Image reconstruction through the opaque medium has great significance in fields of biophotonics, optical imaging, mesoscopic physics, and optical communications. A transmission matrix (TM) can be used to characterize the linear input–output relationship of a fixed scattering medium based on the superposition principle. By measuring the TM of the scattering medium, the image reconstruction can be realized. Scattering medium is typically used as a linear operator in most previous research. In fact, there have been many nonlinear effects that provide superior performance in the field of biological imaging, such as two-photon excitation fluorescence (TPEF) microscopy, second-harmonic generation (SHG) microscopy, and coherent anti-Stokes Raman scattering (CARS) microscopy. Compared with conventional imaging techniques, nonlinear optical imaging has the advantages of deeper imaging depth (TPEF and SHG microscopy) and higher spatial resolution (CARS microscopy). Therefore, the corresponding nonlinear scattering optical imaging is also a fundamental problem in the field of imaging. However, in nonlinear scattering media, which can radiate nonlinear signals, the coupling of multiple scattering and nonlinear processes makes it difficult to characterize the nonlinear scattering processes. To our best knowledge, there is no report on the image reconstruction through nonlinear scattering medium.

Figure Process of reconstructing the original image by SH speckle. Different phase distribution of the image uploaded on FF beam will interact with the nonlinear scattering medium and generate a different SH speckle pattern. The original image and SH speckle patterns are fed into NSDN for joint training. The acquired SH speckle is fed into the learned NSDN to reconstruct the original image.

In this paper, we develop an image reconstruction technique that can restore the phase information of the fundamental frequency (FF) wave through the nonlinear scattering signal of the nonlinear scattering medium via DL method. We use part of the images and the corresponding nonlinear speckle patterns as the training set to train the nonlinear speckle decoder network (NSDN) and the others as the test set. The trained NSDN can be used to reconstruct the wavefront information of the FF wave through a nonlinear speckle pattern. Through different data sets and different diffuser experiments for training and analysis, it is found that the system we proposed here has great ability in nonlinear image reconstruction and robustness in different conditions.

We develop an image reconstruction method through a nonlinear signal of the scattering medium by using our NSDN. As far as we know, this is the first time to precisely reconstruct image information of FF from nonlinear speckles generated from a nonlinear scattering medium. Further, the proposed NSDN is able to restore the initial information through different sets of diffusers and reconstruct the image of a kind of completely unseen object category. Our approach promises highly stable, large-scale nonlinear information transport through a complex scattering medium. We expect that this technique can be applied to arbitrary image reconstruction process with the nonlinear presence and information encryption.

This work is published in“Shuo Yan, Yiwei Sun, Fengchao Ni, Zhanwei Liu, Haigang Liu, and, Xianfeng Chen, Image reconstruction through a nonlinear scattering medium via deep learning, Photonics Research, 12(9), 2047-2055 (2024)”。

Link：https://opg.optica.org/prj/fulltext.cfm?uri=prj-12-9-2047&id=558386