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Liu X, Chen Q, Zeng J, Cai YJ, Liang CH. Measurement of optical coherence structures of random optical fields using generalized Arago spot experiment. Opto-Electron Sci 2, 220024 (2023). doi: 10.29026/oes.2023.220024
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Measurement of optical coherence structures of random optical fields using generalized Arago spot experiment
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Abstract
The optical coherence structures of random optical fields can determine beam propagation behavior, light–matter interactions, etc. Their performance makes a light beam robust against turbulence, scattering, and distortion. Recently, we proposed optical coherence encryption and robust far-field optical imaging techniques. All related applications place a high demand on precision in the experimental measurements of complex optical coherence structures, including their real and imaginary parts. Past studies on these measurements have mainly adopted theoretical mathematical approximations, limited to Gaussian statistic involving speckle statistic (time-consuming), or used complicated and delicate optical systems in the laboratory. In this study, we provide: a robust, convenient, and fast protocol to measure the optical coherence structures of random optical fields via generalized Arago (or Poisson) spot experiments with rigorous mathematical solutions. Our proposal only requires to capture the intensity thrice, and is applicable to any optical coherence structures, regardless of their type or optical statistics. The theoretical and experimental results demonstrated that the real and imaginary parts of the structures could be simultaneously recovered with high precision. We believe that such a protocol can be widely employed in phase measurement, optical imaging, and image transfer.-
Keywords:
- optical coherence /
- statistical optics /
- Arago spot /
- optical encryption /
- optical imaging
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References
[1] Mandel L, Wolf E. Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995). [2] Liu YL, Dong Z, Chen YH, Cai YJ. Research advances of partially coherent beams with novel coherence structures: engineering and applications. Opto-Electron Eng 49, 220178 (2022). doi: 10.12086/oee.2022.220178 [3] Karamata B, Lambelet P, Laubscher M, Salathé RP, Lasser T. Spatially incoherent illumination as a mechanism for cross-talk suppression in wide-field optical coherence tomography. Opt Lett 29, 736–738 (2004). doi: 10.1364/OL.29.000736 [4] Dhalla AH, Migacz JV, Izatt JA. Crosstalk rejection in parallel optical coherence tomography using spatially incoherent illumination with partially coherent sources. Opt Lett 35, 2305–2307 (2010). doi: 10.1364/OL.35.002305 [5] Kang JQ, Zhu R, Sun YX, Li JN, Wong KKY. Pencil-beam scanning catheter for intracoronary optical coherence tomography. Opto-Electron Adv 5, 200050 (2022). doi: 10.29026/oea.2022.200050 [6] Ricklin JC, Davidson FM. Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication. J Opt Soc Am A 19, 1794–1802 (2002). doi: 10.1364/josaa.19.001794 [7] Lu XY, Wang ZY, Zhang SX, Konijnenberg AP, Ouyang YQ et al. Microscopic phase reconstruction of cervical exfoliated cell under partially coherent illumination. J Biophotonics 14, e202000401 (2021). doi: 10.1002/jbio.202000401 [8] Lu XY, Shao YF, Zhao CL, Konijnenberg S, Zhu XL et al. Noniterative spatially partially coherent diffractive imaging using pinhole array mask. Adv Photonics 1, 016005 (2019). doi: 10.1117/1.AP.1.1.016005 [9] Anand V, Han ML, Maksimovic J, Ng SH, Katkus T et al. Single-shot mid-infrared incoherent holography using Lucy-Richardson-Rosen algorithm. Opto-Electron Sci 1, 210006 (2022). doi: 10.29026/oes.2022.210006 [10] Schneider R, Mehringer T, Mercurio G, Wenthaus L, Classen A et al. Quantum imaging with incoherently scattered light from a free-electron laser. Nat Phys 14, 126–129 (2018). doi: 10.1038/nphys4301 [11] Dravins D, Lagadec T, Nuñez PD. Optical aperture synthesis with electronically connected telescopes. Nat Commun 6, 6852 (2015). doi: 10.1038/ncomms7852 [12] Liang CH, Monfared YE, Liu X, Qi BX, Wang F et al. Optimizing illumination’s complex coherence state for overcoming Rayleigh’s resolution limit. Chin Opt Lett 19, 052601 (2021). doi: 10.3788/COL202119.052601 [13] Batarseh M, Sukhov S, Shen Z, Gemar H, Rezvani R et al. Passive sensing around the corner using spatial coherence. Nat Commun 9, 3629 (2018). doi: 10.1038/s41467-018-05985-w [14] Liu YL, Chen YH, Wang F, Cai YJ, Liang CH et al. Robust far-field imaging by spatial coherence engineering. Opto-Electron Adv 4, 210027 (2021). doi: 10.29026/oea.2021.210027 [15] Liu YL, Zhang X, Dong Z, Peng DM, Chen YH et al. Robust far-field optical image transmission with structured random light beams. Phys Rev Appl 17, 024043 (2022). doi: 10.1103/PhysRevApplied.17.024043 [16] Pan RX, Liu X, Tang JH, Ye H, Liu ZZ et al. Enhancing the self-reconstruction ability of the degree of coherence of a light beam via manipulating the cross-phase structure. Appl Phys Lett 119, 111105 (2021). doi: 10.1063/5.0063939 [17] Peng DM, Huang ZF, Liu YL, Chen YH, Wang F et al. Optical coherence encryption with structured random light. PhotoniX 2, 6 (2021). doi: 10.1186/s43074-021-00027-z [18] Liang CH, Wang F, Liu XL, Cai YJ, Korotkova O. Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry. Opt Lett 39, 769–772 (2014). doi: 10.1364/OL.39.000769 [19] Cai YJ, Chen YH, Wang F. Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [Invited]. J Opt Soc Am A 31, 2083–2096 (2014). [20] Hyde IV MW, Bose-Pillai S, Voelz DG, Xiao XF. Generation of vector partially coherent optical sources using phase-only spatial light modulators. Phys Rev Appl 6, 064030 (2016). doi: 10.1103/PhysRevApplied.6.064030 [21] Voelz D, Xiao XF, Korotkova O. Numerical modeling of Schell-model beams with arbitrary far-field patterns. Opt Lett 40, 352–355 (2015). doi: 10.1364/OL.40.000352 [22] Zhu SJ, Li P, Li ZH, Cai YJ, He WJ. Generating non-uniformly correlated twisted sources. Opt Lett 46, 5100–5103 (2021). doi: 10.1364/OL.442264 [23] Wang F, Lv H, Chen YH, Cai YJ, Korotkova O. Three modal decompositions of Gaussian Schell-model sources: comparative analysis. Opt Express 29, 29676–29689 (2021). doi: 10.1364/OE.435767 [24] Ponomarenko SA. Complex Gaussian representation of statistical pulses. Opt Express 19, 17086–17091 (2011). doi: 10.1364/OE.19.017086 [25] Divitt S, Novotny L. Spatial coherence of sunlight and its implications for light management in photovoltaics. Optica 2, 95–103 (2015). doi: 10.1364/OPTICA.2.000095 [26] González AI, Mejía Y. Nonredundant array of apertures to measure the spatial coherence in two dimensions with only one interferogram. J Opt Soc Am A 28, 1107–1113 (2011). doi: 10.1364/JOSAA.28.001107 [27] Partanen H, Turunen J, Tervo J. Coherence measurement with digital micromirror device. Opt Lett 39, 1034–1037 (2014). doi: 10.1364/OL.39.001034 [28] Mendlovic D, Shabtay G, Lohmann AW, Konforti N. Display of spatial coherence. Opt Lett 23, 1084–1086 (1998). doi: 10.1364/OL.23.001084 [29] Halder A, Partanen H, Leinonen A, Koivurova M, Hakala TK et al. Mirror-based scanning wavefront-folding interferometer for coherence measurements. Opt Lett 45, 4260–4263 (2020). doi: 10.1364/OL.398704 [30] Bhattacharjee A, Aarav S, Jha AK. Two-shot measurement of spatial coherence. Appl Phys Lett 113, 051102 (2018). doi: 10.1063/1.5041076 [31] Tran CQ, Williams GJ, Roberts A, Flewett S, Peele AG et al. Experimental measurement of the four-dimensional coherence function for an undulator x-ray source. Phys Rev Lett 98, 224801 (2007). doi: 10.1103/PhysRevLett.98.224801 [32] Cho S, Alonso MA, Brown TG. Measurement of spatial coherence through diffraction from a transparent mask with a phase discontinuity. Opt Lett 37, 2724–2726 (2012). doi: 10.1364/OL.37.002724 [33] Wood JK, Sharma KA, Cho S, Brown TG, Alonso MA. Using shadows to measure spatial coherence. Opt Lett 39, 4927–4930 (2014). doi: 10.1364/OL.39.004927 [34] Shao YF, Lu XY, Konijnenberg S, Zhao CL, Cai YJ et al. Spatial coherence measurement and partially coherent diffractive imaging using self-referencing holography. Opt Express 26, 4479–4490 (2018). doi: 10.1364/OE.26.004479 [35] Wang ZY, Lu XY, Huang WR, Konijnenberg AP, Zhang H et al. Measuring the complete complex correlation matrix of a partially coherent vector beam via self-referencing holography. Appl Phys Lett 119, 111101 (2021). doi: 10.1063/5.0061838 [36] Liu XL, Wang F, Liu L, Chen YH, Cai YJ et al. Complex degree of coherence measurement for classical statistical fields. Opt Lett 42, 77–80 (2017). doi: 10.1364/OL.42.000077 [37] Huang ZF, Chen YH, Wang F, Ponomarenko SA, Cai YJ. Measuring complex degree of coherence of random light fields with generalized Hanbury Brown-Twiss experiment. Phys Rev Appl 13, 044042 (2020). doi: 10.1103/PhysRevApplied.13.044042 [38] Rennie R. A Dictionary of Physics 7th ed (Oxford University Press, New York, 2015). [39] Ma PJ, Kacerovská B, Khosravi R, Liang CH, Zeng J et al. Numerical approach for studying the evolution of the degrees of coherence of partially coherent beams propagation through an ABCD optical system. Appl Sci 9, 2084 (2019). doi: 10.3390/app9102084 [40] Shen YC, Sun H, Peng DM, Chen YH, Cai QL et al. Optical image reconstruction in 4f imaging system: Role of spatial coherence structure engineering. Appl Phys Lett 118, 181102 (2021). doi: 10.1063/5.0046288 [41] Schmidt JD. Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, Bellingham, 2010). [42] Rosales-Guzmán C, Forbes A. How to Shape Light with Spatial Light Modulators (SPIE, Bellingham, 2017). [43] Liu X, Monfared YE, Pan RX, Ma PJ, Cai YJ et al. Experimental realization of scalar and vector perfect Laguerre–Gaussian beams. Appl Phys Lett 119, 021105 (2021). doi: 10.1063/5.0048741 [44] Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13, 600–612 (2004). doi: 10.1109/TIP.2003.819861 [45] Yu JY, Cai YJ, Gbur G. Rectangular Hermite non-uniformly correlated beams and its propagation properties. Opt Express 26, 27894–27906 (2018). doi: 10.1364/OE.26.027894 -
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Liu X, Chen Q, Zeng J, Cai YJ, Liang CH. Measurement of optical coherence structures of random optical fields using generalized Arago spot experiment. Opto-Electron Sci 2, 220024 (2023). doi: 10.29026/oes.2023.220024
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Figure 1.
Schematic of an experimental setup for generation (part 1) and measurement (part 2) of the complex optical coherence structures of random optical fields. (a) Example of the computer-generated holograms loaded on the screen of SLM1, which is used to customize the complex spatial optical coherence structure of the random optical fields. (b) An instantaneous speckle intensity captured by the CCD1 camera, wherein the irregular area denotes an obstacle. HP, half-wave plate; BE, beam expander; BS1 and 2, beam splitters; SLM1 and 2, phase-only spastial light modulators; L1–3, thin lenses with same focal length f=25 cm; CCD1 and 2, charge-coupled devices. The irises are used to select the positive (or negative) 1st diffraction beam; The CCD1 and CCD2 cameras are used to capture the individual mode intensity patterns in the source plane and the Fourier plane, respectively.
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Figure 2.
(a–c) Simulation and (d–f) experimental results for the [(a) and (d)] real part; [(b) and (e)] imaginary part; and the [(c) and (f)] square of the modulus of the optical coherence structure function μ(Δr) of the complex partially coherent beam. The letter “A” is adopted as the power spectrum density function P(κ), and K(r, κ) = exp (−i2πr·κ). Such a partially coherent beam has been produced by the RM method in the experiment, and an irregular obstacle has been chosen, as shown in Fig. 1 (b).
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Figure 3.
Experimental results for the same partially coherent Schell-model beams with different optical statistics. In the upper (a–d) and lower (e–h) rows, they have Gaussian (produced by RM method) and non-Gaussian (produced by PM method) statistics, respectively. (a) and (e) show the individual RM and PM patterns, respectively; (b) and (f) show the experimentally measured intensity PDF curves in space and time. The beam intensity captured by the CCD camera is saved as a grayscale image. The magnitude of grayscale value represents the intensity value of the beam. The spatial intensity PDF is obtained by calculating the gray value of all pixels of a single mode pattern image (consisting of 1288×964 pixels). The temporal intensity PDF is obtained by calculating the gray value of all mode patterns (refreshed by time) at the fixed spatial position; (c, d, g, h) show the experimentally measured real and imaginary parts of the complex optical coherence structures.
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Figure 4.
Simulation (upper row) and experimental (lower row) results for the optical coherence structures of the non-Schell-model partially coherent beams subjected to non-Gaussian statistics, with the reference point positions (a–d) r0= (0 mm, 0 mm) and (e–h) r0 = (1 mm, 0 mm). In the experiment, such a partially coherent beam has been produced by the PM method, and the Dirac obstacle has been replaced by a circular obstacle with a radius of 0.15 mm.
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Figure 5.
Experimentally recovered optical coherence structures and decrypted dynamic images. (a–c) Real and (d–f) imaginary parts of the optical coherence structures are reconstructed by our measurement protocol. (g–i) Corresponding instantaneous recovered images from the optical coherence structures.
