Reference-less Measurement of the Transmission Matrix using DMD and Phase Retrieval Techniques
This paper presents a method for measuring the transmission matrix (TM) of highly scattering materials using a digital micromirror device (DMD) and intensity measurements, avoiding the need for a reference beam. Such methods are particularly relevant in optics for imaging applications, where light scattering poses significant challenges. Through signal processing techniques of phase retrieval, the authors estimate the TM, validating their approach by comparing four different phase retrieval algorithms on experimental data.
The primary contribution of the paper is the experimental demonstration of a reference-less TM measurement using DMD for wavefront shaping. The paper utilizes binary amplitude modulation efficiently, as binary modulators can operate at high speeds and pixel counts compared to phase modulators, which are generally slower. By employing Bayesian phase retrieval algorithms in a variational framework, the authors claim to achieve a reasonable balance between computational complexity and precision of TM estimates.
Experimental Setup and Methodology
The experiment relies on DMD technology for spatial light modulation at high rates. A thick layer of white paint serves as the scattering medium through which light passes after impinging from the DMD. The camera captures the resultant speckle pattern, which signifies random scattering events. Measurements are conducted under the stability constraints of the medium, typically only stable for a limited duration in biological tissues.
The authors used pioneering Bayesian approaches such as prVBEM and prGAMP for phase retrieval in the context of intensity-only measurements and binary inputs. These algorithms were calibrated using multiples of the number of DMD mirrors (900 mirrors) across several iterations or calibration steps. The authors highlight the performance variations among the algorithms concerning the quality of prediction, MSE, and computation time.
Key Results and Implications
The research validates the estimated TM against criteria like prediction quality, distribution of singular values, and focusing quality. A significant observation is that the TM follows the predictions of the Marčenko-Pastur law, indicative of random matrix theory. Notably, prVBEM was found to outperform others for a minimum number of real measurements relative to complex unknowns, with commendable correlation scores in predicted versus actual measurements.
Regarding technological and theoretical implications, the reference-less ability to measure TM could lead to advancements in imaging techniques through scattering media, allowing faster and more robust systems without the need for complex interferometric setups. It promises improvements in real-life applications including but not limited to multimode fibers for endoscopes. Furthermore, the Bayesian phase retrieval techniques suggest potential theoretical developments in optical signal processing and estimation methods in complex media.
Future Directions and Speculation
The paper opens avenues for substantial exploration of TM in different settings, especially in biological contexts where scattering remains a hurdle for optical imaging. Future research may involve scaling these techniques to accommodate larger matrix sizes with improved computational frameworks or adapting them for dynamic media where stability varies more markedly.
Overall, the method provides innovative insights into accomplishing wavefront shaping faster and simpler, leveraging both theoretical advancements in signal processing and practical optimization in optical components. As moderate simplicity of the setup is maintained with high efficiency, this becomes particularly valuable for scenarios requiring rapid data acquisition and handling under conditions like fluctuating biological tissue dynamics.