Sensitivity Analysis of Periodic Errors in Heterodyne Interferometry

Résumé du livre

ABSTRACT: Non-linearities in displacement measurement when using heterodyne interferometry arise due to frequency mixing in the interferometer. These non-linearities are typically characterized as first and second order periodic errors which cause a cyclical (non-cumulative) variation in the reported displacement about the true value. First order periodic error has a spatial frequency of one cycle per displacement fringe, while second order periodic error has a frequency of two cycles per fringe. An analytical model for these non-linearities was suggested by Cosijns et al. which takes into account rotational misalignments of the polarizing beam splitter, mixing polarizer, nonorthogonality of the two laser frequencies, ellipticity in the polarizations of the two independent laser beams, and different transmission coefficients in the beam splitter. This study implements the Cosijns et al. model in order to identify the sensitivities of the periodic errors with respect to the input parameters. A local sensitivity analysis is conducted to examine the sensitivities of the first and second order periodic errors with respect to each input parameter about the nominal input values. Also, a variance-based approach is used to study the global sensitivities of the periodic errors by calculating the Sobol' sensitivity indices using a Monte Carlo approach. A Latin hypercube sampling.