## Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling |

Optics Express, Vol. 22, Issue 6, pp. 6597-6604 (2014)

http://dx.doi.org/10.1364/OE.22.006597

Acrobat PDF (1085 KB)

### Abstract

A dual-comb nonlinear asynchronous optical sampling method is proposed to simplify determination of the time interval and extend the non-ambiguity range in absolute length measurements. Type II second harmonic generation facilitates curve fitting in determining the time interval between adjacent pulses. Meanwhile, the non-ambiguity range is extended by adjusting the repetition rate of the signal laser. The performance of the proposed method is compared with a heterodyne interferometer. Results show that the system achieves a maximum residual of 100.6 nm and an uncertainty of 1.48 μm in a 0.5 ms acquisition time. With longer acquisition time, the uncertainty can be reduced to 166.6 nm for 50 ms and 82.9 nm for 500 ms. Moreover, the extension of the non-ambiguity range is demonstrated by measuring an absolute distance beyond the inherent range determined by the fixed repetition rate.

© 2014 Optical Society of America

## 1. Introduction

1. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science **288**(5466), 635–639 (2000). [CrossRef] [PubMed]

2. R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. **85**(11), 2264–2267 (2000). [CrossRef] [PubMed]

3. S.-W. Kim, “Metrology: combs rule,” Nat. Photonics **3**(6), 313–314 (2009). [CrossRef]

4. N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics **5**(4), 186–188 (2011). [CrossRef]

5. N. Schuhler, Y. Salvadé, S. Lévêque, R. Dändliker, and R. Holzwarth, “Frequency-comb-referenced two-wavelength source for absolute distance measurement,” Opt. Lett. **31**(21), 3101–3103 (2006). [CrossRef] [PubMed]

8. X. Wu, H. Wei, H. Zhang, L. Ren, Y. Li, and J. Zhang, “Absolute distance measurement using frequency-sweeping heterodyne interferometer calibrated by an optical frequency comb,” Appl. Opt. **52**(10), 2042–2048 (2013). [CrossRef] [PubMed]

9. K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. **39**(30), 5512–5517 (2000). [CrossRef] [PubMed]

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

11. M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. **34**(13), 1982–1984 (2009). [CrossRef] [PubMed]

14. P. Balling, P. Křen, P. Mašika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express **17**(11), 9300–9313 (2009). [CrossRef] [PubMed]

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

16. J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. **23**(6), 065203 (2012). [CrossRef]

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

18. 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]

19. K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express **14**(13), 5954–5960 (2006). [CrossRef] [PubMed]

22. 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]

23. 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]

24. J. D. Kafka, J. W. Pieterse, and M. L. Watts, “Two-color subpicosecond optical sampling technique,” Opt. Lett. **17**(18), 1286–1288 (1992). [CrossRef] [PubMed]

25. C. Janke, M. Först, M. Nagel, H. Kurz, and A. Bartels, “Asynchronous optical sampling for high-speed characterization of integrated resonant terahertz sensors,” Opt. Lett. **30**(11), 1405–1407 (2005). [CrossRef] [PubMed]

26. M. Maier, W. Kaiser, and J. Giordmaine, “Intense light bursts in the stimulated Raman effect,” Phys. Rev. Lett. **17**(26), 1275–1277 (1966). [CrossRef]

## 2. Principle

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

27. L. Antonucci, X. Solinas, A. Bonvalet, and M. Joffre, “Asynchronous optical sampling with arbitrary detuning between laser repetition rates,” Opt. Express **20**(16), 17928–17937 (2012). [CrossRef] [PubMed]

*f*

_{r}+ Δ

*f*

_{r}. The light pulses emitted from the SL are incident on both the reference mirror (M

_{ref}) and the target mirror (M

_{tar}). The optical path difference of the two arms is recorded as a function of time intervals between adjacent pulses. In order to spot the time intervals, another femtosecond fiber laser with a slightly different repetition rate

*f*

_{r}serves as the local oscillator (LO). Pulses from the SL and the LO are sent to the SHG structure for cross-correlation measurement. Taking pulses from the SL as static reference, pulses from the LO walk through with a step ofin time domain to fulfill optical scanning.

*I*

_{2}

*, can be expressed as [26*

_{ω}26. M. Maier, W. Kaiser, and J. Giordmaine, “Intense light bursts in the stimulated Raman effect,” Phys. Rev. Lett. **17**(26), 1275–1277 (1966). [CrossRef]

*I*

_{ω,}_{SL}and

*I*

_{ω,}_{LO}are the intensities of fundamental pulses from the SL and the LO and

*τ*is the temporal offset between pulses. According to Eq. (2),

*I*

_{2}

*reflects the temporal offset since the overlap between pulses is quantified and the maximum of SHG intensity is obtained when the LO and SL pulses completely overlap in time.*

_{ω}*τ*while the SHG generates the relevant

*I*

_{2}

*. The LO repetition rate*

_{ω}*f*

_{r}is taken as the sampling rate to record

*I*

_{2}

*. Pulses from the LO can serve as a probe to depict the pulses from the SL. By judging the peak position of*

_{ω}*I*

_{2}

*, the time interval between adjacent pulses from the SL can be obtained. However, because of the fixed time step of Δ*

_{ω}*T*

_{r}, the SHG intensities

*I*

_{2}

*are discrete data points with a step size of 1/*

_{ω}*f*

_{r}, which corresponds to the sampling rate. It will lead to a quantization error as peak positions are found by the maximum SHG intensities. For an enhanced resolution, a sech

^{2}function is used to fit the detected

*I*

_{2}

*. The time interval between adjacent pulses from the SL,*

_{ω}*τ*, can be calculated bywhere

_{d}*t*

_{ref}and

*t*

_{tar}are the peak positions in time domain determined by curve fitting,

*f*

_{r}is the sampling rate and Δ

*T*

_{r}is the time step in Eq. (1).

*L*is given bywhere

*c*is the speed of light in vacuum,

*n*

_{g}is the group refractive index of air and

*τ*is the time interval in Eq. (3). But the non-ambiguity range (NAR) of the absolute distance is limited by the repetition rate of the SL, i.e. Λ

_{d}_{NAR}=

*c*/[2(

*f*

_{r}+ Δ

*f*

_{r})]. In order to extend the NAR, the repetition rate of the SL is changed from

*f*

_{r}+ Δ

*f*

_{r}to

*f*

_{r}+ Δ

*f*

_{r}’, corresponding to a variation of the NAR from Λ

_{NAR}=

*c*/[2(

*f*

_{r}+ Δ

*f*

_{r})] to Λ’

_{NAR}=

*c*/[2(

*f*

_{r}+ Δ

*f*

_{r}’)], while the repetition rate of the LO is fixed. With Λ

_{NAR}and Λ’

_{NAR}, the absolute length

*L*

_{abs}can be expressed by where

*m*and

*m*’ are positive integers while

*L*and

*L*’ are the ‘wrapped’ distances with the given NARs [18

18. 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]

*m*and

*m*’ can be forced to be

*m*=

*m*’ under active control. With Eqs. (5) and (6), the absolute distance

*L*

_{abs}can be obtained as illustrated in Fig. 2.

## 3. Experimental setup

## 4. Experimental results

*L*can be expressed aswhere Δ

*t*equals to |

*t*

_{ref}-

*t*

_{tar}|, representing the time interval between the peak position

*t*

_{ref}and

*t*

_{tar}. From Eq. (7), the uncertainty of the

*L*,

*U*, can be calculated bywhere

_{L}*U*

_{Δ}

*is the uncertainty of Δ*

_{t}*t*and

*U*

_{f}_{r}is that of

*f*

_{r}. Noting

*U*

_{f}_{r}is 3 mHz and

*f*

_{r}is 250 MHz in our experiment, the third term on the right of Eq. (8) is much smaller than the first and the second terms on the right of Eq. (8) and is hence neglected. During the measurement, the temperature varies from 23.624 °C to 23.728 °C. Meanwhile, the humidity is kept at 21.1% and the pressure increases from 102.284 kPa to 102.291 kPa. According to Ciddor equation and its uncertainty, the fourth term in the Eq. (8) is no larger than 10

^{−7}. Compared with the repetition rate stability and the curve fitting accuracy,

*n*

_{g}can be assumed as a constant. Equation (8) can be further represented aswhere

*U*

_{Δ}

*stands for the curve fitting accuracy and*

_{t}*U*

_{f}_{r}illustrates the repetition rate stability. In Eq. (9) Δ

*f*

_{r}is 2 kHz,

*L*is 39.2 mm,

*c*is 299792458 m/s,

*n*

_{g}is 1.00027 calculated through Ciddor equation based on measured temperature, pressure and humidity, and

*U*

_{Δ}

*is 1 ns estimated by introducing functions with similar signal to noise ratio in experiment into curve fitting algorithm.*

_{t}*U*is no larger than 1.2 μm, which matches the standard deviation for 0.5 ms illustrated in Fig. 4(a). According to Eq. (9), the curve fitting accuracy dominates the uncertainty of a single measurement when the measurement is restricted to short distances. In this case, a clear pulse in the SHG measurement is in need to pursue a higher accuracy. When a long distance is measured, the uncertainty of a single measurement is mainly decided by the uncertainty of the repetition rate, since pulse shapes can be controlled by adjusting fiber length of the EDFA and

_{L}*U*

_{Δ}

*is basically maintained. Taking current parameters into account,*

_{t}*U*

_{f}_{r}is more important than

*U*

_{Δ}

*when the absolute length*

_{t}*L*is larger than 0.56 m. In addition, fluctuation of refractive index ought to be considered when measured distance is large.

*m*= 0 and

*m*= 1 because with the same variation of the repetition rate, the change from

*L*to

*L*’ is minimum in this case. The results are shown in Fig. 5, compared with results from the heterodyne interferometer. In Fig. 5(a), distances are measured without the integer

*m*. In comparison, in Fig. 5(b) the integer

*m*is judged by the method proposed above with a change of the repetition rate of 4 kHz from 250.002 MHz to 249.998 MHz. Residuals and standard deviations of Fig. 5(b) is shown in Fig. 5(c). The residuals range from −141.1 nm to 175.8 nm while the standard deviations vary from 87.5 nm to 194.0 nm for 500 ms, which are slightly larger than those in the short distance measurement caused by turbulence of atmosphere. The results prove that changing the repetition rate can extend the NAR of the system.

## 5. Conclusion

## Acknowledgments

## References and links

1. | D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science |

2. | R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. |

3. | S.-W. Kim, “Metrology: combs rule,” Nat. Photonics |

4. | N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics |

5. | N. Schuhler, Y. Salvadé, S. Lévêque, R. Dändliker, and R. Holzwarth, “Frequency-comb-referenced two-wavelength source for absolute distance measurement,” Opt. Lett. |

6. | Y. Salvadé, N. Schuhler, S. Lévêque, and S. Le Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. |

7. | S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. |

8. | X. Wu, H. Wei, H. Zhang, L. Ren, Y. Li, and J. Zhang, “Absolute distance measurement using frequency-sweeping heterodyne interferometer calibrated by an optical frequency comb,” Appl. Opt. |

9. | K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. |

10. | J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. |

11. | M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. |

12. | D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Experimental observation of pulse trains’ destructive interference with a femtosecond optical frequency-comb-based interferometer,” Opt. Lett. |

13. | D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Time-of-flight method using multiple pulse train interference as a time recorder,” Opt. Express |

14. | P. Balling, P. Křen, P. Mašika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express |

15. | J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics |

16. | J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. |

17. | I. Coddington, W. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics |

18. | 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. |

19. | K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express |

20. | J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of air with frequency combs,” Opt. Lett. |

21. | M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, and H. P. Urbach, “Long distance measurement with femtosecond pulses using a dispersive interferometer,” Opt. Express |

22. | 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. |

23. | 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 |

24. | J. D. Kafka, J. W. Pieterse, and M. L. Watts, “Two-color subpicosecond optical sampling technique,” Opt. Lett. |

25. | C. Janke, M. Först, M. Nagel, H. Kurz, and A. Bartels, “Asynchronous optical sampling for high-speed characterization of integrated resonant terahertz sensors,” Opt. Lett. |

26. | M. Maier, W. Kaiser, and J. Giordmaine, “Intense light bursts in the stimulated Raman effect,” Phys. Rev. Lett. |

27. | L. Antonucci, X. Solinas, A. Bonvalet, and M. Joffre, “Asynchronous optical sampling with arbitrary detuning between laser repetition rates,” Opt. Express |

**OCIS Codes**

(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology

(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation

(320.7100) Ultrafast optics : Ultrafast measurements

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: January 27, 2014

Revised Manuscript: March 5, 2014

Manuscript Accepted: March 10, 2014

Published: March 13, 2014

**Citation**

Hongyuan Zhang, Haoyun Wei, Xuejian Wu, Honglei Yang, and Yan Li, "Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling," Opt. Express **22**, 6597-6604 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6597

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### References

- D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef] [PubMed]
- R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000). [CrossRef] [PubMed]
- S.-W. Kim, “Metrology: combs rule,” Nat. Photonics 3(6), 313–314 (2009). [CrossRef]
- N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011). [CrossRef]
- N. Schuhler, Y. Salvadé, S. Lévêque, R. Dändliker, R. Holzwarth, “Frequency-comb-referenced two-wavelength source for absolute distance measurement,” Opt. Lett. 31(21), 3101–3103 (2006). [CrossRef] [PubMed]
- Y. Salvadé, N. Schuhler, S. Lévêque, S. Le Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. 47(14), 2715–2720 (2008). [CrossRef] [PubMed]
- S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009). [CrossRef]
- X. Wu, H. Wei, H. Zhang, L. Ren, Y. Li, J. Zhang, “Absolute distance measurement using frequency-sweeping heterodyne interferometer calibrated by an optical frequency comb,” Appl. Opt. 52(10), 2042–2048 (2013). [CrossRef] [PubMed]
- K. Minoshima, H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000). [CrossRef] [PubMed]
- J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29(10), 1153–1155 (2004). [CrossRef] [PubMed]
- M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, J. J. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009). [CrossRef] [PubMed]
- D. Wei, S. Takahashi, K. Takamasu, H. Matsumoto, “Experimental observation of pulse trains’ destructive interference with a femtosecond optical frequency-comb-based interferometer,” Opt. Lett. 34(18), 2775–2777 (2009). [CrossRef] [PubMed]
- D. Wei, S. Takahashi, K. Takamasu, H. Matsumoto, “Time-of-flight method using multiple pulse train interference as a time recorder,” Opt. Express 19(6), 4881–4889 (2011). [CrossRef] [PubMed]
- P. Balling, P. Křen, P. Mašika, S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009). [CrossRef] [PubMed]
- J. Lee, Y.-J. Kim, K. Lee, S. Lee, S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010). [CrossRef]
- J. Lee, K. Lee, S. Lee, S.-W. Kim, Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012). [CrossRef]
- I. Coddington, W. Swann, L. Nenadovic, N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009). [CrossRef]
- J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013). [CrossRef]
- K.-N. Joo, S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006). [CrossRef] [PubMed]
- J. Zhang, Z. H. Lu, L. J. Wang, “Precision measurement of the refractive index of air with frequency combs,” Opt. Lett. 30(24), 3314–3316 (2005). [CrossRef] [PubMed]
- M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, “Long distance measurement with femtosecond pulses using a dispersive interferometer,” Opt. Express 19(7), 6549–6562 (2011). [CrossRef] [PubMed]
- S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012). [CrossRef] [PubMed]
- T.-A. Liu, N. R. Newbury, 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]
- J. D. Kafka, J. W. Pieterse, M. L. Watts, “Two-color subpicosecond optical sampling technique,” Opt. Lett. 17(18), 1286–1288 (1992). [CrossRef] [PubMed]
- C. Janke, M. Först, M. Nagel, H. Kurz, A. Bartels, “Asynchronous optical sampling for high-speed characterization of integrated resonant terahertz sensors,” Opt. Lett. 30(11), 1405–1407 (2005). [CrossRef] [PubMed]
- M. Maier, W. Kaiser, J. Giordmaine, “Intense light bursts in the stimulated Raman effect,” Phys. Rev. Lett. 17(26), 1275–1277 (1966). [CrossRef]
- L. Antonucci, X. Solinas, A. Bonvalet, M. Joffre, “Asynchronous optical sampling with arbitrary detuning between laser repetition rates,” Opt. Express 20(16), 17928–17937 (2012). [CrossRef] [PubMed]

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