Optimization of system parameters for a complete multispectral polarimeter

We optimize a general class of complete multispectral polarimeters with respect to signal-to-noise ratio, stability against alignment errors, and the minimization of errors regarding a given set of polarization states. The class of polarimeters that are dealt with consists of at least four polarization optics each with a multispectral detector. A polarization optic is made of an azimuthal oriented wave plate and a polarizing filter. A general, but not unique, analytic solution that minimizes signal-to-noise ratio is introduced for a polarimeter that incorporates four simultaneous measurements with four independent optics. The optics consist of four sufficient wave plates, where at least one is a quarter-wave plate. The solution is stable with respect to the retardance of the quarter-wave plate; therefore, it can be applied to real-world cases where the retardance deviates from λ/4. The solution is a set of seven rotational parameters that depends on the given retardances of the wave plates. It can be applied to a broad range of real world cases. A numerical method for the optimization of arbitrary polarimeters of the type discussed is also presented and applied for two cases. First, the class of polarimeters that were analytically dealt with are further optimized with respect to stability and error performance with respect to linear polarized states. Then a multispectral case for a polarimeter that consists of four optics with real achromatic wave plates is presented. This case was used as the theoretical background for the development of the Airborne Multi-Spectral Sunphoto- and Polarimeter (AMSSP), which is an instrument for the German research aircraft HALO.