The straight-through calibration approach is used in ellipsometry measurement to calibrate system model parameters for accurate sample measurement. The advanced parameter model of dual-rotating compensator Mueller matrix ellipsometer (DRC-MME) is complex, with several large parameters. Some advanced parameters are cascaded and coupled together. The independent relationship between parameters in the experiment must be studied to ensure the accuracy of the results of the calibration; thus, the degree of freedom of the DRC-MME through calibration experiments was theoretically analyzed in this study using singular value decomposition, Pauli matrix, and other tools. The “useless” parameters in data fitting methods are elucidated, and a simulation experiment supports the conclusion. Finally, the experimental platform is built, the straight-through calibration experiment is conducted, and the advanced parameter calibration results are obtained which are consistent with the actual physical significance. The thickness of the silicon dioxide film on the silicon substrate was measured using the calibrated advanced parameter model. The measurement result differs from the nominal value by 1.4 nm, and the repeated measurement accuracy is 10.2 pm. In this study, the proposed degree of freedom of the system analysis approach is applied to ellipsometer and provides an analysis idea for other multiparameter optimization processes.