A method for measuring the nonlinearity of laser interferometer using optical frequency tuning technique is presented in this paper. The basic principle of this method is to make the fractional part of an interference fringe change by tuning the laser frequency and determining the nonlinearity of interferometer by comparing the fractional fringe change measured by the interferometer to that calculated from the laser frequency change. An experimental interferometric system with a wavelength tunable laser source is set up and the nonlinearity of the interferometer is measured. Since it does not require the precise displacement mechanism to produce the optical path difference change, this method is more convenient to use and may achieve a higher accuracy than the conventional measurement methods. The nonlinearity of the arbitrary interferometric phase can be measured by changing the laser frequency with this method. Experiments results have shown that the repeatability of nonlinearity measurement is less than 0.2 nm. This method can be applied to interferometry-based high precision dimensional measurements, such as coordinate measurement and displacement sensor calibration.

A novel four-parameter sine wave curve-fitting method for partial period and non-uniform sampling is presented. Based on the three-parameter sine wave curve-fitting method, the principle of this method is to turn the optimization of four parameters (amplitude, frequency, phase and offset) into the optimization of only one parameter (frequency). Compared to other curve-fitting methods, the characteristics of this method is that it does not need initial parameter estimation, and can be used to fitting partial period sinusoid, even with only 1/5 signal periods or less. It is shown that this method has wide convergence interval and excellent robustness. The validity and feasibility of this method have been proved by both the simulations and experiment. The four-parameter sine wave curve-fitting method can be applied to the parameter estimation of sinusoidal wave with non-uniform sampling series of partial period, especially it is very useful in the control of ultra lower frequency sine wave parameters.