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 a 2 and a 3 of the rotating mechanical part deviate from the default.
Highlights
It can be seen from Equation (9) that, assuming an optimized combination of controllable small errors when measuring under stable system conditions, the errors of the measurement results caused by different error sources are independent of each other, i.e., εx j is independent of εxi (j, i); we can separately calibrate the polarizing section and imaging section
We reviewed the configuration for the Mueller microscope, modeled it mathematically, and presented an intuitive and quantitative scheme for error analysis and calibration
Using the Taylor expansion together with an optimized combination of controllable error sources, we established a relationship between the source of the errors and the calculated Mueller matrix elements
Summary
The technique of polarized light imaging can provide microstructural information on samples, and the Mueller matrix offers a comprehensive description of the polarization properties of samples.when the polarized light imaging technique is combined with the Mueller matrix measurement technique, microstructural information can be obtained with great effectiveness [1].A Mueller matrix microscope is usually designed by adding both the polarization state generator and analyzer (polarizing section) to a microscope (imaging section) and has the ability to measure the Mueller matrix of samples via imaging, which enhances the contrast ratio of the anisotropic structures and has been reported to be extremely helpful in biomedical diagnosis, especially for cancer detection [2,3].The elements of the Mueller matrix contain all the polarization information necessary for clear and physically meaningful characterization of the measured samples; these elements, either singly or in combination, include diattenuation, retardation, and depolarization. The technique of polarized light imaging can provide microstructural information on samples, and the Mueller matrix offers a comprehensive description of the polarization properties of samples. When the polarized light imaging technique is combined with the Mueller matrix measurement technique, microstructural information can be obtained with great effectiveness [1]. The elements of the Mueller matrix contain all the polarization information necessary for clear and physically meaningful characterization of the measured samples; these elements, either singly or in combination, include diattenuation, retardation, and depolarization. Mueller matrix polar decomposition [4], Mueller matrix transformation [5], and other similar techniques based on transforming polarization parameters are useful and proven tools in biomedicine [6,7], material testing [8], and other fields.
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