IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 23, DECEMBER 1, 2012
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PGC Demodulation Technique With High Stability and Low Harmonic Distortion Guo-qing Wang, Tuan-wei Xu, and Fang Li
Abstract— In the field of interferometric fiber-optic sensing, the differential-cross-multiplication type of phase-generated carrier (PGC) demodulation technique has a low stability defect and the arc tangent PGC demodulation technique has a high harmonic distortion defect. Thus, we present an improved PGC demodulation technique based on arc cotangent function and differential-self-multiplying. Both theoretical and experimental results show that the interferometric fiber-optic sensing system that has adopted the improved PGC demodulation technique has the merits of high stability of resisting the rapid change of light intensity and low harmonic distortion; experimental results show that √ the demodulation system has a resolution of 2 × 10−5 rad/ Hz, a total harmonic distortion less than 0.1%, a linearity of better than 0.9999, and a dynamic range of 112 dB at 50 Hz. Index Terms— Optical fiber interference, optical fiber measurement applications, optical signal processing, phase modulation.
I. I NTRODUCTION
I
NTERFEROMETRIC fiber-optic sensors have attracted considerable research interest due to their advantages of high sensitivity, high stability, high linearity, and easiness of multiplexing [1]–[3]. They have good application prospect in the field of sonar systems, seismic detection and natural resources exploration. The high resolution phase demodulation for interfero-metric fiber-optic sensor is based on interferometry. An interferometric fiber-optic sensor is employed to convert the external signal into the phase shift [2], [3]. Several phase demodulation techniques have been reported, including active homodyne, passive homodyne using a 3 × 3 coupler or phase generated carrier (PGC), and heterodyne [4]–[6]. The PGC demodulation technique is considered as the most widely used method among them due to the distinct advantages of high resolution, large dynamic range, and the capability of real-time demodulation for large-scale interferometric fiber-optic sensors array. In the PGC demodulation technique, a high-frequency sinusoidal phase modulation is applied to the tunable laser to generate a phase carrier, which up-converts the desired phaseshift signal onto the sidebands of the carrier frequency. By Manuscript received July 4, 2012; revised September 7, 2012; accepted September 12, 2012. Date of publication September 27, 2012; date of current version November 20, 2012. This work was supported in part by the National Science Foundation of China and in part by the Science and Technology Innovation Program of Beijing. The authors are with the Optoelectronics System Laboratory, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 912, China (e-mail:
[email protected];
[email protected];
[email protected]). Digital Object Identifier 10.1109/LPT.2012.2220129
1×2 Coupler Tunable Laser PGC Carrier
PC
sensors
A/D
PD&Amplifiers Fig. 1. Interferometric fiber-optic sensing system based on PGC demodulation technique.
detecting one odd harmonic and one even harmonic of the PGC interference signal, a pair of quadrature components containing the phase-shift signal are then acquired, with which the bias-induced-fading can be overcome. To recover the phase shift of interferometric fiber-optic sensors from the quadrature components, the traditional PGC demodulation technique employs the differential-and-cross-multiplying demodulation technique (PGC-DCM) [7] or the arctangent demodulation technique (PGC-Arctan) [8]. However, the PGC-DCM demodulation technique is correlated with the light intensity and has poor stability when light intensity changes rapidly [9], while the PGC-Arctan demodulation technique has serious harmonic distortions when the PGC modulation depth C deviates from 2.63 rad. Recently, we have proposed an improved PGC demodulation technique based on arc cotangent function and differential-self-multiplying (PGC-Arccot-DSM), which has both high stability and low harmonic distortion. II. P RINCIPLES Figure 1 shows the interferometric fiber-optic sensing system based on PGC demodulation technique. The tunable laser is modulated by the PGC carrier circuit board, which generates a high frequency sinusoidal signal, to generate phase carrier. The modulated light enters interferometric fiber-optic sensor array via 1 × 2 coupler. The interferom-etric fiberoptic sensor adopts the structure of unbalanced Michelson, with Faraday rotation mirrors at its ends to eliminate the decline phenomenon of interference signals, which induced by the polarization change of light. The external signals
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 23, DECEMBER 1, 2012
(a)
(b) Fig. 2. Schematic of PGC demodulation technique. (a) PGC-DCM demodulation technique. (b) PGC-Arctan demodulation technique.
are converted to the phase shifts of the interference signals simultaneously by interferometric fiber-optic sensor via the structure of unbalanced Michelson. The modulated interference signal of each channel is detected by a low-noise p-i-n photodiode and an amplifier circuit. Then signals are sampled simultaneously using an analog-to-digital converter (ADC), and the digital data is transmitted into a personal computer (PC) to perform the PGC demodulation technique to recover the external signals.
Fig. 3.
Schematic of the PGC-Arccot-DSM demodulation technique.
where a is a constant, for the result is related with the input light intensity and the visibility of the interference, it has low stability when the light intensity changes rapidly. For PGC-Arctan demodulation technique, Eq.(4) is divided by Eq.(5), then unwrapping the phase from tangent function and after band-pass filter, the result of PGC-Arctan is obtained as Ar ctan[ J1 (Cs )/J2 (Cs )tan(ϕs + ϕ0 )] − ϕ0 .
(5)
A. Principle of Traditional PGC Demodulation Technique
From the above result, we can see that J1 (Cs ) and J2 (Cs ) is no longer equal when C deviates from 2.63, thus leads a high harmonic distortion.
The output of the interference light intensity of interferometric fiber-optic sensor is
B. Principle of Improved PGC Demodulation Technique
Is = I0 [1 + vcos(Cs cosω0 t + ϕs + ϕ0 )]
(1)
where the subscript sindicates the channel serial number, s = 1, 2, 3, 4 represents the sensor; I0 is the light intensity; v is the visibility of the interference, v
