Error analysis and calibration improvement of the imaging section in a Mueller matrix microscope

Abstract

Currently, there are various calibration methods available to reduce the errors caused by the polarizing section of a dual-rotating-retarder polarimeter. Although these methods have high measurement accuracy, their robustness must be improved and the influence of the imaging section needs be discussed when they are applied in Mueller matrix microscopes. In this paper, a method of error source analysis and element calibration for the Mueller matrix microscope is proposed by using error transform coefficient matrices to account for the polarizing effect of the imaging section. Using Taylor expansion, an approximate linear relationship is established between the sources of errors and the Mueller matrix elements of the measured sample. From this relationship, error magnification coefficient matrices are calculated to determine the specific parameter errors in both the polarizing and imaging sections. Furthermore, elements in the fourth row or column of the error magnification coefficient matrix are especially important for the imaging section. The measurement and simulation results for an air sample and a quarter-wave plate sample as the standard samples, as well as a Daphnia organism sample with complex internal structure, are investigated and discussed. Furthermore, the comparison results reveal the effect of the imaging section on the birefringence characteristics of the Mueller matrix. With the proposed method, the maximum error can be reduced to be less than 0.01 for all the matrix elements and for the amplitude parameter of birefringence, even when the two system parameters a2 and a3 of the rotating mechanical part deviate from the default.