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 scattering media is valuable for many areas, such as biomedicine and communication. Recent progress enabled by deep learning (DL) has shown superiority especially in the model generalization. However, there is a lack of research to physically reveal the origin or define the boundary for such model scalability, which is important for utilizing DL approaches for scalable imaging despite scattering with high confidence. In this paper, we find the amount of the ballistic light component in the output field is the prerequisite for endowing a DL model with generalization capability by using a “one-to-all” training strategy, which offers a physical meaning invariance among the multisource data. The findings are supported by both experimental and simulated tests in which the roles of scattered and ballistic components are revealed in contributing to the origin and physical boundary of the model scalability. Experimentally, the generalization performance of the network is enhanced by increasing the portion of ballistic photons in detection. The mechanism understanding and practical guidance by our research are beneficial for developing DL methods for descattering with high adaptivity.