Operation principle of the line-scan TOF camera. The operation principle of the demonstrated line-scan TOF camera is shown in Fig. 1. Space-to-wavelength encoding11,32,33 with a broad spectrum of a mode-locked Er-fibre optical frequency comb is used to accomplish the line-scan illumination with few-micrometre lateral resolution along several millimetres range. The spectrum of an optical frequency comb (1537 nm − 1577 nm in this work) is spatially dispersed by a diffraction grating to encode one-dimensional spatial coordinates into the wavelengths. The beam size incident on the diffraction grating is expanded until its spectral resolution reaches ~ 0.038 nm, resulting in ~ 1000 resolvable sub-pulses from ~ 40 nm bandwidth of the frequency comb, which corresponds to the pixel number of the used line-scan camera (1024 pixels in this work). When focused on a sample, the dispersed sub-pulses generate a long and narrow line with 9.5-µm width and > 4.4-mm length (see Fig. 2c), wherein each sub-pulse undergoes different TOF corresponding to the instantaneous surface profile. Note that, while the space-to-wavelength encoding was recently used for other frequency comb-based imaging methods, they suffered from low pixel-number and axial resolution of tens of micrometres32–35 due to the degraded temporal confinement of sub-pulses. To overcome this limitation, we employed an electro-optic-sampling-based timing-detector (EOS-TD)36–39 for parallel detection of the TOFs of sub-pulses (see Supplementary Note 1, Supplementary Fig. 1 and refs. 37–40 for more information on the operation principle of the EOS-TD). Here the EOS-TD can detect the relative timing and TOF changes between optical pulses and frequency-locked periodic electric waveforms, such as photocurrent pulses derived from high-speed photodetection40 or timing-synchronized microwave signals36,38,41, with attosecond-level resolution. While the EOS-TD was recently used to measure the single-point TOF of ~ 300-fs-long optical pulses with sub-nanometre resolution42, in this work, we showed that sub-nanometre axial resolution can be obtained for sub-pulses with > 90 ps pulse width as well, allowing massively parallel TOF detection of > 1000 sub-pulses over a several mm-long horizontal coordinate.
When the reflected sub-pulses are applied to the EOS-TD, a unidirectional electro-optic phase modulator inside the differential-biased fibre Sagnac-loop phase-modulates them with respect to the timing ruler provided by the periodic electric waveform, resulting in the conversion of their TOF variations into the spectral intensity variations at the Sagnac-loop output. In this work, the rising edge of photocurrent pulses extracted from a modified-uni-travelling carrier (MUTC) photodiode or the microwave signal generated from a frequency-locked voltage-controlled oscillator (VCO) were employed as the periodic electric waveform for realizing a precise yet long-range timing ruler of optical pulses. The EOS-TD converts the timing error between each sub-pulse and the centre of the timing ruler signal into a parallel intensity change at the EOS-TD output via the Sagnac-loop action. As the 1024-pixel InGaAs line-scan camera analyses the optical spectrum of the EOS-TD output, the TOF profile of more than 1000 resolvable positions is simultaneously reconstructed by mapping the spectral wavelength and intensity into the position and TOF, respectively. Note that, although the divided sub-pulses have > 90 ps pulse width due to their ~ 0.038 nm wavelength resolution, the electro-optic sampling process in the EOS-TD still enables sub-nm precision while maintaining the few-micrometric spatial resolving power.
Axial and lateral resolutions. Figure 2a shows the measured axial precision performance in terms of overlapping Allan deviation. The axial precision is tested under different bias voltages applied to the 22-GHz MUTC photodiode. Higher bias voltage causes photocurrent pulses to have a sharper rising edge, resulting in 3 mm, 1.6 mm, and 1.2 mm measurable range for 4 V, 8 V, and 16 V bias voltages, respectively (see inset of Fig. 2a). Due to the sharper rising edge, the axial precision can be improved with higher bias voltage at the expense of slightly narrower measurable range. At 3.9-µs acquisition time (260 megapixels/s pixel rate), which is the shortest acquisition time of the used line-scan camera, the axial precision under 16-V bias voltage is 155 nm. Note that, as the EOS-TD can output the spectrum-encoded TOF profile with every pulse repetition period (4-ns in this work), the maximum acquisition rate can be improved with a faster line-scan camera. As increasing the acquisition time (i.e., data accumulation or increasing exposure), the averaging effect enables precision improvement until slow timing drift kicks in; when using a 16-V bias voltage, the best precision of 580 pm can be obtained at 2.6-s averaging time (394 pixels/s). When such high-precision performances are combined with > mm measurable ranges, large dynamic-ranges up to 126 dB can be realized. The achievable axial precision at each pixel is limited by the signal-to-noise ratio (SNR) of the camera background noise (white noise). As a result, as shown in Fig. 2b, the achievable axial precision at each pixel has a spectral intensity dependence, ranging from 3.5 nm to 7.4 nm for 10-ms acquisition time (~ 100 kilopixels/s pixel-rate) under 16-V bias condition.
Note that, by saturating the camera, the precision performance can be further improved while slightly sacrificing the measurable range. For example, as shown in Fig. 2a, when increasing the camera electrical gain by 5 times, the camera becomes saturated when the relative timing exceeds ~ 400 µm (when 16 V bias is used). Due to the increase in TOF detection sensitivity, 47 nm precision can be obtained at 3.9 µs acquisition time (260 megapixels/s), which is a ~ 3 times improvement. By accumulating data points, the best precision reaches 330 pm at 0.87 s acquisition time (~ 1.2 kilopixels/s). Since the SNR is almost maintained, the dynamic range is maintained at ~ 122 dB.
When a lens with 30-mm focal length (f) is used, the beam sizes (1/e2) of the sub-pulses are measured to be ~ 9.5 µm, and the total horizontal field-of-view (FOV) reaches > 4.4 mm (Fig. 2c). A resolution test target (1951 USAF) is used to assess lateral (spatial) resolution. The measured 2D image of the normalized return power spectra is shown in Fig. 2d when the target is laterally scanned along the Y direction. As the patterns of Element 6 in Group 6 are resolved with ~ 23% contrast, the spatial resolution is determined to be ~ 114 lp/mm (4.38 µm)43. Note that the lateral resolution and horizontal FOV can scale with the effective focal length.
Surface profile imaging and step heights measurement results. By rapidly scanning the target in the direction perpendicular to the line (Y direction) using a motorized stage, both ultrafast 3D imaging of surface profiles and precise measurement of step heights can be achieved using the line-scan TOF camera. First, a gauge block assembly with a 300-µm step height made of the same material (chromium carbide) is imaged as shown in Fig. 3a. At 10-kHz line-scan rate (10 megapixels/s pixel-rate), the step height is determined to be 300.029 µm with repeatability (1–σ) of 31 nm for 100 consecutive measurements. To assess the accuracy of the measurement, a calibrated interferometer44 with an expanded uncertainty of 40 nm (k = 2, level of confidence 95%) is used, and the determined central length is 299.998 µm. The + 31 nm error is within the uncertainty due to the flatness of gauge blocks. The demonstrated TOF camera can also measure the surface profiles and step heights of structures made of different materials with different reflectance. Two steel gauge blocks are wrung on a ceramic optical flat, as shown in Fig. 3b, with a reflectance difference of > 5 times. The two step heights of 100 µm and 500 µm are clearly measured, with 86 nm (93 nm) repeatability at 10-kHz acquisition rate (10 megapixels/s pixel-rate) for 100 consecutive measurements of the 100-µm (500-µm) heights. The determined step height shows + 15 nm and \(-\)22 nm errors from the calibrated interferometry results (100.014 µm and 500.060 µm). Note that, compared to Fig. 3a, the repeatability is slightly degraded due to the lower reflected optical power from the ceramic optical flat, which resulted in a degradation in TOF measurement precision. High axial and lateral resolutions also allow for precise profiling of more complicated structures. As shown in Fig. 3c, a silicon sample coated with 100-nm thick silver is prepared as a periodic structure with trenches and pillars of 100-µm width and ~ 10-µm height, repeated with 100-µm spacings. The mean step height (difference between two mean heights) is measured to be 10.039 µm, which is -14 nm off from a confocal microscopy result (10.053 µm, see Supplementary Fig. 2).
Note that, for accuracy and repeatability evaluations, the 3D imaging results shown in Fig. 3 were obtained by synchronizing the line acquisition and motor movement: each line data is acquired once the motor has settled down to avoid motor vibration-induced uncertainty. Higher-speed 3D imaging can be achieved by rapidly scanning the target without synchronization. When the gauge-blocks are rapidly scanned (with the motor’s fastest scanning speed; 0.7 m/s), as shown in Supplementary Fig. 3, the 3D imaging takes just 1.4 ms to analyse a 6.4 mm⋅1 mm region with 1024⋅358 pixels resolution. Note that the achieved pixel rate (260 megapixels/s) corresponds to > 120 Hz frame rate (3D image refresh rate) 3D profile recording in full high definition (FHD, 1920⋅1080 pixels resolution). Although the target is scanned stepwise in this study due to the mechanical limitations of the motor, the acousto-optic deflection13,45 may be employed to enable vibration-free and high-speed scanning in the future.
Real-time dynamic imaging results. The inertia-free scanning and large dynamic-range capabilities enable us to capture ultrafast mechanical motions with > 400 m/s speed. As the first example of functionality validation, the interaction between two piezoelectric transducer (lead zirconate titanate, PZT)-mounted mirrors that are firmly fastened on a rigid plate (Fig. 4a) is observed. When the two mirrors are driven at resonances of 11.5 kHz and 10.7 kHz, respectively, their interaction builds a beating pattern repeating every 1.25 ms at steady-state. As shown in Supplementary Video 1, the two mirrors’ interacting motion is composed of irregular and multi-harmonic motions, yet can be readily analysed without requiring data accumulation or entire movement repetition1,22,31. During the interaction, the instantaneous speed reaches up to ~ 4 m/s, which can make accurate distance determination difficult in interferometry-based methods. Although there exists just a few ms of non-repetitive transient before settling down to the steady-state, the demonstrated line-scan TOF camera allowed real-time observation of the transient motions (Fig. 4a).
As another example of real-time dynamics capture, we performed the dynamic imaging of mechanical motions of MEMS bridge (i.e., double-clamped beam) device. By aligning the line beam in bridge’s longitudinal direction, various resonant motions can be observed in real-time. For this experiment, a 1010-µm long and 90-µm wide silicon micro-bridge is prepared (see Methods). In order to reduce rotating motion-induced path length error and enhance TOF detection accuracy, instead of a diffraction grating, we designed and implemented another space-to-wavelength encoding device by combining a dense wavelength division multiplexing (DWDM) coupler and fibre bundle (see Methods and Supplementary Fig. 4). When spectrally divided beams are focused on the bridge under test, the 14 beams (14 DWDM channels) are irradiated to the sample with ~ 6.7 µm beam size and ~ 70 µm spacing (see Supplementary Fig. 4). As shown in Fig. 4b and Supplementary Video 2, five flexural modes of the bridge (4.0 kHz, 13.6 kHz, 31.6 kHz, 57.7 kHz, and 80.9 kHz) could be clearly observed. At resonances, the bridge oscillates with amplitudes ranging from hundreds nm to tens µm, and the instantaneous speed of some spatial points exceeds 5 m/s, the motions of which are difficult to measure when using conventional methods (both interferometry- and microwave-based methods). Note that all resonant motions can be observed in real-time with high-resolution by recording TOFs of 14 spatial points on the bridge, and stroboscopic detection (i.e., synchronizing data acquisition with bridge motion22 or beam scanning30) was not required.