In biological microscopy, light scattering represents the main limitation to image at depth. Recently, a set of wavefront shaping techniques has been developed in order to manipulate coherent light in strongly disordered materials. The Transmission Matrix approach has shown its capability to inverse the effect of scattering and efficiently focus light. In practice, the matrix is usually measured using an invasive detector or low-resolution acoustic guide stars. Here, we introduce a non-invasive and all-optical strategy based on linear fluorescence to reconstruct the transmission matrices, to and from a fluorescent object placed inside a scattering medium. It consists in demixing the incoherent patterns emitted by the object using low-rank factorizations and phase retrieval algorithms. We experimentally demonstrate the efficiency of this method through robust and selective focusing. Additionally, from the same measurements, it is possible to exploit memory effect correlations to image and reconstruct extended objects. This approach opens up a new route towards imaging in scattering media with linear or non-linear contrast mechanisms.

在生物显微镜中，光散射代表了深度成像的主要限制。近来，已经开发出一套波前成形技术，以便操纵强烈无序的材料中的相干光。传输矩阵方法已显示出其能够逆转散射效应并有效聚焦光的能力。实际上，通常使用侵入式探测器或低分辨率声星来测量矩阵。在这里，我们介绍了一种基于线性荧光的非侵入性全光学策略，用于重构往返于散射介质内部的荧光对象的传输矩阵。它包括使用低秩分解和相位检索算法对对象发出的非相干模式进行混合。我们通过鲁棒性和选择性聚焦实验证明了这种方法的效率。此外，通过相同的测量，可以利用记忆效应相关性对图像进行成像并重建扩展对象。这种方法为利用线性或非线性对比机制在散射介质中成像开辟了一条新途径。