Modifications of the sine-approximation method for primary vibration calibration by heterodyne interferometry

Abstract

The paper presents modifications of the sine-approximation method (SAM) specified in ISO 16063-11:1998, focusing on two of the various well-established versions: (i) SAM version using heterodyne quadrature signals (HQS) and (ii) SAM version using time interval analysis (TIA), and their implementation in the national medium-frequency vibration standard of NIM, China. For the HQS version, modified techniques and procedures have been introduced applicable to suppress disturbing effects from frequency instability of the carrier signal and from displacement drift. For the TIA version, a new algorithm has been developed for which the frequency demodulation is based on the estimation of time intervals between neighbouring peaks and valleys of the laser Doppler interferometer instead of successive positive or negative zero crossings. A spline approximation has been implemented allowing relatively slow sampling rates (e.g. 5 MS s −1 ) to be applied. The low requirements on hardware techniques allow primary vibration calibrations with high accuracy to be performed efficiently and cost effectively. Some results of investigations of the modified versions of SAM are demonstrated. The results achieved by these modified SAM versions are compared with each other and with PTB results measured within the complementary key comparison CCAUV.V-K1.1 piloted by PTB from 2006 to 2007.

Symmetric Differential Demodulation-Based Heterodyne Laser Interferometry Used for Wide Frequency-Band Vibration Calibration

“…The TLI uses a laser interference signal with high carrier frequency to measure the excitation displacement, which has gradually become the hotspot in the vibration calibration [16], [17]. Sun et al [18] proposed a TLI with the modified sine approximation method (SAM) to calibrate the sensitivity magnitude and phase, which is able to get the accuracy of 1% and 1°in the range of 10 Hz-10 kHz, respectively. Yang et al [19] investigated a TLI that is based on the bandpass sampling (BPS) theorem to efficiently measure the excitation displacement in the range from 5 Hz to 20 kHz, whose amplitude and phase standard deviations are superior to 0.1% and 0.1°.…”

“…The calibration performance of TLI depends on its excitation measurement accuracy, which is related to the acquisition and demodulation of the heterodyne laser interference signal [14]. Currently, the commonly used acquisition methods include the Nyquist sampling (NS) method, the BPS method, and the mixer and low-pass filter sampling (MLPFS) method [14], [18], [19]. The NS method is easy to accomplish the high-frequency vibration calibration with high accuracy, while its frequency is limited.…”

Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer

“…Note that we considered only one of the traditional, conic, least-squares fitting methods. Since they use diverse constraints on conic coefficients, they yield, in general, different ellipses [27,28].…”

A fast vibration-level adjustment method for low-frequency vibration calibration based on modified filtered-x least mean square algorithm

“…Actually, the primary drawback of SAM is the fact that the vibration-level measurement requires at least one period. Some other approaches like least square algorithm 9 and tracking filter method [10][11][12] can realize accurate amplitude estimation with fewer sampling points. Unfortunately, these approaches will increase the computational efforts significantly.…”