## Space position measurement using long-path heterodyne interferometer with optical frequency comb |

Optics Express, Vol. 20, Issue 3, pp. 2725-2732 (2012)

http://dx.doi.org/10.1364/OE.20.002725

Acrobat PDF (2398 KB)

### Abstract

A heterodyne interference system was developed for position measurement. A stabilized optical-frequency comb is used as the laser source. The preliminary experiment to measure a distance of 22.478 m shows a drift of 1.6 μm in 20 minutes after the temperature compensation. Comparison and frequency shift experiments have been done for a distance of about 7.493 m. The experimental results show that the drift is mainly caused by environmental condition changes and the vibration of the table and floor also has some effects. It was verified that the absolute distance measurement can be realized by fringe scanning and frequency-shifting methods.

© 2012 OSA

## 1. Introduction

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]

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

*f*

_{r}, and the carrier envelope offset frequency,

*f*

_{ceo}. The frequency uncertainty of these two parameters can be traced with high precision to the frequency standard in use, so the optical comb is often used as a frequency standard for other laser sources [3

3. 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]

4. S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” CIRP Ann. Manuf. Technol. **59**(1), 555–558 (2010). [CrossRef]

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

## 2. Principle

### 2.1 Temporal coherence interference of optical comb

*f*

_{r}, where

*f*

_{r}is the repetition frequency. An interference measurement system is shown in Fig. 1 , and the temporal coherence interference occurs at discrete positions, where two optical comb pulse trains overlap with each other. Since the duration of a pulse is about 100 fs, the coherence length of an optical comb is several tens of micrometers. The envelope peak of the interference fringe appears when the optical path difference (OPD) between the two arms of the interferometer satisfieswhere

*m*is an integer,

*c*is the light velocity in a vacuum and

*n*is the refractive index of air. The distance

*l*between the target and the position where

*f*

_{r}is 100 MHz, the approximate value of

*l*will be 1.5 m, 3 m, 4.5 m, …, respectively.

*m*can be determined by shifting the repetition frequency

*f*

_{r}. Since

*l*=

*m·c*/2

*nf*

_{r}, the relation between the displacement of the positions where the envelope peaks of interference fringes appear, Δ

*l*, and the shifted frequency, Δ

*f*

_{r}, will be

*m*= 2, and Δ

*f*

_{r}/

*f*

_{r}= 10

^{−6}, Δ

*l*will be 3 μm. Correspondingly, when Δ

*l*and Δ

*f*

_{r}are known, the value of

*m*can be determined, and then the absolute distance of the positions being measured will be known.

### 2.2 Heterodyne interference system with optical comb

*Δ*, which can be written as

*Δ = f*

_{r}

*+ f*

_{h}. Here, the repetition frequency

*f*

_{r}is 100 MHz, and

*f*

_{h}is 100 kHz. Since any mode of an optical comb can be expressed as

*f*=

*f*

_{ceo}+

*N*·

*f*

_{r}, the frequency of the original

*N*-th mode is shifted to be

*N*-th mode will interfere with the original (

*N*+ 1)-th mode of the optical comb, and the heterodyne frequency is

*f*

_{h}(Fig. 3 ). A collimator is used to expand the beam diameter for the long distance measurement. Two corner cubes are set in the measurement arm, after the collimator. One is placed on the position where the OPD between two arms equals zero (M

_{0}), and the other is the target (M

_{m}). The distance between two corner cubes is

*l*. The light beams are combined by a fiber combiner, and the interference signal is detected by a photo detector and then sent to a lock-in amplifier. The reference signal of the lock-in amplifier is generated from the difference between the signals of

*f*

_{r}and

*Δ*.

*T*, and the scanning distance is

*L*. In one period, the corner cube with PZT will be moved far away from the rectangular prism. When

*L*is several tens of micrometers, the interference fringe generated by the two corner cubes will be detected (Fig. 4 ). When two peaks of the interference fringe envelopes are found, the time interval between the two peaks,

*t*, will be got. The measured distance

*l*can be calculated as

*L*is determined by the scanning direction of the PZT and the sequence of the two peaks. The former part,

*l*

_{1}, is the value calculated according to Eq. (1), and the latter part,

*l*

_{2}, is the measured value.

## 3. Experiments and results

*f*

_{r}is 100.0000 MHz, which is stabilized to a rubidium frequency standard, and the stability is on the order of 10

^{−10}. The lock-in amplifier in use is NF LI5630 (frequency < 100 kHz, phase resolution is 0.01°) and the time constant of 100 μs is adjusted for scanning the interference fringe over about 200 μm.

*m*was preliminarily proved (Section 3.3).

### 3.1 Positioning measurement experiment of 22.478 m

*m*= 15) were done. The scanning distance

*L*is about 230 μm, and the scanning period is 50 s, so the scanning speed is 4.6 μm/s. The center wavelength of the optical comb is 1560 nm, so the frequency of the interference fringe is about 5.9 Hz, and the half period of one fringe is about 85 ms. Therefore the maximum time constant of the lock-in amplifier is 10 ms. If the time constant is too long, the signal will be weakened. The typical interference signal from the lock-in amplifier is shown in Fig. 6 . X-data output and R-data output are used. Since the time constant is selected as 100 μs, the original data include some noise due to the mechanical vibration and air turbulence, and the fitted method is adopted to find the envelope function of the interference fringe, then the locations of the peaks can be determined. The PZT is calibrated by a Michelson interferometer using a stabilized laser diode. A quadratic function is found to describe the relation between the scanning distance, and the driver voltage

*U*, which is

*L*= −0.064

*U*

^{3}+ 1.012

*U*

^{2}+ 18.915

*U*-6.541. When the voltage of the two peaks of the interference fringe envelope,

*U*

_{0}and

*U*

_{m}, are known, the distance

*l*

_{2}can be calculated aswhere

*t*is the time interval between the two peaks’ appearance,

*T*is the scanning period, and

*U*is the amplitude of the driver voltage of PZT. The measured distance

*l*can be several hundreds of micrometers, and the accuracy can be several micrometers or sub-micrometers, which equals the accuracy of

*l*

_{2}.

*l*

_{2}is 112.40 μm, and the standard deviation is 1.66 μm. The dash-dot line shows the drift in an hour, which is 2.68 μm. To find the cause of the drift, the temperature of environment is recorded and the refractive index of the air is compensated based on the Edlén formula. Figure 7(b) shows the experimental results before and after the temperature compensation. The 6 values were recorded over 20 min. The standard deviation is reduced from 3.7 μm to 1.6 μm, and the drift is reduced from 8.0 μm to 1.8 μm after temperature compensation. This result proves that the drift is mainly caused by changes of the environmental condition, but the deviation is caused by the vibration of stage and floor.

### 3.2 Comparison experiment with Renishaw interferometer

*m*= 5). Since the He-Ne interferometer is an incremental length-measuring system, the experimental result can only express the drift of the measurement.

### 3.3 Repetition frequency shifted experiment

*f*

_{r}is changed a certain amount Δ

*f*

_{r}, the integer

*m*can be determined by measuring the displacement change Δ

*l*. To verify this method, the repetition frequency

*f*

_{r}is shifted by different values when the integer m is 5 and the displacement change is measured. Table 1 shows the values of Δ

*f*

_{r}and the theoretical value of Δ

*l*.

*f*

_{r}. Figure 9(b) shows the measurement result of Δ

*l*when Δ

*f*

_{r}is changed from 0 to 200 Hz. The green curve is the measured value. The maximum difference between the measured value and the theoretical value is 1.24 μm. Figure 9(c) shows the measured value of

*l*

_{2}over one hour when Δ

*f*

_{r}is 0 and when it is 1 kHz. Although there was a drift during the measurement, the displacement change Δ

*l*remained about 75.56 μm, which showed a difference of 0.63 μm from the theoretical value. The experiment proved that the value of

*m*can be determined by shifting the repetition frequency and measuring the displacement change. The absolute positioning measurement can be realized using this optical comb heterodyne interference system. This method is very useful because

*m*is uniquely determined by using different Δ

*f*

_{r}values according to the measurement error.

## 4. Conclusions

^{−8}of 22.478 m. Since the drift of the measured result of the distance between the two corner cubes was smaller than the drift of the measured result for the position of the target, the effect of the vibration of the table and optical fiber change was reduced by measuring the position where OPD = 0. A comparison experiment with the Renishaw length measurement interferometer at a distance of 7.493 m showed the consistency of the two systems, and proved that the drift of the measured data was caused by the experimental environmental condition changes, and the deviation is caused by the vibration of the table and floor. The reproducibility of the system can be improved if these conditions are detailed recorded along the optical path and then the measured results can be compensated more precisely. The method to determine the value of

*m*was verified by experiment. It was proved that absolute measurement can be realized by this system.

## Acknowledgments

## References and links

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

2. | S.-W. Kim and Y.-J. Kim, “Advanced optical metrology using ultrashort pulse lasers,” Rev. Laser Eng. |

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

4. | S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” CIRP Ann. Manuf. Technol. |

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

6. | J. Jin, Y.-J. Kim, Y. Kim, S.-W. Kim, and C. S. Kang, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express |

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

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

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

10. | P. Balling, P. Kren, P. Masika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express |

11. | S. Yokoyama, T. Yokoyama, Y. Hagihara, T. Araki, and T. Yasui, “A distance meter using a terahertz intermode beat in an optical frequency comb,” Opt. Express |

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

13. | 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. |

14. | N. R. Doloca, K. Meiners-Hagen, M. Wedde, F. Pollinger, and A. Abou-Zeid, “Absolute distance measurement system using a femtosecond laser as a modulator,” Meas. Sci. Technol. |

15. | H. Takahashi, Z. He, and K. Hotate, “Optical coherence domain reflectometry by use of optical frequency comb with arbitrary-waveform phase modulation,” in |

**OCIS Codes**

(070.1060) Fourier optics and signal processing : Acousto-optical signal processing

(120.2830) Instrumentation, measurement, and metrology : Height measurements

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(140.4050) Lasers and laser optics : Mode-locked lasers

(140.7090) Lasers and laser optics : Ultrafast lasers

(060.2840) Fiber optics and optical communications : Heterodyne

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: November 2, 2011

Revised Manuscript: December 23, 2011

Manuscript Accepted: January 3, 2012

Published: January 23, 2012

**Citation**

Xiaonan Wang, Satoru Takahashi, Kiyoshi Takamasu, and Hirokazu Matsumoto, "Space position measurement using long-path heterodyne interferometer with optical frequency comb," Opt. Express **20**, 2725-2732 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2725

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### References

- I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics3(6), 351–356 (2009). [CrossRef]
- S.-W. Kim and Y.-J. Kim, “Advanced optical metrology using ultrashort pulse lasers,” Rev. Laser Eng.36(APLS), 1254–1257 (2008). [CrossRef]
- 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]
- S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” CIRP Ann. Manuf. Technol.59(1), 555–558 (2010). [CrossRef]
- J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett.29(10), 1153–1155 (2004). [CrossRef] [PubMed]
- J. Jin, Y.-J. Kim, Y. Kim, S.-W. Kim, and C. S. Kang, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express14(13), 5968–5974 (2006). [CrossRef] [PubMed]
- K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express14(13), 5954–5960 (2006). [CrossRef] [PubMed]
- K.-N. Joo, Y. Kim, and S.-W. Kim, “Distance measurements by combined method based on a femtosecond pulse laser,” Opt. Express16(24), 19799–19806 (2008). [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(14), 2715–2720 (2008). [CrossRef] [PubMed]
- P. Balling, P. Kren, P. Masika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express17(11), 9300–9313 (2009). [CrossRef] [PubMed]
- S. Yokoyama, T. Yokoyama, Y. Hagihara, T. Araki, and T. Yasui, “A distance meter using a terahertz intermode beat in an optical frequency comb,” Opt. Express17(20), 17324–17337 (2009). [CrossRef] [PubMed]
- D. Wei, S. Takahashi, K. Takamasu, and H. Matsumoto, “Analysis of the temporal coherence function of a femtosecond optical frequency comb,” Opt. Express17(9), 7011–7018 (2009). [CrossRef] [PubMed]
- 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.20(9), 095302 (2009). [CrossRef]
- N. R. Doloca, K. Meiners-Hagen, M. Wedde, F. Pollinger, and A. Abou-Zeid, “Absolute distance measurement system using a femtosecond laser as a modulator,” Meas. Sci. Technol.21(11), 115302 (2010). [CrossRef]
- H. Takahashi, Z. He, and K. Hotate, “Optical coherence domain reflectometry by use of optical frequency comb with arbitrary-waveform phase modulation,” in 2010 36th European Conference and Exhibition on Optical Communication (ECOC), (2010), pp. 1–3.

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