Variable-frequency lock-in detection for the suppression of beat noise in Brillouin optical correlation domain analysis

Ji Ho Jeong; Kwanil Lee; Kwang Yong Song; Je-Myung Jeong; Sang Bae Lee

doi:10.1364/OE.19.018721

1. Introduction

Recently there has been much interest in applying distributed Brillouin sensors to temperature or stain measurements in structural health monitoring [1–7] with unique advantages of a long measurement range over 100 km [8, 9] and a high spatial resolution down to sub-cm [10–12]. Brillouin sensors commonly share the operation principle that the shift of a local Brillouin frequency (ν_B) is proportional to the strain and temperature variation applied to a fiber under test, and various types of measurement schemes have been proposed based on spontaneous or stimulated scattering by time- or correlation-domain approach [2–7]. In particular, Brillouin optical correlation domain analysis (BOCDA) is featured by a continuous-wave operation of both pump and probe waves with random accessibility of the sensing position, high-speed operation, and high spatial resolution at the cost of a limited measurement range [6, 10, 13,14].

In BOCDA, a sinusoidal frequency modulation (FM) is applied to both pump and probe waves for localizing the generation of stimulated Brillouin scattering (SBS) to a single position (i.e. correlation peak) within a sensing fiber. The acquisition of the Brillouin gain spectrum (BGS) is carried out by applying various types of lock-in detection with the chopping of the pump or both pump and probe waves [6, 10, 15]. To measure the distribution of the BGS, the position of the correlation peak needs to be swept along the fiber by changing the FM frequency f_m. Since several frequency components appear in the operation of the BOCDA, it is not straightforward to avoid an intensity noise coming from the beating of the frequencies which may lead to the failure of the measurement by distorting the acquired BGS. So far such a beat noise in a BOCDA system has not been analyzed in detail, and no established solution has been reported. In this paper, we analyze the beat noise in an ordinary BOCDA system, and show that the rise of the noise depends on the frequency relation between f_m and a chopping frequency f_l of the lock-in detection. An optimal frequency configuration is suggested based on the analysis, and the experimental confirmation is also provided where variable-frequency lock-in detection is newly applied to a BOCDA system as an effective way to circumvent the beat noise.

2. Theory

In BOCDA, a pump and a probe waves counter-propagating along a fiber under test (FUT) are frequency-modulated with a sinusoidal waveform by direct current modulation of a laser diode (LD) to generate a single correlation peak within the FUT where the stimulated Brillouin scattering (SBS) occurs strongly and exclusively. The Brillouin gain of the probe wave is measured through a lock-in amplifier (LIA) operated synchronously to a reference wave used for the chopping of the pump wave [6]. The BGS is obtained by sweeping the frequency offset between the pump and the probe waves, and the measurement position is swept by changing the FM frequency (f_m) applied to the LD. The direct current modulation of the LD is necessarily accompanied by an intensity modulation in the output at the same frequency f_m, which generally distorts the shape of the measured BGS in the BOCDA [16].

In order to analyze the effect of the intensity modulation on the lock-in detection we assume the measurement configuration of the BOCDA as shown in Fig. 1 .

Fig. 1 The interaction of the pump and the probe waves near a correlation peak in the BOCDA with an intensity chop of a square wave (dashed in red) applied to the pump wave.

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When a sinusoidal intensity modulation is applied, the intensity of the pump and the probe waves at a correlation peak can be expressed as follows:

I_{P u m p} = I_{1} (1 + A \cos ω_{m} t)

I_{P r o b e} = I_{0} (1 + A \cos ω_{m} t)

where A is the modulation depth with

0 \leq A \leq 1

and

ω_{m} \equiv 2 π f_{m}

. According to the basic principle of the BOCDA, the frequency modulations of the pump and the probe waves are always in-phase at a correlation peak [6]. Therefore, it is notable that the intensity modulations of the pump and the probe waves are also in-phase at the correlation peak since the relative phases of the frequency and the intensity modulations are constant under the direct current modulation of a LD. In addition, the shapes of the intensity modulation for the pump and the probe waves are expected to be identical when a common sideband-generation method is adopted for the control of the frequency offset between the pump and the probe waves [3, 6]. If the effective length of the correlation peak (i.e. the spatial resolution of the BOCDA) is Δz and the Brillouin gain is small enough (like ordinary cases), the probe intensities through the correlation peak in the presence (I_a) and the absence (I_b) of the pump wave (i.e. (a) and (b) in Fig. 1) are calculated as follow:

I_{a} = I_{P r o b e} e^{g_{B} I_{P u m p} Δ z} \approx g_{B} Δ z \cdot I_{0} I_{1} {(1 + A \cos ω_{m} t)}^{2} + I_{0} (1 + A \cos ω_{m} t)

I_{b} = I_{0} (1 + A \cos ω_{m} t)

where g_B is the Brillouin gain coefficient of the fiber. We assume the intensity chop of the pump wave is applied in the form of a square wave at an angular frequency ω_l (dashed rectangle in Fig. 1), and the intensity of the probe wave is converted to a voltage by a photo detector (PD) with a conversion coefficient B to be input to the phase-detector of the LIA. Using the square wave at ω_l as a reference wave, the voltage output from the phase-detector of the LIA is calculated by integration as follows:

\begin{array}{l} V_{o u t} = B [\int_{τ}^{τ + \frac{π}{ω_{l}}} I_{a} d t - \int_{τ + \frac{π}{ω_{l}}}^{τ + \frac{2 π}{ω_{l}}} I_{b} d t] \\ = \int_{τ}^{τ + \frac{π}{ω_{l}}} {C_{1} {(1 + A \cos (ω_{m} t + φ (τ)))}^{2} + C_{2} (1 + A \cos (ω_{m} t + φ (τ)))} d t \begin{matrix}  \end{matrix} \\ - \int_{τ + \frac{π}{ω_{l}}}^{τ + \frac{2 π}{ω_{l}}} {C_{2} (1 + A \cos (ω_{m} t + φ (τ)))} d t \end{array}

where τ is a starting time of the phase-detection,

φ (τ) \equiv (ω_{m} - ω_{l}) τ + φ_{0}

is a relative phase between the modulation and the chopping waves (φ₀ is a constant offset),

C_{1} \equiv B g_{B} Δ z I_{0} I_{1}

, and

C_{2} \equiv B I_{0}

. The integration is easily evaluated and the result is rearranged in terms of C ₁ and C ₂ as follows:

\begin{array}{l} V_{o u t} (τ) = \begin{matrix}  \end{matrix} \\ C_{1} {(1 + \frac{A^{2}}{2}) \frac{π}{ω_{l}} + \frac{4 A}{ω_{m}} \cos (ω_{m} τ + φ (τ) + \frac{π ω_{m}}{2 ω_{l}}) \sin (\frac{π ω_{m}}{2 ω_{l}}) + \frac{A^{2}}{2 ω_{m}} \cos (2 ω_{m} τ + 2 φ (τ) + \frac{π ω_{m}}{ω_{l}}) \sin (\frac{π ω_{m}}{ω_{l}})} \\ + C_{2} {\frac{2 A}{ω_{m}} \sin (ω_{m} τ + φ (τ) + \frac{π ω_{m}}{ω_{l}}) - \frac{2 A}{ω_{m}} \sin (ω_{m} τ + φ (τ) + \frac{π ω_{m}}{ω_{l}}) \cos (\frac{π ω_{m}}{ω_{l}})} \end{array}

As seen in Eq. (6), V_out is a function of τ including beat-frequency components such as $2 ω_{m} - ω_{l}$ and $4 ω_{m} - 2 ω_{l}$ In practice, the waveform of the intensity modulation or the intensity chop of the pump wave may include higher-order harmonic terms by modification, which would contribute more frequency components to V_out. Since ω_m is swept according to the position of the correlation peak in distributed measurements, it is possible for some of the beat-frequency components to pass the low-pass filter of the LIA and distort the acquired BGS to give rise to a beat noise.

In particular cases of $ω_{m} = 2 n ω_{l}$ (n is a positive integer) in Eq. (6), all the τ-dependent components of V_out vanish to yield a simple equation as follows:

V_{o u t} = C_{1} (1 + \frac{A^{2}}{2}) \frac{π}{ω_{l}} = B g_{B} I_{0} I_{1} Δ z (1 + \frac{A^{2}}{2}) \frac{π}{ω_{l}}

Therefore, one can expect to acquire a pure BGS that is free from the beat noise of the LIA by controlling f_l according to f_m in the following way:

f_{l} = \frac{f_{m}}{2 n} (n : positive integer)

It is worthwhile to comment on the ω_l-dependence of V_out in Eq. (7). According to Eq. (5), V_out is calculated by the integration during the time interval of 1/f_l for simplicity, so finally includes the term of 1/f_l. However, in common use of a lock-in amplifier, the integration time (i.e. time constant) is fixed and V_out does not depend on the chopping frequency f_l. Theoretically it is also possible to apply a phase modulation with an external modulator to circumvent the spurious intensity modulation. However, such an external modulation is not a practical solution since one would need an arbitrary function generator with the operation bandwidth as much as the modulation amplitude (> 10 GHz, in general).

3. Experimental results

We built up a BOCDA system to confirm our theoretical analysis as shown in Fig. 2 . A 30 m single-mode fiber (SMF) was used as a FUT, the v_B of which was about 10.853 GHz. A 1548 nm distributed feedback LD (DFB-LD) was used as a light source, and a sinusoidal frequency modulation was applied to generate a correlation peak within the FUT. The modulation frequency f_m was varied between 2.993 and 3.004 MHz depending on the measurement position (i.e., the correlation peak), and the modulation amplitude (Δf) was about 3.4 GHz, from which the spatial resolution and the measurement range were estimated to be about 10 cm and 32 m, respectively. The variation of the output power of the LD is depicted in Fig. 3 , where the parameter A in Eq. (2) is measured to be about 0.6. The output from the LD was divided into two beams by a 50/50 coupler. One of the beams was used as the Brillouin pump wave after passing through a 10 km delay fiber to control the order of correlation peak and a high power erbium doped fiber amplifier (EDFA) to boost up the pump power to 23 dBm. The other beam was injected into a single sideband modulator (SSBM) which was driven by microwave signal generator, so that the first lower sideband, serving as the probe wave, was generated and propagated along the FUT in the opposite direction to the pump wave. Additionally, a polarization switch (PSW) was inserted after the SSBM for suppressing the polarization dependence of the Brillouin signal [17], and another EDFA was used to compensate for the insertion loss of the SSBM. The pump light was chopped by an intensity modulator with a square waveform for lock-in detection. A 125 MHz photo receiver was used as a detector and the BGS was obtained through a LIA (SR844). In the distributed measurement, the BGS was acquired every 10 cm along the FUT, sweeping Δv from 10.3 to 11.3 GHz. The sweep time was 0.1 s and the number of data point for a single BGS was 1200.

Fig. 2 Experimental setup of a BOCDA system.

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Fig. 3 Sinusoidal intensity modulation of the output from the DFB LD with a direct current modulation of f_m = 3 MHz.

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At first, the time constant and the output filter of the LIA were set 300 μs and 24 dB/octave, respectively, as a common configuration for BOCDA systems, and the BGS were measured varying f_l under f_m fixed to 3 MHz so that the ratio f_m to f_l was swept from 1 to 20 with a step of 0.01. Figure 4 shows some of the measured BGS together with corresponding shapes of the pump wave. As seen in Fig. 4(a) and 4(b), strong distortions of the BGS with low and high frequency noises appear in some cases, while a clear BGS is also observed in other cases like Fig. 4(c) depending on the frequency ratio. It is notable that the amplitude of the beat noise periodically became larger when the frequency ratio approaches odd numbers as exampled by Fig. 4(a) and 4(b) and minimized near the ratio of even numbers like Fig. 4(c). We think this feature could be explained by Eq. (6) where the acquired BGS becomes temporally and also spectrally modulated due to the τ-dependent parts of V_out which periodically vanishes at frequency ratios of even numbers. It is also remarkable that in this first measurement the occurrence of the beat noise was limited to narrow frequency bands near particular frequencies of f_l corresponding to the range within ± 0.02 in terms of the frequency ratios (for example, 3 ± 0.02, 5 ± 0.02 etc.), which is due to the existence of the output filter in the LIA suppressing high frequency beat noises.

Fig. 4 Examples of the measured Brillouin gain spectrum (right) and the corresponding pump waveform (left) with different frequency ratio f_m to f_l: (a) 17 (b) 3.01 and (c) 2.

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For inspecting the detailed properties of the beat noise, we turned off the output filter of the LIA and measured the BGS varying f_l under f_m fixed to 3 MHz so that the ratio f_m to f_l was swept from 1 to 20 with a step of 0.1. This time, the BGS was acquired 20 times for each f_l. Figure 5(a) depicts the standard deviation (σ) of the signal amplitude in the 20 measurements as a function of the frequency ratio which indicates the amplitude of the beat noise. One can clearly see that the noise amplitude fluctuates with a period of 2 and was minimized at the frequency ratio of even numbers (red spots), which matches well with our theoretical expectation in Eq. (8). Figure 5(b) is the standard deviation of the Brillouin frequency ν_B fitted from the BGS of the 20 repetitive measurements as a function of the frequency ratio which indicates the measurement error. This result shows that the measurement error is also decreased to below ± 1 MHz when the frequency ratio is chosen among even numbers (red spots) as expected in Eq. (8). On the other hand, the beat noise tends to reach local maxima when the frequency ratio approaches odd numbers, which is partly explained by the fact that effects of τ-dependent terms in Eq. (6) related to $\sin (π ω_{m} / 2 ω_{l})$ and $\cos (π ω_{m} / ω_{l})$ are maximized at such cases.

Fig. 5 (a) Standard deviation of the signal amplitude in 20 repetitive measurements as a function of f_m / f_l. (b) Standard deviation of the detected Brillouin frequencies in 20 repetitive measurements as a function of f_m / f_l. Note that red spots correspond to f_m / f_l of even numbers, and the insets are the zoomed views.

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From the above results, it is expected that the beat noise can be minimized by varying f_l of the lock-in detection in such a way that the ratio of f_m to f_l remains equal to an even number during the position sweep in BOCDA systems. To confirm the performance of the proposed scheme, we carried out distributed measurements with BOCDA systems based the ordinary and the variable frequency lock-in detection. The time constant and the output filter of the LIA were reset to 300 μs and 24 dB/octave, respectively. In the case of the ordinary lock-in detection f_l was fixed to a prime number (1.004987 MHz), and in the case of the variable frequency lock-in detection f_l was varied according to Eq. (8) with the frequency ratio of 4. The measurement results are shown in Fig. 6 , where the acquired BGS’s were strongly distorted at some positions (i.e. f_m’s) by the beat noise in the ordinary lock-in detection as depicted in Fig. 6(a). On the contrary, it is confirmed that stable and clear BGS’s are maintained along the FUT with the variable frequency lock-in detection as shown in Fig. 6(b).

Fig. 6 Comparison of the distributed measurements of the BGS along a 30 m FUT by BOCDA system based on (a) ordinary lock-in detection with a fixed chopping frequency f_l = 1.004987 MHz and (b) variable frequency lock-in detection with f_l = f_m /4.

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4. Conclusion

In summary, we have theoretically and experimentally analyzed the beat noise phenomenon related to the intensity modulation and the lock-in detection in the Brillouin optical correlation domain analysis, and newly proposed the variable frequency lock-in detection as a simple way to circumvent the beat noise. Additionally, we think our scheme can be applied to a standard modulator with double sidebands as well as the SSBM, since the rise of the beat noise is connected only with the frequency relation between the current modulation of the LD and the chopping for the lock-in detection.

We expect our new scheme will be useful in stabilizing the operation of BOCDA systems in the strain monitoring of civil structures, especially for long-range measurement where large variation of the FM frequency is necessary for the position sweep.

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Variable-frequency lock-in detection for the suppression of beat noise in Brillouin optical correlation domain analysis

Abstract

1. Introduction

2. Theory

3. Experimental results

4. Conclusion

References and links

Cited By

Figures (6)

Equations (8)

Optics Express