Fig. 1. 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.

Fig. 2. 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.

Fig. 3. 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.

Fig. 4. (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.

Fig. 5. 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.

Fig. 6. Experimental results of the dependence of the quality of the recovered image on the strength factor u in the focal plane in free space.

Fig. 7. (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.

Fig. 8. (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.