Optimal polarization modulation and calibration schemes

TL;DR

This paper extends the algebraic framework for polarization modulation efficiency to accommodate varying throughput and noise characteristics, enabling optimized calibration and instrument design in spectro-polarimetry.

Contribution

It introduces a generalized algebraic definition of polarization modulation and calibration efficiency, accounting for different optical paths and noise, facilitating optimization of polarimetric instruments.

Findings

Generalized efficiency model for spatial polarization modulation

Merit function for calibration sequence optimization

Enhanced modeling of instrument-specific polarization performance

Abstract

We review the algebraic definition of the efficiency of a polarization modulation scheme, which is commonly adopted for solar and stellar spectro-polarimetry applications, and generalize it to allow distinct states of the modulation cycle to have arbitrary throughput and different photon-noise statistics for each state. Such a generalization becomes necessary to model and optimize the polarimetric efficiency of instruments implementing spatial polarization modulation schemes, where different optical paths are assigned to different polarization analysis states, which may be characterized by different throughput values. The proposed algebraic extension also proves essential for introducing a workable concept of the efficiency of a polarization calibration scheme, which can then be used to create a merit function for the optimization of calibration sequences, which take into account the specific characteristics of the polarimetric instrument and of its calibration optics.