Nonlinearity in measurements of length by optical interferometry

The periodical nonlinearity of an interferometer usually ranges from sub-nanometre scale to several nanometres. This nonlinearity limits the usefulness of an interferometer to the sub-nanometre level of accuracy in length measurements. A theoretical analysis of length measurement nonlinearities both in heterodyne and in one-frequency interferometers is reported in this paper. The nonlinearity of a heterodyne interferometer arises mainly from the cross talk between different frequencies of two linearly polarized beams. Both one-cycle and two-cycles nonlinearities were observed as the difference in optical path length changed from 0 to 2 pi. Unlike the heterodyne interferometer, the nonlinearity of the one-frequency interferometer arises mainly from the cross talk between two linearly orthogonal beams of the same frequency and only two cycles of periodical nonlinearity were observed as the difference in optical path length changed from 0 to 2 pi.