Correction of periodic displacement non-linearities by two-wavelength interferometry

Non-linearities in interferometric displacement measurements commonly affect both homodyne and heterodyne optical interferometers. Unwanted back reflections (ghost reflections) or polarisation leakage introduce non-linearity terms at harmonics of the illuminating wavelength that cannot be fully corrected for with standard non-linearity correction techniques. A two-wavelength interferometric approach, operating at 632.8 and 785 nm, is presented here that is capable of correcting such non-linearities. Non-linearities are separated from the difference between two displacement measurements made at differing wavelengths with a Fourier approach. Compared to a standard Heydemann ellipse fitting correction, the proposed approach reduces estimated residual non-linearities from 84 to 11 pm in the case of a linear displacement profile. In particular this approach is applicable to the correction of higher order non-linearities that are caused by multiple reflections, and that are therefore very sensitive to alignment conditions.