Application of the continuous wavelet transform in periodic error compensation

Abstract

This paper introduces a new discrete time continuous wavelet transform (DTCWT)-based algorithm, which can be implemented in real time to quantify and compensate periodic error for constant and non-constant velocity motion in heterodyne displacement measuring interferometry. It identifies the periodic error by measuring the phase and amplitude information at different orders (the periodic error is modeled as a summation of pure sine signals), reconstructs the periodic error by combining the magnitudes for all orders, and compensates the periodic error by subtracting the reconstructed error from the displacement signal measured by the interferometer. The algorithm is validated by comparing the compensated results with a traditional frequency domain approach for constant velocity motion. The algorithm demonstrates successful reduction of the first order periodic error amplitude from 4nm to 0.24nm (a 94% decrease) and a reduction of the second order periodic error from 2.5nm to 0.3nm (an 88% decrease). The algorithm also reduces periodic errors for non-constant velocity motion overcoming limitations of existing methods.