Open Access
Add to BibSonomyAbstract
Multi-pass cells (MPCs) are commonly used in trace-gas detection and weak spectrum measurement. It is essential to accomplish a high-precision measurement of MPCs’ effective optical path length (EOPL). A direct high-precision measuring method of MPCs’ EOPL with optical frequency domain reflectometer (OFDR) was reported and demonstrated in this paper. Several important parameters of a MPC, such as EOPL and base length, were derived with high-precision by identifying the complicated signal of OFDR. The MPC’s EOPL was also verified with the prevailing absorbance method. The results showed that the MPC’s EOPL measured by each of these two methods is highly consistent. However, the relative uncertainty with the OFDR dramatically decreased 2 orders of magnitude (about 0.0085%) than that with the absorbance method. It demonstrated that the OFDR method with fewer measurement links is more conducive to a direct measurement. The performances of beam spread and stray light in the White-cell were also evaluated with the method.
© 2016 Optical Society of America
1. Introduction
Multi-pass cells (MPCs) are commonly used in spectroscopy to measure low-concentration components or observe weak spectra in gases or liquids. The application of this type of cell can improve detection sensitivity by increasing the total optical path length that travels through a small, constant sample volume, when it is not convenient to get enough length using single pass detection. Several important advances are made in this area beginning in the 1930s, and the research into a wide range of applications continues to the present days [1–6 ]. Investigations show that MPCs have been widely used in varies areas, including environmental monitoring [4–6 ], combustion processes [7], medical diagnostics [8], and fundamental atomic and molecular physics [9,10 ].
The determination of effective optical path length (EOPL) of gas cells is very important for quantitative spectroscopic analysis, which aims at absolute measurements. In this case an incorrect path length of the gas cell would automatically lead to an incorrect result. When traceability should be an issue for the final spectroscopic analysis results, the determination of the EOPL has to be traceably determined as well [11]. Hence, the EOPL measurement of MPCs with high-accuracy is essential in quantitative spectroscopy when MPCs are used.
It is very challenging to determine the MPC’s EOPL since multiple reflections are involved [11]. Various means have been used to measure the EOPL of a MPC, which in general divide into three broad categories. Firstly, the base path and the reflection times of the MPC are used to calculate the EOPL of the MPC; the second method is by measuring and comparing the gas absorbance of the MPC with a reference cell of known EOPL, which filled with the same gas sample; the third is by measuring the phase difference of the intensity modulation laser travelling through the MPC and a known length path respectively. In practice, the first method is rarely used alone due to its low accuracy. Nwaboh et al. [11] get the optical path length of a MPC by the absorbance method, and obtain a relative uncertainty about ± 0.4%. Das and Wilson [12] obtain an uncertainty of ± 0.03 m in a 50 m MPC with the phase difference method. However, the relative uncertainties of these existing methods are a bit large for the absolute spectroscopic measurements when the ultra-high precision result and result traceability are needed. Andrea Pogány et al. [13] discuss traceability of all parameters used for amount fraction determination including the optical path length of a MPC which measured with a calibrated laser distance meter with relative uncertainty of 0.042%. The uncertainties associated with the cross-section and absorbance in quantitative spectroscopy database maybe in relationship with the path length uncertainty, such as HITRAN [14,15 ] with 10% maximum absorbance uncertainty, PNNL and NIST with 2.1% respectively [16]. In other words, improving the EOPL measurement accuracy may benefit to the measurement accuracy of the absorbance in spectra databases as well.
In order to get higher-precise measurement of MPCs’ EOPL, the present paper reports a direct measuring method to get a MPC’s EOPL with an optical frequency domain reflectometer (OFDR), which shortens the transmission chain of accuracy traceability. We analyzed the signal characteristics and measurement uncertainty of this method, and compared its measuring result with the prevailing absorbance method.
2. Principle of OFDR in space optical path
OFDR benefits the measurement with great resolution and precision, typically used in detecting the character of optical fibers, optical fiber connector and fiber systems [17,18 ]. The key of OFDR is linear frequency tuning in time of a tunable laser (TL). And the optical path difference (OPD) between the two arms (the measuring and reference arm) in optical system which is within the coherence length of the TL can be defined by the beat frequency of interference signal in OFDR system.
This paper tries to directly measure the space optical path of a MPC with OFDR equipped with a fiber collimator (FCM). The schematic diagram of the OFDR measuring system is shown in Fig. 1 . It consists of a TL, an optical interferometer comprising a reference arm and a measuring arm, the space optical path under test with several mirrors (M1, M2 and M3) and signal receiving and signal processing unit with Fast Fourier transform (FFT). The laser beam from TL is divided into two beams at the first fiber coupler (FCP1) which propagate along the two arms. One beam through the reference arm ① is regard as the reference; the other travels through OC and FCM, reflected or scattered by mirrors of the space optical path, and enters the arm ② as the measuring beam; both of the beams are recombined into the FCP2 and form a interference signal. The signal is detected by a photoelectric detector and a FFT allows the visualization of beat frequency.
Fig. 1 Schematic diagram of OFDR. TL: Tunable Laser; PD: Photoelectric Detector; FFT: Fast Fourier Transformation; FCP1, FCP2: Fiber coupler; OC: Optical circulator; FCM: Fiber collimator; M1, M2, M3: plane mirror; A: Amplifier. ① is the reference arm, ② is the measuring arm, and ③ is the beat signal.
In this system, the TL is swept at a constant rate γ = Δf/Δt, where f is the frequency of laser, and t is the tuning time. Frequency difference between the two beams which is equal to the beat frequency of interference signal fb is proportional to the optical path differences 2ΔL between the two paths. And the half optical path differences ΔL can be determined with respect to the beat frequency fb in Eq. (1) as
where the frequency sweep is assumed to be absolutely linear with constant tuning rate γ, c is the speed of light in vacuum, n is the refractive group index of the space optical path. Finally, according to the beat frequencies of the interference signal with FFT, the OPDs between the reference beam and the light from the reflector or scattering facet in the measuring arm including the echo from the space optical path can be obtained. According to the OPDs of these, the relative positions of the M1, M2 and M3 can be calculated with the reference arm of known length.In consideration of the beam properties measureable by means of the OFDR method, the detectability should be determined by such arbitrary factors as laser power, detector sensitivity, mirrors’ reflectivity, and the beam attenuation in the space optical path. In practical measurement, the applicability of the OFDR method must be affected by the beam properties received as well as the inherent nature of OFDR including the properties of the TL and the efficiency of data acquisition.
The measurement, based on laser interference, is well-suited for applications that require a combination of high speed, sensitivity and resolution over intermediate length ranges. The OFDR measurement has achieved higher sensitivity, higher signal-to-noise ratio, higher spatial resolution (with microns) and great dynamic range along with the development in high speed data acquisition, laser linear tuning and phase noise reducing in recent years [19–22 ]. The present paper using the same theory of this method to confirm the EOPL of a MPC is must be feasible and ensured by experiments.
3. Experiments and results
This section specifically shows the measurement procedures of a MPC’s EOPL by analyzing the measurement signal of OFDR and the optical path under test, and compares the method with OFDR with the prevailing absorbance method. Figure 2(a) shows the measuring system with OFDR, and Fig. 2(c) is absorbance method which measures the same MPC. Finally, we analyzed the uncertainties of the two methods according to experimental results of them.
Fig. 2 Experiment set-up with OFDR (a), the explanation of the OFDR measurement signal (b) and experiment set-up with absorbance methods (c). OFDR: Optical frequency domain reflectometer; M: Plane mirror; FCM: Fiber collimator; CCA: Corner cube array; W1, W2: Optical window; f0 is the fiber incident end; f1 is the fiber exit end; f2 is the facet of collimation lens; RGC: Reference gas cell; MPC: Multi-pass cell; LDC: Laser diode controller; TL: Tunable laser; PD: Photoelectrical detector; EOPL: Effective optical path length; A, B and C are the mirrors in the MPC; (b) show the enlargement of measurement signal which can clearly identify the upper and lower facet of the incident window W1u, W1l and the exit window W2u, W2l.
3.1 Experimental set-up with OFDR and signal analysis
In the EOPL measuring system of a MPC with OFDR showed in Fig. 2(a), linear frequency tuning light from the OFDR (OBR4600, LUNA Inc., with 10 μm spatial resolution) with wavelength rage 1525.00-1610.39 nm transmits through the fiber and the fiber collimator into a White-cell (16-v, Infrared Analysis Inc.), which is a glass-bodied cell, 4 inch I.D., base path 10 inches, variable path from 1 to 16 meters, volume approx. 2.3 liters. The maximum length measurable of the instrument is 2 kilometer with no dead-zone. And the detectable sensitivity is −130 dB according to the data sheet of this instrument. The corner cube array (CCA) at the exit of the White-cell is used for the auxiliary judgment of the echo peaks which represent the reflector or scattering facets in the optical path.
Figure 2(b) shows the echo signal which is received and processed by the OFDR. X-axis of the Fig. 2(b) represents the optical distance between the light outlet of the instrument and the reflector or scattering facet. The Y-axis is very much involved with the reflected optical intensity. Although the echo signal in the measuring signal with the OFDR is very complicated, most of them are confirmed by observing the reflected signal of CCA in different distance from the cell. The echo of each reflectors or scattering facets can be confirmed visually and exactly including the up and low facet of the two windows of the White-cell, the reflected signal of CCA and the stray light of the 11-reflection (12-pass) of the three mirrors A, B and C in White-cell which should be the source of the optical fringes for its basic property of multi-pass causing. There are some other echoes might from scattering facet somewhere in MPC which do not have any influence on accurate analysis of the EOPL.
From the signal enlargement in Fig. 2(b), echo peak appeared some beam spread which possibly comes from the laser wavefront aberration caused by micro-shift of beam propagation in radial direction. This phenomenon objectively causes the uncertainty of EOPL measurement which will result in the small uncertain optical path when the detector (or output fiber) is placed at different positions in practical applications. This should be an innate character of the cell, and not measuring error of the method, which might be used for evaluation of the uncertainty degree of cell optical path. In order to reduce the influence on EOPL evaluation by this uncertainty, this paper gave the spread signals by Gaussian curve fitting shown in Fig. 3 . In this figure the red line is the Gaussian curve fitting results, where xc represents the relative positions of the reflector or scattering surface and FWHM is the full width half maximum of the fitting peak by which the situation of beam spread in gas cell might be get simultaneously. It is this fitting method that determines the relative positions of the up-facet of the two windows (W1u, W2u) of White-cell, and the exact value of EOPL will be determined consequently by their relative distances.
Fig. 3 Gaussian curve fitting of spread signals and the parameters of fitting result. The red line is Gaussian curve fitting results.
What the EOPL measuring method of MPC with OFDR needs to do is judging the positions of incident window W1 and exit window W2. Hence, this method can be widely applied to the EOPL direct measurement of MPCs of various types.
3.2 Absorbance method experiment
In order to verify the measuring result with OFDR, this paper uses the absorbance method [11] for the EOPL measurement of a White-cell at the same configuration. The experimental system is shown in Fig. 2(c), where the White-cell under test and a straight through reference gas cell (RGC) with known length are filled with the same reference gas. In this experiment, the probe light of a tunable laser (FRL15DCWD-A82-18990-C, Furukawa) with wavelength scanning tuned by a laser diode controller (LDC-3908, ILX) is divided by a beam splitter and coupled into the White-cell and the RGC, and two same type of photoelectric detector (PDA10CS-EC, Thorlabs) are used to detect the light intensity signal out of the two paths respectively.
The absorbance method is based on the Beer Lambert law which describes the relationship between the incident and the transmitted radiation through a gas cell containing a molecular gas sample.
Where, the Φ0 and Φ are the incident and the transmitted radiant powers; 𝑆𝑇 is the molecular transition line strength of the probed absorption line at gas temperature 𝑇; the function 𝑔 is the normalized absorption profile centered at ν0 and L is the absorption path length. 𝑛0 is the density of the absorbing species.
With making use of the area normalization of 𝑔, it is obviously that the integrated area of the absorption line A is proportional to L when other situation is same with the relationship of Eq. (3).
Therefore, the EOPL of a gas cell under test can be obtained by
where A1 and A2 is the integrated absorbance of molecular gas absorption spectrum through the RGC with known length L1 and the cell under test respectively.In this experiment, first of all, the background signal of the White-cell and the RGC is obtained with the two cells full of dry nitrogen. Then, CO2 with 10% concentration is filled to the two cells, respectively, and the absorption signal is obtained. Finally, based on the Beer Lambert law, the absorbance through out of MPC and RGC can be obtained. Making use of Eq. (4), the EOPL of the White-cell can be acquired.
3.3 Experimental results and discussion
The EOPL measurement of a White-cell with OFDR and absorbance method was done in this paper based on the measuring system described in Fig. 2. In order to ensure the experimental conditions of the two methods are consistent, we evacuate the White-cell and fill it with the dry reference gas (90% N2 + 10% CO2) regardless of the method’s independence on the gas type in cell. In addition, the other conditions are the same as well, such as, temperature of 25 °C and relative humidity of 40%. Prior to the EOPL measurement experiment of the White-cell, the pass times of White-cell is adjusted by an auxiliary visible-light laser to 12 times (11-reflection) and fastened. Experiments with the two methods were done for 30 times, the mean and standard deviation of the two methods and their measurement uncertainty was analyzed and compared with each other. The EOPL of the RGC used in absorbance method (L1 = 301.10 mm) is determined with mechanical measurement (0.01 mm uncertainty).
According to the signal analysis in section 3.1 with the OFDR method, combining the experimental system with OFDR Fig. 2(a) and its measurement signal description Fig. 2b, the two facets of the incident and exit window of the White-cell can be accurately confirmed. With the Gaussian curve fitting result of the measured signal, the distance between W1u and W2u in the White-cell can be directly read which is equal to the MPC’s EOPL. In this experiment, the number of passes of the White-cell is adjusted to 12 times and the 30 times EOPL measurement results of the MPC in this situation with OFDR are shown in Fig. 4 . From Fig. 4, the mean of the EOPL measurement with OFDR is about 3125.74 mm, and the standard deviation (SD) of 30 times measurement is 0.01 mm. Therefore, the relative standard deviation (RSD) measurement with OFDR is calculated to be as low as 3.2 × 10−6.
After the EOPL measuring experiment with OFDR, keeping the reflection times and FCM at inlet of the White-cell still, the EOPL measurement with absorbance method is carried in the same experimental condition. In order to let the working wavelength of absorbance method close to the OFDR method, the absorption spectrum of CO2 at 1578.665 nm is measured based on the Beer Lambert Law Eq. (2) with an appropriate TL which the wavelength of was swept by saw modulation of the laser current at a frequency of 200 Hz. In order to decrease the influence from noise and other interference, the Lorentzian fitting of the gas spectrum absorbance is done as shown in Fig. 5 . Figure 6 is the result of the integrated absorbance of the MPC and RGC in the 30 experiments respectively. With the relationship between integrated absorbance and optical path length Eq. (4), the EOPL mean of MPC is 3125 mm, and the measurement SD is 13 mm, and the RSD of 30 experiments is 4.2 × 10−3.
Fig. 5 The direct absorption spectrum of 10% CO2. The number of passes in the White-cell is 12 times.
Fig. 6 The integrated absorbance results of 10% CO2 (30 times) in the RGC (a) and the White-cell (b).
From the results, the EOPL of the White-cell is highly consistent which the result with OFDR is 3125.74 mm and 3125 mm with absorbance method. While OFDR gives a RSD dramatically lower than the absorbance method by 3 orders of magnitude. Hence, the method with OFDR has a higher precision of EOPL measurement.
The EOPL measurement with OFDR is only need one step to link the target and the direct measurement. In absorbance method, there are three steps from the direct measurements and the goal EOPL of MPC, including the relation between optical path length and absorption spectrum, the spectrum involved to the EOPL of RGC, and the EOPL measurement of RGC.
EOPL of the MPC is calculated with the positions of the two windows with OFDR. According to the composition principle of the measurement uncertainty, the MPC’s EOPL combined measurement uncertainty with OFDR can be written as
where uOFDR represents the uncertainty of OFDR instrument which is subject to the ambient temperature and a given index of refraction error according to the measurement accuracy report of the instrument. The group index of air (n = 1) is well known so that the error associated with it is relatively small. The maximum relative uncertainty of the length measurement with the OFDR is 0.006% with the assurance of ambient temperature where the instrument is located remains within +/−3 °C from when the instrument was last calibrated, which is calibrated by an internal HCN gas cell and traced to the optical frequency of the HCN gas absorption line. umeasure represents the uncertainty of the experimental results with 30 times. In other words, the results relative uncertainty of the White-cell’s EOPL is about 0.0085%.The measurement uncertainty of absorbance method can be defined as
where the A1, A2, L1 are the indirectly measured results, and uA1, uA2, uL1 are their uncertainties respectively. umeasure represents the uncertainty of the experimental results with the absorbance method. The measuring results comparison between the two methods is shown in Table 1 . The OFDR method greatly reduces the measurement uncertainty with 3 orders of magnitude. With the comparison of method with OFDR and absorbance method, the high precision of OFDR is more obvious due to its direct measurement with fewer links.
Table 1. Measuring results comparison between OFDR and absorbance methods
It is necessary to be pointed out that the absorbance method in this paper used a weaker absorption line of CO2, to close the working wavelength of the OFDR, so the measured signal is susceptible to be effected by the noise of detector and amplifier in system, which lead to the uncertainty degree lager than that in reference [11] by about an order of magnitude. But this doesn’t affect the correctness of this result of absorbance method. Therefore, it is more reasonably to say that the uncertainty of the method with OFDR is lower than the absorbance method about by 2 orders of magnitude.
4. Performance evaluation of White-cell with OFDR
Using the direct high-precision measurement with OFDR, the performance of the White-cell was further evaluated in this paper. And the base length with high accuracy was obtained by analysis of the relationship between the EOPL and number of passes in MPC. In the end, beam spread situation and the stray light in the MPC will be stated.
The EOPL of the White-cell is measured by the same experimental system shown in Fig. 2(a) with the number of passes in cell changed with the assistant adjustment of a red light source. Figure 7 shows relationship of the EOPL and the number of passes in MPC. By linear fitting of the results, the function of the path length and the number of passes is defined as y = a + b﹒x, where y represents the EOPL of the MPC, x is the number of passes (equal to the reflection times plus one). And the physical relation between each parameter determines that b represents the base path of the White-cell and a is the representative of the spatial light path length in EOPL of MPC removal of the reflection between the mirrors. And from the result, it is clear that b ( = 254.23mm) is approximately equal to 10 inches which is the base path parameter of the White-cell in product information. With the function fitted, EOPL of the White-cell can be obtained with known number of passes.
The beam spread with different EOPL in the White-cell is carried out according to the Gaussian fitting shown in Fig. 3. With the increase of path length, the FWHM approximately increases in linear, showed as Fig. 8 , which will lead to slightly difference of optical path when the detector (or output fiber) placed at different positions in radial direction. Obviously, it can be ignored in quantitative measurement of non-high precision. And this feature of the OFDR measurement result might be used to determine the beam property by the reflected light at that measurable position.
In addition, from the regular pattern of relative distance of each echo peaks between the two windows in Fig. 2b, it's easy to find that they are consistent to the regulation of beam in White-cell. And these several echo signals should be in corresponding with the mirrors in the MPC. In the experiment, it was also noted that the amplitude of the echo signal is changing along with the micro-adjustment of the White-cell. Hence, the echo signals in cell may be related to the optical fringes which seriously influence the performance of cell will be investigated in the further working.
5. Conclusion
In this paper, a EOPL measuring method of MPCs is reported and validated with OFDR which has been used as the diagnostic and characterization tool for optical fibers, optical fiber connector and fiber systems for long time. According to the comparison with prevailing absorbance method, the method with OFDR has a higher precision by 2 orders of magnitude which will help to improve the measurement accuracy of quantitative spectrum. To our knowledge, the relative uncertainty with the OFDR method is the minimum compared with the previous methods which are used in the determination of MPCs’ EOPL. Obviously, this method can also be used in the high-precision EOPL determination of a single cell as well. Except for the EOPL measurement, the other important characteristic parameters of a MPC can be given by this method, such as the base path, beam spread and stray light which might be source of the optical fringes, which is extremely important for the comprehensive evaluation of a MPC. Apparently, this method can also be used for optical path length measurement and performance evaluation of other types of MPC (such as Herriott cell) or other optical path with a complicate optical system. Especially, OFDR has great potential in the analysis and evaluation of stray light in optical system.
Acknowledgments
This research was supported in part by the Special-funded Program on National Key Scientific Instruments and Equipment Development (2012YQ06016501) of china and the 111 Project (B07014) of China.
References and links
1. H. D. Smith and J. K. Marshall, “Method for Obtaining Long Optical Paths,” J. Opt. Soc. Am. 30(8), 338–342 (1940). [CrossRef]
2. J. U. White, “Long Optical Paths of Large Aperture,” J. Opt. Soc. Am. 32(5), 285–288 (1942). [CrossRef]
3. J. Hodgkinson and R. P. Tatam, “Optical gas sensing: a review,” Meas. Sci. Technol. 24(1), 012004 (2013). [CrossRef]
4. P. Werle, R. Mücke, and F. Slemr, “The limits of signal averaging in atmospheric trace-gas monitoring by tunable diode-laser absorption spectroscopy (TDLAS),” Appl. Phys. B 57(2), 131–139 (1993). [CrossRef]
5. J. A. Silver and W. R. Wood, “Miniature gas sensor for monitoring biological space environments,” Proc. SPIE 4817, 82–87 (2002). [CrossRef]
6. B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013). [CrossRef] [PubMed]
7. P. Minutolo, C. Corsi, F. D’Amato, and M. De Rosa, “Self- and foreign-broadening and shift coefficients for C2H2 lines at 1.54 μm,” Eur. Phys. J. D 17(2), 175–179 (2001). [CrossRef]
8. M. Gianella and M. W. Sigrist, “Infrared Spectroscopy on Smoke Produced by Cauterization of Animal Tissue,” Sensors (Basel) 10(4), 2694–2708 (2010). [CrossRef] [PubMed]
9. 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(21), 3212–3214 (2007). [CrossRef] [PubMed]
10. D. X. Qu and C. Gmachl, “Quasichaotic optical multipass cell,” Phys. Rev. A 78(3), 033824 (2008). [CrossRef]
11. J. A. Nwaboh, O. Witzel, A. Pogány, O. Werhahn, and V. Ebert, “Optical Path Length Calibration: A Standard Approach for Use in Absorption Cell-Based IR-Spectrometric Gas Analysis,” Int. J. Spectrosc. 2014(9), 132607 (2014).
12. D. Das and A. C. Wilson, “Very long optical path-length from a compact multi-pass cell,” Appl. Phys. B 103(3), 749–754 (2011). [CrossRef]
13. A. Pogány, S. Wagner, O. Werhahn, and V. Ebert, “Development and Metrological Characterization of a Tunable Diode Laser Absorption Spectroscopy (TDLAS) Spectrometer for Simultaneous Absolute Measurement of Carbon Dioxide and Water Vapor,” Appl. Spectrosc. 69(2), 257–268 (2015). [CrossRef] [PubMed]
14. L. S. Rothman, A. Barbe, D. Chris Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, “The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant. Spectrosc. RA. 82(1–4), 5–44 (2003). [CrossRef]
15. C. Clerbaux, R. Colin, P. C. Simon, and C. Granier, “Infrared cross sections and global warming potentials of 10 alternative hydrohalocarbons,” J. Geophys. Res. 98(D6), 10491–10497 (1993). [CrossRef]
16. S. W. Sharpe, T. J. Johnson, R. L. Sams, P. M. Chu, G. C. Rhoderick, and P. A. Johnson, “Gas-phase databases for quantitative infrared spectroscopy,” Appl. Spectrosc. 58(12), 1452–1461 (2004). [CrossRef] [PubMed]
17. W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single‐mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981). [CrossRef]
18. K. Shimizu, T. Horiguchi, and Y. Koyamada, “Measurement of Rayleigh backscattering in single-mode fibers based on coherent OFDR employing a DFB laser diode,” IEEE Photonics Technol. Lett. 3(11), 1039–1041 (1991). [CrossRef]
19. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express 13(2), 666–674 (2005). [CrossRef] [PubMed]
20. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. 32(22), 3227–3229 (2007). [CrossRef] [PubMed]
21. K. Yuksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express 17(7), 5845–5851 (2009). [CrossRef] [PubMed]
22. F. Ito, X. Y. Fan, and Y. Koshikiya, “Long-Range Coherent OFDR With Light Source Phase Noise Compensation,” J. Lightwave Technol. 30(8), 1015–1024 (2012). [CrossRef]
