Birefringence-Dispersion-Induced Frequency Domain Nonlinearity ...

4842

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 23, DECEMBER 1, 2015

Birefringence-Dispersion-Induced Frequency Domain Nonlinearity Compensation for Polarized Low-Coherence Interferometry Demodulation Shuang Wang, Junfeng Jiang, Tiegen Liu, Kun Liu, Jinde Yin, Junfeng Shi, Shengliang Zou, and Mingjiang Zhang

Abstract—A high precision demodulation method in frequency domain is proposed for a polarized low-coherence interferometer with location-dependent birefringence dispersion. By minimizing the frequency nonlinearity caused by dispersion effects, the proposed method avoids the jump errors of traditional frequency domain analysis method and exactly retrieve the absolute phase at multiselected-wavenumber point simultaneously, which makes it superior in accuracy, stability, and measurement range. We carried out experiments with an optical fiber Fabry–Pérot pressure sensing system to verify the effectiveness of the proposed method. The experiment result showed that the measured error was less than 0.049 kPa and the measurement range was widened to 285 kPa, which could be wider with suited experimental equipment and is no limit in theory. Index Terms—Fabry–Perot, interferometry, pressure measurement.

I. INTRODUCTION OW-COHERENCE interferometry (LCI), as an effective technique for absolute displacement measurements, has attracted considerable attention for measuring three-dimensional profile [1], optical coherence tomography [2], and optical fiber sensing applications such as for temperature [3], pressure [4] and refractive index [5]. In order to enhance the performance of LCI, a number of demodulation methods have been proposed, including

L

Manuscript received July 15, 2015; revised October 9, 2015; accepted October 9, 2015. Date of publication October 11, 2015; date of current version November 1, 2015. This work was supported by the National Natural Science Foundation of China under Grants 61505139, 61227011, 61378043, and 61475114, National Instrumentation Program of China under Grant 2013YQ030915, National Basic Research Program of China under Grant 2010CB327802, Science and Technology Key Project of Chinese Ministry of Education under Grant 313038, Tianjin Natural Science Foundation under Grant 13JCYBJC16200, Shenzhen Science and Technology Research Project under Grant JCYJ20120831153904083, Key Lab of Advanced Transducers and Intelligent Control System of Ministry of Education and Shanxi Province (Taiyuan University of Technology) under Grant 201403, Key Laboratory of Opto-electronic Information Technology of Ministry of Education (Tianjin University) under Grant 2014KFKT021. (Corresponding author: Junfeng Jiang.) S. Wang, J. Jiang, T. Liu, K. Liu, J. Yin, J. Shi, and S. Zou are with the Key Laboratory of Optoelectronics Information Technology, College of Precision Instrument and Optoelectronics Engineering, Tianjin University,Ministry of Education China, Tianjin 300072, China (e-mail: sarahwang02166@ gmail.com; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). M. Zhang is with the Key Laboratory of Advanced Transducers and Intelligent Control Systems, Ministry of Education and Shaanxi Province,Taiyuan University of Technology, Taiyuan 030024, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2015.2490083

fringe-contrast-based methods and phase-based methods. With the advantage of high computational speed, fringe-contrastbased methods are widely used in early stage [6]. However, since the position of peak fringe contrast is sensitive to dispersion [7] and spectral distribution of light source [8], these methods are not as accurate as phase-shifting interferometry (PSI). For example, when the system includes a location-dependent dispersion element and a dual wavelength low-coherence light source, both the envelope peak and the central fringe peak are difficult to determine [9]. As phase-based methods take advantage of sensitive phase information in low-coherence interference fringes (LCIF), these methods can theoretically achieve the same high measurement accuracy as PSI, so long as the fringe order is correctly identified. In 1993 de Groot and Deck proposed frequency domain analysis (FDA) for three-dimensional imaging [10], which was built on established methods in the analysis of optoelectronic waveguide devices [11]. As a powerful phase-based technique, FDA utilizes the rich Fourier-transformed phase information of several monochrome interference patterns to exactly measure distances. Compared to the fringe-contrast-based methods of LCI, FDA requires no imposed conditions on the spectral distribution and is not sensitive to the spectral distribution variation of light source [12]. Moreover, FDA can be used in combination with sub-sampling technique to increase the data acquisition and processing speed of LCI [13]. The slope of the unwrapped phase information in frequency domain is usually used to identify the fringe order [14]. However, the phase value is severely influenced by the unbalanced dispersion in the system, which will lead to the improper fringe order. In 2002 de Groot et al., improved FDA by use of the phase gap between phase and coherence profiles to compensate the fringe order error [15]. Another improved FDA based on dual wavelength approach was proposed by Ghim and Davies in 2012 to reduce misidentifications of fringe order [16]. But these compensation methods are specifically designed for surface profiling, which either need a priori knowledge or have complicated determination process of fringe order. The relationship between the phase and frequency, including a consideration of dispersion effects, has been discussed and applied to correct the path-length in distance measurement [17] and calculate the refractive index of a silicon wafer [13]. However, these researches just concern location-independent dispersion elements, such as partially transparent measuring objects and an additional glass plate in one arm of Michelson interferometer. The location-dependent dispersion effect in FDA, which

0733-8724 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

WANG et al.: BIREFRINGENCE-DISPERSION-INDUCED FREQUENCY DOMAIN NONLINEARITY COMPENSATION FOR PLCI DEMODULATION

4843

birefringence wedge, ds is the difference of the wedge thickness between adjacent pixels, Dstar t is the wedge thickness of the first pixel corresponding to the starting position, h is the cavity length of the F-P sensor, and n(k) is the refractive index difference (RID) between the E ray and O ray. The dependence of the RID on the wavenumber can be expressed by a linear function n(k) = αk + β,

Fig. 1. sensor.

Schematic diagram of PLCI configuration for demodulating F-P

where α and β represent the birefringence dispersion slope and intercept, respectively. From Eq. (1) we can see that the absolute phase ϕ(k) increases in proportion to the cavity length at a single wavenumber and the cavity length can be calculated using the following formula: h = [kDstar t n(k) − ϕ(k)] / (2k) .

causes frequency nonlinearity and leads to absolute phase jump errors, is explored little in other literature. In this paper, we propose an effective method, which is based on the characteristics of location-dependent birefringence dispersive in frequency domain and multi-point absolute phase, to compensate the frequency nonlinearity and improve the measurement accuracy for polarized low-coherence interference (PLCI). We experimentally verified the performance of the proposed method with an optical fiber Fabry–Pérot (F-P) pressure sensing system. The experimental results showed that, comparing with traditional FDA method without nonlinearity compensation of frequency, the proposed method avoided jump errors of absolute phase and improved the precision and stability in a wider measurement region. II. THEORETICAL ANALYSIS Fig. 1 is a simplified diagram of PLCI configuration for F-P cavity length demodulation. The PLCI demodulator with a birefringence wedge is a modified version of the system demonstrated by Dändliker et al., in 1992 [18]. The light from broadband light source is launched into a F-P sensor via a 3 dB coupler. The reflected light signal from the sensor is guided into the PLCI demodulator. In the PLCI, the light beam passes through a polarizer, a birefringence wedge and an analyzer in sequence. The birefringence wedge converts the optical path difference (OPD) of ordinary (O) ray and extraordinary (E) ray into a spatial distribution. When the OPD of the birefringence wedge matches with twice the cavity length of the F-P sensor, the low-coherence interferogram is visible and can be received by a linear charge-coupled device (CCD). The LCIF in the experiment is an approximate double-beam interference, which can be considered as the superposition of numerous monochrome interference signals. Each interference fringe pattern, having a unique frequency or wavenumber, can be expressed as I(x, k) = C(k) cos [k (ds x + Dstar t ) n(k) − 2hk] ,

(1)

where C(k) represents the light source spectrum, k is the wavenumber defined by k = 2π/λ, x is the coordinate in the CCD array and can be used to denote the location on the

(2)

(3)

Fourier technique is an effective method to extract the phase information of single wavenumber from LCIF. The FDA method shows that we can select a single wavenumber and recover its absolute phase for demodulation, utilizing the relative phase information of the Fourier-transformed data, which is wrapped into the interval(−π, π). In practice, we acquire the relative phase in frequency domain by Discrete Fourier Transform (DFT). Let kl be the selected wavenumber corresponding to the DFT serial number l, the recovered absolute phase ϕ(kl ) can be obtained by [14] ϕ(kl ) = Φ(kl ) − 2mπ,

(4)

where Φ(kl ) is the relative phase at kl obtained by DFT, m = floor(T/2π) is the fringe-order of the selected wavenumber kl , T is the intercept of the unwrapped phase linear fit curve in the range around the selected wavenumber. The function floor() returns the nearest integer which is smaller or equal to the value in the brackets. In the conventional FDA method, it is regarded that the different value of wavenumber between two adjacent DFT points is uniform, therefore the phase unwrapping and linear fitting are generally performed on the DFT series directly. However, when considering birefringence dispersion, the RID is dependent on wavenumber, thus the sample interval of interference signals in spatial domain changes with wavenumber. This leads to the nonlinear sampled data occurs in frequency domain after DFT. In this case, the unwrapped phase on the DFT series is no longer in a line, and that will give rise to erroneous intercept T of the linear fit curve. The intercept error increases with the increment of the cavity length. If the deviation of the intercept is greater than 2π, a misidentification of the fringe order occurs. This improper fringe order will lead to the jump error in the demodulated result, which corresponds to a deviation π/kl of cavity length. Therefore, in order to ensure the correct identification of fringe-order, we have to compensate the frequency nonlinearity by establishing the exact relationship between wavenumber and DFT serial number. The wavenumber, corresponding to the DFT serial number u, can be expressed as ku = 2πufs /N,

(5)

where N is the sampling number of LCIF, i.e., the number of effective pixels in the linear CCD, and fs = [ds n(ku )]−1

4844

Fig. 2.


Relation curve between the wavenumber and the DFT serial number.

represents the sampling frequency of the interference fringe with monochrome wavenumber ku . According to the Eq. (5), the wavenumber at each DFT serial number can be calculated by β 2 + 8παu/ (N ds ) − β . (6) ku = 2α The relationship between wavenumber and DFT serial number calculated with the experimental parameters is shown in Fig. 2. Knowledge of the actual wavenumber at each DFT serial number helps us totally compensate the influence of the frequency nonlinearity. After obtaining the wavenumber value of DFT series, we can carry out absolute phase recovery process in wavenumber domain, and finally demodulate the cavity length. In theory, to perform the linear fit of the unwrapped phase, we only need a few discrete values of wavenumber with high amplitudes after DFT, which can be located by an amplitude threshold. And then choose one point of this region as the selected wavenumber to recover the absolute phase and demodulate the cavity length. The phase unwrapping process of different selected wavenumbers is shown in Fig. 3. Based on the amplitude characteristic of Fourier-transformed data shown in Fig. 3(a), the wavenumber region (k69 , k82 ) for unwrapping process in the experiment and the selected wavenumber for absolute phase recovery can be predetermined. In this small wavenumber region, we can unwrap the relative phase centered on the selected wavenumber. For difference selected wavenumbers, the unwrapped phase-wavenumber curves are different, as shown in Fig. 3(b), except the fringe-order of the selected wavenumbers are same. Then by using the unwrapped phase information we can easily obtain the absolute phase and cavity length according to Eq.(3) and Eq.(4), respectively. When air pressure is applied to the F-P sensor, the silicon diaphragm will has elastic deformation. According to the small deflection theory of circular diaphragm with clamped edges, the cavity length change Δh and pressure change ΔP is linearly related by Δh = 3(1 − υ 2 )r4 ΔP/(16Et3 ), where r, t, E, υ are the effective radius, thickness, Young’s modulus and Poisson’s ratio of silicon diaphragm, respectively [19]. Moreover, from Eq. (3) we can see that the absolute phase increases linearly with the cavity length at a single wavenumber. Therefore, absolute phase and cavity length are both linear with the measurand

Fig. 3. Phase unwrapping process in wavenumber domain based on the interferogram under 120 kPa in experiment. (a) Partial amplitude-wavenumber curve obtained by DFT. (b) The relative phase and the unwrapped phase corresponding to different selected wavenumbers.

of air pressure and can be used for demodulation. However, at a certain pressure absolute phase is different for different selected wavenumbers, but cavity length is the same in theory. Fig. 4 shows the demodulated absolute phase and cavity length in the pressure range of 5–290 kPa, which correspond respectively to k75 , k76 and k77 . From Fig. 4(b) we can see that after compensating the frequency nonlinearity, the demodulation results of cavity length at different selected wavenumbers present a good consistency. Thus, with one set of the Fourier-transformed phase information in the determined wavenumber region after DFT, we can demodulate the cavity length several times corresponding to different selected wavenumbers and use the mean value as the final demodulation result to improve the measurement accuracy. While for the traditional FDA method, because of no birefringence dispersion effects being considered, it is assumed that the RID of all the wavenumbers in the spectrum range of the light source have the same value. Here we use n (kc ), where kc ≈ 0.0109 rad/nm is the central wavenumber in our experiment, as the value of RID for cavity length demodulation by the traditional FDA method. The demodulation results by


Fig. 4. Demodulated absolute phase and cavity length after frequency nonlinearity compensation at k 7 5 , k 7 6 andk 7 7 , respectively. (a) Relationship between the pressure and the recovered absolute phase. (b) Relationship between the pressure and the cavity length.

4845

Fig. 5. Demodulated absolute phase and cavity length by traditional FDA method at k 7 5 , k 7 6 andk 7 7 , respectively. (a) Relationship between the pressure and the recovered absolute phase. (b) Relationship between the pressure and the cavity length.

use of the traditional FDA method are shown in Fig. 5. The jump errors are serious and a cavity length shift exists among different selected wavenumbers, which arise from the influence of location-dependent dispersion. As a result, when we use the traditional FDA method for PLCI, the measurand is limited to a certain range, which has no jump error and is different with various selected wavenumbers, and only a single selected wavenumber can be used for demodulation. Therefore, comparing to traditional FDA method, the proposed method can avoid jump errors and alleviate the measurement error caused by random noise in LCIF and system errors, which slightly increases the computational burden. III. EXPERIMENTAL RESULTS

Fig. 6. Schematic diagram of the optical fiber F-P pressure measurement system configuration.

We carried out pressure experiment to verify the effectiveness of the proposed method. The schematic diagram of experiment setup is shown in Fig. 6. A F-P sensor, placed in an air-pressuretunable chamber with a pressure control accuracy of 0.02 kPa, is used to sense and transfer air pressure into cavity length. The broadband light source used in the system is phosphorbased white light-emitting diode (LED), whose power spectrum with two distinct peaks is shown in Fig. 6. The fiber type is commercial multimode fiber with a core/cladding diameter of

62.5/125 μm. In our PLCI experiment setup, a MgF2 birefringence wedge is used. The slope of MgF2 birefringence dispersion α ≈ 0.049 nm/rad and the intercept β ≈ 0.0113, which are calculated with refractive index data in the spectral region from 520 to 631 nm [20]. A linear CCD with 3000 pixels is used to record the interferogram. The pixel pitch of the linear CCD is 7 μm, whose corresponding sample interval of the birefringence wedge thickness ds is 1.216 μm and the starting position

4846


Fig. 7. Raw interferogram collected by CCD, envelope, and filtered interferogram under 120 kPa pressure.

Fig. 9. (a) Measure error between the set pressure and demodulated pressure by the four methods. (b) Measure error by envelope peak method. (c) Measure error by central fringe peak method. (d) Measure error by traditional FDA method. (e) Measure error by the proposed method.

Fig. 8. Relationship between the pressure and detected cavity length or position by different methods (an offset of –130 pixels was added for the curve of central fringe method to make the profiles distinguishable).

Dstart is 1.981 cm. After digitizing the signals by a data acquisition card, we obtain the intensity data for further processing in computer. The raw output of the CCD array, envelope, and filtered interferogram are shown in Fig. 7. From Fig. 7 we can clearly see that under the influence of birefringence dispersion and dual wavelength broadband light source, both the LCIF and the envelope have a large deformation and are obviously asymmetric. This makes the central fringe with maximum amplitude and the envelope peak difficult to trace. When central fringe peak or envelope peak is misidentified, a jump error corresponding to one or more fringes of CCD pixels occurs. That will give rise to erroneous measurement results if we use the fringe-contrast-based methods. In the experiment, we increased the air pressure from 5 to 290 kPa at intervals of 1 kPa by controlling the air pressure chamber, and acquired 100 consecutive LCIF under each pressure for demodulation. We calculated the cavity length corresponding to the selected wavenumbers k75 , k76 and k77 , which are around the central wavenumber, and then used the mean value as the final demodulation results. The performance of the proposed method is compared with the traditional FDA method with the selected wavenumber k76 and the fringe-contrast-based methods, including envelope peak method and central fringe peak method. The demodulated results by the use of these methods are shown in Fig. 8. From this figure we can see that all the methods give rise to different degrees of jump errors except the

Fig. 10. (a) SD of the measure error for 100 consecutive interference data under each pressure by the four methods. (b) SD by envelope peak method. (c) SD by central fringe peak method. (d) SD by traditional FDA method. (e) SD by the proposed method.

proposed method. In the experiment the measure errors of air pressure, caused by the jump errors of traditional FDA method, envelope peak method and central fringe peak method, are about 9.89, 27.22 and 9.65–29.41 kPa, respectively, with the sensitivity of F-P sensor 28.73 nm/kPa. The measurement errors caused by jump errors are unacceptable. Therefore, the demodulation processing only can be carried out in the available measure-


TABLE I COMPARISON OF THE FOUR METHODS Methods

Envelope method Central fringe method FDA method Proposed method

Measure range (kPa)

30–290 93–193 65–265 5–290

Maximum error (kPa)

Measure accuracy

Standard deviation range

Plus

Minus

(F.S.)

(kPa)

0.665 0.095 0.148 0.038

−0.838 −0.117 −0.144 −0.049

0.322% 0.117% 0.074% 0.017%

0.179–0.440 0.014–0.082 0.021–0.040 0.012–0.023

ment range without jump errors. In the experiment the available measurement range of traditional FDA method, envelope peak method and central fringe peak method are about 200, 260 and 100 kPa, respectively. Fig. 9 shows the measurement error of air pressure by the traditional FDA method atk76 , the envelope peak method and central fringe peak method in their respective available measure regions, and the proposed method in the whole experimental region of 5–290 kPa. While the standard deviation (SD) of the demodulated pressure error under each pressure by the four methods are shown in Fig. 10. Table I shows the available measure range, maximum demodulation error, measure accuracy for the full scale (F.S.) and the SD range by use of the four methods, respectively. From the table we can see that, in the same experimental conditions the proposed method has the maximum measure range and the minimum measure error and SD. It clearly demonstrates that we can obtain more precise and stable demodulated results in a wider measurement region by the proposed method. IV. CONCLUSION We proposed a new method to exactly retrieve the absolute phase at multi-selected-wavenumber point simultaneously for demodulation of PLCI, by means of frequency nonlinearity compensation caused by location-dependent birefringence dispersion. The method effectively avoids the jump errors of the traditional FDA method and can average the results demodulated at different selected wavenumbers, which makes it superior in accuracy, stability and measurement range. The method was demonstrated successfully in an optical fiber F-P barometric pressure sensing experiment system. The measurement error is less than 0.049 kPa, and the measurement range is widened to 285 kPa, which could be much wider in theory but limited by the experimental condition.

4847

[4] F. Xu, J. Shi, K. Gong, H. Li, R. Hui, and B. Yu, “Fiber-optic acoustic pressure sensor based on large-area nanolayer silver diaphragm,” Opt. Lett., vol. 39, no. 10, pp. 2838–2840, 2014. [5] S. H. Kim, S. H. Lee, J. I. Lim, and K. H. Kim, “Absolute refractive index measurement method over a broad wavelength region based on white-light interferometry,” Appl. Opt., vol. 49, no. 5, pp. 910–914, 2010. [6] P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett., vol. 22, no. 14, pp. 1065–1067, 1997. [7] P. Pavliˇcek and J. Soubusta, “Measurement of the influence of dispersion on white-light interferometry,” Appl. Opt., vol. 43, no. 4, pp. 766–770, 2004. [8] W. K. Chong, X. Li, and S. Wijesoma, “Effects of phosphor-based LEDs on vertical scanning interferometry,” Opt. Lett., vol. 35, no. 17, pp. 2946– 2948, 2010. [9] S. Wang, J. Jiang, T. Liu, K. Liu, J. Yin, X. Meng, and L. Li, “A simple and effective demodulation method for polarized low-coherence interferometry,” IEEE Photon. Technol. Lett., vol. 24, no. 16, pp. 1390–1392, Aug. 2012. [10] P. De Groot and L. Deck, “Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms,” Opt. Lett., vol. 18, no. 17, pp. 1462–1464, 1993. [11] B. L. Danielson and C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt., vol. 30, no. 21, pp. 2975–2979, 1991. [12] P. De Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt., vol. 42, no. 2, pp. 389–401, 1995. [13] K. N. Joo, “Sub-sampling low coherence scanning interferometry and its application: Refractive index measurements of a silicon wafer” Appl. Opt., vol. 52, no. 36, pp. 8644–8649, 2013. [14] J. Jiang, S. Wang, T. Liu, K. Liu, J. Yin, X. Meng, Y. Zhang, S. Wang, Z. Qin, F. Wu, and D. Li, “A polarized low-coherence interferometry demodulation algorithm by recovering the absolute phase of a selected monochromatic frequency,” Opt. Exp., vol. 20, no. 16, pp. 18117–18126, 2012. [15] P. De Groot, X. Colonna De Lega X, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt., vol. 41, no. 22, pp. 4571–4578, 2002. [16] Y. S. Ghim and A. Davies, “Complete fringe order determination in scanning white-light interferometry using a Fourier-based technique,” Appl. Opt., vol. 51, no. 12, pp. 1922–1928, 2012. [17] P. De Groot, “Chromatic dispersion effects in coherent absolute ranging,” Opt. Lett., vol. 17, no. 12, pp. 898–900, 1992. [18] R. Dändliker, E. Zimmermann, and G. Frosio, “Electronically scanned white-light interferometry: A novel noise-resistant signal processing,” Opt. Lett., vol. 17, no. 9, pp. 679–681, 1992. [19] S. Timoshenko and S. Woinowsky-Krieger, Theory Plates Shells. New York, NY, USA: McGraw-Hill, 1959, pp. 51–55. [20] A. Duncanson and R. W. H. Stevenson, “Some properties of magnesium fluoride crystallized from the melt,” Proc. Phys. Soc., vol. 72, no. 6, pp. 1001–1006, 1958.

Shuang Wang was born in Tianjin, China, in 1982. She received the B.S. degree from Shandong University, Shandong, China, in 2005 and the M.S. degree from Tianjin University, Tianjin, China, in 2007. She is currently a Lecturer at Tianjin University. Her research interests include optical fiber sensing and demodulation algorithm.

REFERENCES [1] V. Heikkinen, I. Kassamakov, T. Paulin, A. Nolvi, and E. Hæggström, “Stroboscopic scanning white light interferometry at 2.7 MHz with 1.6 μm coherence length using a non-phosphor LED source,” Opt. Exp., vol. 21, no. 5, pp. 5247–5254, 2013. [2] D. Sacchet, M. Brzezinski, J. Moreau, P. Georges, and A. Dubois, “Motion artifact suppression in full-field optical coherence tomography,” Appl. Opt., vol. 49, no. 9, pp. 1480–1488, 2010. [3] T. Liu, J. Yin, J. Jiang, K. Liu, S. Wang, and S. Zou, “Differential-pressurebased fiber-optic temperature sensor using Fabry–Perot interferometry,” Opt. Lett., vol. 40, no. 6, pp. 1049–1052, 2015.

Junfeng Jiang received the B.S. degree from the Southwest Institute of Technology, Sichuan, China, in 1998, and the M.S. and Ph.D. degrees from Tianjin University, Tianjin, China, in 2001 and 2004, respectively. He is currently an Associate Professor at Tianjin University. His research interests include fiber sensors and optical communication performance measurement.

4848


Tiegen Liu received the B.Eng., M.Eng., and Ph.D. degrees from Tianjin University, Tianjin, China, in 1982, 1987, and 1999, respectively. He is currently a Professor at Tianjin University. He is also a Chief Scientist of the National Basic Research Program of China under Grant 2010CB327802. His research interests include photoelectric detection and fiber sensing.

Junfeng Shi received the B.Eng. degree from Tianjin University, Tianjin, China, in 2013, where he is currently working toward the M.Eng. degree in optical engineering. His research interest includes low-coherence interference demodulation.

Kun Liu received the B.Eng., M.Eng., and Ph.D. degrees from Tianjin University, Tianjin, China, in 2004, 2006, and 2009, respectively. He is currently an Associate Professor at Tianjin University. His research interests include fiber physics and chemistry sensing systems.

Jinde Yin received the B.Eng. degree from Tianjin University, Tianjin, China, in 2010, where he is currently working toward the Ph.D. degree in optical engineering. His research interest includes optical fiber sensing technology.

Shengliang Zou received the B.Eng. degree from Tianjin University, Tianjin, China, in 2013, where he is currently working toward the M.Eng. degree in optical engineering. His research interests include Fabry–Pérot sensor.

Mingjiang Zhang (M’11) received the Ph.D. degree in optics engineering from Tianjin University, Tianjin, China, in 2011. He is currently an Associate Professor at the College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, China. His current research interests include optical communication, optical fiber sensing, and microwave photonics. Dr. Zhang is a Member of the Optical Society of America.