Fig. 1. Schematic and setup of picometric homodyne laser interferometry-based remote acoustic detection. (a) Laser interferometer detects acoustic information engraved on the picometric vibration of the window. The interferometric signal is converted into a waveform of sound in the time domain. (b) Measurement interferometer setup with an ultrastable few-hertz linewidth laser. BPD, balanced photodetection; PZT, piezoelectric transducer; TX/RX, transmitter and receiver; PI, proportional and integral servo control.

Fig. 2. Measured displacement amplitude spectral density through optical path stabilization using the interferometric homodyne signal. (a) In-loop measurement of the optical path after interferometric homodyne stabilization, sampled over 6μs and plotted in the time domain. Right panel: histogram of the stabilized optical path showing Gaussian distribution with 1σ standard deviation of 2.3 nm. Inset: measurement stability verification through Allan deviation. (b) The left axis is the measured displacement amplitude spectral density from the error signal (red) and control signal (blue) of the interferometric homodyne stabilization. The laser homodyne displacement noise floor is determined to be 0.5pm/Hz1/2 over 60 m optical path length, near 10 kHz. The right axis indicates the corresponding strain, with a noise floor of 1.7×10−14ε/Hz1/2. For comparison, free-running homodyne signal without locked optical path stabilization is overlaid in the dark gray plot. Outside the ≈1.5kHz servo bandwidth, displacement from the error signal is dominant, whereas displacement from the control signal is dominant inside the servo bandwidth.

Fig. 3. Frequency spectra of acoustic sensing for 140 Hz to 15 kHz input signals and varied sound levels, along with mechanical displacement responses. (a) Spectral densities of laser homodyne control and the error signal in the frequency domain. The blue and red lines indicate background displacement noise measured by the control and error signals, respectively. A minimum background displacement noise is found to be ≈0.5pm/Hz1/2 near 10 kHz. The dashed lines indicate theoretical predictions of optical path length power spectral density for wind speeds of 0.1, 1, and 10m/s.^53,54 (b) Intensity-dependent displacement amplitude spectral density displacement in linear scale. Sound level is first measured by a commercial sound meter with a unit of dBA. This is then converted into decibel units for direct conversion to sound pressure. For (i) 200 Hz, displacements are measured by the control signal. For (ii) 2 kHz and (iii) 15 kHz, displacements are measured by the error signal. (c) Summary displacement response of the target window. Measurement results show that from 140 Hz to 15 kHz, it is a function of sound level (dB) and sound pressure (Pa). The dashed lines indicate linear fitted lines and open circles are estimated minimum and maximum measurable ranges for each frequency.

Fig. 4. Real-time sound reconstruction of “UCLA fight song” and corresponding spectrograms. (a)–(c) Time-domain waveforms of the original sound (gray), control signal-based reconstruction measurement (blue) (Multimedia 1, WAV, 1.91 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s1]), and error signal-based reconstruction measurement (pink) (Multimedia 2, WAV, 1.91 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s2]). (d)–(f) Spectrograms corresponding to panels (a)–(c), respectively. The control signal-based reconstruction has a larger signal and higher signal-to-noise ratio than the error signal-based reconstruction. By contrast, the error signal-based reconstruction has higher frequency components.

Fig. 5. Comparison of real-time music recording reconstructions across different acoustic overtones. (a) Reconstructed control signal waveform and spectrogram of “Shallow1.wav” (Multimedia 3, WAV, 3.81 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s3]). (b) Reconstructed error signal waveform and spectrogram of “Shallow1.wav” (Multimedia 4, WAV, 3.81 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s4]) with a lower amplitude but with higher frequency components distinguished. (c) Reconstructed control signal waveform and spectrogram of “Shallow2.wav” (Multimedia 5, WAV, 0.39 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s5]). (d) Reconstructed error signal waveform and spectrogram of “Shallow2.wav” (Multimedia 6, WAV, 0.39 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s6]). Likewise, a lower amplitude is observed but higher frequency components are distinguished. (e) Reconstructed control signal waveform and spectrogram of “HotelCalifornia.wav” (Multimedia 7, WAV, 1.91 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s7]). (f) Reconstructed error signal waveform and spectrogram of “HotelCalifornia.wav” (Multimedia 8, WAV, 1.91 MB; [URL: https://doi.org/10.1117/1.APN.4.4.046006.s8]) with a lower amplitude and higher frequency metrology.