Demodulation and uncertainty evaluation of quadrature interferometer signals when the errors are autoregressive

Quadrature homodyne interferometers are frequently used in dimensional metrology. Their measurement signals exhibit offsets, unequal amplitudes and phase difference. Frequently, there exists a significant component of the measurement noise common to both (Sine and Cosine) quadrature signals, such that the noise of quadrature signals is correlated. Presented is a method for estimation the unknown correlation coefficient from the measured data, provided that the Sine and Cosine signal noise follow particular autoregressive process (here we consider the AR(1) process). The estimate of the correlation coefficient and of the parameters of the noise autoregressive process are utilized in the iterative algorithm for demodulation and evaluation of the amplitude noise related uncertainty contribution of correlated quadrature interferometer signals, originally proposed by Koning, Wimmer and Witkovsky in [1] for uncorrelated interferometer signals.