LETTERS https://doi.org/10.1038/s41566-020-0586-0 Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea. *e-mail: jungwon.kim@kaist.ac.kr Displacement measurement is a fundamental functionality in modern science and technology. Although there has been remarkable progress in the precision of such measurements with various laser ranging methods 1–8 , they are incapable of capturing fast and complex mechanical displacements. Here, we have established a displacement measurement method using time-of-flight detection 9 with femtosecond opti- cal pulses and frequency-locked electrical waveforms. This method uniquely combines ultrafast measurement speed, sub-nanometre precision and non-ambiguity range of more than several millimetres. The achieved performance features unprecedented detection speed and precision. Starting from 24 nm precision for 4 ns acquisition time, the precision can reach 180 pm for 5 ms acquisition time. Using this method, we show real-time detection of single-event, fast and high- dynamic-range mechanical displacements. This capability can lead to the realization of new measurement and analy- sis platforms for studying broadband, transient and nonlin- ear mechanical dynamics in real time, which will be useful for directly probing optomechanics 10 , the onset of cracks 11 , dynamic deformations 12 , nonlinear vibrations 13 , ultrasonic phenomena 14 and cell-generated forces 15 . Laser-based ranging and displacement measurements 1–8 have been widely used in various areas of science and technology, from gravitational-wave detection 16 to connected sensors for advanced manufacturing 17 . The three important performance parameters for displacement measurements are precision, measurement speed and non-ambiguity range (NAR). In general, improvement in one parameter is achieved at the expense of degradation in other param- eters. For example, although Fabry–Pérot cavity-based displace- ment measurements 1 can reach sub-picometre-level precision, it takes > 1 s to achieve this precision and the detectable range is lim- ited to ~10 μm. The applicability is also limited to objects directly attachable to the end mirror of the cavity. Here, we present a simple, yet powerful, time-of-flight (TOF)- based displacement measurement method with ultrafast, ultra- precise and large-NAR performance. Our approach not only allows high flexibility in its configurations (including multi-channel TOF detection using wavelength division multiplexing (WDM)) and a wide range of applications (including three-dimensional (3D) surface profilometry and strain sensing), but also features a new capability of precisely capturing fast, very small and non-repeating mechanical displacements in real time, which can open up new measurement platforms for the analysis of complex, broadband and nonlinear mechanical movements in microscale devices. Figure 1a illustrates the operation principle. It measures a change in the optical pulse TOF by comparing the timing between femto- second optical pulses, generated from a mode-locked laser (MLL), and the frequency-locked periodic electric waveform. After the optical pulse train is split into two paths, one pulse train is sent to a high-speed photodiode to generate a photocurrent pulse train. The other optical pulse train experiences the TOF change. One can measure the TOF by detecting the relative temporal position of the optical pulses with respect to the rising edges of the photocurrent pulses. To measure the timing change with high precision and large range, an electro-optic-sampling-based timing detector (EOS-TD) is used. Previously, several types of EOS-TD 9,18–20 , most notably dif- ferential-biased Sagnac loop interferometers 18 , have been demon- strated for laser–microwave synchronization. In this work, we use a fibre Sagnac loop with a phase modulator and a non-reciprocal π/2-phase bias 19 as the EOS-TD. Figure 1b shows the measured EOS-TD output signal as a function of the relative temporal posi- tion of the optical pulses and photocurrent pulses when a 22 GHz modified uni-travelling carrier (MUTC) photodiode is used. As the rising edge of the photocurrent pulse is ~40 ps long, one can use this for TOF detection with ~6 mm roundtrip NAR. Curve (i) in Fig. 1c shows the measured residual timing jitter power spectral density (PSD) between the optical pulses and photocurrent pulses (when the optical pulse is positioned at the middle of the rising edge of the photocurrent pulse) for a MUTC photodiode. The relative timing jitter between optical pulses and photocurrent pulses is only 137 as for a bandwidth of 10 MHz. High-dynamic-range TOF detection is possible by combining the attosecond-level timing fluctuation and a measurable range of greater than tens of picoseconds. Instead of photocurrent pulses, note that microwaves from phase-locked volt- age-controlled oscillators (VCOs) can be used to provide the tim- ing frame (see Methods and Fig. 1c(ii)), as used in our preliminary study 21,22 . The main advantage of using VCOs is that one can use any harmonic frequencies of repetition rate and can tune the NAR as needed. Figure 2 presents the measurement precision analysis for the demonstrated TOF detection method. We examined the achievable displacement measurement precision as a function of acquisition time (that is, the averaging time for taking one TOF data point). The precision is determined from the overlapped Allan deviation (Fig. 2b(i)) for roundtrip displacements, which corresponds to type-A uncertainty analysis 23 . The fastest acquisition rate and cor- responding acquisition time are 250 MHz and 4 ns, respectively, due to the MLL repetition rate. In this case, the precision is 24 nm. As the acquisition time increases, due to the averaging effect (Fig. 2a; from case A to case C) the measurement precision improves down to the sub-nanometre level. Sub-10 nm and sub-nanometre preci- sions can be achieved at 50 ns and 50 μs acquisition times, respec- tively (20 MHz and 20 kHz rates), and the minimum precision reaches 180 pm at 5 ms acquisition time (200 Hz rate). When the acquisition time increases beyond ~0.01 s, due to the timing drift between the optical pulses and the photocurrent pulses, the preci- sion becomes worse. Overall, compared to previous laser ranging Ultrafast, sub-nanometre-precision and multifunctional time-of-flight detection Yongjin Na, Chan-Gi Jeon, Changmin Ahn, Minji Hyun, Dohyeon Kwon, Junho Shin and Jungwon Kim  * NATURE PHOTONICS | www.nature.com/naturephotonics