Rethinking conditioning in polarimetry: a new framework beyond $\ell^2$-based metrics

Abstract

A standard procedure to achieve accurate, precise, and fast polarization measurement is to choose analyzing and generating polarization states that yield an $\ell^2$-condition number optimized instrument matrix. This strategy works well for rotating-waveplate systems, where the accessible polarization states trace a curve on the Poincar\'e sphere and the corresponding optimization problem is generally well posed. However, it becomes degenerate for liquid-crystal-based systems, which can generate arbitrary polarization states, and whose additional degrees of freedom allow the optimization of metrics beyond the $\ell^2$-condition number. Leveraging this unique advantage of liquid-crystal polarimeters, we introduce additional performance measures derived from alternative norms and error distributions computed via Monte Carlo simulations to inform the design of measurement schemes. We then experimentally demonstrate their effectiveness in suppressing errors, paving the way for more robust and efficient polarization measurements.