With length as one of the fundamental physical quantities, ultra-precise length metrology is pervasive across diverse areas of science and technology.1^–3 The current SI definition of the meter is based on the optical path length traveled during 1/299,792,458 of a second in vacuum, with optical metrology serving a pivotal role in ultra-precise dimensional metrology.4^,5 Laser interferometry—in homodyne or heterodyne principles for displacement measurement with sub-wavelength precision—has enabled optical dimensional metrology with the advancement of its precision and measurement range.6^–10 However, the precision of interferometric phase–based displacement or distance measurements is practically bounded by several tens of picometer level, from the precision of phase measurements.11^–15 Alternatively, Fabry–Perot (FP) interferometry, which tracks the cavity resonance frequency16^–19 or frequency domain analysis of interferometric signals,20^–23 enables picometer-level displacement measurement and has been demonstrated in applications involving extremely small displacement measurement. Such platforms are widely used to examine gravitational wave searches,1 dynamics on optomechanics,24 membranes,25 and nanomechanical structures.26^,27 In addition to length metrology, various optical and laser sensors have contributed to applications ranging from pressure measurement,28 acoustic sensing,29^–32 force and acceleration measurements,33^–35 gyroscopes,36 strain sensing,37 and earthquake detection38 to chedetection.39 In this study, acoustic sensing can aid in applications such as voice recognition, biological-medical imaging, and ultrasonic sensing.

Through interferometric homodyne stabilization with our hertz linewidth laser, the 60 m optical path length is stabilized within a 1σ standard deviation of 2.29 nm, with a measured displacement noise floor of 0.5pm/Hz1/2 near 10 kHz. Examining the control and error signals in the homodyne metrology up to 100 kHz, the corresponding distance strain noise floor is observed at 1.7×10−14ε/Hz1/2 with a 1.5 kHz servo bandwidth. Subsequently, we demonstrated the remote motional vibrational sensing of a glass beamsplitter under acoustic drives, from 140 Hz to 15 kHz, and quantified the laser homodyne displacement sensitivity as 782.77nm/V and acoustic sensing sensitivities as subnanometer/Pascal across our conversational frequency overtones. The minimal sound level and pressure are determined to be ≈40dB and ≈2mPa, respectively, bounded only by the laser frequency noise. Across the acoustic frequencies, the dynamic range is determined to be between 60 and 100 dB, within the laser λ/4 displacement. With the picometric noise metrology and distance stabilization thus demonstrated, we reconstructed real-time sound waveforms and analyzed their frequency spectrograms at the remote 60 m optical path length, comparing the control signal and error signal mapping, along with different acoustic overtones. Our demonstrated platform not only allows for remote acoustic sensing in targeted areas but also allows for ultrasound sensing and the adaptation of optical frequency standards toward sound metrology.

Figure 1(a) shows the concept of our laser homodyne interferometry–based acoustic detection. Sound propagation, when reflected by an interface structure, including a window, results in minute vibrations on the window surface. The sound amplitude and frequency information are embedded in window vibrational overtones. With precision laser interferometry, the vibration overtones are retrieved, enabling remote and rapid sensing. Figure 1(b) depicts the experimental setup for the picometric displacement measurement realization with our precision laser homodyne interferometry. A 1565.54 nm FP cavity-stabilized ultrastable laser (SLS-INT-1550-100-1, Stable Laser Systems, Munich, Germany) with 1 Hz linewidth and 10−15 fractional stability at 1 s is used as the light source in this study. After a single-mode fiber splitter with a 9:1 ratio, the shorter arm (10%) is used as the reference path, whereas the longer arm (90%; signal) is used as the measurement path goes through a 40 m fiber, which corresponds to an optical path length about 60 m (30 m distance for Michelson-type interferometer) between target and sensing position. A piezoelectric (PZT) actuator, with displacement sensitivity of 2.8μm/V considering the interferometer roundtrip beam path, controls the optical phase delay line. The laser beam is launched into free space by a collimating lens and reflected by a beamsplitter window (BSW30, Thorlabs, Newton, New Jersey, United States) with 2 in. (1 in. = 304.8 mm) diameter and 8 mm thickness. The reflected beam is collimated into a single-mode fiber and combined with a reference arm by a 2×2 optical coupler. The combined reference and signal arm is sent to a balanced photodiode (BPD) to extract the interference signal without DC offset. The reflected beam is attenuated to ≈25μW to enable a homodyne signal amplitude of ≈±500mV, such that the displacement sensitivity of the homodyne signal is 782.77nm/V.

The BPD homodyne signal is sent to a proportional-integral (PI) servo controller, with a small fraction of the homodyne signal sent to a fast Fourier transform (FFT) analyzer and high-speed oscilloscope for data analysis. The control signal from the PI servo controller stabilizes the homodyne signal to zero point for long-term operation and highly sensitive sensing via the PZT actuator. As the control signal range is fixed at ±10V, the PZT actuator can compensate for a ±28μm displacement. A speaker is installed behind the beamsplitter to generate the acoustic input and music. Although recording the acoustic frequencies, a passive DC block electrical filter with >1Hz passband suppresses the long-term drift of optical phase delay due to refractive index change and thermal expansion on the interferometer.

The homodyne detection–based optical path stabilization has been widely used in frequency transfer40^,41 and unbalanced arm interferometry.42Figure 2(a) shows the measurements of in-loop optical path stabilization by homodyne detection and PZT actuator over the long delay line, with Fig. 2(a) as an example path stabilization over 6.5μs at 50 kHz update rate. The Gaussian-shaped histogram has a 2.3 nm (1σ) standard deviation. To quantitatively evaluate the optical path length stability, the inset in Fig. 2(a) shows the resulting Allan deviation. For the short-time scale (20μs to 0.1 s), the optical path length stability is determined to be 2.3 nm at 20μs and gradually improves to 40 pm at 0.1 s, with the measurement fitted relation of 12pm×τavg−0.5, where τavg is the averaging time. For a longer averaging time of more than 0.1 s, the stability remains near 40 pm, equivalent to a time offset of 1.33×10−19s (133 zs).

Figure 2(b) shows the displacement amplitude spectral densities obtained from the error and control signals. After the stabilization of the optical path, the error (red line) and control signals (blue line) are plotted together. For comparison, the error signal without the stabilization is plotted in a black line, representing the background displacement noise of the target window. From Fig. 2(b), we can estimate the PZT servo bandwidth in the optical path stabilization system to be ≈1.5kHz. Inside the servo bandwidth (<1.5kHz), displacement amplitude spectral density from the control signal is dominant and its structure is similar to the amplitude spectral density from the error signal without stabilization. In other words, the displacement amplitude spectral density from the control signal inside the servo bandwidth is equivalent to the background noise of the interferometer. The error signal inside the servo bandwidth is the residual component of the optical path stabilization. Outside the servo bandwidth (>1.5kHz), the displacement amplitude spectral density from the error signal is dominant and its structure is overlaid directly onto the amplitude spectral density of the error signal without stabilization. Above 10 kHz, the displacement amplitude spectral density is bounded by the ultrastable laser and it fluctuates based on the ultrastable laser frequency noise (further detailed in Sec. S1 and Fig. S1 in the Supplementary Material).19^,43^–51 The lowest background noise attained is at the few pm/Hz1/2 level near the Fourier frequency of 10 kHz, based on the frequency noise of the ultrastable 1 Hz laser. As shown in Fig. 2(b), the lowest background noise is estimated to be 0.5pm/Hz1/2, corresponding to a strain of 1.7×10−14ε/Hz1/2. By combining the control signal amplitude spectral density inside the servo bandwidth and the error signal amplitude spectral density outside the servo bandwidth, the amplitude spectral density of displacement can be fully reconstructed over a wide range of Fourier frequencies.52

Figure 3(a) shows the resulting frequency spectra with input acoustic signals from 140 Hz to 15 kHz by analysis of the error and control signals. The blue and red lines indicate the background noise level from control and error signals, respectively, with sensitivities below 10pm/Hz1/2 up to 100 kHz. Control signals for sound detection are used from 140 Hz to 1 kHz and error signals are used from 2 to 15 kHz (the periodic 60 to 300 Hz peaks are from the 60 Hz harmonics of the electrical power line noise). At lower frequency ranges up to 5 kHz, the background noise is mostly limited by environmental noise as the whole system is not isolated from its surroundings. Note that diagonal dashed lines (light gray, gray, and black) indicate theoretically predicted fluctuation of optical path length power spectral density for wind speeds of 0.1, 1, and 10 m/s by the theoretical Kolmogorov’s spectrum of weak turbulence.53^,54 Based on the previous study on long-distance outdoor measurement,55 the optical path variation over a 60 m distance in an outdoor environment with temperature fluctuation and air turbulence is expected to be on the order of a few micrometers, which can be sufficiently compensated by the PZT actuator used in this study. At higher frequencies over 10 kHz, the background noise is limited by the frequency noise of the ultrastable laser.

Figure 3(b) shows the acoustic intensity–dependent displacement amplitude spectral densities for 200 Hz, 500 Hz, 2 kHz, and 15 kHz, with clearly detected acoustic signatures. The vertical y-axis is linear; we use a sound level unit of dB, which does not consider the weighting factor for human ear response to directly convert sound intensity to sound pressure with units of Pascal. We measure the sound level for all frequencies from the speaker using a sound level meter with units of dB. We use control signals for 200 and 500 Hz sound detection and error signals for 2 and 15 kHz sound detection. Within intensities from 60 to 100 dB for all frequencies, we observe linear transduction from the input acoustic intensity to the detected intensity in the optical spectrum.

Figure 3(c) shows the summary mapping of the sound intensity (sound pressure)–dependent displacement response of the target window from 140 Hz to 15 kHz. The upper horizontal axis is the equivalent sound pressure converted from the sound intensity shown in the lower x-axis. Sound intensity is determined by the peak intensity measured in the frequency domain. Sound signals start to appear at 140 Hz due to the relatively high background noise and low output of the driving speaker below this frequency. Detected sound signals of all frequencies have a linear proportion to the input sound pressure and are proportional to the square of sound level in dB units. Across the eight frequencies shown in Fig. 3(c), the typical displacement-to-acoustic intensity sensitivity is determined to be subnanometer/Pascal. The difference in the sound signal intensity response for each (mechanical and acoustic) frequency arises from the mechanical response transfer function of the target window. In addition, we note that as the PZT used in this study can cover displacement of ±28μm, our system detects much louder sound within the servo bandwidth frequency range. Considering the background noise level marked with the open circle, the possible sound level measurement range for all frequencies is plotted with the dashed line. For the higher frequency (2 to 15 kHz) where the error signal is used, the minimum detectable sound level is ≈40dB, corresponding to a sound pressure of ≈2mPa. In this range, we define a maximum measurable range as less than the ±λ/4 vibration level with a marginal safety coefficient of 2, corresponding to an ≈100dB dynamic range in our measurements. For the lower frequency (140 Hz to 1 kHz) where the control signal is used, the minimum detectable sound level varies from 40 to 65 dB, equivalent from 2 to 36 mPa. In this range, the maximum measurable range for lower frequencies is estimated to be much higher than the case for higher frequencies as the optical delay line range of the PZT actuator is ±28μm these lower frequencies, a dynamic range up to ≈100dB is estimated. We further note that vibration amplitudes larger than λ/2 can drop the locking state, and hence a tighter level of locking is required to measure a large sound when the control signal is used, with a less definite pinpoint of the maximum measurable range for the lower frequencies. As a sound level of 60 dB is typical for conversations, our scheme is sufficient to detect human voices over the remote window. If our system is operated with a shorter than 60 m optical path, the detectable sound level would be lower than 60 dB as the background noise is decreased.

With the hertz-level laser metrology in place, subsequently, we recorded and reconstructed several music pieces in the laboratory environment using a high-speed 16-bit oscilloscope to show the feasibility of remote and covert sound detection. Figure 4(a) shows the real-time sound detection of “UCLA fight song” and its spectrogram, with Fig. 4(a) as the original sound waveform and Fig. 4(b) as its spectrogram over 10 s. Figures 4(b) and 4(c) show the recorded and reconstructed waveforms from the control (blue) and error (pink) signals, respectively. Slow-varying drift of the control signal is suppressed by a radio frequency (RF) high pass filter (EF599, Thorlabs, Newton, New Jersey, United States) with a 400 Hz cutoff frequency. Even though the error signal is locked to the zero point, the unsuppressed components have sound signal information. As the control signal has more information below 1.5 kHz where most human voice is distributed, the control signal-based sound information is clearer than the error signal-based information. However, the error signal-based sound signal includes higher frequency overtones than the control signal-based one, from the impulse response measurements noted in Sec. S2 and Figs. S2 and S3 in the Supplementary Material. As shown in Multimedias 1 and 2, respectively, the reconstructed lyrics of “UCLA fight song” are clearly audible for both control and error signal-based music records. In the frequency domain, error signal-based sound signal shows a relatively clearer sound signal over the locking bandwidth, as described in the previous section. A comparison of our millimeter-thickness beamsplitter with a few micrometer-thickness pellicle beam splitter is also noted in Sec. S3 and Figs. S4 and S5 in the Supplementary Material. Sound signal higher than 5 kHz is attenuated as it is above the mechanical transfer function of the target window but it is still sufficient to receive and distinguish male and female voices remotely, as illustrated in Multimedias 3, 4, 5, and 6 (female vocals: Shallow1, control signal; Shallow1, error signal; Shallow2, control signal; Shallow2, error signal), and Multimedias 7 and 8 (male vocals: Hotel California, control signal; Hotel California error signal).

Figure 5 shows further examples of the real-time music recording waveform reconstructions and their corresponding spectrograms. Left panels [(a),(c),(e)] are control signal-based results and right panels [(b),(d),(f)] are error signal-based results. Figures 5(a)–5(d) are songs from a female singer, and Figs. 5(e)–5(f) are songs from a male singer. All data are converted into “.wav” file format (Multimedias 1, 2, 3, 4, 5, 6, 7, and 8), and these .wav files are converted into spectrograms as shown in Figs. 5(b), 5(d), and 5(e). As described in the main text, the control signal-based waveforms have a stronger signal than error signal-based waveforms, whereas the error signal-based waveforms have higher frequency components. From these results, we confirm that our metrology can record both male and female voice overtones at the remote site. Table S1 in the Supplementary Material presents a performance comparison with state-of-the-art acoustic sensing techniques.30^,32^,56^–61

In summary, we have shown remote and local sound detection via picometric homodyne laser interferometry. An FP cavity stabilized hertz-level linewidth laser with 10−15 fractional frequency instability enables picometric displacement measurement over ≈60m optical path length. Our precision homodyne laser interferometer achieves displacement noise background of 1.5pm/Hz1/2 near 10 kHz, limited by laser frequency noise. We show the measurement capability of sound detection up to 100 kHz at remote locations about 60 m away, with a measurement range extended using high-speed electronics. The measurement method demonstrated in this study shows long-term operation via stabilization of the homodyne signal regardless of phase wrapping by long-term drift. We measure sounds from 140 Hz to 15 kHz to verify frequency-dependent displacement intensities, with acoustic sensing sensitivities as subnanometer/Pascal across our conversational frequency overtones. We confirm that our methodology is able to measure sounds ranging from 2 mPa to 2 kPa, with a dynamic range determined between 60 and 100 dB, within the laser λ/4 displacement. With the noise floors and sensitivities determined, we successfully recorded and recreated several music sounds, including female and male voices behind a window at typical conversation volumes. Our proposed system enables long-distance measurements through the use of a laser with a long coherence length and achieves picometer-level displacement sensitivity by stabilizing the homodyne signal at the zero point. In addition, it employs near-infrared lasers, which are invisible to the human eye, thereby offering the potential for undetectable laser eavesdropping. We further believe that our proposed system has the potential for laser-based sound sensing, ultrasound sensing, and the practical realization of optical frequency standards for acoustic measurements.

The fiber stretcher (PZ2, Optiphase, Van Nuys, California, USA) based on a piezoelectric actuator has a displacement sensitivity of 5.6μm/V. In this study, we directly use the output port signal of the servo controller as a control signal, without a voltage amplifier to avoid its voltage noise. As the output voltage range of the control signal is ±10V and our interferometer has a double path of the optical beam line, the fiber stretcher compensates for the displacement of ±28μm on the target window with a sensitivity of 2.8μm/V. The control signal is directly converted into displacement in a high-speed oscilloscope and FFT analyzer. The control signal is used inside the locking bandwidth of 1.5 kHz.

The amplitude of the homodyne signal is fixed to ±500mV, equivalent to ±391.39nm (λ/4). We assume that the error signal is linearly proportional to the displacement near the zero-point, which we use in this study. The displacement sensitivity of the homodyne signal is determined to be 782.77nm/V. As the voltage information of the error signal is directly converted into displacement in the time domain, the displacement information can be rapidly recorded by a high-speed oscilloscope and FFT analyzer. As the error signal below the locking bandwidth is suppressed by the servo control mechanism, the outside-locking bandwidth of the error signal is valid to detect the acoustic signatures.

Acknowledgment. The authors appreciate the helpful discussions with Jinkang Lim, Jiagui Wu, and Qingsong Bai. This work was supported by the Office of Naval Research (Grant Nos. N00014-16-1-2094 and N00014-24-1-2547), the Lawrence Livermore National Laboratory (Grant No. B622827), and the National Science Foundation. Y.-S.J. acknowledges support from KRISS (Grant Nos. 25011026 and 25011211).

Yoon-Soo Jang received his BS degree in mechanical engineering from the Inha University, Incheon, Republic of Korea, in 2007, and his MS degree and PhD from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea, in 2013 and 2017, respectively. From 2018 to 2019, he was a postdoctoral fellow at the University of California, Los Angeles, United States. He is a senior research scientist at the Korea Research Institute of Standards and Science (KRISS), Daejeon, Republic of Korea, and an associate professor at the University of Science & Technology (UST), Daejeon, Republic of Korea. His research interests include optical metrology, ultrafast photonics, frequency combs, laser interferometry, and length standards.

Chee Wei Wong received his BS degree in mechanical engineering from the University of California at Berkeley, United States, in 1999, and his MS degree and PhD from the Massachusetts Institute of Technology (MIT), Cambridge, United States, in 2001 and 2003, respectively. He was a postdoctoral fellow at the MIT in 2003. He is a professor at the Electrical Engineering Department of the University of California, Los Angeles, United States. He is a fellow of the American Physical Society. His current research interests include nonlinear and quantum optics in nanophotonics, silicon electronic–photonic circuits and photonic crystals, quantum dot interactions in nanocavities, nano-electromechanical systems, and nanofabrication.

Biographies of the other authors are not available.