Kalman filtering approach to polarimetric calibration of an optical imager

Abstract

The Mueller matrix of an optical instrument describes the polarimetric effects the instrument will have on the optical observations it makes in terms of the Stokes parameters. The calibration of the instrument relies on a robust characterization of the elements of this matrix. In this paper, we present what we believe is a new technique that uses Kalman filtering to characterize the Mueller matrices of optical instrumentation based on a set of lab calibration measurements. Kalman filtering is a ubiquitous statistical optimizer that works by comparing measurements and a model of the observed physical system to minimize error. Typically, this technique is applied as a filter to refine a set of observations, but it can also be used to retrieve the properties of the physical system that are not directly measured. We demonstrate the use of the Kalman approach to polarimetric calibration through simulation of measurements, where the polarimetric behavior of optical elements is represented by the Mueller matrices of individual components. The elements of these Mueller matrices are then retrieved with the uncertainty estimates using the Kalman filter approach. The results of this simulation are compared to the standard polarimetric calibration technique as a benchmark, demonstrating the superior performance of the Kalman approach. Then, both the Kalman technique and the standard technique are applied to real measurements from a multispectral polarimetric imager used for atmospheric aerosol remote sensing.