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.

Figure 1

Wave front shaping experiments for nonlinear microscopy. (a) Simplified experimental layout. The optical wave front is shaped by an SLM and focused inside the scattering medium. The speckle generated outside the scattering medium excites the nonlinear sources (nano-KTP) placed at a plane further imaged on different detectors (emCCD, CMOS, PMT). (b) Methodology used for refocusing using the Hadamard basis. The wave front phase is swept in respect to a reference field (the unmodified periphery outside a Hadamard base), under broadband excitation. At the detectors (a pixel on the emCCD or on the CMOS), a sinusoidal modulation of the intensity is observed, from which each individual phase is stored (per base). After scanning the basis set, the optimal wave front is used for either enhancing the nonlinear signal (emCCD) or linearly refocusing (CMOS) with the nonlinear signal detected in parallel (PMT).

Figure 2

Nonlinear signal enhancement based on a nonlinear feedback of a single 150-nm-diam nano-KTP crystal through a scattering medium (diffuser). (a) SHG wide field images, taken with the emCCD, before (top) and after WS (bottom). The nonoptimized image is an average over nonoptimal wave fronts, whereas the optimized image is a single frame. Scale bar: 1.6 $\mu \mathrm{m}$. (b) SHG enhancement of a single particle versus the number of independently controlled SLM segments (blue markers, dashed line). The red box refers to the point depicted in (a). The continuous green line is a quadratic dependence of the nonlinear enhancement with respect to linear enhancements estimated after Ref. [9].

Figure 3

Nonlinear signal enhancement based on a linear feedback through a scattering medium (diffuser). (a) After acquisition of the linear TM, wave fronts are tailored to refocus the beam at desired positions through the scattering medium. The optimal wave fronts obtained for two different refocus positions (right) are shown (left). The SHG image is formed by a raster scanning of the refocus positions obtained from the linear-feedback-based TM, and acquisition of the SHG signal simultaneously. (b) Comparison between a bright field image (left) and the obtained corresponding SHG image (right). Number of controlled SLM segments: $2^{12}$. Scale bar: 0.9 $\mu \mathrm{m}$.

Figure 4

Linear refocusing and nonlinear efficiencies obtained after linear feedback in two different scattering media, diffuser and $20-\mu \mathrm{m}-\mathrm{thick}{\mathrm{TiO}}_2$ film. (a) Linear enhancement obtained as a function of the numbers of SLM segments, ${\mathrm{N}}_{\text{SLM}}$. (b) SHG signal dependence on the linear enhancement.

Figure 5

SHG imaging of rat tail tendon collagen. Scattering medium: diffuser. Number of controlled SLM segments: $2^{10}$. Scale bar: 2.3 $\mu \mathrm{m}$.

Figure 6

(a) Relative intensity of the refocus in the field of view presented in Fig. 5. This image is a normalization image to correct for a nonuniform refocus in the field of view. (b) Because of the strong SHG background level arising from a nonsparse sample, normalization of the raw SHG signal by the squared normalization image leads to a noisier image.