Realizing high-fidelity optical information transmission through a scattering medium is of vital importance in both science and applications, such as short-range fiber communication and optical encryption. Theoretically, an input wavefront can be reconstructed by inverting the transmission matrix of the scattering medium. However, this deterministic method for retrieving light field information encoded in the wavefront has not yet been experimentally demonstrated. Herein, we demonstrate light field information transmission through different scattering media with near-unity fidelity. Multi-dimensional optical information can be delivered through either a multimode fiber or a ground glass without relying on any averaging or approximation, where their Pearson correlation coefficients can be up to 99%.

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.

Imaging through multimode fiber (MMF) provides high-resolution imaging through a fiber with cross section down to tens of micrometers. It requires interferometry to measure the full transmission matrix (TM), leading to the drawbacks of complicated experimental setup and phase instability. Reference-less TM retrieval is a promising robust solution that avoids interferometry, since it recovers the TM from intensity-only measurements. However, the long computational time and failure of 3D focusing still limit its application in MMF imaging. We propose an efficient reference-less TM retrieval method by developing a nonlinear optimization algorithm based on fast Fourier transform (FFT). Furthermore, we develop an algorithm to correct the phase offset error of retrieved TM using defocused intensity images and hence achieve 3D focusing. The proposed method is validated by both simulations and experiments. The FFT-based TM retrieval algorithm achieves orders of magnitude of speedup in computational time and recovers 2286 × 8192 TM of a 0.22 NA and 50 μm diameter MMF with 112.9 s by a computer of 32 CPU cores. With the advantages of efficiency and correction of phase offset, our method paves the way for the application of reference-less TM retrieval in not only MMF imaging but also broader applications requiring TM calibration.

与标量涡旋光束不同，矢量涡旋光束同时具有各项异性的空间偏振分布和螺旋相位分布，并携带与相位分布有关的轨道角动量(Orbital angular momentum，OAM)。根据柯林斯衍射积分理论，得到了傍轴近似条件下矢量涡旋光束的OAM密度，实验采集了矢量涡旋光束通过光阑-透镜系统后的光场，详细讨论了光阑截断参数以及光阑-透镜间距等参数对矢量涡旋光场及其OAM密度的影响。结果表明：相比标量涡旋光束，矢量涡旋光束OAM通过光阑系统后随传输距离的衰减更慢，受光阑截断参数影响更小。矢量涡旋光束偏振态不受光阑-透镜系统影响，截断参数大于4.2时，轨道角动量密度和光强不受截断参数影响。在透镜焦点位置处，OAM密度达到最大值。研究结果为矢量涡旋光束OAM特性的应用提供理论依据。