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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 30, NO. 8, APRIL 15, 2018
Absolute Distance Measurement Using an Optical Comb and an Optoelectronic Oscillator Pengfei Cui , Linghui Yang , Yin Guo , Jiarui Lin , Yang Liu , and Jigui Zhu
Abstract— We demonstrate a method for absolute distance measurement based on an optical frequency comb and an optoelectronic oscillator. The unknown distance is measured using optical sampling by cavity tuning. A 1000-m-long fiber is used as a reference path and actively stabilized by the optoelectronic oscillator without ambiguous range. The optical path length of the long fiber is converted to oscillation frequency of the optoelectronic oscillator and locked to an atomic clock. A 0.357-µm standard deviation of the long fiber reference path is verified by the experimental results, corresponding to a 10−10 level relative stability. The proof-of-principle absolute distance measurement is implemented and compared with a commercial interferometer. An agreement better than 4 µm is achieved in 22-mm tuning range with the 1000-m imbalanced interferometer setup. Index Terms— Optical frequency comb, absolute distance measurement, optical sampling by cavity tuning, optoelectronic oscillator.
I. I NTRODUCTION
H
IGH precision and cost-efficient absolute distance measurement plays an important role in advanced engineering and science such as aircraft assembly, space missions and geodetic applications. Rapid development in these fields bring more and more requirements and promote consecutive research in absolute distance measurement. The invention of the optical frequency comb offers more possibilities to researchers [1]. Since Minoshima and Matsumoto [2] used an optical frequency comb to measure 240 m long distance in 2000, many novel methods have been developed in last decade [3]–[7]. One of them, optical sampling method, has advantages by its desirable features of high scan rate, large scan range, and no mechanical delay line. It is also divided into two categories by different configurations, asynchronous optical sampling (ASOPS) and optical sampling by cavity tuning (OSCAT). ASOPS performs distance measurement based on the Vernier effect in the time domain, which is created by two optical frequency combs with a slight offset in their Manuscript received February 12, 2018; revised March 6, 2018; accepted March 8, 2018. Date of publication March 12, 2018; date of current version March 27, 2018. This work was supported in part by the National Natural Science Foundation of China under Grant 51705360 and Grant 51775380, and in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 51721003. (Corresponding author: Jigui Zhu.) The authors are with the State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin 300072, China (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2018.2814680
repetition rates. A nanometer level precision has been achieved by this method with an ambiguity range of 1.5 m and update time of 60 ms in 2009 [8]. However, the requirement of two optical frequency combs and the phase coherence between them adds obvious complexity and cost, which limits broader applications. OSCAT overcomes this problem by using one optical frequency comb and implements optical sampling by laser cavity tuning with a high imbalanced interferometer setup [9], [10]. The cavity tuning range is usually quite small compared with pulse repetition frequency. Thus, the long fiber reference path should be several hundred or even thousand meters to achieve a satisfactory sampling range. Such a long fiber could introduce a huge drift to the measurement result when it suffers vibration and temperature variation during the experiment. Therefore, it is of importance to stabilize the long fiber in OSCAT. A homodyne interferometry has been used to solve this problem in a Fourier-transform spectroscopy in 2015 [11]. An optical frequency comb interferometer with a 10−12 level relative stability long fiber reference path has been proposed in the same year [12]. Furthermore, a 10−8 level relative precision distance measurement has been performed by OSCAT with a 10−10 level relative stability long fiber in 2016 [13]. However, in these experiments, the long fiber is stabilized by an additional monitor interferometer, so the laser source of the monitor interferometer must be stabilized strictly. In both experiments, the cw laser is locked to another optical frequency comb, which obviously adds much cost and complexity. In this case, the critical advantage of OSCAT, using one optical frequency comb, is removed. And the theoretical ambiguous range of the interferometer also limits the robustness of measurement. In this letter, we propose an absolute distance measurement method combining OSCAT and an optoelectronic oscillator (OEO). Only one optical frequency comb is used in our setup for distance measurement. Optical length of the long fiber reference path in OSCAT is converted to oscillation frequency of the OEO and locked to a Rb atomic clock which the optical frequency comb is referenced to. Since Yao and Maleki [14] proposed OEO in 1996, it has been well developed and applied in communication and sensing. An OEO, consisting of an optical intensity modulator, long fiber, photodetector, microwave amplifier and a filter, is a resonant system with high oscillation frequency and high spectral purity [15]. The oscillation frequency of the OEO is decided by the loop delay and could be directly measured with high precision. Assuming the electrical link is constant, we could compensate the optical length drift of the long fiber by oscillation frequency without ambiguous
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CUI et al.: ABSOLUTE DISTANCE MEASUREMENT USING OPTICAL COMB AND AN OPTOELECTRONIC OSCILLATOR
Fig. 1. Experimental setup combining OSCAT and an OEO. OFC, optical frequency comb; FG, function generator; PD, photodetector; BS, beam splitter; BPF, bandpass filter; PZT, piezoelectric ceramic transducer; Rb, rubidium atomic clock.
range. Experimental results show that a 1000-m fiber reference path is stabilized at sub-micrometer level, corresponding to a 10−10 level relative stability. Absolute distance measurement is demonstrated by a proof-of-principle experiment compared with a commercial interferometer. Our method is proved by an agreement within 4 μm and uncertainty analysis. II. A BSOLUTE D ISTANCE M EASUREMENT C OMBINING OSCAT AND AN OEO The experimental setup combining OSCAT (red dashed line) and an OEO (black dashed line) is presented in Fig. 1. A femtosecond fiber laser (MenloSystems C-Fiber, 100MHz repetition frequency) is used as the laser source of OSCAT and its repetition frequency is locked to a function generator (Tektronix AFG3252) by the synchronization electronics (MenloSystems RRE-SYNCRO). The repetition frequency could be tuned several hundred kHz by an intra-cavity stage and several hundred Hz by an intra-cavity PZT. The function generator, which is referenced to a Rb atomic clock, is used to generate a linear sweeping frequency signal to drive the intracavity PZT. The pulse train emitted from the fiber laser is split into two parts, which are introduced into the reference path and the measurement path, respectively. The 1000-m long fiber reference path consists of a single-mode fiber, a dispersion compensation fiber, and a ring PZT for feedback controlling. After recombination at BS, the pulse train is detected and recorded. In the case of the OEO for long fiber stabilization, the laser source is a commercial CW laser with a central wavelength of 1560 nm. The laser propagates through a modulator (Photline MX-LN-40), the same long fiber path and an optical filter, and then is converted to an electrical signal by a photodetector. After being amplified and filtered by a bandpass filter of 1 GHz, the electrical signal feeds back to the modulator. The oscillation frequency is determined by the loop delay and the bandpass filter, and can be expressed as: f O E O = N/τ
(1)
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where f O E O is the oscillation frequency, τ is the loop delay, and N is the mode number of the oscillation chosen by the bandpass filter. More detailed analysis of the OEO could be found in our previous work [16]. The loop delay consists of the delay of electrical devices and the long fiber. Thus, length drift of the long fiber is converted to frequency drift and measured precisely without ambiguous range. In our setup, a power divider is inserted in the OEO to send some power to servo controller for feedback controlling. The long fiber is stabilized by locking the oscillation frequency to the Rb atomic clock. In the configuration of OSCAT, when the repetition frequency of the comb is tuned by PZT, the cross-correlation pattern between pulse trains is obtained and used for peak determination. The instantaneous repetition frequency when measurement pulses and reference pulses are overlapped could be calculated by mapping the peak and the PZT driving signal. The optical length difference L between two paths could be expressed as: L = (m × c)/( f rep × n g )
(2)
where m is an integer corresponding to pulse number difference between measurement pulses and reference pulses. c is light speed in vacuum, n g is group refractive index of air, and frep is instantaneous repetition frequency when measurement pulses and reference pulses are overlapped. m could be determined easily by a pre-measurement of L with an uncertainty better than L pp /2. L pp is the pulse-to-pulse interval, about 3 m in our case. The long fiber reference path is measured by an optical time domain reflectometry with an uncertainty of 1 m. Other fiber paths and free space paths are measured by a tape with an uncertainty of about 0.1 m. Then, L is obtained roughly with a combined uncertainty of about 1 m. Based on the pre-measurement of L, m is calculated from (2) precisely. To measure unknown absolute distances, an initial position is chosen first. After the target mirror is set to the initial position, the absolute optical length difference between two paths L i = (m i × c)/( f repi × n g ) could be got by (2). Then, the target mirror is moved to the end position and the absolute optical length difference L t = (m t × c)/( frept × n g ) is got by the same way. frepi , m i , frept and m t are measured instantaneous repetition frequency and corresponding integer in initial position and end position respectively. The measured absolute distance D could be expressed as: D = (L i − L t )/2
(3)
III. E XPERIMENTAL R ESULTS The performance of the OEO-based long fiber stabilization is evaluated experimentally at first. Fig. 2 shows the RF spectrum of the OEO got by a spectrum analyzer (Keysight N9020A) after it is established. A main oscillation of about 1020.310 MHz is shown with several suppressed oscillations on both sides, which are caused by gain competition. As mentioned above, the mode number of the oscillation is chosen by the bandpass filter. Since the bandwidth of the bandpass filter (tens of MHz) is much larger than 1/τ (about 200 kHz),
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Fig. 2.
IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 30, NO. 8, APRIL 15, 2018
RF Spectrum of the OEO (SPAN 1 MHz, RBW 9.1 kHz). Fig. 4.
Fig. 3. Experimental results of OEO-based long fiber stabilization. (a) Error signal of the servo controller for the fiber stabilization. (b) Optical path length variation of the long fiber with fiber stabilization on.
dozens of oscillation modes could pass the filter. One of them will be the main oscillation with others suppressed. When the oscillation frequency is measured by a frequency counter (Keysight 53230A), a 10−11 level resolution measurement could be achieved for long fiber stabilization as an error signal. The experimental results of long fiber stabilization are shown in Fig. 3. Fig. 3(a) demonstrates the error signal of the servo controller. There is an obvious drift in long fiber when the fiber stabilization is off. In our setup, a frequency drift of 1 Hz corresponds to an optical length variation of about 1.45 μm. When the controller is active to stabilize the long fiber, the stable error signal shows the feedback controlling is successful. The stabilization of the long fiber is proved by a standard deviation of 0.357 μm of optical length variation shown in Fig. 3(b), corresponding to a 10−10 level relative stability. After long fiber stabilization is proved, cross-correlation patterns are measured by repetition frequency tuning. As mentioned above, repetition frequency could be tuned by the stage
Experimental cross-correlation pattern.
manually with a large tuning range or the PZT automatically with a high precision. In addition, the PZT is driven by the function generator which is also synchronized with the oscilloscope. Hence, we design a two-step frequency tuning to combine the large tuning range and synchronization of data. First, the repetition frequency is adjusted to the peak of crosscorrelation patterns roughly by the stage. Then, it is scanned by the PZT with a range of 100 Hz and a period of 10 s. During scanning, the data is acquired with a sampling rate of 5 kS/s and recorded for peak determination by Gaussian curve fitting that demonstrated in our previous work [17]. Fig. 4 shows a typical observed cross-correlation pattern in our experiment. The performance of the method is demonstrated by an absolute distance measurement in a tuning range of 22 mm and the experimental results are compared with a commercial interferometer. During the experiment, environmental conditions are recorded for calculation of the refractive index of air. The small measurement range is limited by the tuning range of the repetition frequency. In our setup, the external reference range of the synchronization electronics is only several hundred Hz, corresponding to a repetition frequency tuning range of several kHz. This limitation is not related to the principle itself and could be solved by a high-performance synchronization controller. A repetition frequency tuning range of 200 kHz could satisfy the need of arbitrary absolute distance measurement by our setup. The target mirror is moved by 11 steps at an increment of 2 mm. At each position, the absolute distance is measured by (3) for 10 times and the average result is taken. Fig. 5 shows the comparison between the absolute distance measurement results and the interferometer results. A good agreement within 4 μm is demonstrated experimentally. The measurement uncertainty is mainly affected by instantaneous repetition frequency determination, the air refractive index, and the long fiber reference path. The combined uncertainty of distance measurement u d could be got from (3) and expressed as: Li Lt D u 2d = ( )2 +( )2 u 2frep +( )2 u 2n g +u 2f iber 2× f repi 2 × frept ng (4) where u frep is the uncertainty of the instantaneous repetition frequency determination, u n g is the uncertainty of the air
CUI et al.: ABSOLUTE DISTANCE MEASUREMENT USING OPTICAL COMB AND AN OPTOELECTRONIC OSCILLATOR
Fig. 5.
Comparison of the experimental results.
refractive index, and u f iber is the uncertainty of the long fiber stabilization. There are three terms in (4), and the first one is the most crucial term in our experiment. This term contributes about 6.8 μm to the combined uncertainty with a coverage factor of k = 2 and almost bears no relation to measured distance. It could be calculated from (4) that this term corresponds to a u frep of about 1 Hz. u frep could be attributed to a number of factors such as fitting method, the accuracy of the oscilloscope, and the repetition frequency scanning of the comb. Since the signal to noise ratio of crosscorrelation patterns is not so satisfactory as shown in Fig. 4, fitting method should be the dominant contributor of u frep . In our setup, the output of reference beam is really small after suffering a large loss. An improvement is possibly achieved by beam optimization or adding optical amplifiers. The second term is distance-dependent uncertainty related to the refractive index of air. This part is affected by environmental conditions measurement error and the inherent uncertainty in the Ciddor’s formula. In our experiment, the measurement uncertainty of temperature, air pressure, and humidity are 0.2 K, 100 pa, and 2% respectively, corresponding to contribute 1.8 × 10−7 , 2.6 × 10−7 , and 2.2 × 10−8 to u n g . After combined with formula’s uncertainty of 2 × 10−8 , the u n g is 3.1 × 10−7 × D, which is mainly limited by poor measurement of temperature and air pressure. Fortunately, the measurement range is so small that the second term could be neglected even with a terrible u n g in our experiment. For a future long distance measurement, the measurement uncertainty of temperature and air pressure should be an order of magnitude better to achieve a 10−8 level distance-dependent uncertainty. The last term is the uncertainty caused by long fiber stabilization which is measured to be 0.7 μm. Thus, u d is [(6.8μm)2 + (3.1 × 10−7 × D)2 ]1/2 . Please note that a 1000-m long fiber is used as reference path in our setup, so a distance measurement with a tens of meter range and a 10−7 level relative precision is highly expected. IV. C ONCLUSION This letter has proposed a method using an optical frequency comb and an OEO for absolute distance measurement. The measured distance is obtained by OSCAT with a highly imbalanced interferometer setup. The 1000-m long fiber reference path in OSCAT is stabilized by using the oscillation frequency
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of the OEO as an error signal for feedback controlling. A 10−10 level relative stability of the long fiber has been experimentally proved without ambiguous range. It could increase the robustness of measurement system and benefit this method in many practical applications where the environment could not be strictly controlled. Absolute distance measurement is performed in a tuning range of 22 mm and compared with a commercial interferometer. Uncertainty analysis shows that a 10−7 level relative precision is promisingly achieved in a tens of meter range by our setup. By combining OSCAT and an OEO, our method enables a high precision, cost-efficient and robust distance measurement suitable for many precision engineering applications. R EFERENCES [1] N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nature Photon., vol. 5, no. 4, pp. 186–188, Apr. 2011. [2] 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., vol. 39, no. 30, pp. 5512–5517, Oct. 2000. [3] J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nature Photon., vol. 4, no. 10, pp. 716–720, Aug. 2010. [4] P. Balling, P. Mašika, P. Kˇren, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol., vol. 23, no. 9, pp. 094001, Jul. 2012. [5] R. Yang, F. Pollinger, K. Meiners-Hagen, J. Tan, and H. Bosse, “Heterodyne multi-wavelength absolute interferometry based on a cavity-enhanced electro-optic frequency comb pair,” Opt. Lett., vol. 39, no. 20, pp. 5834–5837, Oct. 2014. [6] S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Moderesolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep., vol. 5, p. 14661, Sep. 2015. [7] Y. S. Jang et al., “Comb-referenced laser distance interferometer for industrial nanotechnology,” Sci. Rep., vol. 6, p. 31770, Aug. 2016. [8] I. R. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nature Photon., vol. 3, no. 6, pp. 351–356, May 2009. [9] T. Hochrein, R. Wilk, M. Mei, R. Holzwarth, N. Krumbholz, and M. Koch, “Optical sampling by laser cavity tuning,” Opt. Exp., vol. 18, no. 2, pp. 1613–1617, Jan. 2010. [10] L. Yang, J. Nie, and L. Duan, “Dynamic optical sampling by cavity tuning and its application in lidar,” Opt. Exp., vol. 21, no. 3, pp. 3850–3860, Feb. 2013. [11] K. Lee et al., “Fourier-transform spectroscopy using an Er-doped fiber femtosecond laser by sweeping the pulse repetition rate,” Sci. Rep., vol. 5, p. 15726, Oct. 2015. [12] Y. Nakajima and K. Minoshima, “Highly stabilized optical frequency comb interferometer with a long fiber-based reference path towards arbitrary distance measurement,” Opt. Exp., vol. 23, no. 20, pp. 25979–25987, Sep. 2015. [13] H. Wu, F. Zhang, T. Liu, P. Balling, J. Li, and X. Qu, “Long distance measurement using optical sampling by cavity tuning,” Opt. Lett., vol. 41, no. 10, pp. 2366–2369, May 2016. [14] X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Amer. B, Opt. Phys., vol. 13, no. 8, pp. 1725–1735, 1996. [15] X. Zou et al., “Optoelectronic oscillators (OEOs) to sensing, measurement, and detection,” IEEE J. Quantum Electron., vol. 52, no. 1, pp. 1–16, Jan. 2016. [16] T. Zhang, J. Zhu, T. Guo, J. Wang, and S. Ye, “Improving accuracy of distance measurements based on an optoelectronic oscillator by measuring variation of fiber delay,” Appl. Opt., vol. 52, no. 15, pp. 3495–3499, May 2013. [17] Y. Liu, L. Yang, Y. Guo, J. Lin, P. Cui, and J. Zhu, “Optimization methods of pulse-to-pulse alignment using femtosecond pulse laser based on temporal coherence function for practical distance measurement,” Opt. Lasers Eng., vol. 101, pp. 35–43, Feb. 2018.
