Multiplexing of fiber-optic ultrasound sensors via swept frequency interferometry

Haniel Gabai; Idan Steinberg; Avishay Eyal

doi:10.1364/OE.23.018915

1. Introduction

Ultrasound (US) based techniques for measurements and imaging are widely used in a broad spectrum of research fields, ranging from Non-Destructive Testing (NDT) and Structural Health Monitoring (SHM) [1], to biomedical ultrasonography [2] and even underwater acoustics and sonar applications [3]. Traditionally, ultrasound transducers technology is based on piezoelectric materials (e.g. Lead Zirconium Titanate - PZT or Polyvinylidene Fluoride - PVDF) [4]. Despite their excellent attributes, these sensors suffer from several inherent disadvantages. They require electrical contacts and they are usually rigid. Hence, their integration into structures or in-vivo devices is quite challenging. They are prone to electromagnetic interference (EMI) and they are opaque. Additionally, detection sensitivity is proportional to the area of the sensing element. As a result, the use of piezo-electric transducers in applications where small sensors are required is limited. This poses serious restrictions on ultrasonography which relays on tens or even hundreds of sensors which should be compactly wrapped into a small probe [5].

Another family of sensors which was studied extensively in recent years is based on optical fibers [6]. In contrast to the conventional ultrasonic sensors, fiber based sensors are practically immune to EMI. Additionally, they are transparent, small-sized, flexible and can operate under extreme conditions. Ultrasound fiber sensors can be operated as either point-detectors [7] or line-detectors. Recently, the theory of ultrasound tomography based on line-detectors was formulated (separately) by Rosenthal and Burgholzer [8,9] and experimentally demonstrated by Bauer-Marschallinger et al. [10]. Moreover, fiber-optic ultrasound sensing is highly compatible with another emerging technology known as photo-acoustics or opto-acoustics which is based upon the thermo-elastic expansion due to absorption of optical excitation [11]. Photoacoustics is intensively studied today predominantly for applications of bio-medical imaging where both functionality, high penetration-depth and speckle-free imaging are desired. Together, photoacoustics and optical fiber sensors can be used to implement all optical networks of ultrasound probes which can be used in situations where traditional piezoelectric probes are limited [12].

In light of the aforementioned advantages, significant efforts have been made in recent years to facilitate reliable, fiber-based, ultrasonic sensors [7,12–15]. Several approaches exist for ultrasonic fiber sensing. One approach is based on two-arms interferometers, where the sensing arm is exposed to the acoustic wave [10,12,13].Consequently, pressure induced phase variations are translated to measurable intensity fluctuations which are correlated with the acoustic wave. Another approach is to use optical resonators such as Fiber Bragg Gratings (FBGs) or etalons [7,16–18]. In this type of systems, when the acoustic wave perturbs the resonating sensing element, the resonance frequency shifts and with it the intensity of the light which is transmitted-through or reflected-by the resonator.

Although both types of sensors have shown great potential for ultrasound sensing, the important issue of implementing a multiple transducer arrays (i.e. multiplexing) remains a major challenge. Multiplexing several resonator-based-sensors can be achieved by using an equal number of narrowband lasers [19]. However, such approach is cumbersome and costly, and thus impractical for implementing a large number of sensors such as in commercial piezo-electric arrays. Another approach is to use a wideband source and interrogate several resonators simultaneously [15]. This, however, also involves a bulky and expensive optical setup. Moreover, methods based on such sources are often affected by excessive noise due to the stochastic nature of the wideband probing light. Although, as was recently shown, the use of wideband pulse interferometry can alleviate this issue [18]. In the case of interferometer based sensors, multiplexing is also very difficult to achieve. Regardless to the multiplexing method used, each sensor in the array has to be stabilized to its quadrature point [10,20]. This is crucial for achieving sensitive and linear measurement. Such stabilization further increases both system complexity and costs and prohibit the possibility of a large sensor array.

Recently, we proposed a new interferometric approach for US sensing and multiplexing [21]. The method is based on Swept Frequency Interferometry (SFI) interrogation of fiber based US sensors [22]. It can be implemented in either reflection or transmission modes. In reflection mode, which is the one that was implemented in the current work, the method is equivalent to using Optical Frequency Domain Reflectometry (OFDR) [23] to interrogate a parallel connection of sensing fibers. This work, further expands the initial concept and characterizes the performance of the proposed method. A robust normalization procedure is described and tested to overcome interferometric instabilities. Its implementation allowed averaging of 10,000 consecutive measured responses leading to SNR of ~25dB. The system successfully measured microsecond ultrasonic pulses in all four sensors without noticeable crosstalk. Compensation of the optical differential delays enabled proper array operation which was validated by an accurate measurement of the speed of sound in water.

2. Theory

A schematic of a SFI-interrogated, US sensor array is shown in Fig. 1 in both reflection and transmission modes. Both configurations are based on a similar interrogation system and the main difference is in the sensing network. As in SFI (or OFDR), the instantaneous frequency of the laser is linearly swept at a constant rate $γ$ , over a frequency range $Δ F$ . Denoting the amplitude of the laser output as $E_{0}$ and its nominal angular frequency at $t = 0$ as $ω_{0}$ , the linearly chirped laser output can be expressed as: $E (t) = E_{0} \exp {j (ω_{0} t + π γ t^{2})}$ . A fiber coupler is used to split the laser output between a reference and a sensing arm which comprises a parallel connection of sensing fibers. To facilitate multiplexing each sensing section in the sensing fibers is preceded by a different delay. At the detector input, the light from the sensing arm is a sum of N components as follows:

E_{S i g n a l} (t) = E_{0} \sum_{i = 1}^{N} A_{i} \exp {j (ω_{0} (t - τ_{i}) + π γ {(t - τ_{i})}^{2} - θ_{i} (t))}

where

τ_{i}

is the propagation delay (transmission mode) or the round trip time delay (reflection mode) for the i^-th sensor,

A_{i}

is a complex factor which describes reflection or transmission magnitude and (slowly varying) phase, coupling losses etc. and

θ_{i} (t)

is the phase modulation induced by the acoustic perturbation at the i^-th sensor. The light from the sensing arm is combined with the reference light and directed to a photodetector. The recorded signal at the detector output can be expressed as:

V (t) = α E_{0}^{2} W_{p} (t) \sum_{i = 1}^{N} A_{i} \exp {j (ω_{i} t + φ_{i} + θ_{i} (t))} + c . c

where

W_{p} (t)

is a processing window which defines the portion of the signal that is used to calculate the transmission (or reflection) profile of the array (Fig. 2), and

α

a constant describing the detector's responsivity.

ω_{i} = 2 π γ τ_{i}

is the angular beat frequency of the i^-th sensor and

φ_{i} = ω_{0} τ_{i} - γ π τ_{i}^{2}

is a constant phase term. Note that this expression does not include DC terms which are avoided by using a balanced detector. Such detector was implemented in this work. It can be seen, therefore, that the complex response of each sensor is a harmonic signal with phase modulation

θ_{i} (t)

.

Fig. 1 Optical setup for US SWI sensing and multiplexing. (a) Reflection mode configuration using a circulator and 1xN coupler, (b) Transmission mode configuration using two 1xN couplers.

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Fig. 2 SFI sensing timing scheme.

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An important aspect of the proposed method arises from Eq. (2): slow phase variations in the sensing and reference arms change the phases of the $A_{i}$ 's but not their magnitude. Hence, no phase-related fading [20] is observed and there is no need for stabilization of the interferometer to its quadrature. Nevertheless, the changes in the phases of the $A_{i}$ 's do affect the recorded response of the system. They manifest as phase variations in the measured US signals. As will be shown below, however, this undesired effect can be easily compensated by normalizing the sensor's responses with the phases of the components at the beat frequencies.

Figure 2, describes the instantaneous frequencies of the light in the reference arm and the light components from the sensing arm, as seen at the detector input. As illustrated in this figure, each of the sensing lightwaves arrives at the detector with a different delay and hence generates a different beat frequency (i.e. carrier frequency). The acoustically-induced phase modulations are schematically presented as short pulses.

The time-dependent phase perturbation is proportional to the acoustic field at the sensor and can be expressed as:

θ_{i} (t) = η_{i} P_{US} (t) = η_{i} A_{US} (t - τ_{US}) \cos [ω_{US} (t - τ_{US})]

where,

P_{US} (t)

is the acoustic pressure field,

ω_{U S}

and

τ_{U S}

are, respectively, the angular frequency and delay of the acoustic signal,

A_{US} (t)

is the acoustic pulse envelope and

η_{i}

is the pressure-to-phase conversion efficiency which takes the role of a modulation index. It should be noted that the additional time delay of

τ_{i} / 2

should be introduced case of reflection mode due to the additional back propagation of the sensing lightwave after being perturbed in the sensing section (Fig. 1).

For low modulation index ( $η_{i} < < 1$ ) the perturbed phase, $\exp {j θ_{i} (t)}$ can be approximated by the truncated Tylor expansion as follows:

\begin{array}{l} \exp {j η_{i} \cos [ω_{US} (t - τ_{U S})] A_{US} (t - τ_{US})} \\ \approx 1 + j η_{i} \cos [ω_{US} (t - τ_{U S})] A_{US} (t - τ_{US}) \end{array}

Thus, the resulting signal from each sensor will comprise a carrier term and a term modulated by the acoustic US signal. Substituting Eq. (4) into Eq. (2), and taking its Fourier transform the recorded output can be expressed as follow (for

ω \geq 0

):

\begin{array}{l} \tilde{V} (ω) = E_{0}^{2} α \sum_{i = 1}^{N} A_{i} \exp {j φ_{i}} δ (ω - ω_{i}) \\ + 0.5 A_{i} η_{i} \exp {j (φ_{i} - ω_{US} τ_{US})} {\tilde{A}}_{US} (ω - ω_{i} - ω_{US}) \\ + 0.5 A_{i} η_{i} \exp {j (φ_{i} + ω_{US} τ_{US})} {\tilde{A}}_{US} (ω - ω_{i} + ω_{US}) \end{array}

where

\tilde{V} (ω) = ℱ {V (t)}

and

{\tilde{A}}_{US} (ω) = ℱ {A_{US} (t)}

are Fourier transforms of their temporal counterparts and

δ (\cdot)

is the Dirac delta function. It can be seen that the ultrasound modulation can be readily extracted from each sensor by AM demodulation. Undesired slow phase variations, as well as amplitude imbalance between detectors, can be compensated by normalizing each sensor response with the complex amplitude of its carrier:

{\hat{P}}_{US, i} (t) \propto ℱ^{- 1} {(\tilde{V} (ω) \frac{W_{D} (ω - ω_{i})}{\tilde{V} (ω_{i})}) * δ (ω + ω_{i})}

where

W_{D} (\cdot)

is a double-sided filter which zeros the entire response except the acoustically-induced sidebands of the i^-th sensor. Hence, multiplexing is achieved due to the spectral separation of the sensors and normalization with the carrier complex amplitude ensures elimination of undesired phase shifts and amplitude imbalance.

3. Experimental setup

The OFDR interrogator that was used was described in details elsewhere [24]. Briefly, light from an ultra-coherent tunable laser source (NKT Koheras Adjustik), with a central wavelength of 1550.12nm, was split between a reference arm and a sensing arm. The sensing network was connected to the sensing arm via a circulator. The output of the circulator was combined with the reference beam and the resulting optical signals were detected by a balanced detector. The detected signal was sampled and stored by an oscilloscope (600MHz, Agilent Infiniium MSO9064A). The laser frequency was swept over a range of 96MHz during a time window of 12μs. The sensing network used a 1x4 coupler to construct a four sensor array. Multiplexing was facilitated by using communication-type single-mode lead-in fibers with different lengths (100m, 200m and 300m). It ensured at least 8MHz separation between the carrier frequencies of each two adjacent sensors. The sensing elements were made of short sections of the same fibers, with polyimide-coating, pigtailed to high-reflectivity mirrors. Since high reflectivity mirrors were employed, the Rayleigh backscattering in the lead fibers could be considered negligible.

Figure 3, illustrates the sensing network and ultrasonic setup. The four fiber-based US sensors were stretched between two plates. The array was immersed in an anechoic immersion bath (an aquarium lined with Aptflex F28 by Precision Acoustics) in order to avoid reverberations effects and aligned perpendicularly to the transverse plane of the transducer. It should be noted that the spatial separation between the four sensors was not uniform (see Fig. 3). Acoustic excitation was generated via an ultrasonic transducer (Harisonic I3-0208-S) driven by a pulser-receiver (Olympus 5077PR). The transducer had a central frequency of 2.25MHz and bandwidth of 1.1MHz. The excitation signal was a train of pulses at a repetition rate of 4.5kHz, pulse duration of about 1μs and peak amplitude of 200V. The pulse train was synchronized with the OFDR interrogation. Accordingly the frequency scan repetition rate was also 4.5kHz and the processing window was 12μs. Synchronization of the bursts with the scan period of the tunable laser enabled collection of repeated responses and an enhancement in the signal to noise ratio via averaging.

Fig. 3 Experimental setup.

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Amplitude demodulation was performed for each of the four sensors as described in Eq. (6). A digitally implemented, double-sided band-pass filter, which matched the transducer bandwidth (1.1MHz wide), was used to extract each of the sensors' responses.

4. Results

First, we tested the proposed normalization method. Figure 4(a) shows the demodulated signal from a single sensor without normalization by the complex amplitude of the carrier frequency. The plot shows the sensor responses to 10,000 consecutive excitation pulses. The effects of the phase and amplitude variations, from one scan to the next, are evident. To overcome this detrimental effect most interferometric systems require stabilization. However, by using the normalization procedure as described above (Eq. (6)) the measurements could be 'stabilized' in post-processing with no additions or modifications to the optical setup. Figure 4(b) shows the acoustic field that was reconstructed using Eq. (6). It can be seen that the measured acoustic pulses remain stable over thousands of measurements. Both their phase and amplitude are locked and allow reliable measurements as well as averaging.

Fig. 4 Consecutive measurements of US pulses, acquired by a single sensor, without (a) and with (b) normalization.

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Next, the multiplexing capabilities of the proposed method were demonstrated. Figure 5 illustrates the experimental results obtained using the four-sensors setup described in Fig. 3. The averaged responses (over 10,000 measurements) from the four sensors without compensation of the optical time-delay are shown in Fig. 5(a). The pulses delays are the sum of the optical time delay and the acoustic time of arrival to each sensor (Eq. (5)). Figure 5(b) shows these signals after compensation of the optical time delays. Evidently, in this plot the pulses are ordered in accord with the geometry of the measurement (Fig. 3). For reference, the excitation pulse, as was measured by the pulse echo method [25] is shown in Fig. 5(c).The SNR of the averaged response can be estimated by calculating the ratio between the mean power of the pulse to the mean power in a shifted time window where the pulse has already decayed. Using this procedure the SNR of the averaged sensor response was found to be ~25dB.

Fig. 5 Experimental results - multiplexing of four US sensors. The measured pulses before (a) and after (b) optical delay compensation. (c) The excitation pulse as was measured by the pulse-echo technique.

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To verify the delay-compensation approach we calculated the time-delays between all pulse-pairs in the optical-delay-compensated response. This was done according to the maximum cross-correlation criterion. Such estimator is known in the literature as the time delay maximum likelihood estimator and is used extensively in acoustic and sonar applications [26]. The time-delay versus distance between sensors is plotted in Fig. 6. The slope of the plot gives an estimate to the speed of sound in water. The error in measurement was estimated using the following error calculation:

σ_{V} = {[{(σ_{Δ z} \frac{\partial}{\partial Δ z} \hat{V})}^{2} + {(σ_{Δ t} \frac{\partial}{\partial Δ t} \hat{V})}^{2}]}^{0.5}

Where

\hat{V} = Δ z / Δ t

is the estimated speed of sound,

σ_{V}

is the error (standard deviation) of the speed estimation,

σ_{Δ z}

is the error in determining the distance between sensors and

σ_{Δ t}

is the error in determining the Time Difference Of Arrival (TDOA) between sensors.

Fig. 6 Qualitative estimation of the speed of sound in water.

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The estimated speed of sound obtained in this part of the experiment was 1543 ± 139 m/s. It agrees with the value reported in the literature (1495m/s at 25°C [24]) however, the uncertainty in this measurement was rather large.

For further test of the method and a more accurate estimation of the speed of sound an additional measurement was performed. In this measurement the transducer was shifted three times towards the sensor array with increments of 0.635mm using a micrometer. The responses of sensors 2 and 4 for all positions of the transducer are shown in Fig. 7. Once again the measurement yielded a valid estimate to the speed of sound, 1514 ± 30m/s, but this time with a much better accuracy.

Fig. 7 Measured US pluses for four positions of the transducer.

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5. Discussion and conclusions

Swept source interferometry in optical fibers has been studied extensively in recent years. Its potential for ultrasound detection, however, was rarely explored. In this work, a novel SFI-based approach for multiplexing fiber-optic ultrasound sensors was proposed and studied. A major advantage of the proposed approach is that it does not require stabilization of the interferometric setup to its quadrature.

Polarization instabilities, however, may still be a source of signal degradation. To overcome this issue in the current work we optimized the polarization states of all carriers by adjusting the configurations of the lead-in fibers at the beginning of every measurement set. Since each set was performed over a relatively short period of time with respect to the typical polarization drift time, no significant performance degradation was observed. Moreover, this insensitivity to polarization drifts may also be the result of the abovementioned normalization procedure which assisted to reduce any polarization-induced responsivity variations. For a continuous operation, however, polarization induced instabilities can be alleviated by using a polarization diversity scheme [28,29].

Another key attribute of the proposed method is that a single electronic channel (which performs amplification, signal conditioning, digitization etc.) is used for all sensors. This is in contrast to the commonly used PZT-based ultrasound detector arrays which employ parallel electronic channels. Consequently, a considerable simplification of the electronics required to handle sensor arrays is obtained.

An important feature of the proposed method is the flexibility in which the bandwidth of each sensor can be adjusted. The acoustic bandwidth of each sensor is given by half of the spectral distance between adjacent sensor carrier frequencies: $Δ f = 0.5 γ Δ τ$ . Thus, a straightforward adjustment of the bandwidth can be performed by changing the frequency sweep rate.

The preliminary results demonstrated in this paper show the potential of the proposed approach for multiplexing fiber based ultrasonic sensors. One simple theoretical bound to the number of sensors that can be multiplexed is given by $N < Δ F_{Optical} / Δ F_{Ultrasound}$ where $Δ F_{Optical}, Δ F_{Ultrasound}$ are, respectively, the optical detector bandwidth and the bandwidth of the ultrasound sensor. Since $Δ F_{Optical}$ can be very high (optical detectors can provides bandwidths of tens of GHz) this bound of N is also very high. For example, a single (readily available) 0.6GHz optical detector, can potentially accommodate up to 120 US channels with 5MHz bandwidth or 40 wideband US channels with 15MHz bandwidth.

There is however an additional important bound. As the proposed configuration splits the total optical power between $N$ parallel channels and there are additional combining losses in the $1 \times N$ coupler, the power per channel (in dB) decreases as $- 10 \log_{10} N^{2}$ . Namely, doubling the number of sensors will reduce the channel power by 6dB. This, in turn, will lead to a 6dB decrease in the carrier peaks of ${| \tilde{V} (ω) |}^{2}$ and its acoustically induced sidebands. The number of channels, $N$ , for which these sidebands are reduced to the noise-floor level (which in reflection mode is determined by Rayleigh backscattering) is another bound to the multiplexing capability of the method. In this work the difference (in log scale) between the sidebands of ${| \tilde{V} (ω) |}^{2}$ and the Rayleigh level was $~ 18 d B$ . This means that $N$ could be increased to $4 \times 2^{18 / 6} = 32$ before the sidebands would reach the Rayleigh level . Clearly, this limit can be significantly improved by working in a transmission mode, by increasing the number of averaged responses, increasing the total power and optimizing the pressure-to-phase conversion efficiency $η$ .It was recently shown that the use of polymer fibers or polymeric coatings of silica fibers can enhance pressure-to-phase conversion efficiency by an order of magnitude and even more [12,30]. Implementation of these techniques can increase the power splitting bound on the achievable number of sensors to well above 100.

In conclusion, SFI is a promising technique for implementing fiber-based US sensor arrays. It can facilitate a large number of sensors, with no need for stabilization, in a cost-effective and compact manner.

Acknowledgments

This research was supported by the Ministry of Science, Technology & Space, Israel. Idan Steinberg acknowledges the generous support of the Clore Israel Foundation.

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Multiplexing of fiber-optic ultrasound sensors via swept frequency interferometry

Abstract

1. Introduction

2. Theory

3. Experimental setup

4. Results

5. Discussion and conclusions

Acknowledgments

References and links

Cited By

Figures (7)

Equations (7)

Optics Express