Massively parallel electro-optic sampling of space-encoded optical pulses for ultrafast multi-dimensional imaging

High-speed and high-resolution imaging of surface profiles is critical for the investigation of various structures and mechanical dynamics of micro- and nano-scale devices. In particular, recent emergence of various nonlinear, transient and complex mechanical dynamics, such as anharmonic vibrations in mechanical resonators, has necessitated real-time surface deformation imaging with higher axial and lateral resolutions, speed, and dynamic range. However, real-time capturing of fast and complex mechanical dynamics has been challenging, and direct time-domain imaging of displacements and mechanical motions has been a missing element in studying full-field structural and dynamic behaviours. Here, by exploiting the electro-optic sampling with a frequency comb, we demonstrate a line-scan time-of-flight (TOF) camera that can simultaneously measure the TOF changes of more than 1000 spatial coordinates with hundreds megapixels/s pixel-rate and sub-nanometre axial resolution over several millimetres field-of-view. This unique combination of performances enables fast and precise imaging of both complex structures and dynamics in three-dimensional devices and mechanical resonators.

before TOF measurements, a flat mirror is axially scanned by a precision motorized stage (±100 nm repeatability, M-126, Physik Instrumente) to measure the EOS-TD response over the entire measurable range and make look-up tables (LUTs). Fig. S9 shows the measured EOS-TD output spectra when the optical pulses' relative timing is linearly scanned with respect to the rising edges with different bias voltages until detection ambiguity occurs (the total travel ranges are defined as measurable ranges; 3.0 mm, 1.6 mm, and 1.2 mm for 4 V, 8 V, and 16 V bias voltages, respectively).
As shown in the left panels of Fig. S9, the nonuniform response along wavelength (pixel) is due to the spectral intensity-dependent sensitivity variation, and for each pixel, the nonlinear response along axial position is due to the nonlinear shapes of rising edges. Using the LUT method, the EOS-TD response is linearized to 4´10 -6 level, which is the motor's linearity, over the entire measurable ranges as shown in the middle panels of Fig. S9. Due to the EOS-TD's high repeatability, most of the remained nonlinearity lies within the motor's repeatability (±100-nm).
The LUTs can be acquired either by scanning the timing of the probing pulses or the photocurrent pulses.
Since the TOF detection sensitivity is proportional to the input optical power to the EOS-TD, the return power variation due to reflectance variation or out-focusing should be addressed while measuring the TOF. To minimize the systematic uncertainty from power variation, ~20% of the returned power is split for monitoring the return spectrum variation. The EOS-TD's response curves and the spectra of split power are measured as shown in Fig. S10. For each pixel (wavelength), the EOS-TD responses at several spectral powers are obtained. When measuring the target, the actual response at each pixel is estimated by interpolating the measured responses. As shown in Fig. S10c, the high linearity between input optical power and sensitivity enables accurate calibration of the input power dependence of the TOF detection sensitivity.
As the axial precision performance has power dependence, at lower optical power, several methods can be employed to recover the signal power as well as the precision performance. For example, increasing the exposure time increases signal power at the expense of slower measurement speed. Increasing the camera's electrical gain maintains the measurement speed at the expense of slightly increased noise power and worse precision (Fig. S11). When exposure time and gain are increased to 200 μs and 100 times, respectively, 14-nm precision can be acquired with only ~1 μW of EOS-TD input optical power (equivalently, each pixel is supplied <200 pW) (Fig.   S12). The maximum (i.e., the maximum optical power not to saturate line camera) and the minimum (i.e., the minimum optical power enabling TOF detection) sub-pulse's average powers into EOS-TD also depends on the camera operation conditions (see Table S1). When the camera is operated with high camera gain (gain=100) and long exposure time (500-μs exposure time), our method could detect the TOF when sub-pulse with only 0.82 pW power is applied to the EOS-TD.
Two methods were used to measure the spectra of EOS-TD output and the returned optical power: (a) using an optical switch and (b) using two line-scan cameras. For the optical switch method, a PM optical switch with 300-kHz switching speed (NSSW-130110333, Agiltron) is installed before the line-scan camera to switch between the EOS-TD output and the power monitor port. At each line measurement, the line-scan camera measures the spectra of the EOS-TD output and the power monitor in turn. Since this method does not require wavelength-to-pixel calibration between line-scan cameras, the EOS-TD output and the return power spectra have exact pixel correspondence. The 3D imaging results in Fig. 3 are obtained with the optical switch method.
However, as this method requires synchronization between motor movement, optical switch and the line-scan camera, it may suffer from motion-blur and imaging speed limitation for dynamic motion recording (Fig. 4) or high-speed imaging (Fig. S3). Thus, two cameras method with two identical spectrum-acquisition configurations is utilized, where two cameras simultaneously measure the EOS-TD output and return power. This method enables a real-time measurement; therefore, the rapid motions can be measured without motion-blur. Also, since the step-wise movement of the motor stage is not required, the sample can be continuously scanned with maximum motor speed (Fig. S3). Calibration target with equally spaced lines is measured to calibrate wavelength-to-pixel correspondence between the two cameras. Since the target has 50 μm divisions, the uncertainty during two camera calibration is below 50 μm, which is ~4 pixels. A calibration target with smaller spacing can be used for better synchronization.

Supplementary Note 3. The use of different electric waveforms as timing ruler signal
By using different microwave waveforms, the measurable range and precision can be tuned. Since the photocurrent pulses are composed of numerous harmonic frequencies of the comb repetition rate (up to the photodiode bandwidth), any harmonic frequency signal can be extracted as a timing ruler. For example, as shown in Fig. S7, a 1.5-GHz signal (i.e., 6 th harmonic frequency) can be generated by an RF band-pass filter. The MUTC-photodiode is driven with 8 V bias voltage and terminated with 50 Ω. The extracted signal is then amplified and band-pass filtered again for removing high-harmonic components. As a result, a 1.5-GHz signal of ~12 dBm power is generated and applied to the EOS-TD as a 100 mm-long timing ruler signal. The probing pulses undergo TOF variation by the precision motor stage (50 mm travel, ±100 nm repeatability), and an optical delay line is inserted to locate optical pulses at the zero-crossing point of microwave signal. As a result, the 1.5-GHz microwave signal extends the measurable range up to ~50 mm (i.e., half of wavelength, in round-trip), which is ~40 times longer than the measurable range of rising edges. The reduced TOF detection sensitivity linearly scales the precision performance: 5.3 -μm precision at 260 megapixels s -1 of acquisition rate, and when averaged, down to 16-nm precision at 4.7 kilopixels s -1 . Since the optical power is adjusted to fully utilize the camera's nonsaturation range, the dynamic range performance is maintained to ~130 dB.
An independent microwave source, such as a voltage-controlled oscillator (VCO), can be utilized to generate timing rulers. As shown in Fig. S6, the VCO signal is frequency synchronized to the multiple of the repetition rate. For the mode shape observation in Fig. 4b, another EOS-TD is used for ultralow-noise synchronization of an 8-GHz VCO. Using a continuous sinusoidal timing ruler enables TOF detection of sub-pulses present at arbitrary relative timings.             and pixel 700 at region A (when only PZT 2 is modulated with 10.7 kHz (f2) frequency) and region B (when only PZT 1 is modulated with 11.5 kHz (f1) frequency) are Fourier transformed. At region A, in PZT 2mounted mirror, the resonance mode (f2) is excited with highest amplitude and high-harmonic components up to 3 rd harmonic frequency are also excited, and the first two harmonic modes are coupled to PZT 1mounted mirror. The coupled two modes show similar amplitudes, resulting in non-single-tone fluctuation in the time-domain. At region B, while the resonance frequency (f1) has highest amplitude, high-harmonic components up to 8 th harmonic frequency are excited in PZT 1-mounted mirror. In PZT 2-mounted mirror, the coupled harmonic components up to 7 th harmonic frequency are observed in the Fourier transformed spectrum, and the 2 nd harmonic component (2f1) appears with the highest amplitude. As a result, while PZT Figure S15 | Round-shape surface measurement result. a, Microscopic image of micro-bumps. The bumps have ~125 μm diameter, ~100 μm height, and spaced by ~250 μm in pitch. b, Returned power map (measured by line camera) after illuminating with line beam and scanning the bumps in Y-direction. The dark blue region is where there is no power return. A f = 50 mm lens is used for longer Rayleigh range (>100 μm) and calculated NA of the system is 0.25. c, Cross section of a bump measured by a confocal microscopy and slopes. The grey region is where confocal microscopy fails to measure height. d, Return power and measured TOF for the three bumps in b. Figure S16 | Schematic diagram of optical path length variation when target surface rotates or has a slope. To simplify the situation, the collimated single-wavelength beam from optical fiber and collimator is incident to the grating in perpendicular, and after diffraction, the collimated beam is focused on to the target surface. Ray 1 and Ray 2 indicate the upper-end and lower-end rays departing from optical fiber, respectively. CW, clockwise; CCW, counter-clockwise.