Time-domain stereoscopic imaging

Time-domain stereoscopic imaging | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Time-domain stereoscopic imaging Ming Yan, Zijian Wang, Hui Ma, Jinwei Luo, Kun Huang, Jianan Fang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5233274/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Jul, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Stereoscopy harnesses two spatially offset cameras to mimic human vision for depth perception, enabling three-dimensional (3D) optical imaging for various remote sensing applications. However, its depth precision and accuracy are limited by insufficient spatial resolving power. Achieving high precision alongside extensive measurable ranges and high-speed measuring capabilities has long been a challenge in 3D imaging. To address this, we introduce time-domain stereoscopy, a concept inspired by space-time duality in optics. Specifically, it employs two temporally offset optical gating cameras to capture time-domain parallax signals, enabling rapid and precise time-of-flight measurements for depth retrieval. Leveraging two advanced technologies—femtosecond electro-optical comb synthesis and nonlinear optical sampling—this method achieves sub-100 nm depth precision across multimeter-scale imaging ranges and supports millisecond-scale displacement and velocity measurements for 47 million spatial points simultaneously. As such, it provides a versatile tool for applications in surface metrology, mechanical dynamics, and precision manufacturing. Physical sciences/Optics and photonics/Optical techniques/Imaging and sensing Physical sciences/Optics and photonics/Other photonics/Optical metrology Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction In optics, the parallels between concepts in the spatial and temporal domains, often referred to as space-time duality 1 , have led to the development of many revolutionary photonic tools, impacting diverse fields of science and technology, including ultrafast physics, quantum optics, spectroscopy, microscopy, and signal processing. For example, the development of time lenses and time-stretch photonics 2 , 3 , analogous to focusing and dispersing elements in space, has enabled powerful tools, such as wideband analog-to-digital converters and ultrafast signal processors, uncovering phenomena like optical rogue waves, relativistic electron bunching, and quantum chaos, and unlocking new opportunities for applications such as cancer detection, blood testing, optical computing, and 3D light detection and ranging (lidar) 4 . Inspired by this duality, we here devise a time-domain stereoscopic technique (TDS), enabling high-precision, large-dynamic-range, far-field 3D optical imaging. Initially, stereoscopic imaging is performed in the spatial domain, which mimics human eyes to perceive depth using two slightly offset cameras to capture two images of the same scene from different angles. The disparity between the two images yields a depth map, enabling 3D reconstruction 5 . While effective in fields like robotics and autonomous driving, stereo imaging is limited in axial resolution and accuracy due to insufficient spatially resolving capability, especially in low-contrast, reflective, or textureless environments. Analogous to its spatial-domain counterpart, TDS uses two temporally offset cameras to capture two images from the same laser pulse reflected by a target (Fig. 1 a). The disparity between these images manifests in the time domain (Fig. 1 b), and this temporal difference, decisive for depth retrieval, is determined precisely and rapidly by leveraging advanced time-domain techniques such as ultrafast optical sampling. Consequently, TDS addresses two key challenges for 3D imaging 6 – 8 : 1) integrating high axial resolution and precision with an extended imaging range or depth-of-field (DOF); and 2) performing 3D measurements in a high-speed, real-time fashion. Overcoming these challenges is crucial for surface metrology, remote sensing, mechnical dynamics, and tasks like object recognition, navigation, and scene reconstruction, which have widespread applications in areas like advanced manufacturing, security and defense 9 , 10 . As a brief introduction, existing 3D optical imaging techniques can be crudely divided into two groups. The first covers large measurement distances (from a few meters to hundreds of meters) but with limited depth resolution and precision (at the millimeter or centimeter levels), including techniques such as stereoscopic imaging, time-of-flight (ToF) ranging cameras 11 , structured light projection 15 , and the 3D lidar family 12 – 14 . The second achieves nanometer precision but is limited to short ranges or DOF (typically to just a few millimeters), including techniques like confocal microscopy 16 , optical sampling imaging based on electro-optical or nonlinear effects 17 – 20 , and interferometric imaging and tomography 21 – 24 , primarily utilizing an interferometer with a moving arm. Meanwhile, the emergence of optical combs, a coherent light source precisely controlled in both time and frequency domains, opens up new opportunities for lidar 25 – 28 and high-dimensional imaging 29 , 30 . Particularly, dual-comb interferometry, without the limitation of moving parts, enables rapid, long-range absolute distance measurements via heterodyne detection of two mutually coherent combs 25 . This dual-comb concept has been successfully adopted for hyperspectral digital holography 29 . However, the requirement for two tightly locked coherent combs, along with the high computational load and low refresh rate, limits its applicability due to complexity, cost, and real-time constraints. Therefore, despite its importance, high-precision, large-range 3D imaging with real-time measurement capability has remained a missing element in the field. The TDS method we propose offers a promising solution to bridge this gap. Basic concept and principle Figure 1 a conceptually compares TDS with conventional stereo imaging (see details in Supplementary Fig. 1 and Supplementary Table 1). In both cases, achieving high depth precision and accuracy hinges on precisely measuring minute disparities. This task proves challenging in the space domain (fundamentally due to the diffraction limit); conversely, exploiting the time domain benefits from advancements in optical comb and precise timing technologies. Specifically, in TDS, a laser pulse reflected by a target is captured by two cameras gated with a slight temporal offset, yielding distinct electrical signals (Fig. 1 b). This imbalance (ΔI) is governed by the temporal difference (Δt) between the pulse flight time (T D ) and the paired time gates, where Δt = T D - m /f r and m /f r represents a multiple of the repetition period of the gates (provided the two gates are synchronized). The pulse and the paired gates overlap optimally at a zero-crossing point (the middle case in Fig. 1 b), where Δt = 0 and T D = m /f r . The integer m = f r1 /Δf r , where Δf r =f r2 -f r1 , is obtained in a stroboscopic fashion, as m /f r1 =( m + 1)/f r2 , given two adjacent zero-crossing points at f r1 and f r2 , with f r1 <f r2 . Consequently, a target distance ( D ) is determined as D = c ·T D / 2 n r = c /(2 n r ·Δf r ), where n r is the reflective index of the air and c is the speed of light in a vacuum. Note that there are two prerequisites: 1) timing the gates precisely, which is available using optical combs; 2) the gates shorter than or comparable to the laser pulse, achievable via optical gating. A key advantage of TDS over a conventional ToF camera is its superior noise immunity. A similar analogy can be drawn when comparing single-detector cross-correlation with balanced cross-correlation (BCC) in laser synchronization experiments 31 – 33 . The balanced one significantly improves timing precision to the attosecond level, surpassing the former by orders of magnitude, through the elimination of common-mode optical and electrical noise. This advantage also applies to TDS, rendering it inherently sensitive to minute changes in time as well as in distance—a core feature of this approach. Note that the BCC scheme has been adopted for high-precision single-point rangefinding 34 . Here, we explore its potential for TDS imaging that exploits time-domain parallax. In our proof-of-concept demonstration, TDS is carried out by a novel balanced imaging system (Fig. 2 a) comprising a type-II periodically poled KTiOPO 4 (PPKTP) crystal and two identical cameras. The linearly polarized reference pulse serves as an optical gate for sampling the detection pulse with orthogonal polarization. Optical sampling occurs twice within the same PPKTP crystal via a bidirectional sum-frequency generation process. This type-II crystal induces temporal walk-off between the detection pulse and the reference gate pulse, causing the detection pulse to be sampled twice with a small temporal offset before being captured by the respective cameras. Two points in this scheme should be noted. First, an ultrashort pulsed laser with a well-defined, rapidly tunable repetition frequency across a broad range is essential. To achieve this, we utilize a frequency-swept electro-optical (EO) comb. In practice, to measure distance, we record the balanced signal (ΔI) while linearly sweeping the comb’s f r , and then identify the zero-crossing points during data post-processing, as illustrated in Fig. 2 b. Second, the central region of the balanced curve establishes a direct correspondence between intensity and time (or intensity and displacement), enabling 3D measurements from single frames. Results Experimental setup Our setup begins with an EO comb seeded by a narrow-linewidth CW laser at 1550 nm (Fig. 3 a). This comb shares a configuration similar to previously reported sources 35 , 36 , as detailed in the Methods section and Supplementary Fig. 2. Briefly, the EO comb translates a radio-frequency (RF) sinusoidal wave, generated by a hydrogen-maser-disciplined RF synthesizer, into a sequence of sub-500 fs optical pulses, using a single intensity modulator and dispersion managed nonlinear fibers. Notably, the EO comb’s f r ​is directly set by the RF synthesizer, offering several benefits, including the elimination of frequency locking and counting, as well as wide-range frequency tuning with high linearity (Fig. 3 b). The comb’s response to the RF driving signal is instantaneous, with negligible deviation within the resolution bandwidth of observation (Fig. 3 b inset). Also, the comb maintains its pulse shape and temporal width when increasing the tuning speed or the modulation frequency (f m ), as shown in Fig. 3 c, showing the potential for fast measurement (discussed later). Importantly, the comb inherits the excellent frequency stability of the RF synthesizer (reaching 4×10 − 13 in 300 s, as shown in Fig. 3 d), ensuring precise distance assessment. For remote sensing, the comb output is amplified to 200 mW average power via an erbium-doped fiber amplifier (EDFA) and equally split between the detection and reference arms. In the detection light path, the comb pulses pass through a beam expander, subsequently illuminating a 3D scene with staggered mirrors and a resolution test target (1951 USAF) in front. A quarter-wave plate (QWP) and a polarization beamsplitter (PBS) serve as a free-space circulator, guiding the reflected detection pulses to another beam expander for optical scaling, and then to the balanced imager through a second PBS, which combines the detection and orthogonally polarized reference pulses. The balanced imaging unit comprises twin 4f imaging systems—one with lenses L 1 and L 2 , and the other with lenses L 3 and L 4 —in the opposing light paths (indicated by pink arrows in Fig. 3 a). The two imaging subsystems share a single type-II PPKTP crystal, where object images from both directions converge at its center in the Fourier plane. Inside, the reference pulses convert the detection pulses into sum-frequency signals at 775 nm, which are captured by two synchronized CMOS (complementary metal-oxide-semiconductor) cameras. Note that, to serve as pump light for sum-frequency generation, the 2.2-mm diameter (full width at 1/ e 2 ) reference beam bounces through the crystal without focusing, minimizing spatial filtering effects on lateral resolution. As such, we achieve an optimal lateral resolution of 6 µm (limited by the crytal’s transverse section) with a field-of-view (FOV) of 560×420 µm² (Fig. 3 e). Currently, the 4-mm crystal (operating at room temperature) limits the acceptance angle to 3.5° (Supplementary Fig. 3) due to phase-matching restrictions commonly encountered by nonlinear optical imagers. This problem can be solved by changing the operating temperature or the poling structure of a nonlinear crystal 19 , 20 . Nevertheless, adjusting the magnifications of the two beam expanders in our setup allows for a broader view, such as a FOV of 3.5×2.6 cm² in Fig. 3 f, at the cost of a degraded lateral resolution (315 µm) due to the cameras’ fixed pixel density (1440×1080 pixels). To maintain high lateral resolution over a large FOV, high-resolution images obtained by beam steering can be stitched together, such as a full image of the 1951-USAF target (7.62×7.62 cm²) made from 46 sub-images (Supplementary Fig. 4). Remote 3D imaging and depth measurement First, we demonstrate TDS for 3D imaging by detecting four staggered mirror targets at a standoff distance of > 1.3 m (from a reference point). Figure 4 a exemplifies 2D images recorded by the two cameras at a frame rate of 165 fps (frames per second), with the comb f r linearly changing from 165.33 to 165.60 MHz. For these images, we identify spatially correlated pixel pairs, such as points A 1 and A 2 or B 1 and B 2 (Fig. 4 a), by matching corresponding features with a widely-used scale-invariant feature transform (SIFT) algorithm 37 . We then obtain the balanced signals from the paired pixels A 1 A 2 and B 1 B 2 , as plotted in Fig. 4 b. By linear fitting the central potions of the signals, we determine the zero-crossing points at 165.372 MHz and 165.510 MHz for A 1 A 2 and B 1 B 2 , respectively. We continue tuning f r , searching for the second zero-crossing points and calculating Δf r as 16.54 MHz for A 1 A 2 and 16.55 MHz for B 1 B 2 , which determine their absolute distances to be d 0 + 1.308 m and d 0 + 1.3 m, respectively. The effective optical path difference (d 0 ) between the detection and reference arms at the reference point in Fig. 3 a is pre-calibrated to be 15.5 m. In this measurement, we simultaneously obtain range information for dense spatial points (up to 4.67×10 7 pixel pairs), visualized as a false-color 3D point cloud in Fig. 4 c. For display, the axial ( z ) coordinates are referenced to the point B 1 B 2 . Also, points lacking illumination or without sufficient signal-to-noise ratio (SNR) are not displayed. Note that, the f r tuning step size is 606 Hz/frame, resulting in an axial resolution of 33 µm (Methods). This resolution can be improved to 54 nm with a step size of 1 Hz/frame at the cost of longer tuning time. In another example, we perform 3D imaging on a 30%-reflective unpolished metallic foil attached to a 1-inch glass plate (Fig. 4 d). This target is positioned 1.3 m away. Figure 4 e presents a topographic image showing reflections from both the foil and the glass back surface. This showcases our method’s ability to remotely profile metal component surfaces and complex patterns, which is applicable for industrial inspection. Axial precision and imaging depth Next, we assess measurement precision and accuracy by measuring the displacements of a mirror mounted on a translation stage. We compare the TDS results with the truth data obtained by a CW interferometer. Statistical analysis over 50 individual measurements (without averaging) at each displacement yields a 2-σ standard deviation (SD) within ± 10 µm, where the mean values deviate from the truth data by less than 2 µm (Fig. 5 a). With 500-fold averaging, the ranging precision improves to ± 400 nm with an accuracy reaching sub-100 nm (Fig. 5 b). Note that, as shown in Fig. 5 c, the measured SD linearly depends on signal-to-noise ratio (SNR), which can be improved by using a high-power comb and low-noise cameras. For further evaluation, we perform Allan deviation measurements. Experimentally, we fix the comb’s f r at a zero-crossing point, converting intensity variations of the balanced signal to deviations in distance by a conversion factor of 3.03 µm. The same factor is also used for evaluating background noise of a camera (by blocking the comb light). Figure 5 d shows the results with data acquired at a frame rate of 132 fps. Our method (data in light blue) results in a precision of ~ 80 nm in 25 s, which is close to the camera’s noise background (in purple) and is nearly 50 times better than the unbalanced results (~ 4 µm, shown in pink and green) obtained by single cameras (Methods), demonstrating the key advantage of our method over direct ToF cameras. The off-the-shelf cameras we currently use limit the axial precision due to their moderate sensitivity and uncontrolled electronic noise. Replacing the cameras with two low-noise single-point photodetectors achieves 30 nm ranging precision in 2 s at a distance of > 30 m (see Supplementary Fig. 5). Essentially, TDS is a ranging technique, subject to dead zones dictated by the tunable range of f r . Luckily, the EO comb, without an optical cavity, exhibits a broad tuning range of over 200 MHz, with f r tunable from 90 to 300 MHz (Fig. 5 g), limited by the bandwidth of electronics for EO comb generation. Nevertheless, this tuning range results in a dead zone of 0–0.5 m, which has been offset by the extra optical path in the detection arm and can therefore be neglected. Note that sweeping f r across a broad range changes the comb pulse width (Fig. 5 g) due to unbalanced nonlinearity and dispersion, impacting the SNR and the widths of balanced signals (Supplementary Fig. 6). However, thanks to the balanced architecture, the zero-crossing points remain unaffected, maintaining their frequencies (f r ) and separations (Δf r ). Consequently, our method permits large measurable ranges and imaging depths. An example for range imaging at a folded distance of 9.6 m is shown in Supplementary Fig. 7. With this enhanced ranging capability, our system can image objects at largely different depths. For instance, the images of two staggered objects are dispalyed in Fig. 5 h, and their spatial separation (1.85 m) is measured. Note that, for the displayed lateral resolution of 890 µm, the theoretical DOF allowed by our imaging system is 2.4 m (Supplementary Note 1). A larger DOF can be achieved, but at the cost of reduced lateral resolution. High-speed 3D measurement Finally, we demonstrate the real-time measuring capability of our method, which is based on the intensity-to-displacement relationship established by fixing the f r at a zero-crossing point. As exemplified in Fig. 6 a, the highly linear region of a balanced curve (shadowed in grey) links its intensity to a target displacement (Δd), which is pre-calibrated by scanning the reference arm. Alternatively, calibration can be done without motion by sweeping the f r (Methods). As such, our method enables parallel displacement and velocity measurements of moving targets within a single frame, a task that is difficult for interferometric imagers due to the complexity of signal processing. In an experiment, we capture reflections of two mirrors (behind the 1951-USAF target) moving oppositely at similar speeds of ~ 5 mm/s. Using pre-calibrated intensity-to-displacement relationships (similar to the one in Fig. 6 a), we simultaneously measure displacements at over a million spatial points with 132 Hz data refresh rate, corresponding to a temporal resolution of 7.576 ms and a pixel rate of 205.3 megapixels/s. Figure 6 b exemplifies the 3D images in motion. The trajectories of two counter-propagating imaging points (each on a mirror) are plotted in Fig. 6 c, the derivatives of which reveal the instantaneous velocities of the two mirrors (Fig. 6 d). Our setup currently allows a maximum measurable velocity of 330 mm/s, limited by the linear region (~ 2 mm) and the cameras’ maximum frame rate (165 fps, corresponding to a pixel rate of 256.6 MHz). Employing high-speed CMOS cameras (e.g., Photron, Mini AX200, with a frame rate up to 900k fps) can increase the measurable velocity to, e.g., 520 m/s. Also, the real-time measurable displacements (< 2 mm) can be extended by rapidly tuning the f r , which allows fast adjustment of the zero-crossing point and calibration of Δd, e.g., within 0.5 µs using high-speed photodetectors (Fig. 6 e). Therefore, our method shows great potential for capturing dynamic 3D scenes, enabling studies of mechanical vibrations and deformations 38 . Discussion Benefiting from optical sampling and femostecond EO comb synthesis, our system achieves sub-100 nm precision at a meter-level distance for 3D imaging. As shown in Fig. 7 , the dynamic range of our setup, defined as 10·log(measurable range/precision), reaches 74 dB, underscoring its advantage over the aforementioned systems and other 3D imagers 39 – 44 . Besides, compared to mode-locked laser combs in some advanced lidar or imaging systems 28 , 30 , 45 , 46 , the cavity-free EO comb in our setup offers additional merits in terms of reduced complexity, ease of operation, lower cost, and greater environmental immunity—all crucial for practical use. Also, recent advances in lithium niobate photonics have enabled on-chip fs EO comb generation 47 , paving the way for a more compact and minimized system design. Like other nonlinear optical sampling imagers 19 , 20 , our system encounters challenges in lateral resolution, angular FOV, and, most critically, light detection efficiency. Fortunately, advancements in nonlinear optical materials and semiconductor sensors present potential solutions. For instance, larger PPKTP crystals theoretically permit higher lateral resolution, and linearly chirped ones might expand the angular FOV to, e.g., 36.7°, with minimal conversion efficiency loss (Supplementary Fig. 3). Moreover, the development of electron-multiplying CCDs has enabled nonlinear upconversion imaging at the single-photon level 20 , albeit with longer integration times. This level of sensitivity enables our method to perform scanner-less range imaging, even over long distances, or in low-light conditions, as well as high-precision 3D profiling of rough, low-reflective surfaces. With ongoing advances in semiconductor sensors and digital camera technology—particularly in pixel density, sensitivity, and speed—our method is promising for various applications 6 – 10 , such as identifying defects on semiconductor wafers, examining crucial automotive and aerospace components for micro-level deformations, ensuring precise positioning during laser machining processes, and charaterizing dynamic behaveiours in micromechical devices, among others. Additionally, shifting the comb wavelength to the mid-infrared region would enable broader applications in biomedical imaging and materials science 19 , 20 . In conclusion, we present, for the first time, a time-domain stereoscopic approach that offers high precision over large imaging ranges and facilitates rapid, parallel displacement and velocity measurements, thereby introducing a powerful tool for diverse 3D imaging applications. Methods EO comb generation To generate the EO comb, a CW laser at 1550 nm (Adjustik E15, NKT Photonics; linewidth < 0.1 kHz; 40 mW) is fed into an intensity modulator (IM, 40-GHz bandwidth; KY-MU-15-DQ-A, Keyang Photonics), which is driven by an electrical pulse generator that converts the output of an RF synthesizer (N5173B, Keysight) into 30-ps electrical pulses. The IM output is amplified to 150 mW using a custom-built fiber amplifier, followed by a 180-m-long dispersion-managed highly nonlinear fiber for spectral broadening. This fiber has a zero-dispersion wavelength at 1550 nm, a linear dispersion slope of 0.03 ps/(nm²·km), a loss coefficient of less than 1.5 dB/km, and a nonlinear coefficient greater than 10 W⁻¹km⁻¹. The comb pulses (-10 dB spectral width > 10 nm) are then compressed by fiber Bragg gratings, producing sub-500 fs optical pulses. Balanced TDS imaging system As shown in Fig. 3 a, the imaging system employs two identical CMOS cameras (MV-CA016-10UM) to capture the correlated sum-frequency signals. An electrical circuit triggers the cameras in sync with the frequency tuning of the RF synthesizer. In the BCC unit, a type-II PPKTP crystal (CASTECH, 1×2×4 mm 3 for height, width and length) is used for two key reasons. First, it creates a temporal walk-off between two orthogonally polarized pulses, necessary for balanced signal generation. To make this walk-off adjustable, an additional polarized beamsplitter (PBS) and two mirrors (M 5 and M 6 in Fig. 3 a) are incorporated, with their relative positions adjustable. Note that the walk-off effect inevitably limits the sum-frequency generation efficiency (~ 0.053 mW/W 2 ). Second, the crystal prevents second harmonic generation of each pulse, ensuring a zero background. Calculation of SNR and axial resolution The SNR of a balanced trace is defined as its peak value divided by the SD of a background region where the detection and reference pulses are fully separated. The axial resolution (R z ) of TDS is determined by δf, the tuning step of f r , as R z = c /2 n r ·Δf r /(f r + δf)·δf, where the speed of light c = 299,792,458 m/s and the refractive index in air n r = 1.0003. Therefore, we have an axial resolution of 33 µm for δf = 606 Hz/frame and 54 nm for δf = 1 Hz/frame, when f r =166.3 MHz and Δf r =16.6 MHz. Also, based on the above relationship, we can calibrate the curve in Fig. 6 a by sweeping the f r . Intensity-to-displacement conversion factors For calculating the intensity-to-displacement conversion factor, we measure a balanced trace similar to that in Fig. 6 a and then linearly fit the central region, resulting in a slope of 3 µm, i.e., the conversion factor. For Allan deviation measurement with a single camera, we use a conversion factor of 6.1 µm, obtained by linear fitting the central part of the rising edge of a cross-correlation trace. We then measure the intensity fluctuations at the center point of the rising edge with a fixed f r . Declarations Author contributions M.Y. and H.Z. conceived the idea and designed the experiments. Z.W. and H.M. conducted the experiment and drafted the manuscript. Z.W., H.M. and J.L. analyzed the data. M.Y., K.H., and J.F. build the comb source. M.Y., H.Z., J.G., and K.H. revised the manuscript. All authors provided comments and suggestions for improvements. Competing interests The authors declare no competing interests. Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Author information Correspondence and requests for materials should be addressed to M.Y. ( [email protected] ), or to H.Z. ( [email protected] ). 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ACS Photonics 10 , 2964 (2023). Lowe, D.G. in Proc. IEEE Int. Conf. Comput. Vis. 2 , 1150–1157 (1999).. Kakue, T., Endo, Y., Nishitsuji, T. et al. Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena. Sci Rep 7 , 10413 (2017). Rogers, C., Piggott, A.Y., Thomson, D.J. et al. A universal 3D imaging sensor on a silicon photonics platform. Nature 590 , 256–261 (2021). Qian, R., Zhou, K.C., Zhang, J. et al. Video-rate high-precision time-frequency multiplexed 3D coherent ranging. Nat. Commun 13 , 1476 (2022). Chen, R., Shu, H., Shen, B. et al. Breaking the temporal and frequency congestion of LiDAR by parallel chaos. Nat. Photon. 17 , 306–314 (2023). Jing, X., Zhao, R., Li, X. et al. Single-shot 3D imaging with point cloud projection based on metadevice. Nat Commun 13 , 7842 (2022). Choi, E., Kim, G., Yun, J. et al. 360° structured light with learned metasurfaces. Nat. Photon. 18 , 848–855 (2024). Kato, T., Uchida, M., Tanaka, Y. & Minoshima, K. High-resolution 3D imaging method using chirped optical frequency combs based on convolution analysis of the spectral interference fringe. OSA Contin . 3 , 20 (2020). Xu, G. Y. et al . Digital-micromirror-device-based surface measurement using heterodyne interferometry with optical frequency comb. Appl. Phys. Lett. 118 , 251104 (2021). Zhang, W. et al . Comb-referenced frequency-sweeping interferometry for precisely measuring large stepped structures. Applied optics. 57 , 1247-1253(2018). Yu, M., Barton III, D., Cheng, R. et al. Integrated femtosecond pulse generator on thin-film lithium niobate. Nature 612 , 252–258 (2022). Additional Declarations There is NO Competing Interest. Supplementary Files supplementarymaterialsfinal.docx Supplementary Materials for Time-Domain Stereoscopic Imaging Cite Share Download PDF Status: Published Journal Publication published 24 Jul, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5233274","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":369028182,"identity":"085598ce-824d-4540-9afe-09976efb5d47","order_by":0,"name":"Ming Yan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIiWNgGAWjYLCCDwUINmMDMToYZxiQqoWZhyQtujOSnz22Mbhjz8De/OwxD4ON7IYDzM8e4NNidiPN3DjH4FliA88xc2MehjTjDQfYzA3wa0kwk84xOJzAIJHDJs3DcDhxwwEeNgn8WtK/SVsYHLZnkH8D0vKfGC05ZtIMBocZGyR4QFoOEKHlzJsyyR6gX9p40swk5xgkG888zGaGX8vx9G0SPyru2POzH34m8abCTrbvePMzvFoYBBJA5AEGNjAPFFTMeNUDAf8BiJZRMApGwSgYBTgBAGIKQqinesZmAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-4327-0759","institution":"East China Normal University","correspondingAuthor":true,"prefix":"","firstName":"Ming","middleName":"","lastName":"Yan","suffix":""},{"id":369028183,"identity":"2992d3cd-f284-4493-83bf-3bdc92dba92a","order_by":1,"name":"Zijian Wang","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zijian","middleName":"","lastName":"Wang","suffix":""},{"id":369028184,"identity":"0d6633e3-0c3d-4063-8625-85a38d68c0d7","order_by":2,"name":"Hui Ma","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Hui","middleName":"","lastName":"Ma","suffix":""},{"id":369028185,"identity":"a229d962-3bb6-4fe5-b42f-5e57338d2811","order_by":3,"name":"Jinwei Luo","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Jinwei","middleName":"","lastName":"Luo","suffix":""},{"id":369028186,"identity":"393089ed-63b1-407d-81d0-4b4682ee3a32","order_by":4,"name":"Kun Huang","email":"","orcid":"https://orcid.org/0000-0002-1899-7924","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Kun","middleName":"","lastName":"Huang","suffix":""},{"id":369028187,"identity":"be563aff-4c23-41dd-acb1-8fa7b5e08c30","order_by":5,"name":"Jianan Fang","email":"","orcid":"","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Jianan","middleName":"","lastName":"Fang","suffix":""},{"id":369028188,"identity":"dedfacee-a9f9-4f6a-b81c-2c2924f8640f","order_by":6,"name":"Jingman Ge","email":"","orcid":"","institution":"National Key Laboratory of Science and Technology on Space Microwave","correspondingAuthor":false,"prefix":"","firstName":"Jingman","middleName":"","lastName":"Ge","suffix":""},{"id":369028189,"identity":"73eae361-bddb-4df9-8c04-98002926307b","order_by":7,"name":"Heping Zeng","email":"","orcid":"https://orcid.org/0000-0002-2357-4440","institution":"East China Normal University","correspondingAuthor":false,"prefix":"","firstName":"Heping","middleName":"","lastName":"Zeng","suffix":""}],"badges":[],"createdAt":"2024-10-09 14:10:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5233274/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5233274/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-62228-5","type":"published","date":"2025-07-24T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":69830572,"identity":"14015e1d-d2dc-46d1-bb7a-d349fffcb162","added_by":"auto","created_at":"2024-11-25 15:34:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":144567,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConcepts of TDS. a\u003c/strong\u003e Simplified illustration of stereoscopy in space and in time. The light gray lines represent optical paths or time-of-flight. \u003cstrong\u003eb\u003c/strong\u003e Optical sampling and time-domain disparities. In short, pulses arriving at different times produce different intensities on the two cameras. This intensity difference (ΔI), as a differential function of the pulses’ arrival time (Δt) relative to the time zero (the center of the gates), is used to determine distance.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/ee7c1b673ba7658c9b929e4f.png"},{"id":69832229,"identity":"11652ea1-d0de-4b4b-8c3d-d6765641bd62","added_by":"auto","created_at":"2024-11-25 15:42:24","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":116323,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematics of TDS based on a balanced cross-correlator. a\u003c/strong\u003e Balanced imaging with two optical sampling cameras. PBS, polarization beamsplitter; QWP, quarter wave plate; DM, dichroic mirror; PPKTP, periodically poled KTiOPO\u003csub\u003e4\u003c/sub\u003e; I\u003csub\u003e1\u003c/sub\u003e, I\u003csub\u003e2\u003c/sub\u003e, electrical signal intensity for a pixel of camera 1 (camera 2). \u003cstrong\u003eb\u003c/strong\u003e Balanced signals as a function of repetition frequency (f\u003csub\u003er\u003c/sub\u003e) tuning of an electro-optical (EO) comb. In \u003cstrong\u003ea\u003c/strong\u003e, an EO comb emits ultrashort optical pulses that travel to the target, reflect off surfaces, and return to a balanced cross-correlator. Inside this correlator, the orthogonally polarized detection and reference pulses pass through the PPKTP crystal twice, generating bidirectional sum-frequency signals as they temporally overlap inside the crystal. The sum-frequency beams then project two correlated images of a target onto the respective cameras which are synchronized to the f\u003csub\u003er\u003c/sub\u003e tuning. By subtracting the intensities of two correlated pixels (each from a camera), one can derive the balanced signal (ΔI) at any spatial point. In\u003cstrong\u003e b\u003c/strong\u003e, a target distance is calculated as \u003cem\u003eD\u003c/em\u003e=\u003cem\u003ec\u003c/em\u003e/(2\u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e·Δf\u003csub\u003er\u003c/sub\u003e), where \u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e,\u003cem\u003e c\u003c/em\u003e and Df\u003csub\u003er\u003c/sub\u003e, represent the reflective index of the air, the speed of light in a vacuum, and the frequency difference between two consecutive zero-crossing points (at f\u003csub\u003er1\u003c/sub\u003e and f\u003csub\u003er2\u003c/sub\u003e).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/7e44173bfdb957c09c10c273.png"},{"id":69830571,"identity":"2f93a326-3683-4e53-97dd-19d81659d3c0","added_by":"auto","created_at":"2024-11-25 15:34:24","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":225601,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental setup and characterization of the EO comb. a\u003c/strong\u003e Experimental setup. Col., collimator; EDFA, erbium-doped fiber amplifier; HWP, Half-wave plate; M\u003csub\u003e1-6\u003c/sub\u003e, mirrors; 50/50, fiber coupler. The focus length for lenses L\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003e3\u003c/sub\u003e is 100 mm, and for L\u003csub\u003e2\u003c/sub\u003e and L\u003csub\u003e4\u003c/sub\u003e is 75 mm. The dashed box shows a 110-MHz sine wave being converted into a train of ultrashort pulses by an EO comb. \u003cstrong\u003eb\u003c/strong\u003e Linearly sweeping the comb’s repetition frequency (f\u003csub\u003er\u003c/sub\u003e) from 90 to 300 MHz within 210 ms. Inset: RF spectra obtained by short-time Fourier transform, showing instantaneous frequencies of the RF synthesizer and the EO comb. \u003cstrong\u003ec\u003c/strong\u003e Autocorrelation traces of the EO comb versus modulation frequencies (f\u003csub\u003em\u003c/sub\u003e). The data measured after the detection collimator and the frequency deviation is fixed at 250 kHz. \u003cstrong\u003ed\u003c/strong\u003e Fractional stability of the EO comb and the RF synthesizer. The comb stability deteriorates after 200 s due to the use of fibers. \u003cstrong\u003ee\u003c/strong\u003e and \u003cstrong\u003ef\u003c/strong\u003e High-resolution and large field-of-view images of the resolution taget (1951-USAF) recorded by one of the cameras. The central parttens in \u003cstrong\u003ee\u003c/strong\u003e and \u003cstrong\u003ef\u003c/strong\u003e correspond to groups 6 and 0, respectively.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/94bc6151b457a0727a1b982a.png"},{"id":69830574,"identity":"fb3ff94d-4a17-4447-bc8f-2a88333e4916","added_by":"auto","created_at":"2024-11-25 15:34:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":325005,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDemonstration of TDS for 3D imaging.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e 2D images recorded by the cameras. \u003cstrong\u003eb\u003c/strong\u003e Balanced signals measured for pixel pairs A\u003csub\u003e1\u003c/sub\u003eA\u003csub\u003e2\u003c/sub\u003e and B\u003csub\u003e1\u003c/sub\u003eB\u003csub\u003e2\u003c/sub\u003e. \u003cstrong\u003ec\u003c/strong\u003e 3D point could. The color bar represents the values in the z axis (i.e., the depths). \u003cstrong\u003ed\u003c/strong\u003e Picture of a glass plate with a thin metallic foil attached on it. \u003cstrong\u003ee\u003c/strong\u003e Topographic imaging of the glass plate. The optical path (Δd ·\u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e) between the foil and back surface is measured to be 4.694 mm, resulting in a plate thickness of Δd =3.128 mm for the glass refractive index \u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e=1.5008.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/59f1348d0b7fcc8e1dba693f.png"},{"id":69830576,"identity":"700d8666-f3b2-4d83-a1f1-ac0c96a5a5b5","added_by":"auto","created_at":"2024-11-25 15:34:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":208257,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEvaluation of measurement precision and imaging depth. a\u003c/strong\u003e Comparison measurement between our TDS imager (without averaging) and a CW laser interferometer. The offset distance is 1.3 m. \u003cstrong\u003eb\u003c/strong\u003e Measurements with 500-fold averaging. \u003cstrong\u003ec\u003c/strong\u003e Standard deviation (SD) evolving with signal-to-noise ratio (SNR). \u003cstrong\u003ed\u003c/strong\u003e Allan deviation of measurement versus averaging time (averaging number). The standoff distance is ~2 m. Note that the data in \u003cstrong\u003ea\u003c/strong\u003e, \u003cstrong\u003eb\u003c/strong\u003e and \u003cstrong\u003ed\u003c/strong\u003e are calculated for imaging points with SNR \u0026gt;300. \u003cstrong\u003ee\u003c/strong\u003e Balanced signal and EO comb pulse full width at half maximum (FWHM) recorded with tuning f\u003csub\u003er\u003c/sub\u003e from 90 to 300 MHz. \u003cstrong\u003ef\u003c/strong\u003e Imaging of reflections from parts of a positive (front) and a negative 1951-USAF target (behind). They separate at 1.85 m, limited by our optical platform.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/6e1e3296cc381b4205f1159e.png"},{"id":69830578,"identity":"a5aec908-5a54-4dda-821e-0d604f7ba45b","added_by":"auto","created_at":"2024-11-25 15:34:24","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":270397,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eResults of rapid displacement and velocity measurements. a\u003c/strong\u003e Balanced signal versus target displacements (Dd). \u003cstrong\u003eb\u003c/strong\u003e Rapid imaging of two targets moving towards each other. \u003cstrong\u003ec\u003c/strong\u003e Trajectories at two selected imaging points. \u003cstrong\u003ed\u003c/strong\u003e Results of velocity measurements. \u003cstrong\u003ee\u003c/strong\u003e Balanced signals recorded at modulation frequencies of f\u003csub\u003em\u003c/sub\u003e=100 kHz and 1 MHz. For these measurements, the slow cameras are replaced by two fast photodetectors at 1-GHz bandwidth. In this case, the refresh rate of balanced signals is set by the f\u003csub\u003em\u003c/sub\u003e. For the frequency modulation mode, the center f\u003csub\u003er\u003c/sub\u003e of the EO comb is set at 165 MHz with a frequency deviation fixed at 250 kHz. Note that such a small f\u003csub\u003er\u003c/sub\u003e tuning range negligibly impacts the comb pulse width.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/9abcfc59a2092aa3583f6668.png"},{"id":69832231,"identity":"79d3db58-05d5-4c8d-a12d-a6d6bafce9cf","added_by":"auto","created_at":"2024-11-25 15:42:24","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":142826,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAxialprecision versus measurable range for different 3D imaging systems. \u003c/strong\u003eThese systems can be classified into two groups: one characterized by high precision (marked with a green shadow) and the other by large measurement ranges (orange shadow). A trend in 3D imaging technology is the integration of these two features to broaden the scope of applications.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/5b0be6f5727cdc0d60c01bfb.png"},{"id":87556259,"identity":"028d4c95-467d-4da2-a8e9-cc0c6bae1f50","added_by":"auto","created_at":"2025-07-25 07:09:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2272279,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/fc29e8b3-5577-476f-9275-605bc1239bee.pdf"},{"id":69833335,"identity":"2ab3bb43-04ad-48bb-92d6-fe3cf9e51a53","added_by":"auto","created_at":"2024-11-25 15:50:24","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":587842,"visible":true,"origin":"","legend":"Supplementary Materials for Time-Domain Stereoscopic Imaging","description":"","filename":"supplementarymaterialsfinal.docx","url":"https://assets-eu.researchsquare.com/files/rs-5233274/v1/5861e810994f0581eb0b0e64.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Time-domain stereoscopic imaging","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn optics, the parallels between concepts in the spatial and temporal domains, often referred to as space-time duality\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, have led to the development of many revolutionary photonic tools, impacting diverse fields of science and technology, including ultrafast physics, quantum optics, spectroscopy, microscopy, and signal processing. For example, the development of time lenses and time-stretch photonics\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, analogous to focusing and dispersing elements in space, has enabled powerful tools, such as wideband analog-to-digital converters and ultrafast signal processors, uncovering phenomena like optical rogue waves, relativistic electron bunching, and quantum chaos, and unlocking new opportunities for applications such as cancer detection, blood testing, optical computing, and 3D light detection and ranging (lidar)\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eInspired by this duality, we here devise a time-domain stereoscopic technique (TDS), enabling high-precision, large-dynamic-range, far-field 3D optical imaging. Initially, stereoscopic imaging is performed in the spatial domain, which mimics human eyes to perceive depth using two slightly offset cameras to capture two images of the same scene from different angles. The disparity between the two images yields a depth map, enabling 3D reconstruction\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. While effective in fields like robotics and autonomous driving, stereo imaging is limited in axial resolution and accuracy due to insufficient spatially resolving capability, especially in low-contrast, reflective, or textureless environments.\u003c/p\u003e \u003cp\u003eAnalogous to its spatial-domain counterpart, TDS uses two temporally offset cameras to capture two images from the same laser pulse reflected by a target (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). The disparity between these images manifests in the time domain (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb), and this temporal difference, decisive for depth retrieval, is determined precisely and rapidly by leveraging advanced time-domain techniques such as ultrafast optical sampling. Consequently, TDS addresses two key challenges for 3D imaging\u003csup\u003e\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e: 1) integrating high axial resolution and precision with an extended imaging range or depth-of-field (DOF); and 2) performing 3D measurements in a high-speed, real-time fashion. Overcoming these challenges is crucial for surface metrology, remote sensing, mechnical dynamics, and tasks like object recognition, navigation, and scene reconstruction, which have widespread applications in areas like advanced manufacturing, security and defense\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAs a brief introduction, existing 3D optical imaging techniques can be crudely divided into two groups. The first covers large measurement distances (from a few meters to hundreds of meters) but with limited depth resolution and precision (at the millimeter or centimeter levels), including techniques such as stereoscopic imaging, time-of-flight (ToF) ranging cameras\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, structured light projection\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, and the 3D lidar family\u003csup\u003e\u003cspan additionalcitationids=\"CR13\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. The second achieves nanometer precision but is limited to short ranges or DOF (typically to just a few millimeters), including techniques like confocal microscopy\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, optical sampling imaging based on electro-optical or nonlinear effects\u003csup\u003e\u003cspan additionalcitationids=\"CR18 CR19\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, and interferometric imaging and tomography\u003csup\u003e\u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, primarily utilizing an interferometer with a moving arm. Meanwhile, the emergence of optical combs, a coherent light source precisely controlled in both time and frequency domains, opens up new opportunities for lidar\u003csup\u003e\u003cspan additionalcitationids=\"CR26 CR27\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e and high-dimensional imaging\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Particularly, dual-comb interferometry, without the limitation of moving parts, enables rapid, long-range absolute distance measurements via heterodyne detection of two mutually coherent combs\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. This dual-comb concept has been successfully adopted for hyperspectral digital holography\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. However, the requirement for two tightly locked coherent combs, along with the high computational load and low refresh rate, limits its applicability due to complexity, cost, and real-time constraints. Therefore, despite its importance, high-precision, large-range 3D imaging with real-time measurement capability has remained a missing element in the field. The TDS method we propose offers a promising solution to bridge this gap.\u003c/p\u003e\n\u003ch3\u003eBasic concept and principle\u003c/h3\u003e\n\u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea conceptually compares TDS with conventional stereo imaging (see details in Supplementary Fig.\u0026nbsp;1 and Supplementary Table\u0026nbsp;1). In both cases, achieving high depth precision and accuracy hinges on precisely measuring minute disparities. This task proves challenging in the space domain (fundamentally due to the diffraction limit); conversely, exploiting the time domain benefits from advancements in optical comb and precise timing technologies. Specifically, in TDS, a laser pulse reflected by a target is captured by two cameras gated with a slight temporal offset, yielding distinct electrical signals (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). This imbalance (ΔI) is governed by the temporal difference (Δt) between the pulse flight time (T\u003csub\u003eD\u003c/sub\u003e) and the paired time gates, where Δt\u0026thinsp;=\u0026thinsp;T\u003csub\u003eD\u003c/sub\u003e-\u003cem\u003em\u003c/em\u003e/f\u003csub\u003er\u003c/sub\u003e and \u003cem\u003em\u003c/em\u003e/f\u003csub\u003er\u003c/sub\u003e represents a multiple of the repetition period of the gates (provided the two gates are synchronized). The pulse and the paired gates overlap optimally at a zero-crossing point (the middle case in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb), where Δt\u0026thinsp;=\u0026thinsp;0 and T\u003csub\u003eD\u003c/sub\u003e=\u003cem\u003em\u003c/em\u003e/f\u003csub\u003er\u003c/sub\u003e. The integer \u003cem\u003em\u0026thinsp;=\u003c/em\u003e\u0026thinsp;f\u003csub\u003er1\u003c/sub\u003e/Δf\u003csub\u003er\u003c/sub\u003e, where Δf\u003csub\u003er\u003c/sub\u003e=f\u003csub\u003er2\u003c/sub\u003e-f\u003csub\u003er1\u003c/sub\u003e, is obtained in a stroboscopic fashion, as \u003cem\u003em\u003c/em\u003e/f\u003csub\u003er1\u003c/sub\u003e=(\u003cem\u003em\u003c/em\u003e\u0026thinsp;+\u0026thinsp;1)/f\u003csub\u003er2\u003c/sub\u003e, given two adjacent zero-crossing points at f\u003csub\u003er1\u003c/sub\u003e and f\u003csub\u003er2\u003c/sub\u003e, with f\u003csub\u003er1\u003c/sub\u003e\u0026lt;f\u003csub\u003er2\u003c/sub\u003e. Consequently, a target distance (\u003cem\u003eD\u003c/em\u003e) is determined as \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ec\u003c/em\u003e\u0026middot;T\u003csub\u003eD\u003c/sub\u003e\u003cem\u003e/\u003c/em\u003e2\u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ec\u003c/em\u003e/(2\u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e\u0026middot;Δf\u003csub\u003er\u003c/sub\u003e), where \u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e is the reflective index of the air and \u003cem\u003ec\u003c/em\u003e is the speed of light in a vacuum. Note that there are two prerequisites: 1) timing the gates precisely, which is available using optical combs; 2) the gates shorter than or comparable to the laser pulse, achievable via optical gating.\u003c/p\u003e \u003cp\u003eA key advantage of TDS over a conventional ToF camera is its superior noise immunity. A similar analogy can be drawn when comparing single-detector cross-correlation with balanced cross-correlation (BCC) in laser synchronization experiments\u003csup\u003e\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. The balanced one significantly improves timing precision to the attosecond level, surpassing the former by orders of magnitude, through the elimination of common-mode optical and electrical noise. This advantage also applies to TDS, rendering it inherently sensitive to minute changes in time as well as in distance\u0026mdash;a core feature of this approach. Note that the BCC scheme has been adopted for high-precision single-point rangefinding\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Here, we explore its potential for TDS imaging that exploits time-domain parallax.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn our proof-of-concept demonstration, TDS is carried out by a novel balanced imaging system (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) comprising a type-II periodically poled KTiOPO\u003csub\u003e4\u003c/sub\u003e (PPKTP) crystal and two identical cameras. The linearly polarized reference pulse serves as an optical gate for sampling the detection pulse with orthogonal polarization. Optical sampling occurs twice within the same PPKTP crystal via a bidirectional sum-frequency generation process. This type-II crystal induces temporal walk-off between the detection pulse and the reference gate pulse, causing the detection pulse to be sampled twice with a small temporal offset before being captured by the respective cameras.\u003c/p\u003e \u003cp\u003eTwo points in this scheme should be noted. First, an ultrashort pulsed laser with a well-defined, rapidly tunable repetition frequency across a broad range is essential. To achieve this, we utilize a frequency-swept electro-optical (EO) comb. In practice, to measure distance, we record the balanced signal (ΔI) while linearly sweeping the comb\u0026rsquo;s f\u003csub\u003er\u003c/sub\u003e, and then identify the zero-crossing points during data post-processing, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb. Second, the central region of the balanced curve establishes a direct correspondence between intensity and time (or intensity and displacement), enabling 3D measurements from single frames.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eExperimental setup\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOur setup begins with an EO comb seeded by a narrow-linewidth CW laser at 1550 nm (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). This comb shares a configuration similar to previously reported sources\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e, as detailed in the \u003cspan refid=\"Sec9\" class=\"InternalRef\"\u003eMethods\u003c/span\u003e section and Supplementary Fig.\u0026nbsp;2. Briefly, the EO comb translates a radio-frequency (RF) sinusoidal wave, generated by a hydrogen-maser-disciplined RF synthesizer, into a sequence of sub-500 fs optical pulses, using a single intensity modulator and dispersion managed nonlinear fibers. Notably, the EO comb\u0026rsquo;s f\u003csub\u003er\u003c/sub\u003e ​is directly set by the RF synthesizer, offering several benefits, including the elimination of frequency locking and counting, as well as wide-range frequency tuning with high linearity (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The comb\u0026rsquo;s response to the RF driving signal is instantaneous, with negligible deviation within the resolution bandwidth of observation (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb inset). Also, the comb maintains its pulse shape and temporal width when increasing the tuning speed or the modulation frequency (f\u003csub\u003em\u003c/sub\u003e), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec, showing the potential for fast measurement (discussed later). Importantly, the comb inherits the excellent frequency stability of the RF synthesizer (reaching 4\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;13\u003c/sup\u003e in 300 s, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed), ensuring precise distance assessment.\u003c/p\u003e \u003cp\u003eFor remote sensing, the comb output is amplified to 200 mW average power via an erbium-doped fiber amplifier (EDFA) and equally split between the detection and reference arms. In the detection light path, the comb pulses pass through a beam expander, subsequently illuminating a 3D scene with staggered mirrors and a resolution test target (1951 USAF) in front. A quarter-wave plate (QWP) and a polarization beamsplitter (PBS) serve as a free-space circulator, guiding the reflected detection pulses to another beam expander for optical scaling, and then to the balanced imager through a second PBS, which combines the detection and orthogonally polarized reference pulses.\u003c/p\u003e \u003cp\u003eThe balanced imaging unit comprises twin 4f imaging systems\u0026mdash;one with lenses L\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003e2\u003c/sub\u003e, and the other with lenses L\u003csub\u003e3\u003c/sub\u003e and L\u003csub\u003e4\u003c/sub\u003e\u0026mdash;in the opposing light paths (indicated by pink arrows in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). The two imaging subsystems share a single type-II PPKTP crystal, where object images from both directions converge at its center in the Fourier plane. Inside, the reference pulses convert the detection pulses into sum-frequency signals at 775 nm, which are captured by two synchronized CMOS (complementary metal-oxide-semiconductor) cameras. Note that, to serve as pump light for sum-frequency generation, the 2.2-mm diameter (full width at 1/\u003cem\u003ee\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) reference beam bounces through the crystal without focusing, minimizing spatial filtering effects on lateral resolution. As such, we achieve an optimal lateral resolution of 6 \u0026micro;m (limited by the crytal\u0026rsquo;s transverse section) with a field-of-view (FOV) of 560\u0026times;420 \u0026micro;m\u0026sup2; (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee). Currently, the 4-mm crystal (operating at room temperature) limits the acceptance angle to 3.5\u0026deg; (Supplementary Fig.\u0026nbsp;3) due to phase-matching restrictions commonly encountered by nonlinear optical imagers. This problem can be solved by changing the operating temperature or the poling structure of a nonlinear crystal\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Nevertheless, adjusting the magnifications of the two beam expanders in our setup allows for a broader view, such as a FOV of 3.5\u0026times;2.6 cm\u0026sup2; in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef, at the cost of a degraded lateral resolution (315 \u0026micro;m) due to the cameras\u0026rsquo; fixed pixel density (1440\u0026times;1080 pixels). To maintain high lateral resolution over a large FOV, high-resolution images obtained by beam steering can be stitched together, such as a full image of the 1951-USAF target (7.62\u0026times;7.62 cm\u0026sup2;) made from 46 sub-images (Supplementary Fig.\u0026nbsp;4).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eRemote 3D imaging and depth measurement\u003c/h3\u003e\n\u003cp\u003e \u003c/p\u003e \u003cp\u003eFirst, we demonstrate TDS for 3D imaging by detecting four staggered mirror targets at a standoff distance of \u0026gt;\u0026thinsp;1.3 m (from a reference point). Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea exemplifies 2D images recorded by the two cameras at a frame rate of 165 fps (frames per second), with the comb f\u003csub\u003er\u003c/sub\u003e linearly changing from 165.33 to 165.60 MHz. For these images, we identify spatially correlated pixel pairs, such as points A\u003csub\u003e1\u003c/sub\u003e and A\u003csub\u003e2\u003c/sub\u003e or B\u003csub\u003e1\u003c/sub\u003e and B\u003csub\u003e2\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea), by matching corresponding features with a widely-used scale-invariant feature transform (SIFT) algorithm\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. We then obtain the balanced signals from the paired pixels A\u003csub\u003e1\u003c/sub\u003eA\u003csub\u003e2\u003c/sub\u003e and B\u003csub\u003e1\u003c/sub\u003eB\u003csub\u003e2\u003c/sub\u003e, as plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb. By linear fitting the central potions of the signals, we determine the zero-crossing points at 165.372 MHz and 165.510 MHz for A\u003csub\u003e1\u003c/sub\u003eA\u003csub\u003e2\u003c/sub\u003e and B\u003csub\u003e1\u003c/sub\u003eB\u003csub\u003e2\u003c/sub\u003e, respectively. We continue tuning f\u003csub\u003er\u003c/sub\u003e, searching for the second zero-crossing points and calculating Δf\u003csub\u003er\u003c/sub\u003e as 16.54 MHz for A\u003csub\u003e1\u003c/sub\u003eA\u003csub\u003e2\u003c/sub\u003e and 16.55 MHz for B\u003csub\u003e1\u003c/sub\u003eB\u003csub\u003e2\u003c/sub\u003e, which determine their absolute distances to be d\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1.308 m and d\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1.3 m, respectively. The effective optical path difference (d\u003csub\u003e0\u003c/sub\u003e) between the detection and reference arms at the reference point in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea is pre-calibrated to be 15.5 m.\u003c/p\u003e \u003cp\u003eIn this measurement, we simultaneously obtain range information for dense spatial points (up to 4.67\u0026times;10\u003csup\u003e7\u003c/sup\u003e pixel pairs), visualized as a false-color 3D point cloud in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec. For display, the axial (\u003cem\u003ez\u003c/em\u003e) coordinates are referenced to the point B\u003csub\u003e1\u003c/sub\u003eB\u003csub\u003e2\u003c/sub\u003e. Also, points lacking illumination or without sufficient signal-to-noise ratio (SNR) are not displayed. Note that, the f\u003csub\u003er\u003c/sub\u003e tuning step size is 606 Hz/frame, resulting in an axial resolution of 33 \u0026micro;m (Methods). This resolution can be improved to 54 nm with a step size of 1 Hz/frame at the cost of longer tuning time.\u003c/p\u003e \u003cp\u003eIn another example, we perform 3D imaging on a 30%-reflective unpolished metallic foil attached to a 1-inch glass plate (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). This target is positioned 1.3 m away. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee presents a topographic image showing reflections from both the foil and the glass back surface. This showcases our method\u0026rsquo;s ability to remotely profile metal component surfaces and complex patterns, which is applicable for industrial inspection.\u003c/p\u003e\n\u003ch3\u003eAxial precision and imaging depth\u003c/h3\u003e\n\u003cp\u003e \u003c/p\u003e \u003cp\u003eNext, we assess measurement precision and accuracy by measuring the displacements of a mirror mounted on a translation stage. We compare the TDS results with the truth data obtained by a CW interferometer. Statistical analysis over 50 individual measurements (without averaging) at each displacement yields a 2-σ standard deviation (SD) within \u0026plusmn;\u0026thinsp;10 \u0026micro;m, where the mean values deviate from the truth data by less than 2 \u0026micro;m (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). With 500-fold averaging, the ranging precision improves to \u0026plusmn;\u0026thinsp;400 nm with an accuracy reaching sub-100 nm (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). Note that, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec, the measured SD linearly depends on signal-to-noise ratio (SNR), which can be improved by using a high-power comb and low-noise cameras.\u003c/p\u003e \u003cp\u003eFor further evaluation, we perform Allan deviation measurements. Experimentally, we fix the comb\u0026rsquo;s f\u003csub\u003er\u003c/sub\u003e at a zero-crossing point, converting intensity variations of the balanced signal to deviations in distance by a conversion factor of 3.03 \u0026micro;m. The same factor is also used for evaluating background noise of a camera (by blocking the comb light). Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed shows the results with data acquired at a frame rate of 132 fps. Our method (data in light blue) results in a precision of ~\u0026thinsp;80 nm in 25 s, which is close to the camera\u0026rsquo;s noise background (in purple) and is nearly 50 times better than the unbalanced results (~\u0026thinsp;4 \u0026micro;m, shown in pink and green) obtained by single cameras (Methods), demonstrating the key advantage of our method over direct ToF cameras. The off-the-shelf cameras we currently use limit the axial precision due to their moderate sensitivity and uncontrolled electronic noise. Replacing the cameras with two low-noise single-point photodetectors achieves 30 nm ranging precision in 2 s at a distance of \u0026gt;\u0026thinsp;30 m (see Supplementary Fig.\u0026nbsp;5).\u003c/p\u003e \u003cp\u003eEssentially, TDS is a ranging technique, subject to dead zones dictated by the tunable range of f\u003csub\u003er\u003c/sub\u003e. Luckily, the EO comb, without an optical cavity, exhibits a broad tuning range of over 200 MHz, with f\u003csub\u003er\u003c/sub\u003e tunable from 90 to 300 MHz (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eg), limited by the bandwidth of electronics for EO comb generation. Nevertheless, this tuning range results in a dead zone of 0\u0026ndash;0.5 m, which has been offset by the extra optical path in the detection arm and can therefore be neglected. Note that sweeping f\u003csub\u003er\u003c/sub\u003e across a broad range changes the comb pulse width (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eg) due to unbalanced nonlinearity and dispersion, impacting the SNR and the widths of balanced signals (Supplementary Fig.\u0026nbsp;6). However, thanks to the balanced architecture, the zero-crossing points remain unaffected, maintaining their frequencies (f\u003csub\u003er\u003c/sub\u003e) and separations (Δf\u003csub\u003er\u003c/sub\u003e). Consequently, our method permits large measurable ranges and imaging depths. An example for range imaging at a folded distance of 9.6 m is shown in Supplementary Fig.\u0026nbsp;7. With this enhanced ranging capability, our system can image objects at largely different depths. For instance, the images of two staggered objects are dispalyed in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eh, and their spatial separation (1.85 m) is measured. Note that, for the displayed lateral resolution of 890 \u0026micro;m, the theoretical DOF allowed by our imaging system is 2.4 m (Supplementary Note 1). A larger DOF can be achieved, but at the cost of reduced lateral resolution.\u003c/p\u003e\n\u003ch3\u003eHigh-speed 3D measurement\u003c/h3\u003e\n\u003cp\u003e \u003c/p\u003e \u003cp\u003eFinally, we demonstrate the real-time measuring capability of our method, which is based on the intensity-to-displacement relationship established by fixing the f\u003csub\u003er\u003c/sub\u003e at a zero-crossing point. As exemplified in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea, the highly linear region of a balanced curve (shadowed in grey) links its intensity to a target displacement (Δd), which is pre-calibrated by scanning the reference arm. Alternatively, calibration can be done without motion by sweeping the f\u003csub\u003er\u003c/sub\u003e (Methods). As such, our method enables parallel displacement and velocity measurements of moving targets within a single frame, a task that is difficult for interferometric imagers due to the complexity of signal processing.\u003c/p\u003e \u003cp\u003eIn an experiment, we capture reflections of two mirrors (behind the 1951-USAF target) moving oppositely at similar speeds of ~\u0026thinsp;5 mm/s. Using pre-calibrated intensity-to-displacement relationships (similar to the one in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea), we simultaneously measure displacements at over a million spatial points with 132 Hz data refresh rate, corresponding to a temporal resolution of 7.576 ms and a pixel rate of 205.3 megapixels/s. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb exemplifies the 3D images in motion. The trajectories of two counter-propagating imaging points (each on a mirror) are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec, the derivatives of which reveal the instantaneous velocities of the two mirrors (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed). Our setup currently allows a maximum measurable velocity of 330 mm/s, limited by the linear region (~\u0026thinsp;2 mm) and the cameras\u0026rsquo; maximum frame rate (165 fps, corresponding to a pixel rate of 256.6 MHz). Employing high-speed CMOS cameras (e.g., Photron, Mini AX200, with a frame rate up to 900k fps) can increase the measurable velocity to, e.g., 520 m/s. Also, the real-time measurable displacements (\u0026lt;\u0026thinsp;2 mm) can be extended by rapidly tuning the f\u003csub\u003er\u003c/sub\u003e, which allows fast adjustment of the zero-crossing point and calibration of Δd, e.g., within 0.5 \u0026micro;s using high-speed photodetectors (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ee). Therefore, our method shows great potential for capturing dynamic 3D scenes, enabling studies of mechanical vibrations and deformations\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eBenefiting from optical sampling and femostecond EO comb synthesis, our system achieves sub-100 nm precision at a meter-level distance for 3D imaging. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the dynamic range of our setup, defined as 10\u0026middot;log(measurable range/precision), reaches 74 dB, underscoring its advantage over the aforementioned systems and other 3D imagers\u003csup\u003e\u003cspan additionalcitationids=\"CR40 CR41 CR42 CR43\" citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. Besides, compared to mode-locked laser combs in some advanced lidar or imaging systems\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e, the cavity-free EO comb in our setup offers additional merits in terms of reduced complexity, ease of operation, lower cost, and greater environmental immunity\u0026mdash;all crucial for practical use. Also, recent advances in lithium niobate photonics have enabled on-chip fs EO comb generation\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e, paving the way for a more compact and minimized system design.\u003c/p\u003e \u003cp\u003eLike other nonlinear optical sampling imagers\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, our system encounters challenges in lateral resolution, angular FOV, and, most critically, light detection efficiency. Fortunately, advancements in nonlinear optical materials and semiconductor sensors present potential solutions. For instance, larger PPKTP crystals theoretically permit higher lateral resolution, and linearly chirped ones might expand the angular FOV to, e.g., 36.7\u0026deg;, with minimal conversion efficiency loss (Supplementary Fig.\u0026nbsp;3). Moreover, the development of electron-multiplying CCDs has enabled nonlinear upconversion imaging at the single-photon level\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, albeit with longer integration times. This level of sensitivity enables our method to perform scanner-less range imaging, even over long distances, or in low-light conditions, as well as high-precision 3D profiling of rough, low-reflective surfaces.\u003c/p\u003e \u003cp\u003eWith ongoing advances in semiconductor sensors and digital camera technology\u0026mdash;particularly in pixel density, sensitivity, and speed\u0026mdash;our method is promising for various applications\u003csup\u003e\u003cspan additionalcitationids=\"CR7 CR8 CR9\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, such as identifying defects on semiconductor wafers, examining crucial automotive and aerospace components for micro-level deformations, ensuring precise positioning during laser machining processes, and charaterizing dynamic behaveiours in micromechical devices, among others. Additionally, shifting the comb wavelength to the mid-infrared region would enable broader applications in biomedical imaging and materials science\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn conclusion, we present, for the first time, a time-domain stereoscopic approach that offers high precision over large imaging ranges and facilitates rapid, parallel displacement and velocity measurements, thereby introducing a powerful tool for diverse 3D imaging applications.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eEO comb generation\u003c/h2\u003e \u003cp\u003eTo generate the EO comb, a CW laser at 1550 nm (Adjustik E15, NKT Photonics; linewidth\u0026thinsp;\u0026lt;\u0026thinsp;0.1 kHz; 40 mW) is fed into an intensity modulator (IM, 40-GHz bandwidth; KY-MU-15-DQ-A, Keyang Photonics), which is driven by an electrical pulse generator that converts the output of an RF synthesizer (N5173B, Keysight) into 30-ps electrical pulses. The IM output is amplified to 150 mW using a custom-built fiber amplifier, followed by a 180-m-long dispersion-managed highly nonlinear fiber for spectral broadening. This fiber has a zero-dispersion wavelength at 1550 nm, a linear dispersion slope of 0.03 ps/(nm\u0026sup2;\u0026middot;km), a loss coefficient of less than 1.5 dB/km, and a nonlinear coefficient greater than 10 W⁻\u0026sup1;km⁻\u0026sup1;. The comb pulses (-10 dB spectral width\u0026thinsp;\u0026gt;\u0026thinsp;10 nm) are then compressed by fiber Bragg gratings, producing sub-500 fs optical pulses.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eBalanced TDS imaging system\u003c/h2\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, the imaging system employs two identical CMOS cameras (MV-CA016-10UM) to capture the correlated sum-frequency signals. An electrical circuit triggers the cameras in sync with the frequency tuning of the RF synthesizer. In the BCC unit, a type-II PPKTP crystal (CASTECH, 1\u0026times;2\u0026times;4 mm\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e for height, width and length) is used for two key reasons. First, it creates a temporal walk-off between two orthogonally polarized pulses, necessary for balanced signal generation. To make this walk-off adjustable, an additional polarized beamsplitter (PBS) and two mirrors (M\u003csub\u003e5\u003c/sub\u003e and M\u003csub\u003e6\u003c/sub\u003e in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) are incorporated, with their relative positions adjustable. Note that the walk-off effect inevitably limits the sum-frequency generation efficiency (~\u0026thinsp;0.053 mW/W\u003csup\u003e2\u003c/sup\u003e). Second, the crystal prevents second harmonic generation of each pulse, ensuring a zero background.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eCalculation of SNR and axial resolution\u003c/h2\u003e \u003cp\u003eThe SNR of a balanced trace is defined as its peak value divided by the SD of a background region where the detection and reference pulses are fully separated. The axial resolution (R\u003csub\u003ez\u003c/sub\u003e) of TDS is determined by δf, the tuning step of f\u003csub\u003er\u003c/sub\u003e, as R\u003csub\u003ez\u003c/sub\u003e=\u003cem\u003ec\u003c/em\u003e/2\u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e \u0026middot;Δf\u003csub\u003er\u003c/sub\u003e/(f\u003csub\u003er\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;δf)\u0026middot;δf, where the speed of light \u003cem\u003ec\u0026thinsp;=\u003c/em\u003e\u0026thinsp;299,792,458 m/s and the refractive index in air \u003cem\u003en\u003c/em\u003e\u003csub\u003er\u003c/sub\u003e= 1.0003. Therefore, we have an axial resolution of 33 \u0026micro;m for δf\u0026thinsp;=\u0026thinsp;606 Hz/frame and 54 nm for δf\u0026thinsp;=\u0026thinsp;1 Hz/frame, when f\u003csub\u003er\u003c/sub\u003e=166.3 MHz and Δf\u003csub\u003er\u003c/sub\u003e=16.6 MHz. Also, based on the above relationship, we can calibrate the curve in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea by sweeping the f\u003csub\u003er\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eIntensity-to-displacement conversion factors\u003c/h2\u003e \u003cp\u003eFor calculating the intensity-to-displacement conversion factor, we measure a balanced trace similar to that in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea and then linearly fit the central region, resulting in a slope of 3 \u0026micro;m, i.e., the conversion factor. For Allan deviation measurement with a single camera, we use a conversion factor of 6.1 \u0026micro;m, obtained by linear fitting the central part of the rising edge of a cross-correlation trace. We then measure the intensity fluctuations at the center point of the rising edge with a fixed f\u003csub\u003er\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor contributions\u003c/h2\u003e\n\u003cp\u003eM.Y. and H.Z. conceived the idea and designed the experiments. Z.W. and H.M. conducted the experiment and drafted the manuscript. Z.W., H.M. and J.L. analyzed the data. M.Y., K.H., and J.F. build the comb source. M.Y., H.Z., J.G., and K.H. revised the manuscript. All authors provided comments and suggestions for improvements.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003ch2\u003eData availability\u003c/h2\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the\u0026nbsp;corresponding\u0026nbsp;author upon reasonable request.\u003c/p\u003e\n\u003ch2\u003eAuthor information\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eCorrespondence and requests for materials should be addressed to M.Y. ([email protected]), \u0026nbsp;or to H.Z. ([email protected]).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eSalem, R., Foster, M. A. \u0026amp; Gaeta, A. L. Application of space\u0026ndash;time duality to ultrahigh-speed optical signal processing. \u003cem\u003eAdv. Opt. 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However, its depth precision and accuracy are limited by insufficient spatial resolving power. Achieving high precision alongside extensive measurable ranges and high-speed measuring capabilities has long been a challenge in 3D imaging. To address this, we introduce time-domain stereoscopy, a concept inspired by space-time duality in optics. Specifically, it employs two temporally offset optical gating cameras to capture time-domain parallax signals, enabling rapid and precise time-of-flight measurements for depth retrieval. Leveraging two advanced technologies—femtosecond electro-optical comb synthesis and nonlinear optical sampling—this method achieves sub-100 nm depth precision across multimeter-scale imaging ranges and supports millisecond-scale displacement and velocity measurements for 47 million spatial points simultaneously. As such, it provides a versatile tool for applications in surface metrology, mechanical dynamics, and precision manufacturing.\u003c/p\u003e","manuscriptTitle":"Time-domain stereoscopic imaging","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-25 15:34:19","doi":"10.21203/rs.3.rs-5233274/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"cf5ab2ea-97d6-43f8-a40f-f6fdd7baca3e","owner":[],"postedDate":"November 25th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":39267411,"name":"Physical sciences/Optics and photonics/Optical techniques/Imaging and sensing"},{"id":39267412,"name":"Physical sciences/Optics and photonics/Other photonics/Optical metrology"}],"tags":[],"updatedAt":"2025-07-25T07:09:03+00:00","versionOfRecord":{"articleIdentity":"rs-5233274","link":"https://doi.org/10.1038/s41467-025-62228-5","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-07-24 04:00:00","publishedOnDateReadable":"July 24th, 2025"},"versionCreatedAt":"2024-11-25 15:34:19","video":"","vorDoi":"10.1038/s41467-025-62228-5","vorDoiUrl":"https://doi.org/10.1038/s41467-025-62228-5","workflowStages":[]},"version":"v1","identity":"rs-5233274","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5233274","identity":"rs-5233274","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}