Abstract

The cross correlation between a pair of femtosecond lasers with slightly different repetition rates enables high precision, high update rate time-of-flight (TOF) distance measurements against multiple targets. Here, we investigate the obtainable ranging precision set by the timing jitter from femtosecond lasers. An analytical model governing dual femtosecond laser TOF distance measurement in the presence of pulse train timing jitter is built at first. A numerical study is conducted by involving typical timing jitter sources in femtosecond lasers in the following. Finally, the analytical and numerical models are verified by a TOF ranging experiment using a pair of free running femtosecond Er-fiber lasers. The timing jitter of the lasers is also characterized by an attosecond resolution balanced optical cross correlation method. The comparison between experiment and numerical model shows that the quantum-limited timing jitter of femtosecond lasers sets a fundamental limit on the performance of dual femtosecond laser TOF distance measurements.

© 2015 Optical Society of America

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References

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2014 (3)

2013 (1)

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

2012 (3)

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]

2011 (3)

2010 (5)

J. A. Cox, A. H. Nejadmalayeri, J. Kim, and F. X. Kärtner, “Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers,” Opt. Lett. 35(20), 3522–3524 (2010).
[Crossref] [PubMed]

J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser Photonics Rev. 4(3), 432–456 (2010).
[Crossref]

S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B 27(11), B51–B62 (2010).
[Crossref]

J. H. Lee, Y. J. Kim, K. W. Lee, S. H. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

2009 (1)

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

2005 (1)

2004 (2)

J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29(10), 1153–1155 (2004).
[Crossref] [PubMed]

R. Paschotta, “Noise of mode-locked lasers (Part I): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[Crossref]

2003 (1)

2002 (1)

M. E. Pritchard and M. Simons, “A satellite geodetic survey of large-scale deformation of volcanic centres in the central Andes,” Nature 418(6894), 167–171 (2002).
[Crossref] [PubMed]

2000 (1)

1993 (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[Crossref]

1981 (1)

1962 (1)

L. D. Smullin and G. Fiocco, “Optical echoes from the moon,” Nature 194(4835), 1267 (1962).
[Crossref]

Bae, E.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Balling, P.

P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]

Bartels, A.

Benedick, A. J.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

Bhattacharya, N.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Coddington, I.

T.-A. Liu, N. R. Newbury, and I. Coddington, “Sub-micron absolute distance measurements in sub-millisecond times with dual free-running femtosecond Er fiber-lasers,” Opt. Express 19(19), 18501–18509 (2011).
[Crossref] [PubMed]

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Cox, J. A.

Diddams, S. A.

Diels, J. C.

Doležal, M.

P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]

Fiocco, G.

L. D. Smullin and G. Fiocco, “Optical echoes from the moon,” Nature 194(4835), 1267 (1962).
[Crossref]

Fontaine, J. J.

Först, M.

Fujimoto, J. G.

Gopinath, J. T.

Guelachvili, G.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref] [PubMed]

Han, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Hänsch, T. W.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref] [PubMed]

Haus, H. A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[Crossref]

Hu, M.

Ideguchi, T.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref] [PubMed]

Ippen, E. P.

Janke, C.

Jung, K.

Kaertner, F. X.

Kärtner, F. X.

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser Photonics Rev. 4(3), 432–456 (2010).
[Crossref]

J. A. Cox, A. H. Nejadmalayeri, J. Kim, and F. X. Kärtner, “Complete characterization of quantum-limited timing jitter in passively mode-locked fiber lasers,” Opt. Lett. 35(20), 3522–3524 (2010).
[Crossref] [PubMed]

Kim, H.

Kim, J.

Kim, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Kim, S. W.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. H. Lee, Y. J. Kim, K. W. Lee, S. H. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Kim, Y. J.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. H. Lee, Y. J. Kim, K. W. Lee, S. H. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Kok, G. J.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Kolodziejski, L. A.

Kren, P.

P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]

Kurz, H.

Kuzucu, O.

Kwon, D.

Lee, J.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Lee, J. H.

J. H. Lee, Y. J. Kim, K. W. Lee, S. H. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, K.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Lee, K. W.

J. H. Lee, Y. J. Kim, K. W. Lee, S. H. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Lee, S. H.

J. H. Lee, Y. J. Kim, K. W. Lee, S. H. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Li, Y.

Liu, T.-A.

Mašika, P.

P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]

Matsumoto, H.

Mecozzi, A.

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[Crossref]

Minoshima, K.

Nagel, M.

Nejadmalayeri, A. H.

Nenadovic, L.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Newbury, N. R.

T.-A. Liu, N. R. Newbury, and I. Coddington, “Sub-micron absolute distance measurements in sub-millisecond times with dual free-running femtosecond Er fiber-lasers,” Opt. Express 19(19), 18501–18509 (2011).
[Crossref] [PubMed]

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Paschotta, R.

R. Paschotta, “Noise of mode-locked lasers (Part I): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[Crossref]

Persijn, S. T.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Petrich, G. S.

Picqué, N.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref] [PubMed]

Poisson, A.

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref] [PubMed]

Pritchard, M. E.

M. E. Pritchard and M. Simons, “A satellite geodetic survey of large-scale deformation of volcanic centres in the central Andes,” Nature 418(6894), 167–171 (2002).
[Crossref] [PubMed]

Qin, P.

Sallaba, H.

Schibli, T. R.

Shin, J.

Simons, M.

M. E. Pritchard and M. Simons, “A satellite geodetic survey of large-scale deformation of volcanic centres in the central Andes,” Nature 418(6894), 167–171 (2002).
[Crossref] [PubMed]

Smullin, L. D.

L. D. Smullin and G. Fiocco, “Optical echoes from the moon,” Nature 194(4835), 1267 (1962).
[Crossref]

Song, Y.

Swann, W. C.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Takahashi, S.

Takamasu, K.

Tandon, S. N.

van den Berg, S. A.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Wang, C.

Wang, C. Y.

Wei, D.

Wei, H.

Wu, X.

Yang, H.

Ye, J.

Zeitouny, M. G.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Zhang, H.

Appl. Opt. (1)

Appl. Phys. B (1)

R. Paschotta, “Noise of mode-locked lasers (Part I): timing jitter and other fluctuations,” Appl. Phys. B 79(2), 163–173 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser Photonics Rev. 4(3), 432–456 (2010).
[Crossref]

Meas. Sci. Technol. (2)

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. W. Kim, and Y. J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]

Nat. Commun. (1)

T. Ideguchi, A. Poisson, G. Guelachvili, N. Picqué, and T. W. Hänsch, “Adaptive real-time dual-comb spectroscopy,” Nat. Commun. 5, 3375 (2014).
[Crossref] [PubMed]

Nat. Photonics (3)

A. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

J. H. Lee, Y. J. Kim, K. W. Lee, S. H. Lee, and S. W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Nature (2)

L. D. Smullin and G. Fiocco, “Optical echoes from the moon,” Nature 194(4835), 1267 (1962).
[Crossref]

M. E. Pritchard and M. Simons, “A satellite geodetic survey of large-scale deformation of volcanic centres in the central Andes,” Nature 418(6894), 167–171 (2002).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (6)

Phys. Rev. A (1)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010).
[Crossref]

Phys. Rev. Lett. (1)

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 ASOPS based TOF ranging principle in the presence of LO timing jitter.
Fig. 2
Fig. 2 Ranging performance with different timing jitter noise sources. (a). Simulated pulse train timing jitter power spectral density. (b). The corresponding standard deviation (STD) of calculated distance over one ambiguity range.
Fig. 3
Fig. 3 Simulation result of ASOPS based TOF distance measurement at different ranging update rate in the presence of timing jitter of femtosecond lasers.
Fig. 4
Fig. 4 ASOPS based TOF ranging simulation over 10 ambiguity ranges in the presence of timing jitter of femtosecond lasers.
Fig. 5
Fig. 5 Configurations of the two lasers used in distance measurement (a) and experimental set up for timing jitter measurement (b). BOC, balanced optical cross correlator; BPF, band-pass filter; BD, balanced detector; CNT, carbon nanotube; DM, dichroic mirror; HWP, half-wave plate; ISO, isolator; L, lens; LD, 980 nm laser diode; PBS, polarization beam splitter; PPKTP, periodically poled KTiOPO4; PZT, piezoelectric transducer; WDM, wavelength division multiplexer.
Fig. 6
Fig. 6 Experimental setup of ASOPS based TOF distance measurement. HWP, half wavelength plate; LPF, low pass filter; PD, photo-detector; QWP, quarter wavelength plate. Insert: the signal sampled by the digitizer.
Fig. 7
Fig. 7 Experiment and simulation comparison by using stretched pulse laser as LO for ASOPS based TOF ranging. (a) Timing jitter power spectral density. (b) The standard deviation of measured and calculated distances at a close target-reference separation. Insert: measurement precision in an ambiguity range.
Fig. 8
Fig. 8 Experiment and simulation comparison by using soliton pulse laser as LO for ASOPS based TOF ranging. (a) Timing jitter power spectral density. (b) The standard deviation of measured and calculated distances at a close target-reference separation. Insert: measurement precision in an ambiguity range.
Fig. 9
Fig. 9 The comparison of ranging performance by using two kinds of lasers as LO in ranging experiment. (a) Timing jitter spectrum density (b) The standard deviation of measured distance at a close target-reference separation. Insert: measurement precision in an ambiguity range.

Equations (9)

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L= c 2 n g t TOF
t TOF = t tr N +p T rt,sig
L a = c 2 n g T rt,sig
t TOF =( t tr t rr +p ) T rt,sig
{ Δ t TOF =( t tr +Δ t tr t rr +Δ t rr t tr t rr ) T rt,sig Δ t tr =N m=1 q δ t m , q=N t tr t rr Δ t rr =N m=1 N δ t m
Δt(n)= m=1 n δ t (m)
V ref (n T rt,sig )= T rt /2 T rt /2 e [ t t LO (n) ] 2 T 0 2 e [ t t ref (n) ] 2 T 0 2 dt
V tar (n T rt,sig )= T rt /2 T rt /2 e [ t t LO (n) ] 2 T 0 2 e [ t t tar (np) ] 2 T 0 2 dt, for, np
Δ t tr =N( m=1 q δ t m + m'=1 p δ t m' ), q=N t tr t rr

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