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Stability and Resolution of a Conventional Displacement Measuring Heterodyne Interferometer Using a Single Phase-Locked Loop

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Abstract

Background

Heterodyne interferometry offers an exciting solution for achieving sub-nanometer or ten-picometer-order mechanical displacement measurements because of its high resolution and noise immunity.

Objective

In this paper, we investigate the stability and resolution of a conventional displacement-measuring heterodyne interferometer using a single phase-locked loop (PLL) at a sub-nanometer or 10-pm level over an µm-scale measurement regime in normal air.

Methods

In the experiment, we perform the beat frequency reduction of the heterodyne signals to take advantage of a low-cost frequency sampling data acquisition (DAQ). The primary calculations of the single phase-locked loop (PLL) algorithm are implemented in a point-by-point (pt-pt) construction, providing pt–pt low-pass filters (LPFs) with high noise suppression. The output is appended into an array of N points and averaged to reduce the noise of the outgoing signal again. Using the PLL phase meter with the beat frequency reduction can ensure a mdeg-order phase measurement with Allan deviation stability of ~ 10 µdeg over 1000 s. We consider a combination of the miniaturization of optical paths in air and the PLL phase meter integrated with low-cost devices while ensuring mdeg-order measurement stability to achieve the interferometer's pm-order measurement resolution and stability.

Results

The measurement results show that the interferometer can achieve a resolution of 26 pm over a 5 μm-range mechanical displacement measurement. The Allan deviation stability of the interferometer reaches ~ 10 pm over a sampling time of 30 s, and the displacement noise floor is 10 pm/Hz1/2 above 1 Hz.

Conclusions

The new signal-processing PLL phase meter provides higher noise reduction than the old one presented in our previous work. With low cost but high resolution and stability, the PLL phase meter is incredibly suitable for pm-order displacement-measuring heterodyne interferometry. Combining a well-reduced PLL phase meter and a conventional heterodyne interferometer with a stable, isolated configuration and the minimization of optical paths in the air can give the measurement system a high resolution and stability. The measurement system can have a more significantly improved resolution of a few tens of pm than interferometers presented in previous publications and stability comparable to the modified heterodyne interferometers shown in earlier works over the sampling time of 30 s (possibly up to 100 s). A conventional heterodyne interferometer with a single PLL is expected to perform large-range displacement measurements with resolution at ten picometer levels in air.

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Funding

This research is funded by Hanoi University of Science and Technology (HUST) under project number T2022-TT-003.

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Authors and Affiliations

  1. School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi, 100000, Vietnam

    Nguyen Thanh Dong & Dinh Gia Ninh

  2. School of Engineering and Built Environment, Griffith University, Gold Coast, QLD, 4215, Australia

    Dinh Gia Ninh

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  1. Nguyen Thanh Dong
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  2. Dinh Gia Ninh
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Correspondence to Dinh Gia Ninh.

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Nguyen, T.D., Dinh, G.N. Stability and Resolution of a Conventional Displacement Measuring Heterodyne Interferometer Using a Single Phase-Locked Loop. Exp Mech 63, 1015–1032 (2023). https://doi.org/10.1007/s11340-023-00970-x

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