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Common-path dual-wavelength quadrature phase demodulation of EFPI sensors using a broadly tunable MG-Y laser

Qiang Liu, Zhenguo Jing, Ang Li, Yueying Liu, Zhiyuan Huang, Yang Zhang, and Wei Peng

Open Access Open Access

Abstract

A common-path dual-wavelength phase demodulation technique for extrinsic Fabry–Perot interferometric (EFPI) sensors is proposed on the basis of a broadly tunable modulated grating Y-branch (MG-Y) laser. It can address the three main concerns of existing dual-wavelength phase interrogation methods: the imbalances and disturbances caused by two optical paths utilizing two lasers or two photodetectors, the restrictions between two operating wavelengths and the cavity length of EFPI, and the difficulty in eliminating the direct current (DC) component of the interferometric fringe. Dual-wavelength phase interrogation is achieved in a common optical path through high-speed wavelength switching. Taking advantage of the MG-Y laser’s full spectrum scanning ability (1527 ∼ 1567 nm), initial cavity length and DC component can be directly measured by white light interferometry. Two quadrature wavelengths are then selected to perform high speed phase demodulation scheme. Three polyethylene terephthalate (PET) diaphragm based EFPI acoustic sensors with cavity lengths of 127.954 µm, 148.366 µm and 497.300 µm, are used to demonstrate the effectiveness.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

High-performance dynamic sensing of acoustic or vibration signals has been widely used in various applications such as non-destructive testing [1], process control [2] and structural condition monitoring [3,4]. Fiber optic extrinsic Fabry–Perot interferometric (EFPI) sensors have been extensively investigated as a promising high-speed dynamic sensor technology owing to their unique features of compact size, immunity to electromagnetic interference, remote sensing and multiplexing ability [5–7]. The demodulation techniques for extracting target dynamic signals from the output of EFPI sensors is one of the crucial points to be studied. The spectrum based white light interferometry (WLI) demodulation method is generally applied by a broadband light source and an optical spectrum analyzer (OSA). Absolute cavity lengths can be interrogated from the full spectrum by a cross-correlation algorithm or fast Fourier transformation [8–10]. The WLI method usually attains high precision and large dynamic range, but the high system cost and slow measurement speed limit its application. Intensity demodulation methods employ a laser whose wavelength is fixed at the quadrature point (Q-point) to ensure the maximum sensitivity as well as the linear dynamic range. However, the Q-point may experience large, but relatively low-frequency environmental drifts caused by ambient temperature or static background pressure variations, requiring a complex tuning mechanism with feedback control [11,12]. Moreover, the dynamic range is limited owing to the narrow linear range [13]. Phase demodulation methods, such as phase generated carrier (PGC) methods [14] and passive quadrature phase-shifted demodulation methods [15,16] can address these shortcomings of WLI and Q-point intensity demodulation methods. Recently, researchers have shown an increased interest in the dual-wavelength phase interrogation scheme [17–19] for its advantages of high-frequency response, large dynamic range and high stability.

However, most dual-wavelength quadrature phase demodulation methods utilize two lasers or two photodetectors (PD) [16,17,20,21], bringing power imbalances between the two paths. The imbalances maybe induced by the optical path difference variations relating to ambient temperature or pressure fluctuations, and the different responsivity of two PDs. In order to obtain two orthogonal signals, the two wavelengths need to satisfy a quarter of the free space range (FSR), thereby confining the length of EFPI cavity. In recent years, direct current (DC) compensation or estimated algorithms [21–25] have been reported to solve the restrictions between the EFPI cavity length and the two operating wavelengths. EFPIs with different cavity lengths can be applied in the methods utlizing two fixed wavelengths. A novel ellipse fitting algorithm was used. However, it might introduce additional estimation errors or loss of sensitivity at the same time. Xia [22] established a wavelength-switched phase demodulation system to track the phase variations in one optical path. Wavelength switching at a speed of 10 kHz is achieved by electro-optic modulators (EOMs) and a polarizer, increasing the system complexity and instability. Moreover, the polarization switching device limits its frequency response. Therefore, there is still a lack of universal, practical and high-performance demodulation techniques up to now.

Vernier tuned distributed Bragg reflector (VT-DBR) lasers were developed for telecommunications applications. They are one of the most promising wavelength tunable lasers for their characteristics of broad tuning range (>40 nm), high-speed switching (<20 ns) and high side mode suppression ratio (SMSR) (>40 dB) [26,27]. In addition to the telecommunications field, they are also used in optical coherence tomography (OCT) and lidar applications [28–30]. Their high-speed switching, linear scanning and narrow linewidth characteristics are very important in various fiber sensing applications. Among various types of VT-DBR lasers, the sampled grating DBR (SG-DBR) laser and modulated grating Y-branch (MG-Y) laser [31] are widely used. In this paper, we proposed a common-path dual-wavelength quadrature phase demodulation technique utilizing an MG-Y tunable laser. The MG-Y laser is electronically tuned and precisely switched without mechanical movement, resulting in high wavelength stability and repeatability [29]. Thanks to its wide wavelength tuning range (1527 ∼ 1567 nm), initial cavity lengths of EFPI sensors and the DC component can be directly measured through full spectrum scanning. Two wavelengths with accurate quadrature phase difference are then chosen to perform high-speed quadrature phase demodulation of dynamic signals. Wavelength switching frequency is up to 500 kHz under the current configuration. Two orthogonal signals for extracting phase variations are separated and recovered in the time domain. The proposed system is highly flexible and adaptable. It is capable of demodulating the phase variations of polyethylene terephthalate (PET) diaphragm based EFPI acoustic sensors with different cavity lengths in one optical path completely.

2. Setup and principles

Schematic diagram of the EFPI demodulation setup is illustrated in Fig. 1. The light beam emitted from a MG-Y laser is guided into the acoustic sensor probe via a circulator. Then, the backreflected signals are detected by a PD. We use a field programmable gate array (FPGA) for precise wavelength control and simultaneous data acquisition. The collected data is uploaded to a computer for phase demodulation. There are two modulated grating reflectors to extand the tuning range based on vernier effect. Output wavelength is determined by injection currents of three sections: the right reflector section (IRR), the left reflector section (ILR) and the phase section (IPH) [32–34]. Injection current of the semiconductor optical amplifier segment (ISOA) enables fine adjustment of output power. More details about its tuning characteristics are introduced in the experimental section. First of all, full spectrum scanning is carried out to get the interference spectrum of acoustic sensor. The initial cavity length, FSR and the DC component can be measured. Output wavelength is linearly scanned from 1527 nm to 1567 nm with an interval of 8 pm. Two quadrature wavelengths are then chosen to achieve high-speed phase interrogation. The wavelength switched continuously at a rate of 500 kHz. Unlike traditional dual-wavelength passive demodulation methods which utilized two lasers or two PDs, the two orthogonal signals are separated and extracted in the time domain. PET diaphragm based EFPI acoustic sensors with cavity lengths of 127.954 µm, 148.366 µm and 497.300 µm were used to verify the performance of the technique. The thickness and diameter of the PET diaphragm are 6 µm and 3.4 mm, respectively.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the common-path dual-wavelength quadrature phase demodulation system. (Inset) Diagram of the EFPI sensor with a polyethylene terephthalate (PET) diaphragm.

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Fiber optic EFPI can be considered as a low-finesse two-beam interferometer. Figure 2 presents the interference spectrum of an EFPI acoustic sensor obtained by wavelength scanning of Mg-Y laser. Cavity length of EFPI was calculated as 148.366 µm by a cross-correlation algorithm [10]. The intensity of reflected interferential light corresponding to λ1 and λ2 can be expressed as

$${I_1} = A + B\cos (\frac{{4n\pi }}{{{\lambda _1}}}L + {\varphi _0})$$
$${I_2} = A + B\cos (\frac{{4n\pi }}{{{\lambda _2}}}L + {\varphi _0})$$

 figure: Fig. 2.

Fig. 2. Interference spectrum of the EFPI acoustic sensor with a cavity length of 148.366 µm.

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Where A and B are the DC value and the fringe visibility, respectively. L is the cavity length, φ0 is the initial phase, n is the effective refractive index of the cavity (for air, n = 1). We use L0 to represent the initial cavity length when there is no external vibration signal at the beginning. A, B and L0 can be measured directly from the interference spectrum. The phase difference between the two wavelengths can be defined as β, to get two quadrature signals, let

$$\beta = 4\pi nL(\frac{1}{{{\lambda _1}}} - \frac{1}{{{\lambda _2}}}) \approx 4\pi n{L_0}(\frac{1}{{{\lambda _1}}} - \frac{1}{{{\lambda _2}}}) = \frac{\pi }{2} + k\pi$$
Where k is an integer. To obtain the highest sensitivity and reduce the complexity of wavelength selection [17,35], k = 0, so that β is π/2. The wavelength interval between λ2 and λ1 is
$$\Delta \lambda = {\lambda _2} - {\lambda _1} = \frac{{{\lambda _1}{\lambda _2}}}{{8n{L_0}}} \approx \frac{{{\lambda _1}^2}}{{8n{L_0}}}$$
For convenience, we make λ1 at a fix wavelength, for example, 1541.579 nm. For a given initial cavity length L0, λ2 can be determined according to Eq.u. (4). If L0 = 148.366 µm, λ2 is calculated as 1543.581 nm. Equation (2) can then be expressed as
$${I_2} = A + B\cos (\frac{{4n\pi }}{{{\lambda _1}}}L + {\varphi _0} - \frac{\pi }{2}) = A + B\sin (\frac{{4n\pi }}{{{\lambda _1}}}L + {\varphi _0})$$
Let
$${\varphi _1} = \frac{{4n\pi }}{{{\lambda _1}}}L$$
Equation (1) and (5) can be written as
$${I_1} = A + B\cos ({\varphi _1} + {\varphi _0})$$
$${I_2} = A + B\sin ({\varphi _1} + {\varphi _0})$$
According to Eq. (7) and (8), the phase difference can be calculated by a differential cross multiplication (DCM) method [36] or an arctangent method [18]. In this paper, we utilize an arctangent algorithm to extract the phase signals.
$${\varphi _1} + {\varphi _0} = \arctan (\frac{{{I_2} - A}}{{{I_1} - A}}) + m\pi$$
The φ0 is considered constant, m is a phase compensation integer value used for unwraping the large phase variations. The dynamic phase variations caused by vibration or acoustic signals can be recovered by the calculation of Δφ1. One of the main drawbacks of Q-point intensity demodulation is its limited dynamic range, which appears signal distortion when measuring strong acoustic signals. In this paper, continuous phase variations can be monitored and recovered by phase compensation for high dynamic range measurements [37]. The DC value, A, is measured directly by full spectrum scanning based on the same configuration. Moreover, based on linear wavelength scanning of the MG-Y laser, A and the initial cavity length L0 can be easily re-measured, the two selected output wavelengths can be calibrated to meet the quadrature phase condition when needed, making it suitable for engineering applications in harsh environments.

3. Experimental results and discussion

Linear wavelength sweeping and fast switching is the foundation of common-path quadrature phase demodulation technique. Therefore, precise wavelength output and switching are the prerequisites for this work. The tuning mechanism of MG-Y lasers is much more complicated than that of distributed feedback (DFB) lasers. Output wavelength of the laser is controlled by three injection currents that are applied to IRR, ILR, and IPH [32–34]. In order to determine the initial lookup table of the injected current corresponding to each target wavelength, we have established an automated calibration system based on an optical wavelength meter (Yokogawa, AQ6151) to achieve closed-loop feedback. The calibration system is shown in Fig. 3(a). At the beginning, ISOA was set as a constant value. Tuning paths of three injection currents are shown in Fig. 3(b). With the decreasing of IRR or ILR, the output intensity increased as a result of decreased absorption by injected carriers [28], so that the output intensity will have a saw-tooth like variations. The intensity was then calibrated to a constant value (10.51 dBm) by fine tuning of SOA current ISOA as indicated in Fig. 3(c). After the calibration, the standard deviation (SD) of the output intensity is about 0.028 dBm. It can be considered that the laser output intensity is flat throughout the C-band.

 figure: Fig. 3.

Fig. 3. Automated calibration of MG-Y lasers. (a) Diagram of the laboratory-built automated calibration system. (b) Tuning paths of three injection currents for creating a linear wavelength ramp between 1527 nm and 1567 nm. (c) Output intensity and SOA-injection current ISOA after intensity calibration.

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An EFPI acoustic sensor (148.366 µm cavity length) was interrogated by the proposed common-path dual-wavelength phase demodulation method to verify its demodulation performance. WLI interrogation was firstly carried out to get the interference spectrum. In WLI mode, there is no external acoustic disturbance applied to the EFPI probe. The DC component can be measured directly. Then switched to dual-wavelength phase interrogation mode. Two quadrature wavelengths were chosen (λ1 = 1541.579 nm and λ2 = 1543.581 nm). The channel numbers corresponding to the selected wavelengths are sent to the FPGA program by host computer, enabling two wavelengths switching and simultaneous data acquisition. In the current configuration, the wavelength switching frequency is up to 500 kHz. A signal generator and a speaker were used to generate the acoustic signals. Firstly, the speaker was driven by a 15 kHz sinewave. Two orthogonal signals extracted from the time domain are presented in Fig. 4(a). Owing to the deviation from the linear operation range, the extracted waveform corresponding to λ1 has a distortion compared with that for λ2. The vibrational phase signal, Δφ1, was recovered successfully, as presented in Fig. 4(b). Its power spectrum in the frequency domain is displayed in Fig. 4(c). It can be seen that the demodulated phase variation frequency is 15 kHz, which is consistent with the external acoustic signals. The signal to noise ratio (SNR) at 15 kHz is approximately 75 dB. To verify the demodulation stability of the demodulator, the same acoustic signal was measured 100 times. The peak-to-valley amplitude values of demodulated phase variations are plotted in Fig. 4(d). The relative standard deviation (RSD) of the peak-to-valley amplitude values is about 0.49%, which indicates that the common-path quadrature phase demodulation system can work stably.

 figure: Fig. 4.

Fig. 4. Demodulation of an EFPI acoustic sensor with cavity length of 148.366 µm at 15 kHz acoustic signals: (a) Extracted orthogonal signals corresponding to λ1 and λ2. (b) Demodulated phase variations. (c) Power spectrum in the frequency domain. (d) Peak-to-valley amplitude fluctuations of the demodulated phase variations at 15 kHz acoustic signals.

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Then the EFPI probe was driven at 1 kHz and 8 kHz acoustic signals respectively. The corresponding time domain phase waveforms and power spectrums are shown in Fig. 5. Indicating that the system can correctly demodulate signals at different applied acoustic frequency. Since the wavelength switching frequency is 500 kHz, dual-wavelength phase demodulation frequency is 250 kHz. In practical applications, the sampling frequency should be 5 times larger than the detected acoustic frequency, so that the maximum detectable acoustic frequency is about 50 kHz in this work.

 figure: Fig. 5.

Fig. 5. Power spectrum of phase variations at 1 kHz and 8 kHz acoustic signals. (Inset) Time domain waveform signals. (a) 1 kHz. (b) 8 kHz.

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One of the most concerned shortcomings of conventional dual-wavelength phase demodulation methods is the inability to demodulate another EFPI sensor, usually with a different cavity length. Thanks to the wide tuning range of Mg-Y lasers, this disadvantage can be excluded. For another EFPI sensor, after a simple and fast calibration of full-spectrum scanning, two wavelengths with quadrature phase condition will be redefined. Since we used a WLI method to calculate the initial cavity length of the EFPI sensor, considering the wavelength scanning range of the MG-Y laser, the theoretical minimum cavity length that can be demodulated is about 30 µm. Which demonstrates the advantages of this quadrature phase demodulation system in demodulating short cavity EFPI acoustic sensors. Three EFPI acoustic sensors with different cavity lengths (127.954 µm, 148.366 µm and 497.300 µm) were used to verify the adaptability of our demodulation system. Figure 6 displays their frequency domain power spectrum at 8 kHz acoustic signals. We can see that the acoustic signals applied to all three EFPI sensors can be successfully detected and the three responses are highly consistent.

 figure: Fig. 6.

Fig. 6. Power spectrum of three EFPI acoustic sensors with cavity lengths of 127.954 µm, 148.366 µm and 497.300 µm at 8 kHz acoustic signals.

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In fact, the proposed method is an intelligent combination of the traditional WLI demodulation scheme and the two-wavelength quadrature phase demodulation scheme. WLI demodulation is performed to directly measure the DC component of the interferometric fringe and calculate the initial cavity length of EFPI sensors. Dual-wavelength quadrature phase demodulation is performed to achieve high-speed phase interrogation. Taking advantages of the broad wavelength tuning range and high-speed switching capability of MG-Y lasers, these two practical demodulation methods can be implemented in one compact and robust system, addressing the drawbacks of existing WLI and dual-wavelength phase demodulation techniques.

4. Conclusion

In summary, we have demonstrated a highly flexible common-path dual-wavelength quadrature phase demodulation technique for EFPI sensors. High-speed phase variations can be tracked in a single optical path completely. A widely tunable monolithic MG-Y laser is used to achieve high-speed wavelength switching. Then two orthogonal signals for extracting phase variations are separated in the time domain. Thanks to MG-Y laser’s full spectrum scanning capability, initial cavity length of the EFPI sensor and the DC component can be measured by WLI interrogation without additional OSA, which is very promising in practical engineering applications. The proposed technique is capable of demodulating different lengths of EFPI cavity. Two wavelengths with accurate quadrature phase relationship are selected to perform high-speed phase demodulation for each specific EFPI sensor probe. Considering its high applicability and stability in demodulating dynamic signals, further research will focus on its application in photoacoustic spectroscopy and photoacoustic imaging.

Funding

National Natural Science Foundation of China (61520106013, 61727816); Dalian University of Technology (DUT18RC016).

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Figures (6)
Fig. 1.
Fig. 1. Schematic diagram of the common-path dual-wavelength quadrature phase demodulation system. (Inset) Diagram of the EFPI sensor with a polyethylene terephthalate (PET) diaphragm.

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Fig. 2.
Fig. 2. Interference spectrum of the EFPI acoustic sensor with a cavity length of 148.366 µm.

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Fig. 3.
Fig. 3. Automated calibration of MG-Y lasers. (a) Diagram of the laboratory-built automated calibration system. (b) Tuning paths of three injection currents for creating a linear wavelength ramp between 1527 nm and 1567 nm. (c) Output intensity and SOA-injection current ISOA after intensity calibration.

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Fig. 4.
Fig. 4. Demodulation of an EFPI acoustic sensor with cavity length of 148.366 µm at 15 kHz acoustic signals: (a) Extracted orthogonal signals corresponding to λ1 and λ2. (b) Demodulated phase variations. (c) Power spectrum in the frequency domain. (d) Peak-to-valley amplitude fluctuations of the demodulated phase variations at 15 kHz acoustic signals.

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Fig. 5.
Fig. 5. Power spectrum of phase variations at 1 kHz and 8 kHz acoustic signals. (Inset) Time domain waveform signals. (a) 1 kHz. (b) 8 kHz.

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Fig. 6.
Fig. 6. Power spectrum of three EFPI acoustic sensors with cavity lengths of 127.954 µm, 148.366 µm and 497.300 µm at 8 kHz acoustic signals.

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Equations (9)

Equations on this page are rendered with MathJax. Learn more.

I 1 = A + B cos ⁡ ( 4 n π λ 1 L + φ 0 )
I 2 = A + B cos ⁡ ( 4 n π λ 2 L + φ 0 )
β = 4 π n L ( 1 λ 1 − 1 λ 2 ) ≈ 4 π n L 0 ( 1 λ 1 − 1 λ 2 ) = π 2 + k π
Δ λ = λ 2 − λ 1 = λ 1 λ 2 8 n L 0 ≈ λ 1 2 8 n L 0
I 2 = A + B cos ⁡ ( 4 n π λ 1 L + φ 0 − π 2 ) = A + B sin ⁡ ( 4 n π λ 1 L + φ 0 )
φ 1 = 4 n π λ 1 L
I 1 = A + B cos ⁡ ( φ 1 + φ 0 )
I 2 = A + B sin ⁡ ( φ 1 + φ 0 )
φ 1 + φ 0 = arctan ⁡ ( I 2 − A I 1 − A ) + m π
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