Ultrasonic wave sensing using an optical-frequency-comb sensing cavity for photoacoustic imaging

Takeo Minamikawa; Takashi Masuoka; Takashi Ogura; Kyuki Shibuya; Ryo Oe; Eiji Hase; Yoshiaki Nakajima; Yoshihisa Yamaoka; Takahiko Mizuno; Masatomo Yamagiwa; Yasuhiro Mizutani; Hirotsugu Yamamoto; Tetsuo Iwata; Kaoru Minoshima; Takeshi Yasui

doi:10.1364/OSAC.2.000439

1. Introduction

Optical-frequency-comb (OFC) is a proven modality for optical frequency metrology and spectroscopy owing to the ability of an OFC to act as an optical frequency ruler traceable to frequency standards, and is applicable to visible, near-infrared, infrared, and THz spectral regions [1–6]. The OFC enables highly precise and accurate optical frequency measurement with the dynamic range better than 10¹⁰, ultra-high resolution spectroscopy with the spectral resolution and accuracy better than 1 MHz and the spectral range wider than a few tens of THz [1]. Recent developments of the OFC technology extend the application to not only precise metrology, but also to unique instrumentations such as nonlinear spectroscopy, confocal microscopy, imaging, polarization control and measurement, and so on [7–14].

A recent development of the OFC technology also includes a perturbation-sensitive sensor using an OFC cavity, namely an OFC sensing cavity [15–17]. A fiber-based sensor is well established and is utilized as a flexible and high-sensitivity sensor by encoding a perturbation into optical information such as intensity, wavelength and so on [18–26]. By combining with the OFC sensing cavity, the perturbation-encoded optical information can be decoded by a radio-frequency (RF) signal because the OFC sensing cavity is worked as a dimensional converter of perturbation signal into a RF signal via the direct frequency link nature of OFC between the optical frequency domain (a few hundreds of THz) and the RF domain (a few tens of MHz). When the perturbation is applied to the OFC sensing cavity, the perturbation signal is encoded into the comb structure of the OFC, such as comb spacing and intensity of each comb mode. This perturbation-encoded comb information can be retrieved via radio-frequency (RF) signal by observing it as a beat note of each comb pair. Since the OFC exhibits an inherent direct frequency link between the optical frequency domain and the RF domain without spoiling frequency uncertainty, the perturbation signal can be decoded with the equivalent accuracy of optical signals without the direct measurement of optical frequency. We have demonstrated the feasibility of the OFC sensing cavity in strain sensing with the frequency response of up to a few hundreds of Hz [16], and in refractive index sensing with a multi-mode interference fiber [17].

In the present study, we extended the concept of OFC sensing cavity to the ultrasonic wave sensing with MHz order frequency, especially for photoacoustic imaging. Photoacoustic imaging is a promising modality for deep tissue imaging with high spatial resolution in the field of biology and medicine [27–35]. High penetration depth and spatial resolution of the photoacoustic imaging is achieved by means of the advantages of optical and ultrasonic wave imaging, i.e., a tightly focused beam confines ultrasonic wave-generated region within micrometer scale and the ultrasonic wave can propagate through tissues without significant energy loss. In this study, we provided a proof-of-principle demonstration of the ultrasonic wave detection with the OFC sensing cavity. We confirmed the fundamental characteristics of the OFC sensing cavity in ultrasonic wave sensing with a MHz order ultrasonic wave. Furthermore, we also performed the two-dimensional photoacoustic imaging of a rubber film to confirm potential applicability of the OFC sensing cavity.

2. Theory and methods

2.1. Principle of the OFC sensing cavity-based ultrasonic wave sensor

Experimental setup of the developed OFC sensing cavity-based ultrasonic wave sensor is shown in Fig. 1

Fig. 1 Principle of the OFC sensing cavity-based ultrasonic wave sensor. EDF, Er-doped fiber; LD, laser diode; WDM, wavelength division multiplexer; PZT, piezoelectric transducer; PD, photodetector; DBM, double-balanced mixer; LPF, low-frequency-pass filter; f_rep, repetition rate or comb spacing of OFC; f_syn, frequency of RF synthesizer; I_rep, intensity of RF signal of OFC; I_syn, intensity of RF synthesizer.

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. A custom-built ring-cavity erbium-doped fiber (EDF) laser mode-locked by a nonlinear polarization rotation technique was employed as an OFC generator (the fundamental comb spacing or repetition rate, 26.6 MHz; the center wavelength, 1560 nm; and the spectral bandwidth, 42 nm). A part of the OFC cavity was used as an ultrasonic wave sensing region that was winded loosely four times and bundled to enhance detection sensitivity. Elastic modulation by ultrasonic wave was applied to a part of the cavity fiber, leading to the modulation of the comb structures such as comb spacing or intensity of each comb mode due to the modulation of the cavity state. The modulation of the comb structures directly reflected to the RF signal that appeared as an output signal of the OFC generator, in other words, the modulation generated sidebands at each comb mode that also converted to the sidebands of beat notes of each comb pair in the RF domain.

For the sensitive detection and the characterization of the modulated RF signal that reflected the ultrasonic wave, we employed a phase-sensitive detection system. The output signal of the OFC generator was obtained by a photodetector (PDA10CF, Thorlabs) with the frequency response of about the fundamental beat note of the comb spacing, in other words, the repetition rate of the pulse trains (26.6 MHz) of the OFC generator. The OFC signal was divided into two parts; one for the low-bandwidth stabilization of the comb spacing of the OFC generator, and the other for the ultrasonic wave sensing.

In the low-bandwidth stabilization of the comb spacing of the OFC generator, the OFC signal was led to a double balanced mixer (ZAD-6 + , Mini Circuits) and a low-frequency-pass filter to obtain a phase error signal. The error signal was then processed by a proportional and integral type servo controller and fed back to the OFC cavity tuning via a piezoelectric transducer to stabilize the comb spacing. The cutoff frequency of the low-bandwidth stabilization was set at about 100 Hz, which was much less than the frequency of the ultrasonic wave.

In ultrasonic wave sensing, the OFC signal was also led to another double balanced mixer (ZAD-6 + , Mini Circuits). The lower frequency component of the output signal of the double balanced mixer was obtained by an oscilloscope or an RF spectral analyzer via a low-frequency-pass filter. Since the frequency of the ultrasonic wave-encoded signal was much higher than the cutoff frequency of the comb spacing stabilization system, the ultrasonic wave-encoded signal can be obtained as an unstabilized component of the output signal of the double balanced mixer.

2.2. Sensing mechanism of an ultrasonic wave with an OFC sensing cavity

Firstly, we confirmed the sensing mechanism of an ultrasonic wave using the OFC sensing cavity. Possible sensing mechanisms are phase/frequency modulation or intensity modulation due to the ultrasonic wave perturbation at the sensing region. These two modulations can be evaluated with the output signal of the double balanced mixer by tuning the phase difference between the OFC signal and the RF synthesizer signal.

In the case of the phase/frequency modulation condition, the OFC signal (I_OFC) and the synthesizer signal (I_syn) are expressed as,

I_{O F C} = A_{O F C} \cos (ω_{O F C} t + Δ φ),

I_{s y n} = A_{s y n} \cos (ω_{s y n} t + θ),

where A, ω, Δφ, θ are amplitude, angular frequency, the modulation phase of the OFC signal and the initial phase of the synthesizer signal, respectively. The suffixes of OFC and syn represent the corresponding parameters of the OFC signal and the synthesizer signal. The two signals are mixed with a mixer with the assumption of ω_OFC = ω_syn, which is expressed as,

\begin{array}{l} I_{m i x} = I_{O F C} I_{s y n} \\ = \frac{1}{2} A_{O F C} A_{s y n} {\cos (2 ω_{O F C} t + Δ φ + θ) + \cos (Δ φ - θ} . \end{array}

By using a low-frequency pass filter, we obtained the second term of I_mix,

I_{m i x, L P F} = \frac{1}{2} A_{O F C} A_{s y n} \cos (Δ φ - θ) .

To elucidate the effective initial phase of the synthesizer signal θ, the first derivative of the I_mix,LPF in terms of Δφ is expressed as,

\frac{\partial}{\partial (Δ φ)} I_{m i x, L P F} = - \frac{1}{2} A_{O F C} A_{s y n} \sin (Δ φ - θ) .

Therefore, the highest sensitivity obtained is at which the first derivative of I_mix,LPF is maximized. When the mean expectation of <Δφ> = 0, the initial phase of the synthesizer signal θ should be π/2 rad for effective sensing.

In the case of the intensity modulation condition, the OFC signal (I_OFC) and the synthesizer signal (I_syn) are expressed as,

I_{O F C} = A_{O F C} \cos (ω_{O F C} t),

I_{s y n} = A_{s y n} \cos (ω_{s y n} t + θ),

where A_OFC is a function of time due to the intensity modulation. As the same manner of the phase modulation condition, the low-frequency term of the multiplication signal I_mix with the assumption of ω_OFC = ω_syn can be obtained by the combination of a mixer and low-frequency pass filter as,

I_{m i x, L P F} = \frac{1}{2} A_{O F C} A_{s y n} \cos (θ) .

The first derivative of I_mix,LPF in terms of A_OFC is expressed as,

\frac{\partial}{\partial A_{O F C}} I_{m i x, L P F} = \frac{1}{2} A_{s y n} \cos (θ) .

Therefore, the highest sensitivity is determined at which the first derivative of I_mix,LPF is maximized, which is obtained at the initial phase of the synthesizer signal θ of 0 rad.

As a result of the theoretical estimation, the highest sensitivity of the phase/frequency modulation is obtained at the phase difference of π/2 rad, and that of the intensity modulation is at 0 rad. Figure 2

Fig. 2 Phase dependency of the output signal of the double balanced mixer mixing with the OFC signal and the synthesizer signal. (a) Phase dependency in strain application along the longitudinal direction of the cavity fiber with a piezoelectric transducer operating at low frequency (f = 1 kHz), which provides ideal phase/frequency modulation. (b) Phase dependency in ultrasonic wave sensing. Solid lines indicate the fitting curves with a sinusoidal function.

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shows the phase dependency between the OFC signal and the RF synthesizer signal. Ideal phase/frequency modulation can be realized by the strain application with a piezoelectric transducer operating at low frequency (f = 1 kHz) to the sensing region, which is a general way to modulate or stabilize the comb spacing [16]. In this case, the highest sensitivity of the applied modulation was obtained at the phase difference of π/2 rad as show in Fig. 2a, which agreed well with the theoretical estimation described above. In contrast, in the ultrasonic wave sensing with the frequency of 8 MHz, the peak signal was obtained at the phase difference of 0 rad as shown in Fig. 2b, indicating an intensity modulation was applied to the OFC generator in ultrasonic wave sensing.

3. Results

3.1 Fundamental characteristics of ultrasonic wave detection with an OFC sensing cavity

We evaluated the fundamental characteristics of ultrasonic wave detection with the developed OFC sensing cavity by using an ultrasonic wave transducer. A frequency response of the OFC sensing cavity that obtained with the spectral resolution of 3 kHz is shown in Fig. 3a

Fig. 3 Frequency response and detection linearity of the OFC sensing cavity. (a) Frequency response of the OFC sensing cavity. Dashed line indicates a noise floor. (b) Representative RF spectra of ultrasonic waves operating at 7.5 to 8.5 MHz. (c) Detection linearity of the OFC sensing cavity observing at 9 MHz. Dashed line indicates a noise floor.

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. Ultrasonic wave application was performed with an ultrasonic wave transducer (B10K8I, Japan Probe) operating with a continuous wave at each frequency. The driving voltage of the ultrasonic wave transducer was set at 5 V_p-p. The ultrasonic wave transducer and the sensing region of the OFC sensing cavity were immersed in water. We realized the ultrasonic wave detection from 1 to 13 MHz. The center frequency and the bandwidth defined by the −3 dB down from the spectral peak of the ultrasonic wave spectrum were respectively obtained at 10 MHz and 5 MHz, which corresponded to the specification of the ultrasonic wave transducer. The maximum frequency response of the OFC sensing cavity was reached to the half of the repetition frequency of OFC generator, which might be limited due to the sampling theorem.

Representative ultrasonic wave spectra from 7.5 to 8.5 MHz with the spectral resolution of 3 kHz and the ultrasonic wave driving voltage of 5 V_p-p is shown in Fig. 3b. The bandwidth of each spectrum had below spectral resolution of 3 kHz, and no side bands or harmonic bands were observed, indicating the OFC sensing cavity smoothly responded against the applied ultrasonic wave without any spectral broadening and modulation effects.

The detection linearity of the OFC sensing cavity was also confirmed. We obtained the dependency of the ultrasonic wave signal against the ultrasonic wave driving voltage at the ultrasonic wave frequency of 9 MHz. The spectral resolution was set at 1 Hz to reduce noise contribution. The ultrasonic wave signal exhibited good linearity with a correlation coefficient of 0.991 against the driving voltage of the ultrasonic wave transducer as shown in Fig. 3c.

3.2 Photoacoustic wave detection with an OFC sensing cavity

To provide a proof-of-principle demonstration of the developed OFC sensing cavity in photoacoustic wave detection, we observed photoacoustic signals generated by a pulse laser. The photoacoustic signals of several materials detected by the developed OFC sensing cavity were shown in Fig. 4

Fig. 4 Photoacoustic wave detection by the developed OFC sensing cavity. Temporal behaviors and Fourier-transformed spectra of photoacoustic signals of (a, b) a black ink, (c, d) a pencil lead, and (e, f) a rubber film excited by the pulsed laser operating at 532 nm with the pulse duration of 8 ns.

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. The pulsed lasers operating at 532 nm with the pulse duration of 8 ns and the repetition rate of 200 Hz (SIRIUS-D2P-LNQ, Fractal Laser) was employed for the excitation of photoacoustic wave. The excitation laser illuminated from the upper side of the samples, and the generated photoacoustic wave was observed by a part of the loosely winded and bundled sensing region of the OFC sensing cavity that placed under the sample. The excitation laser was focused on the center of the bundled fibers in xy position and on the center of samples in z position.

The OFC sensing cavity directly obtained the temporal behavior of the photoacoustic signals of a black ink (Fig. 4a), a pencil lead (Fig. 4c), and a rubber film (Fig. 4e) as the output signal of the double balanced mixer. A few-cycle pulsed acoustic signal with the pulse duration of about sub-microseconds was clearly obtained. A typical signal-to-noise ratio of the time-domain signal of the black ink was 38 with the excitation pulse energy of 150 µJ and the signal averaging of 50 times in time domain. The photoacoustic spectra were obtained by the Fourier transformation of each time-domain signal as shown in Figs. 4b, 4d, and 4f. Sample-dependent photoacoustic spectra were clearly observed. These results confirmed the feasibility of the OFC sensing cavity in photoacoustic wave detection.

We also evaluated the excitation laser power dependency of photoacoustic signal detected by the developed OFC sensing cavity as shown in Fig. 5

Fig. 5 Excitation power dependency of photoacoustic signal detected by the developed OFC-based strain sensor. The intensity was obtained by the averaging of the photoacoustic signal of a rubber film from 5 MHz to 11 MHz.

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. A rubber film was used as a sample. The photoacoustic signal was averaged for 50 times in time domain. We obtained linear relationship between the output signal of the double balanced mixer and the pulse energy. In this condition, the detection limit of photoacoustic signal was at the excitation averaged laser power of 3 mW or the excitation pulse energy of 15 µJ.

3.3. Photoacoustic imaging

Finally, we performed photoacoustic imaging with the OFC sensing cavity. Photoacoustic images were obtained with a sample scan scheme with the signal averaging 50 times in time domain. A rubber film with the thickness of 1 mm was used as a sample (Fig. 6a

Fig. 6 Photoacoustic imaging of a rubber film with the OFC sensing cavity. (a) Schematic of the rubber film, the sensing fiber, and the excitation laser. The sensing fiber was placed under the rubber film. (b) Photoacoustic imaging of the region 1 with an edge. (c) Photoacoustic imaging of the region 2 with a “T”-shaped region. (d, e) Photoacoustic signals of parts of the rubber film indicated by A in b and the background indicated by B in b. (f) Photoacoustic spectra of the parts indicated by A in b (solid line) and B in b (dashed line). (g, h) Photoacoustic signals of parts of the rubber film indicated by C in c and the background indicated by D in c. (i) Photoacoustic spectra of the parts indicated by C in c (solid line) and D in c (dashed line).

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). Photoacoustic images of an edge and a “T”-shaped cutting region of the rubber film obtained by the averaging of the photoacoustic spectrum from 1 MHz to 13 MHz were shown in Figs. 6b and 6c, respectively. The step structure of the edge (Fig. 6b) and the “T”-shaped cutting structure (Fig. 6c) were clearly visualized in terms of photoacoustic imaging. These results clearly showed the capability of the photoacoustic imaging by using the developed OFC sensing cavity.

In the temporal behavior of the photoacoustic signal of the rubber film, we observed a few-cycle pulsed photoacoustic signal with the pulse duration of about 200 ns (Figs. 6d and 6g). The temporal behavior near the edge (Fig. 6d) and near the “T”-shaped cutting region (Fig. 6g) are similar to each other, indicating similar response of photoacoustic generation at the rubber film was observed as with the OFC sensing cavity. At the no sample region, we did not obtain any photoacoustic signals (Figs. 6e and 6h), indicating unfavorable effect such as the modification of OFC cavity fiber by the direct excitation of the pulsed laser onto the sensing fiber were not presented in our system. The Fourier transformed spectra of the photoacoustic signal in time domain were shown in Figs. 6f and 6i. Strong spectral intensity was obtained at around 5 to 8 MHz in the rubber film region, while the no spectral peak was obtained in the no sample region. The slight difference between the photoacoustic spectra of the rubber film shown in Figs. 6f and 6i were obtained, which might indicate the difference of local mechanical environments of the rubber film. These results indicate the feasibility of the OFC-based ultrasonic wave sensor in photoacoustic imaging.

4. Discussion

Our previous studies provided a proof-of-principle demonstration of an OFC sensing cavity for a new scheme of physical quantity sensing [16,17]. Here, we extended the OFC sensing cavity to ultrasonic wave sensing. We confirmed the fundamental characteristics of the developed ultrasonic wave sensing system, and realized ultrasonic wave sensing up to 13 MHz with the direct measurement of temporal behavior of ultrasonic waves. We also provided a proof-of-principle demonstration of photoacoustic imaging using the OFC sensing cavity.

Frequency response of the developed OFC sensing cavity is limited by the half frequency of the repetition rate of the OFC generator in this study because of the sampling theorem. In this study, we employed an OFC generator with the repetition rate of 26.6 MHz, resulting in the frequency response of about 13 MHz. To enhance the frequency response of the OFC generator, an OFC generator with higher repetition rate is possibly employed. The repetition rate of an OFC generator can be determined by changing the cavity length of the OFC generator. An available repetition rate with the same setup of this study is from a few tens of MHz to a few hundreds of MHz, indicating that the frequency response of OFC sensing cavity can be reached 100 MHz or higher. Mechanical properties of an optical fiber at the sensing region such as stiffness and damping property and so on, also affect the frequency response of the OFC sensing cavity. Further studies are required by using an OFC generator with such higher repetition rate and various species of sensing fibers to elucidate the actual frequency characteristics of OFC sensing cavity in higher frequency region.

In the ultrasonic wave sensing with the OFC sensing cavity, we clarified that an intensity modulation was observed by the application of ultrasonic wave perturbation at the sensing region. A possible factor of the intensity modulation is polarization modulation of propagating pulses in an OFC cavity. We applied ultrasonic waves from the lateral side of a part of the cavity fiber in this study, which might result the cross-sectional change of the fiber by the lateral stress. It is well known that the cross-sectional change of a fiber will modulate the polarization state of propagating light. Actually, we could obtain a ultrasonic wave-induced polarization change of light propagating in a single-mode-fiber by a polarization-sensitive detection method (data not shown). The change of the polarization state must affect the lasing condition of OFC due to a nonlinear polarization rotation mode locking system was employed in this study. As a result, the intensity modulation might be caused following the modulation of lasing state of OFC. Although further studies are required, the modulation effect of lasing state of OFC is interesting in terms of a dimensional conversion from a perturbation signal to an OFC information, such as not only intensity, but also comb spacing, carrier envelope offset frequency and so on for a perturbation detection with the OFC sensing cavity.

Importantly, in the developed system, the signal as a result of phase/frequency modulation or intensity modulation can be selectively obtained by tuning the phase difference between the OFC signal and the RF synthesizer signal as described in Theory and Methods section. This selective detection mechanism provides an important benefit for the ultrasonic wave sensing with the OFC sensing cavity, i.e., the contribution of phase/frequency modulation such as the extension or contraction of cavity fiber such by thermal instability and mechanical perturbation, phase noise of OFC generator and so on, can be minimized according to Eqs. (5) and 9. In the same manner, in the detection of phase/frequency modulation, the contribution of the intensity modulation will be minimized. Of course, simultaneous observation of phase/frequency modulation and intensity modulation, such for simultaneous observation of ultrasonic wave and low frequency strain, can also be realized by employing two double balanced mixers with respective RF signals having different phases. Although further studies are required to confirm the benefit of the selective or simultaneous observation of phase/frequency modulation and intensity modulation with the OFC sensing cavity, we believe that our unique detection scheme will open up a new way of the detection of physical quantities.

5. Conclusion

In conclusion, we proposed and experimentally demonstrated ultrasonic wave sensing with an OFC sensing cavity. Although further studies are required to confirm actual benefits of the OFC sensing cavity in ultrasonic wave detection by optimizing fiber species, fiber arrangement and optical setup of the OFC generator for practical applications, our feasibility study will extend the potential applicability of the concept of the OFC sensing cavity, and will also expand the potential of the OFC technology.

Funding

Exploratory Research for Advanced Technology (ERATO) MINOSHIMA Intelligent Optical Synthesizer Project (JPMJER1304), Japan Science and Technology Agency (JST), Japan, and Grant-in-Aid for Exploratory Research (15K13384) from the Japan Society for the Promotion of Science (JSPS).

Acknowledgements

The authors thank Ms. Natsuko Takeichi and Ms. Shoko Lewis, Tokushima University, for the English proofreading of the manuscript.

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Ultrasonic wave sensing using an optical-frequency-comb sensing cavity for photoacoustic imaging

Abstract

1. Introduction

2. Theory and methods

2.1. Principle of the OFC sensing cavity-based ultrasonic wave sensor

2.2. Sensing mechanism of an ultrasonic wave with an OFC sensing cavity

3. Results

3.1 Fundamental characteristics of ultrasonic wave detection with an OFC sensing cavity

3.2 Photoacoustic wave detection with an OFC sensing cavity

3.3. Photoacoustic imaging

4. Discussion

5. Conclusion

Funding

Acknowledgements

References

Cited By

Figures (6)

Equations (9)

OSA Continuum