Enhanced nonlinear imaging through scattering media using transmission-matrix-based wave-front shaping

Despite the tremendous progress in wave front shaping for enhancing imaging penetration depths in scattering media, several factors, among which are significantly low signal-to-noise ratios at large depths, prevent feasibility for nonlinear imaging in biological tissues. Here, we propose an alternative to the traditional schemes that use optimization of a nonlinear signal. By exploiting the linear photons instead of nonlinearly generated ones, we show strong enhancements of nonlinear signals of several orders of magnitude, through thicknesses of a few transport mean free paths, which corresponds to millimeters in biological tissues. This is achieved by measuring the linear broadband transmission matrix (TM) of the scattering medium, using a spectral bandwidth comparable to the speckle spectral correlation width. We further highlight several advantages of the use of linear TM for prospective nonlinear imaging deep inside scattering media.