Fig. 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) 1^st 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.

Fig. 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 functionμ(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).

Fig. 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.

Fig. 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.

Fig. 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.