Rapid fluorescent wavefront shaping using incoherent power iterations

Wavefront shaping correction aims to image fluorescent particles deep inside scattering tissue. This requires determining a correction mask to be placed in both excitation and emission paths. Standard optimization-based approaches for finding this correction are prohibitively slow. To reduce 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 apply to fully-coherent imaging systems. We extend such techniques to the incoherent case for the first time. The fact that light emitted from different sources sums incoherently makes linear transmission operators inapplicable. We show that, surprisingly, the non-linearity due to incoherent summation results in an order-of-magnitude acceleration in the convergence of the phase conjugation iteration.