Nonlinearity analysis in homodyne multi-pass interferometer with Jones matrix and correction with Fourier harmonic components method

The nonlinearity of the interferometer is an essential error in nanoscale measurements influenced by anisotropic gain and nonorthogonality of imperfect polarization components. In this paper, polarization error and the corresponding nonlinearity correction method are studied. The paper is divided into two parts, in the first part, main research focuses on the polarization mixing effect of multi-pass interferometer, besides this, polarization beam splitter and retardation plate are also analyzed, then a final synthetic evaluation is obtained through Jones matrix. In the second part, a harmonic separation method of interferometer signals is researched, the method first decomposes signals into Fourier series, then uses least square fitting to estimate coefficients of main terms of series. In the correction process, the primary phase angle is obtained through coefficients of base series and trigonometric formulas; the finer phase angle is obtained through coefficients of harmonics and Taylor expansion. Experimental results demonstrate that the nonlinearity of homodyne interferometer is significantly reduced in nanometer measurements.