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Research Article

Vol. 55, No. 11 / April 10 2016 / Applied Optics

Measurement of the optical path length
difference in an interferometer using asinusoidally frequency-modulated light source
SHUMPEI SHIMADA,1 MAKOTO SHIZUKA,1 NEISEI HAYASHI,2 YOSUKE MIZUNO,1,* AND KENTARO NAKAMURA1
1

Laboratory for Future Interdisciplinary Research of Science and Technology, Tokyo Institute of Technology, 4259, Nagatsuta-cho,
Midori-ku, Yokohama 226-8503, Japan
2
Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8904, Japan*Corresponding author: ymizuno@sonic.pi.titech.ac.jp
Received 22 January 2016; revised 10 March 2016; accepted 10 March 2016; posted 11 March 2016 (Doc. ID 258091); published 5 April 2016

We develop a technique for measuring the optical path length difference (OPLD) in an interferometer using afrequency-modulated light source. Compared with conventional methods, this technique offers a high sampling
rate, high precision, and cost efficiency, and is capable of determining which of the two optical paths is longer.
In addition, we show that this technique works properly even when the OPLD is significantly longer than thecoherence length of the light source. © 2016 Optical Society of America
OCIS codes: (060.4080) Modulation; (120.3180) Interferometry; (280.4788) Optical sensing and sensors.
http://dx.doi.org/10.1364/AO.55.002904

1. INTRODUCTION
For the past several decades, fundamental sensing techniques
based on fiber-optic interferometry have been studied in order
to measure a variety of physical parameters, such as reflectivity,
loss, strain, temperature, displacement, vibration, pressure,humidity, profile, refractive index, concentration, pH, and rotation [1–6]. Some of the fiber-optic interferometers used insuch measurements are composed of two light paths: a signal
path, which contains an optical circulator, and a reference path.
The optical path length difference (OPLD) between these twopaths generally plays a significant role in the operation of thesystem. For instance, let’s consider using a technique known as
optical correlation-domain reflectometry (OCDR) [7–16] inconjunction with a distributed reflectivity sensing system. If
the zero-OPLD point is located in the fiber under test (FUT;i.e., the second port of the circulator), in theory the measurement cannot be performed. Another example is a techniqueknown as Brillouin OCDR [17–19] in conjunction with a distributed strain and temperature sensing system. Even when
the zero-OPLD point is located outside the FUT, unless the
OPLD is carefully selected, the signal-to-noise ratio (SNR) of
the measurement drastically deteriorates because of the overlapof the interference pattern on the Brillouin gain spectrum [19].
Thus, it is of crucial importance to measure and control the
OPLD in an interferometer that includes an optical circulator.
Direct measurement of the OPLD is, however, sometimes
difficult, because general interferometers contain various opticaldevices with unknown fiber lengths, such as optical amplifiers,
1559-128X/16/112904-05 Journal © 2016 Optical Society of America

external modulators, and kilometer-order delay lines. Therefore,
several techniques for measuring the OPLD indirectly have beendeveloped. One such technique works by exploiting the interval
between the interference fringes observed using a spectrum analyzer [19–22]. This method is simple, though it does not allow
us to judge which of the two paths is longer; furthermore, thevisibility of the interference pattern becomes extremely low when
the OPLD is significantly longer than the coherence length ofthe light source (or when the frequency resolution of the spectrum analyzer is not sufficiently high). Another method is basedon the so-called time-of-flight technique [23–25], wherein optical pulses are simultaneously injected into the two paths, andthe delay between the reflected pulses is subsequently measured.
However, preparing such optical pulses can be costly, and thismethod does not provide any information concerning which of
the paths is longer. In addition, numerous reflected pulses are generally utilized in order to improve the SNR, resulting in a relatively
long measurement time (for instance, up to several minutes).
In order to mitigate the aforementioned drawbacks of theconventional techniques, in this work we develop an OPLD
measurement technique for an interferometer that contains an
optical circulator. By using a frequency-modulated light source,
our technique can achieve a high sampling rate (corresponding
to a short measurement time of ∼10 ms ), high precision, andcost efficiency. Moreover, we demonstrate that this technique
can determine which of the two optical paths is longer, and that
the OPLD can be correctly obtained even when it is significantly longer than the laser coherence length.

Research Article
2. PRINCIPLE
The basic configuration of a fiber-optic interferometer that
contains an optical circulator is schematically illustrated inFig. 1, where an FUT is connected to the second port of thecirculator. In order to calculate the OPLD between the signal
and reference paths, here we exploit one of the useful techniques for distributed reflectivity measurements—namely,
OCDR [9–16]—by using a synthesized optical coherencefunction (SOCF) [14]. This system operates based on opticalcorrelation control by the frequency modulation of laser output. The methods involved in frequency modulation can beclassified into two categories: sinusoidal modulation [9–11]
and stepwise modulation [12–14], which includes the use of
optical frequency combs [15,16]; the former method is reported to be more cost efficient [9–11].
In a standard SOCF-OCDR system based on sinusoidal
modulation [9–11], optical heterodyne detection using an
acousto-optic modulator (AOM) is performed in order to shift
the Fresnel spectrum by several tens of megahertz, thereby
avoiding the overlap of low-frequency noise from the electricaldevices. However, we have recently succeeded in excluding
the optical heterodyne detection from the measurement process(i.e., eliminating the need for an AOM) by exploiting the footof the Fresnel spectrum [26]. This results in electrical signal
processing in the frequency range near dc (up to several megahertz) and, furthermore, reduces the cost of the relevant devices. High-speed operation has also been demonstrated bytracking a moving reflection point.
In an SOCF-OCDR system (with or without the use of an
AOM), the optical frequency of the laser output is sinusoidally
modulated at f m , thereby generating periodical correlation
peaks along an FUT [14]. The measurement range d m is determined by the interval between the correlation peaks, whichis inversely proportional to f m as follows:
c
D
;
(1)
2nf m
where c is the velocity of light in a vacuum and n is the refractive index of the fiber core. By sweeping f m , the correlation
peak, which can be regarded as the sensing position, can bescanned along the FUT in order to acquire the reflectivity distribution. The spatial resolution of the system is given by [27]
0.76c
Δz ≅
;
(2)
πnΔf
where Δf is the modulation amplitude of the optical frequency.

Fig. 1. Basic configuration of a fiber-optic interferometer that contains an optical circulator in the signal path. ESA, electrical spectrum
analyzer; FUT, fiber under test; PD, photodiode.

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Here, we develop a new method of calculating the OPLD
between the signal and reference paths by using the operating
principle of SOCF-OCDR. The zeroth-order correlation peakis always located at a zero-OPLD point, the location of which isfixed regardless of the modulation frequency f m (Fig. 2). Whenthe neighboring first-order correlation peak is located at the
FUT end, where optical reflectivity is high due to Fresnel reflection, the OPLD can be calculated as the product of thecore’s refractive index n and twice the correlation peak interval[i.e., the measurement range d m given by Eq. (1)]. In general,
when neighboring correlation peaks are located at the FUTend, the difference in their f m values (denoted by Δf m ) is
the same as the f m value when the first-order correlation peakis located at the FUT end, irrespective of their peak orders.
Therefore, by acquiring the reflectivity (or reflection power)
as a function of f m and obtaining Δf m from an arbitrary
set of two neighboring reflectivity peaks (corresponding to
Fresnel reflection at the FUT end), the OPLD can be calculated
as follows:c
OPLD 
:(3)Δf m
3. EXPERIMENTAL SETUP
Figure 3 depicts the experimental setup, which represents an
AOM-free SOCF-OCDR system. It contains an optical circulator in the signal path; moreover, several dummy devices are
employed in order to demonstrate that this method is applicable to complicated interferometers. A laser diode with a wavelength of 1550 nm and a linewidth of ∼1 MHz (and thus a
coherence length of ∼200 m ) was used as a light source. The
driving current of the laser was directly modulated with a biasof 80 mA. The laser output was amplified to 18 dBm using anerbium-doped fiber amplifier (EDFA) and was injected into the
FUT. Both the reflected light and the reference light were also
amplified to 3 dBm using EDFAs. Polarization controllers(PCs), which were used to adjust the polarization states, wereinserted in both optical paths. Various lengths of delay lines
were inserted in each path in order to adjust the OPLD. The
modulation amplitude Δf was fixed at 0.75 GHz, whichcorresponds to a nominal spatial resolution of 66 mm [seeEq. (2)]. For AOM-free operation, a 2 MHz component of theFresnel reflection spectrum [output of a photodiode (PD)]observed using an electrical spectrum analyzer (ESA) was selectively acquired with an oscilloscope (OSC) in order to maximize the SNR [26]. The resolution bandwidth (RBW) and

Fig. 2. Calculation principle of the optical path length difference(OPLD).

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Research Article

The first demonstration was performed for a signal path thatwas shorter than the reference path by ∼50 m. Figure 4(a)shows the reflection power dependence on the modulation frequency f m in the range from 3 to 15 MHz. Two sets of peaks,
each of which consisted of one small and one large peak, wereobserved. Using the large peaks corresponding to the Fresnel
reflection at the FUT end, the frequency difference Δf m
was calculated to be 6.142 MHz, which agrees with the f mvalue of the large peak at the lower frequency. This is because
the set of peaks at the lower frequency corresponds to the firstorder correlation peak. By substituting the Δf m value into
Eq. (3), the OPLD was calculated to be 48.84 m. (The validityof this value is discussed below.)
The smaller peaks correspond to the reflection from thecirculator. In general, when the signal path is shorter than
the reference path, as f m increases, the correlation peaks movefrom proximal (circulator) to distal (FUT end) positions, resulting in the appearance of the small peak followed by the appearance of the large peak. In contrast, when the signal path islonger than the reference path, as f m increases, the correlation
peaks move from distal to proximal positions, resulting in theappearance of the large peak followed by the appearance of thesmall peak. Thus, using the order in which the small and large
peaks appear within each set of peaks, we can ascertain which of
the two paths is longer; this logical procedure is (to our knowledge) unique to our method.
The calculated value of the OPLD (48.84 m) was thenvalidated by measuring the same OPLD using a standard technique based on an interference pattern, which is shown in
Fig. 4(b). The RBW and VBW of the ESA were set to 10 and
0.1 kHz, respectively. The average period of the interference
pattern Δf p (calculated using multiple peaks/dips) was
6.135 MHz; this corresponds to an OPLD of 48.89 m
 c∕Δf p , thereby indicating impressive agreement between
the two methods. Because the widths of the peaks in Fig. 4(a)are narrower than those in Fig. 4(b), the OCDR-based method
provides higher precision when a simple fringe-counting technique is used.
Subsequently, the same measurements were performed for a
signal path that was longer than the reference path by ∼50 m.
Figure 5(a) shows the reflection power dependence on f m . The
frequency difference Δf m was 5.666 MHz, which corresponds
to an OPLD of 52.95 m; this was verified by the interference
pattern in Fig. 5(b) with a Δf p value of 5.680 MHz, whichcorresponds to an OPLD of 52.82 m. As f m increases, the large
peak appears first and is followed by the small peak. This orderis opposite to that in Fig. 4(a), which indicates that the signal
path is longer than the reference path in this case.
We also measured the OPLD for a signal path that was
shorter than the reference path by ∼1 km, which is longer thanthe coherence length of the laser (∼200 m). From the reflection
power dependence on f m [Fig. 6(a)], Δf m was calculated tobe 210 kHz, which corresponds to an OPLD of 977 m.
From the interference pattern [Fig. 6(b)], Δf p was evaluatedto be 211 kHz, which corresponds to an OPLD of 974 m.
However, the visibility of the pattern was so low that precise
measurement was relatively difficult.
Additionally, we performed the same measurements for a
signal path that was shorter than the reference path by ∼15 km,
which is significantly longer than the laser coherence length.
The reflection power dependence on f m was obtained[Fig. 7(a)], and Δf m was calculated to be 20 kHz, which corresponds to an OPLD of 14.78 km. However, the interference

Fig. 4. (a) Reflection power dependence on the modulation frequency f m, (b) interference pattern measured for a signal path thatis shorter than the reference path by ∼50 m.

Fig. 5. (a) Reflection power dependence on the modulation
frequency f m, (b) interference pattern measured for a signal path thatis longer than the reference path by ∼50 m.

Fig. 3. Schematic setup for experimental demonstration. EDFA,
erbium-doped fiber amplifier; FG, function generator; OSC, oscilloscope; PC, polarization controller.

video bandwidth (VBW) of the ESA were set to 300 and 1 kHz,
respectively. Data averaging was performed 100 times on the
OSC (unless otherwise stated) in order to secure a high SNR,
corresponding to a total measurement time of ∼1 s (10 ms forone sampling).
4. EXPERIMENTAL RESULTS

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path by ∼50 m. Figures 8(a) and 8(b) show the reflection
power dependencies on f m with and without averaging(100 times). Even without averaging (leading to a measurement
time of 10 ms), the OPLD was correctly calculated to be
46.26 m. High-speed measurability is also one of the advantages of this method, as compared with other techniques that
exploit interference patterns or optical pulses.
5. CONCLUSION

Fig. 6. (a) Reflection power dependence on the modulation frequency f m, (b) interference pattern measured for a signal path thatis shorter than the reference path by ∼1 km.

Based on the principle of the AOM-free SOCF-OCDR, a technique for measuring the OPLD in an interferometer wasdeveloped. We demonstrated its high-speed operation, highprecision, and, most importantly, its capability of determining
which of the two optical paths is longer. We also experimentallydemonstrated that this technique works properly even when
the OPLD is significantly longer than the laser coherence
length. We believe that this technique will serve as a promising
candidate for implementing OPLD measurement systems infuture studies.
Funding. Japan Society for the Promotion of Science(JSPS) (25007652, 25709032, 26630180).
REFERENCES

Fig. 7. (a) Reflection power dependence on the modulation frequency f m, (b) interference pattern measured for a signal path thatis shorter than the reference path by ∼15 km.

pattern was not observed, as shown in Fig. 7(b). The ability tomeasure an OPLD that is significantly longer than the coherence length of the laser is one of the important advantages ofthis method. (It is worth noting that SOCF-OCDR has beenshown to possess a measurement range much longer than thelaser coherence length [28].)
Finally, the averaging effect was evaluated using the dataobtained for a signal path that was shorter than the reference

Fig. 8. Reflection power dependencies on the modulation frequency
f m (a) with and (b) without averaging (100 times), measured for a
signal path that is shorter than the reference path by ∼50 m.

1. Y. J. Rao and D. A. Jackson, “Principles of fiber-optic interferometry,”in Optical Fiber Sensor Technology, K. T. V. Grattan and B. T. Meggitt,eds. (Springer, 2000), pp. 167–191.
2. A. D. Drake and D. C. Leiner, “Fiber-optic interferometer for remotesubangstrom vibration measurement,” Rev. Sci. Instrum. 55, 162–165(1984).
3. C. E. Lee and H. F. Taylor, “Fiber-optic Fabry-Perot temperature
sensor using a low- coherence light source,” J. Lightwave Technol.
9, 129–134 (1991).
4. D. P. Hand, T. A. Carolan, J. S. Barton, and J. D. C. Jones, “Profile
measurement of optically rough surfaces by fiber-optic interferometry,” Opt. Lett. 18, 1361–1363 (1993).
5. L. Yuan, “White-light interferometric fiber- optic strain sensor fromthree-peak- wavelength broadband LED source,” Appl. Opt. 36,
6246–6250 (1997).
6. T. K. Yadav, R. Narayanaswamy, M. H. Abu Bakar, Y. M. Kamil, and
M. A. Mahdi, “Single mode tapered fiber-optic interferometer based
refractive index sensor and its application to protein sensing,” Opt.
Express 22, 22802–22807 (2014).
7. R. C. Youngquist, S. Carr, and D. E. N. Davies, “Optical coherencedomain reflectometry: a new optical evaluation technique,” Opt. Lett.
12, 158–160 (1987).
8. E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and
C. A. Puliafito, “High-speed optical coherence domain reflectometry,”
Opt. Lett. 17, 151–153 (1992).
9. K. Hotate, M. Enyama, S. Yamashita, and Y. Nasu, “A multiplexing
technique for fibre Bragg grating sensors with the same reflection
wavelength by the synthesis of optical coherence function,” Meas.
Sci. Technol. 15, 148–153 (2004).
10. Z. He, T. Tomizawa, and K. Hotate, “High-speed high-reflectanceresolution reflectometry by synthesis of optical coherence function,”
IEICE Electron. Express 3, 122–128 (2006).
11. Z. He, M. Konishi, and K. Hotate, “A high-speed sinusoidally
frequency-modulated optical reflectometry with continuous modulation-frequency sweeping,” Proc. SPIE 7004, 70044L (2008).
12. K. Hotate and O. Kamatani, “Reflectometry by means of opticalcoherence modulation,” Electron. Lett. 25, 1503–1505 (1989).
13. Z. He and K. Hotate, “Distributed fiber-optic stress-location measurement by arbitrary shaping of optical coherence function,” J. Lightwave
Technol. 20, 1715–1723 (2002).

2908

Vol. 55, No. 11 / April 10 2016 / Applied Optics

14. K. Hotate, “Application of synthesized coherence function to distributed optical sensing,” Meas. Sci. Technol. 13, 1746–1755 (2002).
15. Z. He, H. Takahashi, and K. Hotate, “Optical coherence-domainreflectometry by use of optical frequency comb,” in Conference on
Lasers and Electro-Optics (2010), paper CFH4.
16. H. Takahashi, Z. He, and K. Hotate, “Optical coherence domainreflectometry by use of optical frequency comb with arbitrarywaveform phase modulation,” in European Conference on OpticalCommunication (2010), paper Tu.3.F.4.
17. Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin opticalcorrelation-domain reflectometry (BOCDR),” Opt. Express 16, 12148–
12153 (2008).
18. Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Operation of Brillouin opticalcorrelation-domain reflectometry: theoretical analysis and experimental validation,” J. Lightwave Technol. 28, 3300–3306 (2010).
19. Y. Mizuno, N. Hayashi, and K. Nakamura, “Fiber-optic interferometry
using narrowband light source and electrical spectrum analyzer:
influence on Brillouin measurement,” J. Lightwave Technol. 32,
4734–4740 (2014).
20. L. V. Ngyuen, D. Hwang, S. Moon, D. S. Moon, and Y. Chung, “Hightemperature fiber sensor with high sensitivity based on core diametermismatch,” Opt. Express 16, 11369–11375 (2008).
21. A. A. Jasim, N. Hayashi, S. W. Harun, H. Ahmad, R. Penny, Y.
Mizuno, and K. Nakamura, “Refractive index and strain sensing using

Research Article
inline Mach-Zehnder interferometer comprising perfluorinated gradedindex plastic optical fiber,” Sens. Actuators A 219, 94–99 (2014).
22. K. S. Park, H. Y. Choi, S. J. Park, U. C. Paek, and B. H. Lee,
“Temperature robust refractive index sensor based on a photonic
crystal fiber interferometer,” IEEE Sens. J. 10, 1147–1148 (2010).
23. K. Aoyama, K. Nakagawa, and T. Itoh, “Optical time domain reflectometry in a single-mode fiber,” IEEE J. Quantum Electron. 17, 862–868(1981).
24. S. V. Shatalin, V. N. Treschikov, and A. J. Rogers, “Interferometric
optical time-domain reflectometry for distributed optical-fiber sensing,”
Appl. Opt. 37, 5600–5604 (1998).
25. T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y.
Koyamada, “Brillouin optical-fiber time domain reflectometry,” IEICE
Trans. Commun. 76, 382–390 (1993).
26. M. Shizuka, S. Shimada, N. Hayashi, Y. Mizuno, and K. Nakamura,“Optical correlation-domain reflectometry without optical frequency
shifter,” Appl. Phys. Express 9, 032702 (2016).
27. K. Hotate and K. Kajiwara, “Proposal and experimental verificationof Bragg wavelength distribution measurement within a long-length
FBG by synthesis of optical coherence function,” Opt. Express 16,
7881–7887 (2008).
28. M. Kashiwagi and K. Hotate, “Long range and high resolution reflectometry by synthesis of optical coherence function at region beyond
the coherence length,” IEICE Electron. Express 6, 497–503 (2009).