## Distance measurements by combined method based on a femtosecond pulse laser

Optics Express, Vol. 16, Issue 24, pp. 19799-19806 (2008)

http://dx.doi.org/10.1364/OE.16.019799

Acrobat PDF (290 KB)

### Abstract

We describe a combined interferometric scheme that enables absolute distance measurements using a femtosecond pulse laser. This method is combined with synthetic wavelength interferometry (SWI), time of flight (TOF) and spectrally-resolved interferometry (SRI) using the optical comb of femtosecond laser. Each technique provides distinct measuring resolutions and ambiguity ranges which are complementary to each other. These separate measurement principles are incorporated and implemented simultaneously and the unified output can enhance the dynamic range of the measuring system. Our experimental results demonstrate an example of absolute distance measurement with the proposed technique and we discuss the possibility of the combined method to measure long distances and the important factors for the implementation.

© 2008 Optical Society of America

## 1. Introduction

1. P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett. **17**, 1626–1628 (1992). [CrossRef] [PubMed]

2. T. Kubota, M. Nara, and T. Yoshino, “Interferometer for measuring displacement and distance,” Opt. Lett. **12**, 310–312 (1987). [CrossRef] [PubMed]

3. Y. Y. Cheng and J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,” Appl. Opt. **24**, 804–807 (1985). [CrossRef] [PubMed]

4. J. Schwider and L. Zhou, “Dispersive interferometric profiler,” Opt. Lett. **19**, 995–997 (1994). [CrossRef] [PubMed]

5. 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**, 5512–5517 (2000). [CrossRef]

6. C. E. Towers, D. P. Towers, D. T. Reid, W. N. MacPherson, R. R. J. Maier, and J. D. C. Jones, “Fiber interferometer for simultaneous multiwavelength phase measurement with a broadband femtosecond laser,” Opt. Lett. **29**, 2722–2724 (2004). [CrossRef] [PubMed]

9. Y. -J. Kim, J. Jin, Y. Kim, S. H., and S. -W. Kim, “A wide-range optical frequency generator based on the frequency comb of a femtosecond laser,” Opt. Express **16**, 258–264 (2008). [CrossRef] [PubMed]

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

^{16}which can be determined by the ratio of the maximum measurement range and the measuring resolution.

## 2. Principles

_{1}) where it is split into two, a reference beam and a measurement beam. After the beams are reflected by the reference mirror and measurement mirror respectively, they are recombined by PBS

_{1}and traverse toward to a beam splitter (BS). The reflected beams at BS are detected by photodetectors (PD

_{R}, PD

_{M}) with PBS

_{2}to distinguish one beam from the other in SWI and TOF. The lengths between BS and photodetectors are previously adjusted to be same. In the meantime, the beams transmitted in BS are measured by spectrometer after going through 45° polarizer (P) and Fabry-Perot etalon (FPE) to generate the dispersive interference. This dispersive interference between the reference and measurement beams is observed by use of a spectrometer that consists of a line grating and a line array of 3648 photodetectors.

*ν*) of SRI varies with the frequency ν and the Fourier-transform analysis allows measuring the phase variation with respect to ν so that the distance L (=L

_{2}-L

_{1}) can be determined by the relation of L=(c

_{0}/4

*π*N)(dϕ/dν), where N represents the group refractive index defined as N=n+(dn/dν)ν and c

_{0}is the speed of light in vacuum [11

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

_{NAR}) is restricted by the Nyquist limit that is given as L

_{NAR}=c

_{0}/4Np, in which p represents the sampling period of the spectrometer. If all the modes of the optical comb could possibly be sampled with one mode per pixel of the spectrometer line CCD, p would be equal to the mode spacing of the comb. In addition, the maximum measurable range L

_{MAX}is far beyond L

_{NAR}up to the temporal coherence length (1.5×10

^{7}m), which can be determined by the mode in the comb having a linewidth below 10 Hz when the femtosecond pulse laser is frequency stabilized [12

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

_{NAR}. In Ref. [11

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

_{NAR}is about 1.46 mm with the FPE of 2 mm thickness made of fused silica.

_{NAR}in SRI, an essential procedure is to determine the integer multiple of L

_{NAR}to obtain absolute distances. For the purpose, the scheme of synthetic wavelength interferometry (SWI) based on the mode spacing of the optical comb has been adopted in our configuration.

_{eq}) can be created from the mode spacing (ν

_{F}) of the femtosecond laser or its high harmonic frequencies as the form of λ

_{eq}=c

_{0}/qν

_{F}, where q is an integer which means the order of harmonics. When this synthetic wavelength is used in the interferometer, the measuring range becomes half the synthetic wavelength and the resolution is usually taken as a thousandth of the wavelength by electronic phase measuring technique. For more precise resolution, higher-order harmonics of the mode spacing may be selected as the synthetic wavelength by using appropriate electronic filters and the measurement results are cascaded and incorporated from the first to higher-order harmonics [5

5. 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**, 5512–5517 (2000). [CrossRef]

_{2}-L

_{1}) by detecting the time interval between two pulses with the time resolution on the order of picoseconds. In principle, TOF is used for determining the multiple integer of synthetic wavelength (m

_{1}) in SWI and SWI plays a role of compensating the number of non-ambiguity range (m2) in SRI as shown in Fig. 2.

_{2}means the integer multiple of L

_{NAR}and can be calculated with

_{s}is the measured distance of SWI which includes the multiples of λ

_{eq}/2 with the aids of TOF as a form of

_{syn}is the measured fraction of distance in SWI and m

_{1}is the integer multiple of λ

_{eq}/2 which can be determined by the similar fashion of Eq. (2) with the measurement result of TOF and λ

_{eq}/2.

_{R}and PD

_{M}which can be implemented by a simple device such as an optical chopper in front of the source. The TOF measurement is then used to approximately the absolute distance. Then, SWI and SRI measure the same distance and the final result is calculated using Eq. (1). When combining the three, the overall system can theoretically measure absolute distances up to 1.5×10

^{7}m, which is the coherence length of the stabilized femtosecond laser mode, with the resolution of a few nanometers from SRI.

## 3. Experimental results and discussion

_{NAR}aliasing. L

_{NAR}was 1.458 mm, which is much larger than the resolution of SWI, 0.154 mm when using the 13

^{th}harmonic as the synthetic wavelength as seen in Fig. 3(b). The measurement results from SWI, Fig. 3(b) was used to compensate for L

_{NAR}ambiguity in Fig. 3(a). The distance obtained has a linear relationship with the displacement as shown in Fig. 3(c). From Fig. 3(c), the measurement range is found from SWI and the measurement resolution is determined by SRI.

_{eq}in SWI, a simple experiment to detect the time difference between the reference and measurement arms with PD

_{R}and PD

_{M}was performed. The time delay was obtained from the first pulse into the two arms by an oscilloscope (DSO6012A, Agilent) and was 7.4×10

^{-9}sec. with a resolution of 50 ps. In these experiments, the distance was calculated to be 1.11 m with a resolution of 7.5 mm. By comparing this to λ

_{eq}in SWI, TOF is sufficient for compensating the measured SWI results, thus making Eq. (1) valid for measuring arbitrarily long distances with resolution on the order of nanometers.

^{7}m according to the principle, the transmission peak must become exceedingly sharp and FPE reflectivity should be very high approximately 0.999. Maintaining this reflectivity in the broad spectrum in practice is impossible, thus every mode cannot be filtered. If the linewidth of the transmission peak in the FPE, however, reach the mode spacing of the femtosecond pulse laser and it can be controlled actively, only two modes exist in the transmission peak and they can be sampled at one pixel of the CCD in the spectrometer as shown in Fig. 5(a). Then, the coherence function is decided by the two modes with the mode spacing in the transmission peak and the measurement results of SRI can be expressed as a form of sinusoidal wave with the period of c/2ν

_{F}(roundtrip path) as described in Fig. 5(b). In this case, the measurement results of SRI appear repeatedly at the half of the synthetic wavelength which is created by the optical comb of the femtosecond pulse laser. As shown in Fig. 5(b), the multiple integer m

_{2}in Eq. (1) is not increased infinitely but has the maximum limit value which can be expressed as ±[(λ

_{eq}/4)/L

_{NAR}] due to the periodicity of the results as the distance is longer. The periods can be also determined by SWI.

_{NAR}and the measurement uncertainty of SRI from Eq. (1), excluding the environmental and geometrical errors. Because m2 is a large number for a long distance, the accuracy of L

_{NAR}becomes a more important factor than the other. In SRI, L

_{NAR}is determined by F.S.R. of the FPE filter and it is the half the optical thickness of FPE theoretically [11

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

^{-5}which is dependent on the accuracy of the spectrometer. To achieve low uncertainty measurements, more research in determining the optical thickness of the FPE and the thermal stability should be investigated.

## 4. Conclusion

^{7}m with the resolution of a few nanometers.

## Acknowledgment

## References and links

1. | P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett. |

2. | T. Kubota, M. Nara, and T. Yoshino, “Interferometer for measuring displacement and distance,” Opt. Lett. |

3. | Y. Y. Cheng and J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,” Appl. Opt. |

4. | J. Schwider and L. Zhou, “Dispersive interferometric profiler,” Opt. Lett. |

5. | 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. |

6. | C. E. Towers, D. P. Towers, D. T. Reid, W. N. MacPherson, R. R. J. Maier, and J. D. C. Jones, “Fiber interferometer for simultaneous multiwavelength phase measurement with a broadband femtosecond laser,” Opt. Lett. |

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

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

9. | Y. -J. Kim, J. Jin, Y. Kim, S. H., and S. -W. Kim, “A wide-range optical frequency generator based on the frequency comb of a femtosecond laser,” Opt. Express |

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

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

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

**OCIS Codes**

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

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(140.7090) Lasers and laser optics : Ultrafast lasers

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: September 5, 2008

Revised Manuscript: September 25, 2008

Manuscript Accepted: September 25, 2008

Published: November 14, 2008

**Citation**

Ki-Nam Joo, Yunseok Kim, and Seung-Woo Kim, "Distance measurements by combined method based on a femtosecond pulse laser," Opt. Express **16**, 19799-19806 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-19799

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### References

- P. de Groot and J. McGarvey, "Chirped synthetic-wavelength interferometry," Opt. Lett. 17, 1626-1628 (1992). [CrossRef] [PubMed]
- T. Kubota, M. Nara, and T. Yoshino, "Interferometer for measuring displacement and distance," Opt. Lett. 12, 310-312 (1987). [CrossRef] [PubMed]
- Y. Y. Cheng and J. C. Wyant, "Multiple-wavelength phase-shifting interferometry," Appl. Opt. 24, 804-807 (1985). [CrossRef] [PubMed]
- J. Schwider and L. Zhou, "Dispersive interferometric profiler," Opt. Lett. 19, 995-997 (1994). [CrossRef] [PubMed]
- 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, 5512-5517 (2000). [CrossRef]
- C. E. Towers, D. P. Towers, D. T. Reid, W. N. MacPherson, R. R. J. Maier, and J. D. C. Jones, "Fiber interferometer for simultaneous multiwavelength phase measurement with a broadband femtosecond laser," Opt. Lett. 29, 2722-2724 (2004). [CrossRef] [PubMed]
- N. Schuhler, Y. Salvadé, S. Lévêque, R. Dändliker, and R. Holzwarth, "Frequency-comb-referenced two-wavelength source for absolute distance measurement," Opt. Lett. 31, 3101-3103 (2006). [CrossRef] [PubMed]
- Y. Salvadé, N. Schuhler, S. Lévêque and S. L. Floch, "High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source," Opt. Express 47, 2715-2720 (2008).
- Y. -J. Kim, J. Jin, Y. Kim, S. H. and S. -W. Kim, "A wide-range optical frequency generator based on the frequency comb of a femtosecond laser," Opt. Express 16, 258-264 (2008). [CrossRef] [PubMed]
- J. Ye, "Absolute measurement of a long, arbitrary distance to less than an optical fringe," Opt. Lett. 29, 1153-1155 (2004). [CrossRef] [PubMed]
- K.-N. Joo and S.-W. Kim, "Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser," Opt. Express 14, 5954-5960 (2006). [CrossRef] [PubMed]
- R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000). [CrossRef] [PubMed]

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