## Femtosecond frequency comb based distance measurement in air

Optics Express, Vol. 17, Issue 11, pp. 9300-9313 (2009)

http://dx.doi.org/10.1364/OE.17.009300

Acrobat PDF (491 KB)

### Abstract

Interferometric measurement of distance using a femtosecond frequency comb is demonstrated and compared with a counting interferometer displacement measurement. A numerical model of pulse propagation in air is developed and the results are compared with experimental data for short distances. The relative agreement for distance measurement in known laboratory conditions is better than 10^{-7}. According to the model, similar precision seems feasible even for long-distance measurement in air if conditions are sufficiently known. It is demonstrated that the relative width of the interferogram envelope even decreases with the measured length, and a fringe contrast higher than 90% could be obtained for kilometer distances in air, if optimal spectral width for that length and wavelength is used. The possibility of comb radiation delivery to the interferometer by an optical fiber is shown by model and experiment, which is important from a practical point of view.

© 2009 Optical Society of America

## 1. Introduction

1.
For a general review see, e.g., S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. **75**, 325–342 (2003). [CrossRef]

4. E. V. Baklanov and A. K. Dmitriev, “Absolute length measurements with a femtosecond laser,” Quantum Electron. **32**, 925–928 (2002). [CrossRef]

5. J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. **29**, 1153–1155 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=ol-29-10-1153. [CrossRef] [PubMed]

6. K.-N. Joo, Y. Kim, and S.-W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express **16**, 19799–19806 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-24-19799. [CrossRef] [PubMed]

7. Y. Salvadé, N. Schuhler, S. Lévêque, and S. Le Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. **47**, 2715–2720 (2008), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-14-2715. [CrossRef] [PubMed]

8. M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid Publ. **3**, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246. [CrossRef]

*et al*. [9

9. K. Minoshima, T. R. Schibli, H. Inaba, Y. Bitou, F.-L. Hong, A. Onae, H. Matsumoto, Y. Iino, and K. Kumagai, “Ultrahigh dynamic-range length metrology using optical frequency combs,” NMIJ-BIPM Joint Workshop on Optical Frequency Comb, Tsukuba, (2007), http://www.nmij.jp/~nmijclub/photo/docimgs/minoshima_2007May_web2.pdf.

10. J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of carbon dioxide with a frequency comb,” Opt. Lett. **32**, 3212–3214 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-21-3212 [CrossRef] [PubMed]

## 2. Principle of interferometric distance measurement with a frequency comb

*l*, an interferogram (cross-correlation function) can be measured. In order to accomplish spatial overlap between the pulses traveling in the long and short arms, respectively, the short arm can be adjusted within the range

_{pp}*l*/2.

_{pp}*f*of 100–1000 MHz, which leads to an interpulse distance

_{r}*l*=

_{pp}*c*/(

_{o}*n*) of 30–300 cm. Here

_{ge}f_{r}*c*is the speed of light in vacuum and

_{o}*n*is the effective group refractive index of air. The range of non-ambiguity of the distance measurement is determined by

_{ge}*l*. An initial measurement with this accuracy can be done easily with other methods, or the integer number

_{pp}*N*of

*l*in a measured distance can be estimated by change of

_{pp}*f*and the measurement of a corresponding shift of the interferogram, if the relative precision of the shift measurement is better then 1/

_{r}*N*. Thus the path length difference in the interferometer is measured as a multiple of the interpulse distance and is retrieved from the center of the measured interferogram. This measurement principle can be applied for absolute distance measurements by placing the measuring reflector to the zero position (of baseline) and adjusting the reference arm for coherence maximum, then moving the measuring reflector to the target point of the long arm and adjusting the short arm to obtain a coherence maximum again. The displacement of the short arm may be measured, e.g., by an auxiliary counting interferometer or a calibrated line scale. There is no need for continuous measurement while moving the reflector (in contrast to counting the interferometer displacement measurement). By scanning the reference arm around the coherence maxima position, an interferogram is obtained. The interferogram can be measured as either first- or second-order correlation functions. The shape of the interferogram depends on the spectral content and the fact that the pulses experience different dispersions in the long and short arms. For second-order correlation, the chirp of the initial pulse comes into play. To obtain an accurate distance measurement, the interpulse distance

*l*needs to be known accurately and thus the effective group refractive index of air.

_{pp}## 3. Numerical model of comb pulse propagation in air

*v*or the group refractive index

_{g}*n*can be calculated analytically as

_{g}*λ*and

_{c}*f*are the central wavelength and frequency of the pulse spectra, respectively, and

_{c}*n*is corresponding phase refractive index.

*∂n*/

*∂f*leads to a relatively complicated expression when using precise refractive index formulas such as Ciddor’s [11

11. Ciddor formula for refractive index of air, http://emtoolbox.nist.gov/Wavelength/Documentation.asp.

*x*as

_{n}*k*=2

_{i}*π n*/

_{i}f_{i}*c*represents the angular wavenumber in air and

_{o}*E*is the (relative) electric field of the frequency comb component

_{i}*i*. The frequency

*f*is given by:

_{i}*f*=

_{i}*f*+

_{o}*if*, with

_{r}*f*as the carrier-envelope offset frequency. For each frequency

_{o}*f*the phase refractive index

_{i}*n*is taken into account, which is calculated using the Ciddor formula [11

_{i}11. Ciddor formula for refractive index of air, http://emtoolbox.nist.gov/Wavelength/Documentation.asp.

12. J. E. Decker and J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia **34**, 479–493 (1997). [CrossRef]

_{2}content—are provided as input. The input pulse properties can be set by specifying

*f*and

_{r}*f*as the central wavelength and the spectral width and shape. Alternatively, an arbitrary (measured) spectral shape can be loaded. For the individual comb components, the relative electric field and the phase index are calculated. From these results the group refractive index for the central wavelength and the mean group refractive index (spectrally weighted according to light intensity) are determined. For the latter, Eq. (2) (with

_{o}*f*instead of

_{i}*f*) is applied for calculation of the contribution of each spectral component to the effective group index.

_{c}*f*. In both cases these values are chosen such that the path length difference between measuring and the reference arm equals an integer multiple of

_{r}*l*. Once the expected position of interferogram “center” is known, a local value of the electric field (at time =0) is calculated as a sum of the contributions of all comb components according to Eq. (3). Both

_{pp}*E*(

_{r}*x*) for the reference pulse (

_{n}*x*around zero) and

_{n}*E*(

_{m}*x*) for the measuring pulse (with

_{n}*x*around the expected path length difference) are determined, each of them in

_{n}*N*points (with

*n*ranging from -

*N*/2 to

*N*/2). We have prepared the spatial profile of the electric field of reference and the measuring pulses (strictly speaking, an instant picture of a profile in time equal to the integer multiple of femtosecond laser periods 1/

*f*). The (relative) interferogram

_{r}*I*(

*x*), i.e., the time-averaged light intensity variation with changing the path length, is obtained from the convolution of the electric fields of both pulses as

*d*. The convolution is calculated numerically; if index

*n*+

*d*is outside the interval -

*N*/2 to

*N*/2, the

*E*is taken equal to zero. The range of x is chosen such that both

_{m}*E*and

_{r}*E*pulses fully fit into the range of calculated path lengths—only negligible tails were outside—and

_{m}*N*is chosen such that the increment of the position is much smaller than the central wavelength.

_{2}. It is observed that air dispersion is significant even for this short distance; the measuring pulse returns stretched (the red curve in the middle picture compared to the green one) and the contrast of the linear interferogram is decreased by a few percent.

*l*. However, due to air dispersion, the coherence is maintained only for some part of the spectra for path length difference

_{pp}*L*equal to non-zero multiples of

*l*. The light intensity for a certain value of

_{pp}*λ*is given by

*f*= 200 MHz, total width of the evaluated spectra 160 THz and for 20 nm steps over the range ±0.1 mm, all 800 000 of the comb components have to be evaluated for each 10 000 position points, i.e., 2×10

_{r}^{9}of cosine evaluations and a few multiplications (with extended precision) have to be done for

*E*field profiles (which take 18 min on a PC with an x86 2 GHz processor). But, the resulting position and shape of the interferogram is the same if a higher

*f*is chosen (equal to an integer multiple of the original value) as long as the remaining number of components is sufficient for a detailed representation of incident radiation spectra. So to save time, the above described calculation can be done for

_{r}*f*= 20 GHz (8 000 components) in just 12 seconds. But if a detailed spectral shape including, e.g., molecular absorption spectral lines is needed [13

_{r}13. Y. Yamaoka, L. Zeng, K. Minoshima, and H. Matsumoto, “Measurements and numerical analysis for femtosecond pulse deformations after propagation of hundreds of meters in air with water-vapor absorption lines,” Appl. Opt. **43**, 5523–5530 (2004). [CrossRef] [PubMed]

*f*and

_{r}*f*) is needed.

_{o}## 4. Results of modeling

^{-10}relative for 100 m distance). For symmetrical spectra the agreement is even much better.

*l*remains constant). Only the second-order interferogram background shows the real pulse length, as can be seen in Fig. 3.

_{pp}*n*and

_{ge}*l*are calculated (the

_{pp}*f*or reference arm length is changed such that the path difference equals an integer multiple of

_{r}*l*). The spectral modulation curve at that position shows spectral bands (Fig. 4) for which coherence is maintained—the broadest one in the center is the optimal one.

_{pp}*f*is a disadvantage, bringing longer

_{r}*l*—a longer movement of the reference arm for finding the interferogram. This problem could be solved by folding the beam on the moving stage (or by measuring distances only close to the integer multiple of

_{pp}*l*/2 (close enough such that an adjustment of

_{pp}*l*by

_{pp}*f*is possible).

_{r}## 5. Experimental setup and measurement procedure

14. P. Balling and P. Kren, “Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm,” Eur. Phys. J. D **48**, 3–10 (2008). [CrossRef]

^{-11}rel. for 1 s averages, k=2) and the cavity length is approximately 0.75 m (

*l*~1.5 m).

_{pp}*l*, respectively, as determined by the CI. The displacement of these positions is measured by the LI as well.

_{pp}_{2}content) and detected pulse spectra (see next section for details about spectra detection).

10. J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of carbon dioxide with a frequency comb,” Opt. Lett. **32**, 3212–3214 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-21-3212 [CrossRef] [PubMed]

## 6. Experimental results

^{-8}. This is illustrated in Fig. 8, which shows the relative difference between LI and CI for various measurements.

^{-7}rel. was caused by the combination of spectral sensitivity of the interferometer and the real change of spectra due to a drift of the fs comb laser after measurement with the spectrometer. The possible instability of fs laser spectra only emphasizes the value of real-time evaluation of spectra from the interferogram, which is by the way easier and directly traceable as compared with the complicated traceable calibration of a spectrometer (wavelength and sensitivity) and a photodiode of an interferometer detector (reflectance of mirrors and beam splitter are not important when measuring the spectra at the interferometer output). Here only the calibration of the amplitude of piezoelectric transducer modulation by counting the number of fringes with a calibrated cw laser is sufficient for a correct evaluation of the actual detected spectral shape (defining actual effective group refractive index).

^{-7}rel. as shown in Fig. 8 is solely due to the instability of laboratory conditions (the temporal inhomogeneity between LI and CI paths) and not by the resolution and reproducibility of the interferogram detection, which was about 10 times better. For each point both CI and LI values were corrected to actual atmospheric conditions.

*et al*. also used the fiber connection between an Er: fiber fs comb laser and the distance measuring equipment [9

9. K. Minoshima, T. R. Schibli, H. Inaba, Y. Bitou, F.-L. Hong, A. Onae, H. Matsumoto, Y. Iino, and K. Kumagai, “Ultrahigh dynamic-range length metrology using optical frequency combs,” NMIJ-BIPM Joint Workshop on Optical Frequency Comb, Tsukuba, (2007), http://www.nmij.jp/~nmijclub/photo/docimgs/minoshima_2007May_web2.pdf.

*l*, we have changed the arrangement so that both CL and LI measure the same distances between common retro reflectors and beam splitter, so the drift influence is suppressed because values of LI and CI are taken the same time. During this test we use narrow beams (diameter ~2mm), which are spatially separated next to common axis. The comb radiation is again delivered via fiber (angle polished with attached lens collimators). When observing interferogram position by eye, the repeatability is not improved much; a scatter of up to 1/3 of the fringe is mostly due to residual amplitude noise and is also affected by the less than perfect coincidence of sampling and fringe peaks. When evaluating interferogram positions by computer, e.g., as the center of gravity of the absolute value of an ac signal or as the center of gravity of the squares of an ac signal, the measured distance between consecutive interferograms is repeatable to better than ±20nm/1.5m (±13.10

_{pp}^{-9}rel). However, a systematic deviation of about 100nm/1.5m was found. The reason is that the center of gravity of a square of the electric field of the reference arm pulse does not coincide exactly with the center of gravity of the interferogram (light intensity produced by interference of reference and measuring arm E-field pulses) when real (asymmetric) spectra or a less than perfect dispersion compensation of arms is used (the model and measurement agree).

*l*defined by a distance of the centers of gravity is not good enough to reach 0.1 ppm relative uncertainty at a short distance in the case of a non-perfect or not perfectly known compensation of dispersion between the arms. But, it should be noted that the above mentioned problem of the center of gravity ambiguity is, in our case, only 1/8 of the fringe or 1% of FWHM of the detected interferogram. For long-distance and optimal spectral filtering, when whole interferogram length is about 0.1 ppm of the distance to be measured (see Table 1), minor differences between different ways of interferogram center evaluation should not be a problem.

_{pp}*x*

_{0}at which the Fourier transform with phases

*φ*(

*λ,x*

_{0}) was calculated, and also where the value of the reference laser interferometer was read. When we added the difference of Δx for the zero and 1*

*l*interferograms to the distance measured by LI, we got better agreement with the predicted

_{pp}*l*than in case of the center of gravity evaluation. Using the distance between the next stationary phase points for a certain wavelength means that only the simple group refractive index at that wavelength is needed. That is, no weighting to the effective group refractive index is needed.

_{pp}*l*(

_{pp}*λ*) or

*n*(

_{g}*λ*) is better than 0.1 ppm for each wavelength used. The relative deviation of

*l*(790 nm) and

_{pp}*l*(810 nm) is 0.36 ppm.

_{pp}^{-8}rel. and it is further compensated by a compensating plate CP (Thorlabs BSW08-1-OC, also 30’) placed anti-parallel behind the beam splitter.

*et al*. used a gauge block as a reference [15

15. Y. Yamaoka, K. Minoshima, and H. Matsumoto, “Direct measurement of the group refractive index of air with interferometry between adjacent femtosecond pulses,” Appl. Opt. **41**, 4318–4324 (2002). [CrossRef] [PubMed]

^{-7}rel. (standard deviation). We use a 633 nm interferometer with a phase refractive index calculated by the Ciddor formula as a reference. We got both scatter and agreement of measured and calculated group refractive indices of better than 1.10

^{-7}rel. (two standard deviations) in this preliminary arrangement.

## 7. Conclusion

^{-8}on average if calculation is done for actually detected spectra. Alternative methods of evaluation using phase information from a Fourier transform is proposed and demonstrated. It could lead to precise measurement of dispersion/group refractive indices after an improvement of the experimental arrangement. It was demonstrated that first-order interferograms remain transform limited, even if highly chirped and elongated pulses enter the interferometer, allowing for delivering the frequency comb radiation to the interferometer by an optical fiber.

## Acknowledgments

16. J.-P. Wallerand, A. Abou-Zeid, T. Badr, P. Balling, J. Jokela, R. Kugler, M. Matus, M. Merimaa, M. Poutanen, E. Prieto, S. van den Berg, and M. Zucco, “Towards new absolute long-distance measurement in air,” 2008 NCSL International Workshop and Symposium, Orlando (USA), http://www.longdistanceproject.eu/files/towards_new_absolute.pdf.

## References and links

1. |
For a general review see, e.g., S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. |

2. | P. Gill, “Optical frequency standards,” Metrologia |

3. | L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, “The measurement of optical frequencies,” Metrologia |

4. | E. V. Baklanov and A. K. Dmitriev, “Absolute length measurements with a femtosecond laser,” Quantum Electron. |

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

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

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

8. | M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, “Experimental demonstration of distance measurement with a femtosecond frequency comb laser,” J. Eur. Opt. Soc. Rapid Publ. |

9. | K. Minoshima, T. R. Schibli, H. Inaba, Y. Bitou, F.-L. Hong, A. Onae, H. Matsumoto, Y. Iino, and K. Kumagai, “Ultrahigh dynamic-range length metrology using optical frequency combs,” NMIJ-BIPM Joint Workshop on Optical Frequency Comb, Tsukuba, (2007), http://www.nmij.jp/~nmijclub/photo/docimgs/minoshima_2007May_web2.pdf. |

10. | J. Zhang, Z. H. Lu, and L. J. Wang, “Precision measurement of the refractive index of carbon dioxide with a frequency comb,” Opt. Lett. |

11. | Ciddor formula for refractive index of air, http://emtoolbox.nist.gov/Wavelength/Documentation.asp. |

12. | J. E. Decker and J. R. Pekelsky, “Uncertainty evaluation for the measurement of gauge blocks by optical interferometry,” Metrologia |

13. | Y. Yamaoka, L. Zeng, K. Minoshima, and H. Matsumoto, “Measurements and numerical analysis for femtosecond pulse deformations after propagation of hundreds of meters in air with water-vapor absorption lines,” Appl. Opt. |

14. | P. Balling and P. Kren, “Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm,” Eur. Phys. J. D |

15. | Y. Yamaoka, K. Minoshima, and H. Matsumoto, “Direct measurement of the group refractive index of air with interferometry between adjacent femtosecond pulses,” Appl. Opt. |

16. | J.-P. Wallerand, A. Abou-Zeid, T. Badr, P. Balling, J. Jokela, R. Kugler, M. Matus, M. Merimaa, M. Poutanen, E. Prieto, S. van den Berg, and M. Zucco, “Towards new absolute long-distance measurement in air,” 2008 NCSL International Workshop and Symposium, Orlando (USA), http://www.longdistanceproject.eu/files/towards_new_absolute.pdf. |

**OCIS Codes**

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(010.3310) Atmospheric and oceanic optics : Laser beam transmission

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

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.3940) Instrumentation, measurement, and metrology : Metrology

(260.2030) Physical optics : Dispersion

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: March 10, 2009

Revised Manuscript: April 17, 2009

Manuscript Accepted: April 18, 2009

Published: May 19, 2009

**Citation**

Petr Balling, Petr Křen, Pavel Mašika, and S. A. van den Berg, "Femtosecond frequency comb based distance
measurement in air," Opt. Express **17**, 9300-9313 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-11-9300

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### References

- For a general review see, e.g., S. T. Cundiff and J. Ye, "Colloquium: Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003). [CrossRef]
- P. Gill, "Optical frequency standards," Metrologia 42, S125-S137 (2005). [CrossRef]
- L. Hollberg, S. Diddams, A. Bartels, T. Fortier, and K. Kim, "The measurement of optical frequencies," Metrologia 42, S105-S124 (2005). [CrossRef]
- E. V. Baklanov and A. K. Dmitriev, "Absolute length measurements with a femtosecond laser," Quantum Electron. 32, 925-928 (2002). [CrossRef]
- J. Ye, "Absolute measurement of a long, arbitrary distance to less than an optical fringe," Opt. Lett. 29, 1153-1155 (2004), opticsinfobase.org/abstract.cfm?URI=ol-29-10-1153">http://www.opticsinfobase.org/abstract.cfm?URI=ol-29-10-1153. [CrossRef] [PubMed]
- K.-N. Joo, Y. Kim, and S.-W. Kim, "Distance measurements by combined method based on a femtosecond pulse laser," Opt. Express 16, 19799-19806 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-24-19799. [CrossRef] [PubMed]
- Y. Salvadé, N. Schuhler, S. Lévêque, and S. Le Floch, "High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source," Appl. Opt. 47, 2715-2720 (2008), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-14-2715. [CrossRef] [PubMed]
- M. Cui, R. N. Schouten, N. Bhattacharya, and S. A. van den Berg, "Experimental demonstration of distance measurement with a femtosecond frequency comb laser," J. Eur. Opt. Soc. Rapid Publ. 3, 08003 (2008), https://www.jeos.org/index.php/jeos_rp/article/view/08003/246. [CrossRef]
- K. Minoshima, T. R. Schibli, H. Inaba, Y. Bitou, F.-L. Hong, A. Onae, H. Matsumoto, Y. Iino, and K. Kumagai, "Ultrahigh dynamic-range length metrology using optical frequency combs," NMIJ-BIPM Joint Workshop on Optical Frequency Comb, Tsukuba, (2007), http://www.nmij.jp/~nmijclub/photo/docimgs/minoshima_2007May_web2.pdf.
- J. Zhang, Z. H. Lu, and L. J. Wang, "Precision measurement of the refractive index of carbon dioxide with a frequency comb," Opt. Lett. 32, 3212-3214 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-21-3212 [CrossRef] [PubMed]
- Ciddor formula for refractive index of air, http://emtoolbox.nist.gov/Wavelength/Documentation.asp.
- J. E. Decker and J. R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical interferometry," Metrologia 34, 479-493 (1997). [CrossRef]
- Y. Yamaoka, L. Zeng, K. Minoshima, and H. Matsumoto, "Measurements and numerical analysis for femtosecond pulse deformations after propagation of hundreds of meters in air with water-vapor absorption lines," Appl. Opt. 43, 5523-5530 (2004). [CrossRef] [PubMed]
- P. Balling and P. Kren, "Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm, and 1540 nm," Eur. Phys. J. D 48, 3-10 (2008). [CrossRef]
- Y. Yamaoka, K. Minoshima, and H. Matsumoto, "Direct measurement of the group refractive index of air with interferometry between adjacent femtosecond pulses," Appl. Opt. 41, 4318-4324 (2002). [CrossRef] [PubMed]
- J.-P. Wallerand, A. Abou-Zeid, T. Badr, P. Balling, J. Jokela, R. Kugler, M. Matus, M. Merimaa, M. Poutanen, E. Prieto, S. van den Berg, and M. Zucco, "Towards new absolute long-distance measurement in air," 2008 NCSL International Workshop and Symposium, Orlando (USA), http://www.longdistanceproject.eu/files/towards_new_absolute.pdf.

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