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A linear polarization scanning method based on the Mueller matrix formulation and Stokes polarimetry is proposed for extracting the effective ellipsometric parameters of isotropic and anisotropic thin films. The effective ellipsometric parameters (Ψp'p', Ψp's', Ψs'p', Δp'p', Δp's', and Δs'p') describe the amplitude ratio and phase difference of two orthogonal waves in any arbitrary coordinate system with a scanning angle θ relative to the X-Y coordinate frame. In the proposed approach, the effective ellipsometric parameters are determined from the Stokes parameters corresponding to one right-hand circular polarization light and four linear polarization lights with orientations in the range of θ = 0 ~ 180°. The validity of the proposed approach is confirmed by comparing the experimental results for the effective ellipsometric parameters with the inversely extracted results obtained using a genetic algorithm (GA). In traditional ellipsometry methods, it is necessary to scan the incident angle of an input light or the yaw angle of the sample using a mechanical stage. By contrast, in the method proposed in this study, it is necessary only to rotate a single polarizer for scanning a linear polarization light from 0 ~ 1801° and this function can be achieved by modulating an EO modulator. Thus, the proposed method not only minimizes the risk of vibration and positioning errors, but also can be easily applied to the production line. It is noted that if physical parameters of a tested sample cannot be completely obtained by only using the polarization scanning way, the other traditional scanning ways on incident angle, sampl- , and/or spectra also can be integrated for inverse extraction.