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Background <p>High-resolution ultrasonic displacement and vibration measurements are crucial in precision machining, advanced manufacturing, and materials characterization. However, achieving both high sensitivity and high acquisition speed typically requires expensive hardware, such as high-speed analog-to-digital converters (ADCs), field-programmable gate array (FPGA) platforms, or commercial lock-in amplifiers, which constrain flexibility and cost-effectiveness.</p> Objective <p>This study aims to develop and validate a low-cost, high-performance phase meter for heterodyne interferometric ultrasonic-vibration measurements, using low-cost software-defined radio (SDR) hardware and open-source software.</p> Methods <p>A &lt; $50 RTL-SDR-based phase meter was designed using flexible beat-frequency up and down conversion to acquire heterodyne signals spanning from kilohertz to hundreds of megahertz. Digital quadrature demodulation, multi-stage filtering, and a computationally efficient quadri-correlator algorithm were implemented in GNU Radio to achieve unwrap-free and real-time phase extraction. System performance was evaluated through simulations and ultrasonic-vibration experiments using a double-path heterodyne interferometer and was directly benchmarked against a commercial lock-in amplifier.</p> Results <p>Simulations showed a phase resolution of ± 0.01° and stability of ± 0.06° at 20&#xa0;kHz. This corresponds to sensitivity levels in the nanometer and sub-nanometer range. Experiments confirmed that the SDR-based system can reliably measure 20&#xa0;kHz ultrasonic vibrations with peak-to-peak amplitudes of less than 500&#xa0;nm. Furthermore, despite the limitations of an 8-bit ADC, the SDR achieved a signal-to-noise ratio (SNR) of 130&#xa0;dB for MHz-level phase-alternating signals through effective digital processing gain. This performance exceeded that of previous SDR models and showed good agreement with the commercial lock-in amplifier.</p> Conclusion <p>The proposed SDR-based phase meter offers a unique combination of low cost, wide heterodyne compatibility, high SNR, and nanometer-scale resolution. These characteristics demonstrate that low-cost SDR hardware, when combined with advanced digital demodulation techniques, provides a practical and high-performance alternative to conventional lock-in and FPGA-based interferometric systems for real-time ultrasonic metrology.</p>

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Nanoscale Ultrasonic Vibration and High-Speed Displacement Measurement with Heterodyne Interferometry and Cost-Effective Software-Defined Radio Phase Meter

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • T. D. Nguyen,
  • N. Van Muoi,
  • H. H. Hai

摘要

Background

High-resolution ultrasonic displacement and vibration measurements are crucial in precision machining, advanced manufacturing, and materials characterization. However, achieving both high sensitivity and high acquisition speed typically requires expensive hardware, such as high-speed analog-to-digital converters (ADCs), field-programmable gate array (FPGA) platforms, or commercial lock-in amplifiers, which constrain flexibility and cost-effectiveness.

Objective

This study aims to develop and validate a low-cost, high-performance phase meter for heterodyne interferometric ultrasonic-vibration measurements, using low-cost software-defined radio (SDR) hardware and open-source software.

Methods

A < $50 RTL-SDR-based phase meter was designed using flexible beat-frequency up and down conversion to acquire heterodyne signals spanning from kilohertz to hundreds of megahertz. Digital quadrature demodulation, multi-stage filtering, and a computationally efficient quadri-correlator algorithm were implemented in GNU Radio to achieve unwrap-free and real-time phase extraction. System performance was evaluated through simulations and ultrasonic-vibration experiments using a double-path heterodyne interferometer and was directly benchmarked against a commercial lock-in amplifier.

Results

Simulations showed a phase resolution of ± 0.01° and stability of ± 0.06° at 20 kHz. This corresponds to sensitivity levels in the nanometer and sub-nanometer range. Experiments confirmed that the SDR-based system can reliably measure 20 kHz ultrasonic vibrations with peak-to-peak amplitudes of less than 500 nm. Furthermore, despite the limitations of an 8-bit ADC, the SDR achieved a signal-to-noise ratio (SNR) of 130 dB for MHz-level phase-alternating signals through effective digital processing gain. This performance exceeded that of previous SDR models and showed good agreement with the commercial lock-in amplifier.

Conclusion

The proposed SDR-based phase meter offers a unique combination of low cost, wide heterodyne compatibility, high SNR, and nanometer-scale resolution. These characteristics demonstrate that low-cost SDR hardware, when combined with advanced digital demodulation techniques, provides a practical and high-performance alternative to conventional lock-in and FPGA-based interferometric systems for real-time ultrasonic metrology.