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Implementation of a Reference Interferometer for Nanodetection
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Lock-in frequency measurement with high precision and efficiency.

Jun Lu1

  • 1Institute of Physics, Chinese Academy of Sciences, Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China.

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|August 6, 2020
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Summary

This study introduces a novel frequency measurement technique using adaptable lock-in amplifiers (LIAs). This method precisely determines frequency, amplitude, and phase of noisy signals, offering improved efficiency over Fast Fourier Transformation (FFT).

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Area of Science:

  • Signal Processing
  • Measurement Science
  • Electrical Engineering

Background:

  • Traditional frequency measurement methods like Fast Fourier Transformation (FFT), zero crossing, and scanning autocorrelation have limitations in noisy environments.
  • Accurate determination of frequency, amplitude, and phase is crucial for analyzing periodic signals, especially those with low signal-to-noise ratios (SNRs).
  • Existing techniques struggle with precision when signals are heavily obscured by noise.

Purpose of the Study:

  • To develop and validate a new high-precision frequency measurement method utilizing adaptable lock-in amplifiers (LIAs).
  • To demonstrate the method's capability in determining frequency, amplitude, and phase of periodic signals even under severe noise conditions.
  • To compare the efficiency and accuracy of the proposed LIA-based method against conventional techniques like FFT.

Main Methods:

  • Developed an adaptable lock-in amplifier (LIA) design for precise signal analysis.
  • Performed mathematical derivation of the local spectrum around the center frequency, revealing a bell-shaped waveform for sinusoidal signals.
  • Utilized sinusoidal fitting on amplitudes of three frequency points to accurately determine the peak frequency.

Main Results:

  • The proposed LIA method achieves high precision in determining frequency, amplitude, and phase, outperforming FFT in efficiency by a factor of log₂(N).
  • Simulation results confirm the algorithm's ability to reach the theoretical Cramer-Rao lower bound and stay within a lock-in upper bound.
  • Implementation on a field-programmable gate array (FPGA)-based device demonstrated robust performance across various frequencies, amplitudes, and noise types.

Conclusions:

  • The novel LIA-based frequency measurement technique offers superior precision and efficiency for analyzing periodic signals, particularly in low SNR environments.
  • The method's accuracy is validated through theoretical derivations, simulations, and experimental testing on an FPGA platform.
  • This approach is highly effective for fine frequency determination when prior knowledge of the approximate frequency is available.