Optimizing the metric in sensorless adaptive optical microscopy with fluorescence fluctuations

Adaptive optics (AO) strategies using optimization-based, sensorless approaches are widely used, especially for microscopy applications. To converge rapidly to the best correction, such approaches require that a quality metric and a set of modes be chosen optimally. Fluorescence fluctuations microscopy, a family of methods that provides quantitative measurements of molecular concentration and mobility in living specimen, is in particular need of adaptive optics, since its results can be strongly biased by optical aberrations. We examined two possible metrics for sensorless AO, measured in a solution of fluorophores diffusing in 3D: the fluorescence count rate and the molecular brightness (or number of photons detected per molecule in the observation volume). We studied their respective measurement noise and sensitivity to aberrations. Then, AO correction accuracy was experimentally assessed by measuring the residual aberration after correcting a known wavefront. We proposed a theoretical framework to predict the correction accuracy, knowing the metric measurement noise and sensitivity. In the small aberration range, the brightness allows more accurate corrections when fluorophores are few but bright, whereas the count rate performs better in more concentrated solutions. When correcting large aberrations, the count rate is expected to be a more reliable metric.