Editor-in-Chief : V.K. Rastogi
Asian Journal of Physics | Vol. 33, Nos 3 & 4 (2024) 205-217 |
Phase space tomography for measuring partially coherent fields of light sources
Rui Qi1 and Miguel A Alonso2,3
1Department of Physics and Optical Science, The University of North Carolina at Charlotte, NC, 28262, USA
2Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, 13013, France.
3The Institute of Optics, University of Rochester, Rochester, NY,14627, USA.
Dedicated to Professor Anna Consortini for her significant contributions and pioneering works in the field of atmospheric turbulence and her continuous commitment to promote optics at global level
We implement experimentally a method for characterizing the two-point coherence properties of fields in two dimensions from measurements of their irradiance at different propagation distances. This method is a form of phase space tomography, based on a definition of the ambiguity function that is appropriate beyond the paraxial regime. In the experiment, a combination of two cylindrical lenses is used to create focused fields that vary slowly in one direction, so they behave approximately like two-dimensional fields. Four types of light sources (an incandescent lamp, a white LED, a green LED, and a green laser) with different coherence properties were measured. The results of the method for nonparaxial fields are compared to those based on the paraxial approximation. © Anita Publications. All rights reserved.
Doi: 10.54955/AJP.33.3-4.2024.205-217
Keywords: Imaging, Cameras, Resolution, LED, Incandescent lamp.
Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve
References
- Consortini A, How much mathematics should optics students know? in Proc SPIE, 98, SPIE vol 1603(1991).
- Consortini A, Should optics students know statistics ? in Education and Training in Optics and Photonics, (Optica Publishing Group, 1999), p OS47.
- Bertrand J, Bertrand P, A tomographic approach to Wigner’s function, Found Phys, 17(1987)397–405.
- Nugent K A, Wave field determination using three-dimensional intensity information, Phys Rev Lett, 68(1992)2261; doi.org/10.1103/PhysRevLett.68.2261.
- Beck M, Raymer M, Walmsley I, Wong V, Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses, Opt Lett, 18(1993)2041–2043.
- Smithey D, Beck M, Raymer M G, Faridani A, Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum, Phys Rev Lett, 70(1993)1244; doi.org/10.1103/PhysRevLett.70.1244.
- Raymer M, Beck M, McAlister D, Complex wave-field reconstruction using phase-space tomography, Phys Rev Lett, 72(1994)1137; doi.org/10.1103/PhysRevLett.72.1137.
- McAlister D, Beck M, Clarke L, Mayer A, Raymer M, Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms, Opt Lett, 20(1995)1181–1183.
- Leonhardt U, Measuring the quantum state of light, vol 22, (Cambridge University Press), 1997.
- Born M, Wolf E, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, (Elsevier), 2013.
- Wigner E, On the quantum correction for thermodynamic equilibrium, Phys Rev, 40(1932)749; doi.org/10.1103/PhysRev.40.749.
- Alonso M A, Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles, Adv Opt Photonics, 3 (2011)272–365.
- Papoulis A, Ambiguity function in Fourier optics, J Opt Soc Am, 64(1974)779–788.
- Lohmann A W, Image rotation, Wigner rotation, and the fractional Fourier transform, J Opt Soc Am A, 10(1993) 2181–2186.
- Cámara A, Alieva T, Rodrigo J A, Calvo M L, Phase space tomography reconstruction of the Wigner distribution for optical beams separable in cartesian coordinates, J Opt Soc Am A, 26(2009)1301–1306.
- Guan J, Cao Y, Li J, Pan J, LanT, Wang Z, Study on beam characteristics of semiconductor laser based on Wigner distribution function, First Optics Frontier Conference, Vol 11850. SPIE, 2021; doi.org/10.1117/12.2599707.
- Zuo C, Chen Q, Tian L, Waller L, Asundi A, Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective, Opt Lasers Eng, 71(2015)20–32.
- Zhang R, Sun J, Zuo C, Chen Q, Phase space retrieval by iterative three-dimensional intensity projections, Fourth International Conference on Photonics and Optical Engineering, 117611C(2021); doi.org/10.1117/12.2586647.
- Zhang R, Zuo C, Sun J, Chen Q, Wigner distribution function retrieval via three-dimensional intensity measurement, Optics Frontier Online:Optics Imaging and Display, 115710S(2020); doi.org/10.1117/12.2580310.
- Zhang R, Sun J, Zuo C, Chen Q, Phase space retrieval and the imaging system effect, Advanced Optical Imaging Technologies, 1154917(2020); doi.org/10.1117/12.2573628.
- Tu J, Tamura T, Analytic relation for recovering the mutual intensity by means of intensity information, J Opt Soc Am A, 15(1998)202–206.
- Cho S, Alonso M A, Ambiguity function and phase-space tomography for nonparaxial fields, J Opt Soc Am A, 28(2011)897–902.
- Dolin L S, Beam description of weakly-inhomogeneous wave fields, Izv Vyssh Uchebn Zaved Radiofiz (Radiophysics), 7(1964)559–563.
- Walther A, Radiometry and coherence, J Opt Soc Am, 58(1968)1256–1259.
- Bastiaans M J, The wigner distribution function applied to optical signals and systems, Opt Commun, 25(1978)26–30.
- Wolf E, Coherence and radiometry, J Opt Soc Am A, 68 (1978)6–17.
- Friberg A T, Effects of coherence in radiometry, Appl Optical Coherence, 194(1979)55–70.
- Wolf K B, Alonso M A, Forbes G W, Wigner functions for helmholtz wave fields, J Opt Soc Am A, 16(1999) 2476–2487.