Scattering of light limits the depth at which a focus can be formed in turbid media. However, light can be focused through and inside thick and strongly scattering samples by spatially modulating the incident light using wavefront shaping techniques . Wavefront shaping requires feedback from a localized reporter, for example, a point detector or a fluorescent ‘guide star’ inside the sample.
In some cases, a localized reporter is not available as a source of feedback. For instance in multiphoton fluorescence microscopy, the only available feedback signal is the total fluorescent signal coming from inside the sample. Even with this non-localized form of feedback, Katz et al.  were capable of forming a single diffraction-limited focus behind a strongly scattering layer. However, the statistics behind this nonlinear optimization procedure are poorly understood, and the location at which this blind focusing method will form a focus could not be predicted or controlled.
We developed an analytical model to predict the outcome of the blind focusing method. Our model allows us to determine under which conditions the optimization algorithm converges to a single diffraction-limited focus, and how the location of this optimized focus can be controlled. Furthermore, we can find the parameters that determine the convergence rate of this blind focusing procedure. The model is validated with experiments through strongly scattering samples, and an excellent agreement was found.
 I.M. Vellekoop, Optics Express 23, 1-18 (2015)
 O. Katz, E. Small, Y. Guan, Y. Silberberg, Optica 1, 170-174 (2014)
Gerwin Osnabrugge, Lyubov V. Amitonova, and Ivo M. Vellekoop, "Blind focusing through strongly scattering samples using nonlinear feedback (Conference Presentation)," Proc. SPIE 10886, Adaptive Optics and Wavefront Control for Biological Systems V, 108860T (Presented at SPIE BiOS: February 04, 2019; Published: 4 March 2019); https://doi.org/10.1117/12.2510507.6008595892001.
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