A. Michelson and F. G. Pease, “Measurement of the diameter of Alpha-Orionis by the interferometer,” Astrophys. J.53, 249–259 (1921). [CrossRef]
  5. Y. Cai and S.-Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E71, 056607 (2005). [CrossRef]
  6. B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photon.2, 405–450 (2010). [CrossRef]
  7. 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]
  8. P. Kolman and R. Chmelík, “Coherence-controlled holographic microscope,” Opt. Express18, 21990–22003 (2010). [CrossRef] [PubMed]
  9. X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express16, 20126–20141 (2008). [CrossRef] [PubMed]
  10. X. Ma and G. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics (Wiley, 2011).
  11. 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]
  12. 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]
  13. 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]
  14. Z. Zalevsky, D. Medlovic, and H. M. Ozaktas, “Energetic efficient synthesis of general mutual intensity distribution,” J. Opt. A2, 83–87 (2000). [CrossRef]
  15. M. J. Bastiaans, “The Wigner distribution function of partially coherent light,” Opt. Acta28, 1215–1224 (1981). [CrossRef]
  16. M. Alonso, “Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles,” Adv. Opt. Photon.3, 272–365 (2011). [CrossRef]
  17. 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.
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. K. A. Nugent, “Partially coherent diffraction patterns and coherence measurement,” J. Opt. Soc. Am. A8, 1574–1579 (1991). [CrossRef]
  23. M. Santarsiero and R. Borghi, “Measuring spatial coherence by using a reversed-wavefront Young interferometer,” Opt. Lett.31, 861–863 (2006). [CrossRef] [PubMed]
  24. 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]
  25. L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon.6, 474–479 (2012). [CrossRef]
  26. 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]
  27. 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.
  28. 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]
  29. 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]
  30. 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]
  31. J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Med. Imag.5, 170–176 (1986). [CrossRef]
  32. J. A. Rodrigo, T. Alieva, and M. J. Bastiaans, Optical and Digital Image Processing (Wiley-VCH Verlag, 2011), chap. 12.
  33. J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express17, 4976–4983 (2009). [CrossRef] [PubMed]
  34. 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]
  35. X. Liu and K. H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun.225, 19–30 (2003). [CrossRef]
  36. 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]
  37. 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]
  38. 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]
  39. 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]
  40. 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]
  41. “Adaptive optics kits, tabletop deformable mirrors and more,” Nature Photon.5, 27–27 (2011).
  42. M. Bastiaans, “Transport equations for the Wigner distribution function in an inhomogeneous and dispersive medium,” Opt. Acta26, 1333–1344 (1979). [CrossRef]
  43. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, Colorado, USA, 2005).
  44. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Multimedia

Multimedia FilesRecommended Software
» Media 1: MOV (3080 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited