Extended eigenvalue calibration method for Mueller matrix polarimetry with four photoelastic modulators

The Mueller matrix polarimeter with four photoelastic modulator (4-PEM MMP), known for its high-speed and high-precision measurement capabilities, holds great potential in material characterization and nanoscale measurements. We propose an extended eigenvalue calibration method (eECM) to the 4-PEM MMP by introducing two temporal basis vectors to project the continuously modulated light intensity into a time-independent projection matrix, which can then be acquired by a nonlinear regression method. The eECM enables complete calibration of system parameters of the 4-PEM MMP in a model-free manner without any approximation, including the parameters associated with each PEM and the alignment errors in the azimuths of all the polarization elements. Moreover, it is unnecessary to precisely adjust the orientations of the polarization elements, and it does not require precise reference sample information either. Consequently, the eECM allows the 4-PEM MMP to achieve accurate Mueller matrix measurement under not only the usual system configurations but also other unusual system configurations in a simple and unified approach. Simulation results have verified the effectiveness and advantages of the eECM.