Kalman Filter Estimation for Focal Plane Wavefront Correction

TL;DR

This paper introduces a Kalman filter-based estimator for focal plane wavefront correction in space telescopes, significantly reducing the number of images needed for electric field estimation and improving correction efficiency.

Contribution

It presents a novel Kalman filter approach combined with an optimal probe shape selection method to enhance wavefront correction in coronagraphs.

Findings

Reduces the number of exposures needed for electric field estimation.

Demonstrates improved estimate accuracy and covariance management.

Introduces a novel probe shape generation method using stroke minimization.

Abstract

Space-based coronagraphs for future earth-like planet detection will require focal plane wavefront control techniques to achieve the necessary contrast levels. These correction algorithms are iterative and the control methods require an estimate of the electric field at the science camera, which requires nearly all of the images taken for the correction. We demonstrate a Kalman filter estimator that uses prior knowledge to create the estimate of the electric field, dramatically reducing the number of exposures required to estimate the image plane electric field. In addition to a significant reduction in exposures, we discuss the relative merit of this algorithm to other estimation schemes, particularly in regard to estimate error and covariance. As part of the reduction in exposures we also discuss a novel approach to generating the diversity required for estimating the field in the image plane. This uses the stroke minimization control algorithm to choose the probe shapes on the deformable mirrors, adding a degree of optimality to the problem and once again reducing the total number of exposures required for correction. Choosing probe shapes has been largely unexplored up to this point and is critical to producing a well posed set of measurements for the estimate. Ultimately the filter will lead to an adaptive algorithm which can estimate physical parameters in the laboratory and optimize estimation.