## Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser |

Optics Express, Vol. 22, Issue 9, pp. 10380-10397 (2014)

http://dx.doi.org/10.1364/OE.22.010380

Acrobat PDF (2010 KB)

### Abstract

We propose an interferometric method that enables to measure a distance by the intensity measurement using the scanning of the interferometer reference arm and the recording of the interference fringes including the brightest fringe. With the consideration of the dispersion and absorption
of the pulse laser in a dispersive and absorptive medium, we investigate the cross-correlation function between two femtosecond laser pulses in the time domain. We also introduce the measurement principle. We study the relationship between the position of the brightest fringe and the
distance measured, which can contribute to the distance measurement. In the experiments, we measure distances using the method of the intensity detection while the reference arm of Michelson interferometer is scanned and the fringes including the brightest fringe is recorded. Firstly we
measure a distance in a range of 10 µm. The experimental results show that the maximum deviation is 45 nm with the method of light intensity detection. Secondly, an interference system using three Michelson interferometers is developed, which combines the methods of light intensity
detection and time-of-flight. This system can extend the non-ambiguity range of the method of light intensity detection. We can determine a distance uniquely with a larger non-ambiguity range. It is shown that this method and system can realize absolute distance measurement, and the
measurement range is a few micrometers in the vicinity of N*l*_{pp}, where N is an integer, and *l _{pp}* is the pulse-to-pulse length.

© 2014 Optical Society of America

## 1. Introduction

1. K. N. Joo, Y. Kim, and S.
W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express **16**(24), 19799–19806 (2008). [CrossRef] [PubMed]

8. S. Hyun, Y. Kim, Y. Kim, J. Jin, and S. Kim,
“Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. **20**(9), 095302 (2009). [CrossRef]

^{−12}) or Cs clock (10

^{−15}), hence the optical frequency comb has the frequency stability and accuracy same as the frequency standard [9]. Due to the super-stability and high accuracy of the frequency, the optical frequency comb can be used as an optical source in a distance measurement system with nm or even pm precision [10

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

11. 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]

^{6}m with an accuracy of subwavelength theoretically [12

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

13. 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]

^{6}m [14

14. 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]

*l*

_{pp}(

*l*

_{pp}is the pulse-to-pulse length) can be directly measured as the distance between temporal coherence peaks of the fringes, and the accuracy is 1 µm over 1.5 m [15

15. D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto,
“Time-of-flight method using multiple pulse train interference as a time recorder,” Opt. Express **19**(6), 4881–4889 (2011). [CrossRef] [PubMed]

16. X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto,
“Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express **20**(3), 2725–2732 (2012). [CrossRef] [PubMed]

17. 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]

18. S. A. van den Berg, S. T. Persijn, G. J.
P. 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]

19. 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]

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

*φ*on the position of the brightest fringe of the correlation patterns. This is important for time-of-flight method and heterodyne interference method. In Section V, we measure a distance in a range of 10 µm based on a Michelson interferometer. The experimental results show that the maximum deviation is 45 nm with a small non-ambiguity range using the model of asymmetric sech

_{ce}^{2}pulse. To extend the range of non-ambiguity, we design an interference system combining the methods of light intensity detection and time-of-flight, which is composed of three Michelson interferometers in Section VI, and the system is not complex. Finally, the main conclusions and future plan of this work are summarized in Section VII.

## 2. Analysis of pulse temporal coherence function

21. D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto,
“Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express **17**(9), 7011–7018 (2009). [CrossRef] [PubMed]

22. M.
G. Zeitouny, M. Cui, N. Bhattacharya, H. P. Urbach, S.
A. van den Berg, and A. J. E. M. Janssen, “From a discrete to a continuous model for inter pulse interference with a frequency-comb laser,” Phys. Rev.
A **82**(2), 023808 (2010). [CrossRef]

_{R}. The other part of the pulse train goes into the measurement arm and is reflected by the target mirror M

_{T}. These two parts of the pulse train are finally recombined at the beam splitter BS. The reference arm is scanned over a fixed range using a piezoelectric transducer, while the measurement arm is displaced over a distance to be determined. In this work, the distance determined is a tiny displacement in a range of 10 µm, another piezoelectric transducer is needed as a length standard. When the two parts of the pulse train overlap in space, the interference fringes can be observed on the oscilloscope OS by scanning the reference arm.

_{n}= c/n = c/(n

_{R}+

*i*n

_{I}), where n, n

_{R}and n

_{I}denote the complex refractive index, the real part and imaginary part, respectively. n

_{R}is the refractive index, and n

_{I}characterizes the wave absorption when traveling through the medium. For the case of temporal coherence function of the light pulses, all the proposed models were created with neglection of absorption. However, the limited power of the laser gets lower and lower when propagating in absorptive medium like air because of the absorption, that is the reason why the distance measured cannot be infinity, thus it is necessary to consider the absorption of the medium. In this section, we develop a model with the consideration of both the dispersion and absorption. The Ciddor formula [23

23. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,”
Appl. Opt. **35**(9), 1566–1573 (1996). [CrossRef] [PubMed]

_{R}of complex refractive index to make the model more comprehensive.

*f*

_{rep}and the carrier-envelope-offset frequency

*f*

_{ceo}.

*ω*

_{m}= m

*ω*

_{rep}+

*ω*

_{ceo}= 2π (m

*f*

_{rep}+

*f*

_{ceo}). m is a positive integer. The spectrum of the optical frequency comb consists of hundreds of thousands of discrete and single lines with the equal space of

*ω*

_{rep}. The shorter the pulse is, the wider the spectrum is. A pulse train from optical frequency comb can be expressed as:where E

_{train}(t,z) is the electric field of the pulse train in the time domain, ∑E

_{z1,m}(t,z

_{1})exp[-

*i*(

*ω*

_{m}

*t*-

*k*

_{m}z

_{1}) +

*i*(

*φ*

_{0}+ Δ

*φ*

_{ce}

*t*)] is the field of the pulse, propagating in the direction of positive z, at z = z

_{1},

*E*

_{z1,m}(

*t*,z

_{1}) is a real amplitude,

*k*

_{m}is the propagation vector of the pulse,

*k*

_{m}= 2π/

*λ*

_{m}=

*ω*

_{m}/

*c*

_{m}=

*n*

_{m}

*ω*

_{m}/

*c*= (

*n*

_{Rm}+

*in*

_{Im})

*ω*

_{m}/

*c*.

*λ*

_{m}is the wavelength corresponding to n

_{R}(

*ω*

_{m}).

*φ*

_{0}is an initial phase of the carrier pulse. Δ

*φ*

_{ce}is carrier phase slip rate because of the difference between the group and phase velocities.

*h*is an integer. It is significant that

*l*

_{pp}is a function of the wavelength

*λ*

_{m}because the wave velocities are different corresponding to the different wavelengths. Here the pulse-to-pulse length

*l*

_{pp}is defined as

*l*

_{pp}(

*λ*

_{m}) =

*c*/(

*n*) =

_{g}f_{rep}*cT*/

_{rep}*n*where

_{g}*n*is the group refractive index.

_{g}*n*is a function of the wavelength

_{g}*λ*

_{m}.

*λ*

_{c}is the center wavelength [3

3. 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]

*T*

_{rep}is the time interval between the pulses.

*f*Δ

_{ceo}=*φ*

_{ce}f_{rep}/2π.*L*is the distance to be determined.

*floor*(2

*L*/

*l*

_{pp}),

*floor*rounds the element of 2

*L*/

*l*

_{pp}to the nearest integer less than or equal to 2

*L*/

*l*

_{pp}.

*T*

_{d}is used to detect the light intensity, and the intensity can be expressed as:where

*g*is a positive integer,

*g*=

*floor*(

*T*

_{d}/

*T*

_{rep}).

*l*

_{pp}, Eq. (6) can be rewritten as

_{I}. The AC part is simply an oscillation cosine function, and the envelop is determine by the factor

*P*

_{m}is defined as the power spectral density. This shows that the temporal coherence function requires the knowledge of the optical source spectrum, and the absorption cannot be neglected. The AC part (arbitrary unit) of the waveform observed on the oscilloscope is determined by n

_{R}(

*ω*

_{m}),

*ω*

_{m},

*L*,

*N*, and Δ

*φ*

_{ce}, and is important for the distance measurement method proposed in this work, which we will discuss in next section. In our experiment,

*f*

_{rep}= 199.817 MHz, the center wavelength is 1548.2 nm, and the spectrum bandwidth is 58.8 nm.

## 3. Distance measurement principle and simulations

^{2}pulse, we compare the simulated interference fringes based on the Gaussian pulse model, the sech

^{2}pulse model, the asymmetric Gaussian pulse model, and the asymmetric sech

^{2}pulse model, respectively. The comparison results can provide a reference to the distance measurement.

*N*is a positive integer, and

*d*is a small length,

### 3.1 Determination of N and simulations

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

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

19. 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]

24. K. N. Joo, Y. Kim, and S.
W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express **16**(24), 19799–19806 (2008). [CrossRef] [PubMed]

*f*

_{rep}= 200 MHz,

*f*

_{ceo}= 2 MHz, d = 0, and the intensity is the average value. Figure 2 shows the simulated results in a period. We can observe that the curve is a standard cosine function, and the intensity varies obviously when N is adjusted. It is necessary to indicate that the results shown in Fig. 2 are only theoretical values with no consideration of the environment conditions.

*ω*

_{c}is the center frequency of the optical frequency comb. We can find that the intensity decreases when N increases, and the decreasing trend is square of a negative exponential function. The method requires the precision measurement of n

_{R}and n

_{I}and a very stable environment conditions. This can be a subject for future research.

### 3.2 Determination of d and simulations

_{R}(

*ω*

_{c})

*ω*

_{c}/

*c*, and the non-ambiguity range of d is πc/(2n

_{R}(

*ω*

_{c})

*ω*

_{c}).

*ω*

_{c}is the center angular frequency of the pulse laser.

25. A. M. Weiner, D. E. Leaird, J.
S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. **15**(6), 326–328 (1990). [CrossRef] [PubMed]

27. M. Bitter, E.
A. Shapiro, and V. Milner, “Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping,” Phys. Rev. A **86**(4), 043421 (2012). [CrossRef]

^{2}pulse model, the asymmetric Gaussian pulse model, and the asymmetric sech

^{2}pulse model, to analysis the interference fringes theoretically, which can bridge the distance and the intensity smoothly.

^{2}pulse can be expressed as:

^{2}pulse can be expressed as:where

*A*

_{1},

*A*

_{2},

*A*

_{3},

*A*

_{4}are the electric field amplitudes, and

*a*

_{1},

*a*

_{2},

*a*

_{3},

*a*

_{4},

*a*

_{5},

*a*

_{6}are the attenuation factors, respectively. When

*a*

_{3}>

*a*

_{4}, the pulse is left asymmetric;

*a*

_{3}<

*a*

_{4}, the pulse is right asymmetric. When

*a*

_{5}>

*a*

_{6}, the pulse is left asymmetric;

*a*

_{5}<

*a*

_{6}, the pulse is right asymmetric. Figure 3 shows the comparison between shapes of different pulses. The pulse width Δ

*t*and the spectral bandwidth Δ

*ν*maintain the relationship of Δ

*t*·Δ

*ν*= K where the constant K equals 0.32 and 0.44 for sech

^{2}and Gaussian pulses [28

28. S. Kim and Y. Kim, “Advanced optical metrology using
ultrashort pulse lasers,” Rev. Laser Eng. **36**(suppl), 1254–1257 (2008). [CrossRef]

*f*

_{rep}= 200 MHz,

*f*

_{ceo}= 2 MHz, the scanning step size of d is 100 nm, and the scanning range is 100 µm. Figure 4 shows the interference fringes based on different pulse models. In the cases it is straightforward that all the fringes are symmetric. The Gaussian fringe and asymmetric Gaussian fringe attenuate a little faster than the sech

^{2}fringe and the asymmetric sech

^{2}fringe, while all the pulse widths in the simulations are about 50 fs. While propagating in dispersive medium, the pulse laser suffers from the shape broadening and deformation in the long distance measurement, known as the dispersion and the chirp. For the case of short distance, or even a tiny displacement measurement, the dispersion is not very obvious, and can be neglected. In this work, the fringes in Fig. 4 are generated based on an interferometer at equal arms, which means the distance is not very long, and the patterns are simulated with no consideration of the dispersion. We will use the intensity of these fringes to measure distances in Sec. V.

## 4. Analysis of the position of the brightest fringe

22. M.
G. Zeitouny, M. Cui, N. Bhattacharya, H. P. Urbach, S.
A. van den Berg, and A. J. E. M. Janssen, “From a discrete to a continuous model for inter pulse interference with a frequency-comb laser,” Phys. Rev.
A **82**(2), 023808 (2010). [CrossRef]

*f*

_{rep}= 200 MHz,

*f*

_{ceo}= 2 MHz, the scanning step size of d is 10 nm, and the scanning range is 6 µm. The pulse-to-pulse length

*l*

_{pp}is 1.5016546 m. Figure 5 shows the position of the brightest fringe corresponding to different N, and the shift displacement is shown in the figures significantly. The increasing step of the shifted displacement of the brightest fringe can be calculated as:where

*λ*

_{c}is the center wavelength.

## 5. Experiment and deviation analysis

*λ*

_{c}is the center wavelength. As shown in Fig. 7, we can observe that there are three peaks in the fringe envelop. The reason is the pulses emitted from the light source are not ideal. The pulse itself has more than one peak in the time domain, and multiple peaks emerge when two pulses overlap in space. In this work, we focus on the intensity around the position of the brightest fringe.

^{2}pulse model, asymmetric Gaussian pulse model and asymmetric sech

^{2}pulse model, respectively. We pick up the distances corresponding to the intensities of 0.05611, −0.8887, 0.32954, 0.85437, −0.34645, −0.5822, 0.63823, 0.4452, −0.42319, −0.11197, respectively, and these distances are the measurement results based on different pulse models introduced in Sec. III. Table 1 shows the measurement results. Figure 11 shows the deviations of different pulse models.

^{2}model and sech

^{2}model at 9 µm. We arrange the maximum difference of different models in Table 2. The maximum differences are all at the position of 9 µm, and the deviation of the asymmetric sech

^{2}model is the smallest. The reasons of introducing deviations include the instability of the pulses, the variation of the environment conditions, the resolution of the electric instruments, the vibration of the precision optical platform, the difference between the numerical models and the real one, and the resolution of the simulation software. We consider that the mean reason is the difference between the numerical models and the real one. To build a more accurate model can reduce the deviation.

^{2}pulse model. In ranging and manufacturing applications, there are two critical parameters: precision and non-ambiguity range. We observe that the non-ambiguity range of this method is just 0.387 µm which can be calculated as λ

_{c}/4 = 1548.2/4 = 0.387 μm theoretically. To solve this problem, we design an interference system which will be introduced in next section.

## 6. A combined interference system using three Michelson interferometers

_{1}is Thorlabs PDB150 Balanced Amplified Photodetector, and the photodetector PD

_{2}is EOT Amplified InGaAs Detector ET-3000A-FC. S

_{1}and S

_{2}are two shutters. L is the distance to be measured. The interference system is a combination of three equal arms Michelson interferometer. As shown in Fig. 12, M

_{R}, BS

_{1}, BS

_{2}, M

_{T1}make up one Michelson interferometer named Mi

_{α}, M

_{R}, BS

_{1}, BS

_{2}, M

_{T2}constitute another Michelson interferometer named Mi

_{β}, and the last Michelson interferometer named Mi

_{γ}is composed of M

_{T1}, BS

_{2}, M

_{T2}.

_{1}is open, S

_{2}is open. The pulses reflected by M

_{T1}and M

_{T2}overlap in space, and PD

_{2}can be illuminated. We record the intensity displayed on the oscilloscope. This intensity can be used to measure the distance according to Sec. III and Sec. V. Secondly, S

_{1}is open, S

_{2}is closed. The pulses reflected by M

_{T1}and M

_{R}overlap and are detected by PD

_{1}. The interference fringe observed on the oscilloscope like Fig. 7 is used to record the relative position of M

_{T1}. Thirdly, S

_{1}is closed, S

_{2}is open. The pulses reflected by M

_{T2}and M

_{R}overlap, and the interference fringe is used to determine the relative position of M

_{T2}. We set the PZT driving signal as a reference of the position. Figure 13 shows the system photograph. The yellow line (CH1, upper line) indicates the interference fringe detected by PD

_{1}, the red line (CH2, middle line) denotes the PZT driving signal, which is stable enough to be a position reference, and the blue line (CH3, lower line) is the intensity detected by PD

_{2}. We use this system to measure a distance, and the distances measured are 5, 10, 15 µm, respectively.

_{1}is open, S

_{2}is open. The intensity detected by PD

_{2}is −0.34645. As shown in Fig. 14, there are several distances corresponding to the intensity of −0.34645, which means we cannot uniquely determine the distance measured.

_{1}is open, S

_{2}is closed. We can record the relative position of M

_{T1}based on the interference fringe, as shown in Fig. 15(a) (upper yellow line, fringe generated by Mi

_{β}). Thirdly, S

_{1}is closed, S

_{2}is open. We can determine the relative position of M

_{T2}, as shown in Fig. 15(a) (lower yellow line, fringe generated by Mi

_{α}). The PZT driving signal (lower red line) is the position reference. As shown in Fig. 15(a), we can observe that the distance between the positions of the two brightest fringes is about 5 µm. Then we can uniquely pick up the distance around 5 µm in the red box, as shown in Fig. 14, and the measured value is 4.995 µm according to Sec. V. The deviation is −5 nm. We also measure the distances of 10 µm and 15 µm, as shown in Figs. 15(b) and 15(c).

*t·c*/n in air, where Δ

*t*is the pulse width and

*c*is the light velocity in vacuum. This system can extend the range of non-ambiguity to be largest. We can find that the non-ambiguity range of the method of intensity detection is small, and this is a big limitation.

_{T1}and M

_{T2}, and we can observe the pure interference fringes. In fact, this system can satisfy the requirement of large scale distance measurement.

## 7. Conclusion and future plan

^{2}pulse model, the asymmetric Gaussian pulse model, and the asymmetric sech

^{2}pulse model. We investigate the relationship between the shifted displacement of the position of the brightest fringe and the pulse-to-pulse phase relation of the optical frequency comb. We do experiments to verify the method of intensity detection under stable environment conditions. The displacement of piezo position platform has been taken as a distance reference. In a range of 10 µm, we measure each distance for 10 times to reduce the random error. The experimental results show that this method can realize absolute distance measurement. The maximum deviation of different pulse models all emerges at the position of 9 µm, which are 56, 57, 47, and 45 nm corresponding to Gaussian, sech

^{2}, asymmetric Gaussian, and asymmetric sech

^{2}model, respectively. We observe that the deviation of the asymmetric models is smaller. There are two critical parameters for ranging system: precision/accuracy and non-ambiguity range. To expand the non-ambiguity range, we design an interference system exploiting three Michelson interferometers. The working process of the system is introduced, and we measure distances of 5, 10, 15 µm using this system, respectively. The experimental results show that this system can measure a distance with a higher accuracy and a larger range of non-ambiguity.

## Acknowledgments

## References and links

1. | K. N. Joo, Y. Kim, and S.
W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express |

2. | 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 |

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

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

5. | M. G. Zeitouny, M. Cui, A. J. E.
M. Janssen, N. Bhattacharya, S. A. van den Berg, and H. P. Urbach,
“Time-frequency distribution of interferograms from a frequency comb in dispersive media,” Opt. Express |

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

7. | H. Matsumoto, X. Wang, K. Takamasu, and T. Aoto,
“Absolute measurement of baselines up to 403 m using heterodyne temporal coherence interferometer with optical frequency comb,” Appl. Phys. Express |

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

9. | J. Ye and S. T. Cundiff, |

10. | J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S. Kim, and Y. Kim,
“Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. |

11. | 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. |

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

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

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

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

16. | X. Wang, S. Takahashi, K. Takamasu, and H. Matsumoto,
“Space position measurement using long-path heterodyne interferometer with optical frequency comb,” Opt. Express |

17. | 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. |

18. | S. A. van den Berg, S. T. Persijn, G. J.
P. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute
distance measurement,” Phys. Rev. Lett. |

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

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

21. | D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto,
“Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express |

22. | M.
G. Zeitouny, M. Cui, N. Bhattacharya, H. P. Urbach, S.
A. van den Berg, and A. J. E. M. Janssen, “From a discrete to a continuous model for inter pulse interference with a frequency-comb laser,” Phys. Rev.
A |

23. | P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,”
Appl. Opt. |

24. | K. N. Joo, Y. Kim, and S.
W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express |

25. | A. M. Weiner, D. E. Leaird, J.
S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. |

26. | S. H. Shim, D. B. Strasfeld, E.
C. Fulmer, and M. T. Zanni, “Femtosecond pulse shaping directly in the mid-IR using acousto-optic modulation,” Opt. Lett. |

27. | M. Bitter, E.
A. Shapiro, and V. Milner, “Enhancing strong-field-induced molecular vibration with femtosecond pulse shaping,” Phys. Rev. A |

28. | S. Kim and Y. Kim, “Advanced optical metrology using
ultrashort pulse lasers,” Rev. Laser Eng. |

**OCIS Codes**

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

(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(320.7160) Ultrafast optics : Ultrafast technology

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: February 14, 2014

Revised Manuscript: March 31, 2014

Manuscript Accepted: April 3, 2014

Published: April 22, 2014

**Citation**

Hanzhong Wu, Fumin Zhang, Shiying Cao, Shujian Xing, and Xinghua Qu, "Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser," Opt. Express **22**, 10380-10397 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10380

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### References

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