Fig. 2. Experimental Results: TM reconstruction and focusing on beads through a ground glass diffuser.

From the experimentally measured I_out, the field-TM T is reconstructed using NMF and a phase retrieval algorithm. To prove the success of the reconstruction, we investigate in the ability of T to focus excitation light. A rank r = 30 is set as input parameter for the NMF. a Examples of focus spots obtained after phase conjugation of T. Since the rank is overestimated (r > N), the NMF may generate spurious eigen-patterns and reconstruction thus partially fails. Corresponding points do not generate a focus, like $I_{\mathrm{focus}}^{\left(2\right)}$. b This validation step can be performed non-invasively by looking at the spatial variance of the epi-detected fluorescent patterns. c Sum of all the r = 30 intensity images recorded on the control camera. It shows that our technique is able to focus on most targets. d Fluorescence image of the object obtained without the scattering medium for control only. Here P = 15,360 − Acq. speed = 50 Hz − N_SLM = 1024.