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In biological microscopy, light scattering represents the main limitation toimage at depth. Recently, a set of wavefront shaping techniques has beendeveloped in order to manipulate coherent light in strongly disorderedmaterials. The Transmission Matrix approach has shown its capability to inversethe effect of scattering and efficiently focus light. In practice, the matrixis usually measured using an invasive detector or low-resolution acoustic guidestars. Here, we introduce a non-invasive and all-optical strategy based onlinear fluorescence to reconstruct the transmission matrices, to and from afluorescent object placed inside a scattering medium. It consists in demixingthe incoherent patterns emitted by the object using low-rank factorizations andphase retrieval algorithms. We experimentally demonstrate the efficiency ofthis method through robust and selective focusing. Additionally, from the samemeasurements, it is possible to exploit memory effect correlations to image andreconstruct extended objects. This approach opens up a new route towardsimaging in scattering media with linear or non-linear contrast mechanisms.

Non-invasive focusing and imaging in scattering media with a fluorescence-based transmission matrix