State estimation of fast-rate systems using slow-rate image sensors

This paper presents algorithms for state estimation of adaptive optics (AO) systems with fast-rate actuators and slow-rate image sensors. Typically, the information obtained from these slow-rate image sensors is the time-averaged output measurement during the exposure time. The additional information available in the image measurement (in the form of an intensity distribution) is discarded. In order to fully extract information from these blurry measurements, the image sensor is modeled as an integrative intensity sensor. The integrative intensity sensor is a transform from temporal outputs to pixel-domain measurements. Thus, the state estimation problem for the AO system is recast into a multi-rate estimation problem from a non-linear output measurement. Based on this formulation, we propose and compare estimation algorithms that exploit the unique properties of the non-linear integrative sensor model. Experimental results on a fast-rate beam steering mirror and a slow-rate image sensor verify that using the integrative sensor model and exploiting its structure for state estimation can result in lower prediction error.