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When viewed under coherent illumination, scattering materials such as tissue exhibit highly varying speckle patterns. Despite their noise-like appearance, the temporal and spatial variations of these speckles, resulting from internal tissue dynamics and/or external perturbation of the illumination, carry strong statistical information that is highly valuable for tissue analysis. The full practical applicability of these statistics is still hindered by the difficulty of simulating the speckles and their statistics. This paper proposes an efficient Monte Carlo framework that can efficiently sample physically correct speckles and estimate their covariances. While Monte Carlo algorithms were originally derived for incoherent illumination, our approach simulates complex-valued speckle fields. We compare the statistics of our speckle fields against those produced by an exact numerical wave solver and show a precise agreement, while our simulator is a few orders of magnitude faster and scales to much larger scenes. We also show that the simulator predictions accurately align with existing analytical models and simulation strategies, which currently address various partial settings of the general problem. 

We exploit memory effect correlations in speckles for the imaging of incoherent fluorescent sources behind scattering tissue. These correlations are often weak when imaging thick scattering tissues and complex illumination patterns, both of which greatly limit the practicality of associated techniques. In this work, we introduce a spatial light modulator between the tissue sample and the imaging sensor and capture multiple modulations of the speckle pattern. We show that by correctly designing the modulation patterns and the associated reconstruction algorithm, statistical correlations in the measurements can be greatly enhanced. We exploit this to demonstrate the reconstruction of mega-pixel sized fluorescent patterns behind the scattering tissue. 

We extend iterative phase conjugation algorithms, previously derived for coherent illumination. We show they can be used to focus on incoherent fluorescent sources, and the incoherent emission largely expands penetration depth and convergence speed. 

Wavefront shaping correction makes it possible to image fluorescent particles deep inside scattering tissue. This requires determining a correction mask to be placed in both the excitation and emission paths. Standard approaches select correction masks by optimizing various image metrics, a process that requires capturing a prohibitively large number of images. To reduce the acquisition cost, iterative phase conjugation techniques use the observation that the desired correction mask is an eigenvector of the tissue transmission operator. They then determine this eigenvector via optical implementations of the power iteration method, which require capturing orders of magnitude fewer images. Existing iterative phase conjugation techniques assume a linear model for the transmission of light through tissue, and thus only apply to fully coherent imaging systems. We extend such techniques to the incoherent case. The fact that light emitted from different sources sums incoherently violates the linear model and makes linear transmission operators inapplicable. We show that, surprisingly, the nonlinearity due to incoherent summation results in an order-of-magnitude acceleration in the convergence of the phase conjugation iteration.