|Citation:||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|
The degree of coherence (DOC) function that characterizes the second-order correlations at any two points in a light field is shown to provide a new degree of freedom for carrying information. As a rule, the DOC varies along the beam propagation path, preventing from the efficient information recovery. In this paper, we report that when a partially coherent beam carrying a cross phase propagates in free space, in a paraxial optical system or in a turbulent medium, the modulus of the far-field (focal plane) DOC acquires the same value as it has in the source plane. This unique propagation feature is employed in a novel protocol for far-field imaging via the DOC, applicable to transmission in both free-space and turbulence. The advantages of the proposed approach are the confidentiality and resistance to turbulence, as well as the weaker requirement for the beam alignment accuracy. We demonstrate the feasibility and the robustness of the far-field imaging via the DOC in the turbulent media through both the experiment and the numerical simulations. Our findings have potential applications in optical imaging and remote sensing in natural environments, in the presence of optical turbulence.
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|Supplementary Information for Robust far-field imaging by spatial coherence engineering|
Variation of the modulus of DOC |μ| of a CGCSM beam with the propagation distance z after the focusing lens, with the CP strength factor (a1−a4) u = 0 mm−2, (b1−b4) u = 2 mm−2, (c1−c4) u = 10 mm−2, and (d1−d4) u = 70 mm−2. The parameters are set as λ = 532 nm, δ0 =0.5 mm and n=1.
Theoretical results of the modulus of the DOC |μ| at different propagation distances z after the lens with the CP strength factor u=−60 mm−2. The inserted letter “S” in (a) is adopted as the power spectral density P(v) function.
Schematic diagram of the experiment setup for generation of Schell-model beams with a controllable CP structure, measurement of the modulus of the DOC in the far field propagation in free space as well as in turbulent atmosphere. Laser, a Nd:YAG laser with wavelength 532nm; M, mirror; BE, beam expander; SLM1, SLM2, spatial light modulator; RGGD, rotating ground glass disk; L1, L2, L3, L4, L5, L6, thin lenses with the identical focal length f=250mm; GAF, Gaussian amplitude filter; BS, beam splitter; CA, circular aperture; SP, source plane; CCD, charge-coupled device; HP, hot plate; PC1, PC2, PC3, personal computers.
(a−d) Experimental results of the modulus of the DOC |μ| in the focal plane with different strength factors u. (e−h) The modulus of the DOC |μ| at different propagation distances z after the lens with the CP strength factor u=−60 mm−2.
Experimental results of the modulus of the DOC |μ| in the focal plane at different temperatures of the HP. The strength factor of the CP is u=−60 mm−2. T=0 °C stands for the free space case.
Experimental results of the dependence of the quality of the recovered image on the strength factor u in the focal plane in free space.
(a−c) Simulation results of the reconstructed image in turbulence of different strength and with different CP strength factor u. (d−f) Experimental results of the reconstructed image at different temperatures with u=−60 mm−2.
(a) A typical instantaneous intensity captured by the CCD. (b) Experimental results of the recovered image through the area surrounded by the yellow dashed square shown in subplot (a) covering 1440×1440 pixels. (c) The recovered image through the area surrounded by the red dashed square shown in subplot (a) covering 500×500 pixels.