Ultrafast, sub-nanometre-precision and multifunctional time-of-flight detection


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 methods1,2,3,4,5,6,7,8, they are incapable of capturing fast and complex mechanical displacements. Here, we have established a displacement measurement method using time-of-flight detection9 with femtosecond optical 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 analysis platforms for studying broadband, transient and nonlinear mechanical dynamics in real time, which will be useful for directly probing optomechanics10, the onset of cracks11, dynamic deformations12, nonlinear vibrations13, ultrasonic phenomena14 and cell-generated forces15.

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Fig. 1: EOS-TD-based TOF detection method.
Fig. 2: Measurement precision analysis of the EOS-TD-based TOF detection method.
Fig. 3: EOS-TD-based TOF sensor demonstration results.
Fig. 4: EOS-TD-based real-time, nanometre-precision, dynamic displacement measurement results.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Schibli, T. R. et al. Displacement metrology with sub-pm resolution in air based on a fs-comb wavelength synthesizer. Opt. Express 14, 5984–5993 (2006).

    ADS  Article  Google Scholar 

  2. 2.

    Pierce, R., Leitch, J., Stephens, M., Bender, P. & Nerem, R. Intersatellite range monitoring using optical interferometry. Appl. Opt. 47, 5007–5019 (2008).

    ADS  Article  Google Scholar 

  3. 3.

    Militky, J., Kadulova, M. & Hlubina, P. Highly sensitive displacement measurement based on spectral interferometry and Vernier effect. Opt. Commun. 366, 335–339 (2016).

    ADS  Article  Google Scholar 

  4. 4.

    Lee, J.-Y. & Jiang, G.-A. Displacement measurement using a wavelength-phase-shifting grating interferometer. Opt. Express 21, 25553–25564 (2013).

    ADS  Article  Google Scholar 

  5. 5.

    Lee, J., Kim, Y. J., Lee, K., Lee, S. & Kim, S. W. Time-of-flight measurement with femtosecond light pulses. Nat. Photon. 4, 716–720 (2010).

    ADS  Article  Google Scholar 

  6. 6.

    Coddington, I., Swann, W. C., Nenadovic, L. & Newbury, N. R. Rapid and precise absolute distance measurements at long range. Nat. Photon. 3, 351–356 (2009).

    ADS  Article  Google Scholar 

  7. 7.

    Trocha, P. et al. Ultrafast optical ranging using microresonator soliton frequency combs. Science 359, 887–891 (2018).

    ADS  Article  Google Scholar 

  8. 8.

    Suh, M.-G. & Vahala, K. J. Soliton microcomb range measurement. Science 359, 884–887 (2018).

    ADS  Article  Google Scholar 

  9. 9.

    Jeon, C.-G., Na, Y., Lee, B.-W. & Kim, J. Simple-structured, subfemtosecond-resolution optical-microwave phase detector. Opt. Lett. 43, 3997–4000 (2018).

    ADS  Article  Google Scholar 

  10. 10.

    Vanner, M. R. et al. Pulsed quantum optomechanics. Proc. Natl Acad. Sci. USA 108, 16182–16187 (2011).

    ADS  Article  Google Scholar 

  11. 11.

    Lu, Y. L., Zhu, T., Chen, L. A. & Bao, X. Y. Distributed vibration sensor based on coherent detection of phase-OTDR. J. Lightwave Technol. 28, 3243–3249 (2010).

    ADS  Google Scholar 

  12. 12.

    Burg, T. P. et al. Weighing of biomolecules, single cells and single nanoparticles in fluid. Nature 446, 1066–1069 (2007).

    Article  Google Scholar 

  13. 13.

    Ke, L. L., Yang, J. & Kitipornchai, S. Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Compos. Struct. 92, 676–683 (2010).

    Article  Google Scholar 

  14. 14.

    Gomopoulos, N. et al. One-dimensional hypersonic phononic crystals. Nano Lett. 10, 980–984 (2010).

    ADS  Article  Google Scholar 

  15. 15.

    Polacheck, W. J. & Chen, C. S. Measuring cell-generated forces: a guide to the available tools. Nat. Methods 13, 415–423 (2016).

    Article  Google Scholar 

  16. 16.

    Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  17. 17.

    Teti, R., Jemielniak, K., O’Donnell, G. & Dornfeld, D. Advanced monitoring of machining operation. CIRP Annu. Manuf. Technol. 59, 717–739 (2010).

    Article  Google Scholar 

  18. 18.

    Kim, J., Kartner, F. X. & Perrott, M. H. Femtosecond synchronization of radio frequency signals with optical pulse trains. Opt. Lett. 29, 2076–2078 (2004).

    ADS  Article  Google Scholar 

  19. 19.

    Jung, K. & Kim, J. Subfemtosecond synchronization of microwave oscillators with mode-locked Er-fiber lasers. Opt. Lett. 37, 2958–2960 (2012).

    ADS  Article  Google Scholar 

  20. 20.

    Peng, M. Y., Kalaydzhyan, A. & Kartner, F. X. Balanced optical-microwave phase detector for sub-femtosecond optical-RF synchronization. Opt. Express 22, 27102–27111 (2014).

    ADS  Article  Google Scholar 

  21. 21.

    Lu, X. et al. Time-of-flight detection of femtosecond laser pulses for precise measurement of large microelectronic step height. Opt. Lett. 43, 1447–1450 (2018).

    ADS  Article  Google Scholar 

  22. 22.

    Lu, X. et al. Ultrasensitive, high-dynamic-range and broadband strain sensing by time-of-flight detection with femtosecond-laser frequency combs. Sci. Rep. 7, 13305 (2017).

    ADS  Article  Google Scholar 

  23. 23.

    Bureau International des Poids et Mesures (BIPM) Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement JCGM 100:2008 (BIPM, 2008).

  24. 24.

    López-Higuera, J. M., Rodriguez Cobo, L., Quintela Incera, A. & Cobo, A. Fiber optic sensors in structural health monitoring. J. Lightwave Technol. 29, 587–608 (2011).

    ADS  Article  Google Scholar 

  25. 25.

    Marra, G. et al. Ultrastable laser interferometry for earthquake detection with terrestrial and submarine cables. Science 361, 486–490 (2018).

    ADS  Google Scholar 

  26. 26.

    Liu, Q. et al. Ultrahigh resolution multiplexed fiber Bragg grating sensor for crustal strain monitoring. IEEE Photon. J. 4, 996–1003 (2012).

    ADS  Article  Google Scholar 

  27. 27.

    Vanner, M. R. & Aspelmeyer, M. Cooling-by-measurement and mechanical state tomography via pulsed optomechanics. Nat. Commun. 4, 2295 (2013).

    ADS  Article  Google Scholar 

  28. 28.

    Ekinci, K. L. & Roukes, M. L. Nanoelectromechanical systems. Rev. Sci. Instrum. 76, 061101 (2005).

    ADS  Article  Google Scholar 

  29. 29.

    Sackmann, E. K., Fulton, A. L. & Beebe, D. J. The present and future role of microfluidics in biomedical research. Nature 507, 181–189 (2014).

    Article  Google Scholar 

  30. 30.

    Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555–559 (2011).

    ADS  Article  Google Scholar 

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This research was supported by the National Research Foundation of Korea (grant no. 2018R1A2B3001793). We thank Y. Song, J. Suh and Y.-J. Kim for discussions. We thank C.-S. Kang for providing gauge-block assemblies and discussions on the uncertainty analysis. We also thank K. Yu for providing the MEMS sample used for surface profile imaging.

Author information




J.K. initiated and managed the project. J.K. and Y.N. conceived the main ideas and designed the experiments. Y.N. led the overall experiments. Y.N., C.-G.J., C.A., M.H. and D.K. performed the experiments and obtained data. Y.N., C.-G.J., J.S. and J.K. analysed the data. Y.N. and J.K. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Jungwon Kim.

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Competing interests

Two patents have been filed based on this work, with Korean patent application numbers 10-2019-0018203 and 10-2019-0018205.

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Supplementary Information

Supplementary Figs. 1–17 and Table 1.

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Na, Y., Jeon, C., Ahn, C. et al. Ultrafast, sub-nanometre-precision and multifunctional time-of-flight detection. Nat. Photonics 14, 355–360 (2020). https://doi.org/10.1038/s41566-020-0586-0

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