Considerations for calibration of Stokes polarimeters

We introduce a framework for evaluating the performance of polarimetric calibration schemes for Stokes polarimeters. Extending the modulation-efficiency formalism of del Toro Iniesta and Collados [Appl. Opt.39, 1637 (2000)], we define an analogous calibration efficiency that relates uncertainties in measurements to errors in inferred modulation matrices. This framework enables direct comparison of calibration strategies and provides a metric for optimizing calibration sequences for a desired accuracy and execution time. We analyze the behavior of typical calibration optics, including linear and elliptical retarders, depolarizing elements, and imperfect polarizers, and identify the conditions under which degeneracies arise in the calibration model. Our results show that all calibration parameters except for global rotation gauges and intensity scaling remain recoverable when the calibration polarizer can be assumed to be perfect. Continuous degeneracies appear if the calibration polarizer deviates from ideal behavior. We discuss how increasing realism expands the dimensionality of the calibration model and argue the need for good initial parameter estimates to ensure convergence of fits. The formalism developed here supports a systems-engineering approach to polarimetry, enabling error budgeting, design optimization, and assessment of calibration efficiency for current and future polarimetric instrumentation.