Phase demodulation of interferometric fiber sensor ... - OSA Publishing

Vol. 25, No. 18 | 4 Sep 2017 | OPTICS EXPRESS 21094

Phase demodulation of interferometric fiber sensor based on fast Fourier analysis XIN FU,1 PING LU,1,* WENJUN NI,1 HAO LIAO,1 DEMING LIU,1 AND JIANGSHAN ZHANG2,3 1Wuhan

National Laboratory for Optoelectronics (WNLO) and National Engineering Laboratory for Next Generation Internet Access System, School of Optics and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China 2Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China [email protected] *[email protected]

Abstract: A demodulation method for interferometric fiber sensors (IFSs) is proposed in this article. The phase variation induced by the measurands can be estimated by calculating the Fourier phase at the intrinsic spatial frequencies of the fiber sensor. Theoretical analysis of the demodulation method is discussed in detail. Numerical simulations are put forward to demonstrate the consistency of the demodulation results under different wavelength sampling interval and noise level, showing a better stability compared with the conventional peak wavelength tracking technique. The proposed method is also experimentally demonstrated by an inline multimode interferometer based on a single-mode fiber (SMF) offset-splicing structure. Experimental results indicate that the phase response of different cladding modes can be analyzed simultaneously. Simultaneous measurement of strain and temperature is realized in our confirmatory experiment by analyzing the phase sensitivities of two selected cladding modes. © 2017 Optical Society of America OCIS codes: (060.2310) Fiber optics; (060.2370) Fiber optics sensors; (280.4788) Optical sensing and sensors.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

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#301288 Journal © 2017

https://doi.org/10.1364/OE.25.021094 Received 29 Jun 2017; revised 15 Aug 2017; accepted 17 Aug 2017; published 21 Aug 2017


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1. Introduction Interferometric fiber sensors (IFSs) are widely investigated due to the remarkable superiorities of high sensitivity and precision. The interferences are formed by two or more beams that have certain phase difference [1–3]. Since the optical wavelength is very short, usually several hundreds of nanometers or a few micrometers, very small optical path difference (OPD) variation can be detected by IFSs, offering relatively high sensitivity and resolution in measurement of parameters such as pressure [4–6], refractive index (RI) [7–11], displacement [12,13], strain [14–18], and curvature [19–21], etc. Wavelength tracking demodulation technique is mostly used for interferometric fiber sensors due to the simple operation and linear response. The mechanism is based on the resonant wavelength shift due to the OPD variation caused by physical parameters. The wavelength shift usually shows a linear response to the measurands. By calibrating the sensitivity, the measurand can be interrogated from the wavelength shift. However, a significant limitation of wavelength demodulation is the accuracy. Since the resonant wavelength is determined by searching the maximum (for resonant peak) or minimum (for resonant dip) intensity value in a certain wavelength window, the results may suffer from unpredictable errors that depend on wavelength sampling rate or spectral noise [22,23]. In order to improve the accuracy, Fast Fourier Transform (FFT) is applied to the optical spectrum to demodulate the sensor signal in the frequency spectrum domain [22–25]. Traditional FFT method to demodulate the fiber sensor is to monitor the peak variations (including both peak intensity variation and peak frequency variation) in the FFT spectrum. It


usually requires a relatively large amount of variation of the measurands. But in some sensing applications, parameters that have very small amount of changes should be detected, such as micro pressure or strain sensing. In these applications, the OPD variation introduced by the measurands is small enough to be neglected compared with the initial OPD value. Therefore, the peak location variation in the FFT spectrum is not able to be recognized. In this article, we propose a demodulation method to calculate the phase variation of the sensor in the Fourier domain. For fiber interferometer, most of the energy is contained in the intrinsic spatial frequencies that are corresponding to the interference components. For this reason, we believe that the information of phase variation between each interference component can be obtained by the Fourier phase at these spatial frequencies. The mechanism is theoretically analyzed. Numerical simulations prove that the demodulation result is insensitive to the spectral noise and sampling interval. Experiment is conducted by testing multimode interferometers to demonstrate the proposed scheme. For multimode interference, phase response of each cladding mode can be obtained by calculating the Fourier phase at each related spatial frequency, so it can be applied to multi-parameters measurement or quasidistributed sensing system. 2. Theoretical analysis To theoretically explain the principle of the demodulation method, we firstly use a model of two-beam interference for analysis. The condition of multimode interference is generalized theoretically and demonstrated in the subsequent experiment. For a two-beam interferometer, the spectrum function can be expressed by Eq. (1). The interference function can be regarded as a trigonometric function of the wavelength within a certain range. In the equation, d represents the optical path difference (OPD). A and B are two constants determined by the optical intensity and coupling ratio between two optical paths. T (λ ) = A + B cos(

2π

(1) ⋅ d ) ≈ A + B cos( βλ ) λ When the OPD of the interferometer is modulated by the environmental parameters, the whole spectrum will show a wavelength shift, as written by Eqs. (2) and (3). d is the OPD variation, while λ is the wavelength shift value. T '(λ )= A + B cos  2π ⋅(d −∆d )= T (λ + ∆λ )  

= ∆λ



λ

λ ⋅ ∆d



≈

(2)

λ0 ⋅ ∆d

(3) d − ∆d d − ∆d From Eq. (3), the shift value is dependent on the wavelength. Within a certain wavelength window that is not too wide, the shift can be regarded as a constant. The free spectrum range (FSR) variation is approximately presented by Eq. (4). Usually the OPD variation is too small compared with the initial OPD value, thus the FSR variation is small enough to be neglected. According to this, we can conclude that the spectrum experiences a constant wavelength shift without shape distortion, as demonstrated by Eqs. (5) and (6), and φ is the additional phase variation item introduced by the wavelength shift. It can be seen from the equation that the wavelength is discretely sampled, just like the spectrum data acquired for analysis in the experiment or practical applications. N and λ0 stand for the number and interval of wavelength sampling points. = ∆FSR λ0 2 (

1 1 ∆d − )≈ ⋅ FSR