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 4 nm to 0.24 nm (a 94% decrease) and a reduction of the second order * Corresponding author. Tel.: +1 803 777 8236; fax: +1 803 777 0106. E-mail address: JAT@sc.edu (J.A. Tarbutton). 2 periodic error from 2.5 nm to 0.3 nm (an 88% decrease). The algorithm also reduces periodic errors for non-constant velocity motion overcoming limitations of existing methods.

Fiber-based two-wavelength heterodyne laser interferometer

“…The modelling and analysis of periodic errors have long been explored in the past decades for the heterodyne interferometry [29][30][31], and various algorithms have been developed for compensation [32][33][34][35][36]. In this paper, we demonstrate the correction of periodic errors by applying a least-square linear fit [37,38] to the measured displacement and the error terms array in Equation 23.…”

Underwater acoustic beacon signal extraction based on dislocation superimposed method

“…The test signal is decomposed into four layers using a db10 orthogonal wavelet basis. 21,22 The third layer detail signal is given in Figure 11(d). A short period of time, where the signal changes, may be missed when processing with the Fourier transform.…”

Mean Centered Kinetic—Spectrophotometric Data—Continuous Wavelet Transform for Simultaneous Determination of Dopamine and Uric Acid in Presence of Ascorbic Acid at Biological Samples

“…In addition to simultaneous quantitative determination of a multi-component mixtures [36,37], CWT has been used for periodic error compensation [38], electrochemical signals [39], spectrophotometric determination of drugs using high performance liquid chromatography [40], solvent effect on MRI probe and [41] sampling structures from molecular dynamics simulations [42]. This approach has the advantages of removing the Fourier transform restriction, increasing the signal-to-noise ratio in comparison to previous approaches, and reducing spectral interference.…”