Error analysis and analytical calibration of the dual vortex retarder Mueller matrix ellipsometry

The dual vortex retarder Mueller matrix ellipsometry (DVRMME) is a spatially modulated ellipsometry that obtains the Mueller matrix elements by analyzing a single-shot intensity image. While it offers the advantage of rapid measurement speed, some inherent non-negligible errors limit the measurement accuracy. We present a comprehensive framework for error analysis and calibration, and a refined error model is developed to quantify perturbations in Mueller matrix elements. This model incorporates six parameters: the azimuthal angles of the polarizer and analyzer, the fast-axis orientations, and the retardance deviations of two vortex retarders. First-order Jacobian matrix analysis is employed to evaluate these perturbations. The analysis identifies errors caused by inaccuracy of the azimuthal arrangement and retardance deviation of the optical components via a two-zone averaging measurement strategy. An analytical calibration method based on Fourier decomposition is proposed, which enables six parameters of the error model to be calibrated using a single-shot air medium image. Experimental validation with linear polarizers and quarter-wave plates demonstrates a 25.1-32.7% reduction of RMS error for normalized Mueller matrix elements. Our framework enhances measurement accuracy while maintaining the system's intrinsic advantage of millisecond-level single-shot operation, advancing spatially modulated ellipsometry for precision-critical applications.