Fig. 1. Schematic illustration of the operational principles for various transmission matrix measurement methods. (a) Interferometric holographic configuration: Reference light is introduced after the complex medium, enabling transmission matrix measurement using a three-step phase-shifting method. (b) Coaxial interferometric setup: Reference light is introduced before the complex medium, facilitating transmission matrix measurement. (c) Non-interferometric phase retrieval: No reference light is used, relying on phase retrieval techniques to determine the transmission matrix. (d) Proposed coded self-referencing method: Probing light (Hadamard bases) and reference light (three-step phase-shifted) are synthesized, enabling transmission matrix measurement while preserving all controllable elements.

Fig. 2. Experimental setup of the system. M1–M5: mirrors; HWP: half-wave plate; PBS: polarizing beam splitter; L1–L5: lenses; DMD: digital micromirror device; SF: spatial filter; MMF: multimode fiber; P: polarizer; BS: beam splitter; APD: avalanche photodiode; CMOS: complementary metal-oxide-semiconductor camera.

Fig. 3. Experimental demonstration of focusing light through the MMF with 256 controllable elements. (a) Illustration of the binary-amplitude mask used to synthesize a complex optical field by combining a Hadamard basis of order 128 with reference light at a phase of 2/3π. (b) Time-dependent intensity captured by the APD, illustrating the transformation of random speckle patterns into a bright focus within 22 ms. Scale bar: 1 mm.

Fig. 4. Multi-spot focusing through the MMF and stacked ground glass diffusers with 1024 controllable elements. (a) Schematic of the coded self-referencing method used to measure 225 rows of the transmission matrix and compute the input complex fields for phase conjugation. (b) Experimental results showing the projection of the letters “S,” “Y,” and “U” through the MMF, with average enhancements of 25, 38, and 29, respectively, achieving over 25.3% of the theoretical value. (c) Experimental results showing the projection of the same letters through stacked ground glass diffusers, with average enhancements of 25, 27, and 28, respectively achieving over 22.5% of the theoretical value. Scale bars: 1 mm.

Fig. 5. Evaluation of optical focusing against dynamic scattering with 256 controllable elements. (a) Schematic of the experimental setup using moving stacked ground glass diffusers to create a dynamic scattering environment. (b) Plot of correlation time as a function of inverse diffuser velocity, with a linear fit mapping correlation time to velocity. (c) Experimental results demonstrating optical focusing at diffuser velocities of 0.001, 0.01, and 0.1 mm/s, corresponding to correlation time of 2100, 210, and 21 ms, respectively. The optical focus achieved at these speeds demonstrates the system’s robustness, with enhancements reaching 159 at slower velocities and decreasing to 62 as the operational time approaches the scattering correlation time, consistent with theoretical predictions. Scale bar: 0.5 mm.

Fig. 6. Illustration of full-field modulation using the superpixel method. (a), (b) Intensity and phase distributions of the target field. (c), (d) Intensity and phase distributions of the generated field, demonstrating a high correlation of over 99%.

Fig. 7. Performance of different orthogonal bases under noisy conditions. (a) Comparison of Hadamard, random, and Cartesian bases under Gaussian noise. (b) Comparison of Hadamard, random, and Cartesian bases under DC noise. Error bars: standard deviations of 100 independent trails.

Fig. 8. Plot of computation time as a function of the number of independent modes.

Fig. 9. Sequence diagram outlining the operational process of the wavefront shaping system.