Transmission matrix (TM) allows light control through complex media, such as multimode fibers (MMFs), gaining great attention in areas, such as biophotonics, over the past decade. Efforts have been taken to retrieve a complex-valued TM directly from intensity measurements with several representative phase-retrieval algorithms, which still see limitations of slow or suboptimum recovery, especially under noisy environments. Here, we propose a modified nonconvex optimization approach. Through numerical evaluations, it shows that the optimum focusing efficiency is approached with less running time or sampling ratio. The comparative tests under different signal-to-noise levels further indicate its improved robustness. Experimentally, the superior focusing performance of our algorithm is collectively validated by single- and multispot focusing; especially with a sampling ratio of 8, it achieves a 93.6% efficiency of the gold-standard holography method. Based on the recovered TM, image transmission through an MMF is realized with high fidelity. Due to parallel operation and GPU acceleration, our nonconvex approach retrieves a 8685 × 1024 TM (sampling ratio is 8) with 42.3 s on average on a regular computer. The proposed method provides optimum efficiency and fast execution for TM retrieval that avoids the need for an external reference beam, which will facilitate applications of deep-tissue optical imaging, manipulation, and treatment.
Controllable optical propagation, such as forming diffraction-limited optical focusing, beyond the diffusion limit in biological tissue or tissue-like scattering media, has been desired for long yet considered challenging. In the past two decades, optical wavefront shaping (WFS) has been proposed and has progressed, demonstrating its remarkable potential. That said, inherent tradeoffs still exist among optimization speed, control degree of freedom, and energy gain, which has hindered wide applications of the technology. Most recently, an analogue optical phase conjugation system was developed, equipped with stimulated emission light amplification that effectively achieves the least tradeoff ever, yielding high-gain and high-speed performance of optical focusing through dynamic thick media.
Focusing light into an arbitrary pattern through multimode fiber is highly desired in energy delivery-related biomedical applications and has been demonstrated feasible with wavefront shaping. Here, the strategy relying on natural gradient ascent-based parameter optimization is shown to search the optimal wavefront rapidly towards high-quality pattern projection through a multimode fiber. Meanwhile, a new fitness function based on cosine similarity is adopted to replace the commonly used Pearson correlation coefficient, which leads to higher pattern contrast without sacrificing the fidelity with the target. With the proposed scheme, long-distance projection of arbitrary pattern was demonstrated through a 15-meter unfixed multimode fiber, showing fast convergence and better anti-interference ability. The superior performance of our approach for generating arbitrary pattern may gains special interest in multimode fiber based deep-tissue photon therapy and optogenetics.
A new multimode fiber micro-endoscopy that integrates fiber calibration and imaging phase is proposed. The approach utilizes the back-scattered patterns emitted by the fluorescence targets at the fiber distal end to reconstruct the reflection matrix by phase retrieval algorithm. Simulations show that selective focusing through the fiber is directly achieved using the eigenvectors decomposed from the reflection matrix. It is possible to reconstruct the full fluorescent objects based on speckle correlations. Further experiments will be conducted to explore the focusing and imaging performance. The fluorescence-based reflection matrix method has the potential for re-calibration in situ and robust imaging under moderate perturbations, promising for practical micro-endoscopic applications.
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