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Abstract
High-frequency fiber laser sensor is a new acoustic detector for photoacoustic imaging. However, its performance has not been thoroughly studied. Here, we present a comprehensive characterization of a fiber laser sensor for photoacoustic imaging. Ultrasound waves deform the fiber laser cavity and induce frequency changes in the heterodyning output signal. The sensitivity peaks at 22 MHz, which is associated with an azimuthal mode number l = 2 and a radial mode number n = 1. The broadband acoustic sensitivity in terms of frequency shift is 2.25 MHz/kPa and the noise-equivalent pressure reaches 45 Pa with a sampling rate of 100 MHz. The 3-dB bandwidth is 18 MHz for spherical-wave detection. We characterized the spatial distribution of acoustic sensitivity. The sensitivity along the fiber longitudinal direction varies with the laser spatial mode and is determined by the grating and cavity parameters. The sensitivity at the azimuthal direction presents a |cos(2θ)| dependence as a result of fiber core asymmetry. In the radial direction, the sensitivity is inversely proportional to the square root of the distance between the source and the detector. The acoustic sensitivity can be enhanced by reducing the cavity length. We experimentally show that a short sensor can enhance the contrast and penetration depth of PAM than a long one.
© 2017 Optical Society of America
1. Introduction
Photoacoustic microscopy (PAM) provides optical-absorption contrasts and non-invasive imaging in superficial and deep tissues [1–4]. In optical-resolution PAM (OR-PAM), focused pulsed light is partially absorbed to induce ultrasound waves via photoacoustic effect. Generally, the ultrasound signals are detected with an ultrasound transducer (UT) confocally aligned with the excitation light. PAM maps the distribution of optical absorbers by raster scanning the optical/acoustic beams [5]. OR-PAM requires ultrasound sensors with miniature sizes for implantable or wearable instrumentation. However, existing PAM probes often use big piezoelectric acoustic transducers or bulky focusing/alignment components, not suitable for these applications. Recently, a number of optical ultrasound detectors have been developed with compact sizes and flexible configurations [6]. Optical sensors based on Fabry-Perot (FP) or whispering-gallery-mode resonators, Mach-Zehnder interferometers, in-fiber Bragg gratings and surface plasmon resonance (SPR) have been used to detect photoacoustic signals [7–16]. FP sensors are fabricated on a glass substrate or an optical fiber tip by sandwiching a polymer between two layers of thin dichroic reflectors [7, 8]. Incident pressure wave deforms the cavity and induces a shift in the resonant wavelength. An FP detector with a noise-equivalent pressure (NEP) of 40 Pa has been used to monitor tumor growth [9]. A π-shifted fiber Bragg grating, with 100-Pa NEP in response to ultrasound waves, has been incorporated in PAM [10]. An imprinted polymer micro-ring resonator presents a detection bandwidth from 1 to 350 MHz range offered by the extremely thin waveguide [11, 12]. An SPR ultrasound detector measures acoustically induced variation in reflective power at the gold-glass interface [13]. It presents a flat frequency response over 120-MHz bandwidth but the sensitivity is limited. A similar optical configuration without the use of SPR has been demonstrated, which measured ultrasound signals by detecting polarization-dependent reflection [14]. Recently, optical resonators in silicon photonics platform also demonstrate the ability of ultrasound detection [15, 16].
Fiber optic sensors are preferable for ultrasound detection because of their light weight, inherent connection to optical measurement instrumentations and the multiplexing capability [17,18]. An optical fiber can inherently present ultrasound sensitivity in optical delay or birefringence change [19,20]. A dual-polarization fiber laser, whose output intensity oscillates at a radio-frequency signal due to beating between two orthogonal laser modes, has shown frequency shift due to the interaction between the acoustic wave and the solid fiber. It is highly resistant to external perturbations due to common-mode cancellation between the two orthogonal modes. Fiber laser sensors have been used in the detection of low-frequency or single-frequency acoustic waves. Our recent work has developed a broadband fiber-laser sensor and extend its application to PAM [21]. However, the performance of the broadband fiber-laser sensor has not been thoroughly studied.
Here we comprehensively characterize the frequency response and spatial sensitivities of the ultrasound sensors which are related to PAM performances. The noise-equivalent pressure (NEP) for planar-wave detection is 45 Pa over 50 MHz. The sensor presents a 3-dB bandwidth 18 MHz for spherical-wave detection. The spatial distribution of the sensitivity has been characterized by scanning a point-like acoustic source. Results suggest (a) the fiber laser sensor presents maximum sensitivity at the principle axis facing the middle region of the laser cavity; (b) the acoustic sensitivity can be enhanced by shortening the laser cavity to yield a more confined laser mode, which increases PAM imaging contrast and penetration depth.
2. Theory
We first consider the acoustic response of an ideal line detector. As shown in Fig. 1(a), a point source S generates a spherical acoustic wave with a frequency fa. The acoustic wave is totally absorbed by the line detector placed at a distance d. The acoustic pressure with propagation can be written as p(ω, r) = exp(-ikar)/r, where ka denotes the acoustic wave number and r = (d2 + z2)1/2 is the propagation distance, z represents the longitudinal position (a strict expression can be found in [22]). The spherical wavefront arrives at the line detector with different phases, as shown in Fig. 1(b). The response of the line detector can be expressed as an integration and simplified as . Figure 1(c) plots the frequency response of the line detector to a spherical acoustic wave. Higher acoustic frequency leads to reduced sensitivity which follows 1/fa1/2 variation, because the acoustic phase oscillates faster along the line detector and the self-cancellation effect is stronger. The response can be equivalently considered as an effect of a uniform pressure peq = 1/d (the amplitude at the position facing to the source z = 0) with a length Leq. Based on the above relation, we can write the equivalent interaction length as, which is ten to hundred times shorter than the sensitive region (typically 2 to 10 mm) of a fiber laser sensor. For a 50-MHz spherical ultrasound wave (wavelength: 30μm, speed in water: 1500 m/s) with a source-detector distance d = 500 μm, the equivalent interaction length is Leq = 122 μm.
Fig. 1 (a) Schematic of an ideal line detector and a point source S which emits spherical ultrasound waves. (b) Real part of received acoustic pressure along the detector. (b) Calculated response of the integrated line detector with different distances to S.
For a fiber laser with a cavity length Lc, The lasing frequency at each polarization is determined by the resonant condition:
where denotes the effective refractive index of each polarization mode, M represents the resonant order and c is the speed of light in vacuum. Their lasing frequencies are slightly different because of a weak fiber birefringence B = |nx-ny|. The two polarized light beat at a frequencywhere n0 = (nx + ny)/2 denotes the average refractive index. Equation (2) suggests a proportional relation between the beat frequency and fiber birefringence. Note that the sensitivity of the fiber laser sensor should be weighted by the intracavity intensity density , which is normalized via. The profile of , denoted as laser mode profile, is determined by cavity length as well as grating parameters [23].The interaction between planar ultrasound waves and the optical fiber can be treated as a scattering problem [24]. The incident ultrasound waves deform the fiber and create a stress distribution [23–31]. The acoustic pressure and the stress distributions over the optical fiber can be calculated by solving decoupled Helmholtz equations in combination with the continuity boundary conditions [28, 29]. Based on photoelastic effect, the acoustically induced birefringence change can be calculated with the principle stresses at the fiber core. The scattering model can apply to both normal and oblique incidences. A full picture which depicts the dependence on incidence angle α has been demonstrated in [30]. For the fiber laser sensor, different longitudinal position z (from z = 0 to ± ∞) receives acoustic waves with different incident angle α = arctan(z/d) (from α = 0 to ± π/2). Therefore, the local birefringence change can be obtained. In addition, the frequency response can be calculated by repeating the above procedure with scanning acoustic frequency. The spherical wave can be considered as a superposition of individual angular components of planar waves [30, 31]. Therefore, the spherical-wave response can be written as
The acoustic phase oscillates fast with position z at large incidence angles, and the acoustic sensitivity is mainly a result of the perturbation over a confined region facing to the source. As a result, Eq. (3) can be approximately expressed aswhere is the birefringence change induced by normal incident planar waves. Equation (4) demonstrates the three determinative factors that contribute to the spherical-wave ultrasonic response: Leq() is a result of the line shape of the fiber and reflects the effect of phase cancellation; is determined by fiber cross-sectional geometry and elastic properties; denotes the contribution of the laser mode.3. Sensor characterization
Figure 2 shows an experimental setup for sensor characterization. The ultrasound sensor comprises of two highly reflective UV-inscribed Bragg gratings in a single mode Er/Yb-codoped fiber (EY305, CorActive) to form a laser cavity. The fiber has a diameter of 125 μm, a numerical aperture (N. A.) of 0.18 and a cutoff wavelength of 1277 nm. Its absorption at 980 nm is 1337 dB/m. Each grating has a length of 3 mm and a coupling strength of about 760 m−1. The Germanium doped fiber core offers high photosensitivity which forms highly reflective gratings. A 980-nm semiconductor laser pumps the cavity via a wavelength division multiplexer (WDM). The lasing wavelength is 1531.8 nm and the output power is about 1 mW. The laser outputs two orthogonal polarization modes with different lasing frequencies due to weak birefringence. The two laser modes beat at the output, and a 2.7-GHz beat signal can be detected with a high-speed photodetector. Its amplitude can be maximized by tuning the polarization states with a polarization controller and a polarizer. The acoustically induced frequency shift can be readout with an I/Q demodulator. Two carrier waves with the same frequency and a phase offset of 90° are mixed with the beat signal, respectively. After a low-pass filter, the I/Q quadrature signals are obtained to extract the phase φ of the beat signal. The frequency change can be determined by computing . The sampling rate is 100 MHz in the experiment, which allows for an acquisition bandwidth of 50 MHz. The changes in lasing frequency can also be measured with other strategies, e. g., Mach-Zehnder interferometer, but they usually require frequency locking to compensate the low frequency drift. In contrast, the self-heterodyning manner between the two polarization modes yields a radio-frequency signal, which does not require additive frequency locking to yield a stable performance. This sensing scheme also offers resistance to external perturbations including temperature change, vibration and bending, due to the common-mode cancellation and broadband frequency response, as described in [21].
Fig. 2 Experimental setup for ultrasound detection with a fiber laser sensor. PAM imaging uses the same setup for spherical-wave detection by raster scanning the sample. L: Lens; WDM: Wavelength-division multiplexer; PD: Photodetector.
3.1 Frequency response
We first characterized the planar-wave response. Ultrasound waves generated by an unfocused transducer (V358-SU, Panametrics) are normally applied to the sensor. The aperture of the acoustic beam is 6 mm. The ultrasonically induced perturbation is approximately uniform over the whole sensitive region. Figures 3(a) and 3(b) show the measured temporal and frequency responses. The beat frequency shifts by 198 MHz at 88 kPa acoustic pressure, yielding an acoustic sensitivity of 2.25 MHz/kPa. The applied acoustic pressure has been calibrated with commercial reference ultrasound hydrophone (HMB-0500, ONDA). Each polarized laser mode has a linewidth of 13 kHz and the beat signal has extremely low frequency noises at the frequency range of interest. As demonstrated in [21], the noise of the demodulation system is limited by the shot noise of the photodetector as well as the dynamic range of the frequency demodulation. Considering the noise floor of 83 kHz with 50 MHz acquisition bandwidth, the NEP of the fiber sensor is about 45 Pa. The frequency response curve presents two maxima at 22 MHz and 39 MHz. Relaxation oscillation can induce fluctuations in laser output intensity as well as lasing frequency. However, we did not observe corresponding variation in beat frequency, which is probably a result of common-mode cancellation.
Fig. 3 (a) Transient response to a pulsed planar wave. (b) Measured and calculated frequency responses. (c) Calculated displacement of excited fiber vibrations at 22 and 39 MHz, i. e, the (2, 1) and (2, 2) modes.
The acoustically induced deformation, as well as the resultant optical response, is calculated with the acoustic scattering model. The following parameters have been employed in this model: longitudinal and shear wave velocities cL = 5878 m/s and cS = 3706 m/s in silica glass, acoustic velocity in water cw = 1500 m/s, the mass density of glass and water ρg = 2240 kg/m3 and ρw = 1000 kg/m3, the Pockel’s coefficient p11 = 0.113 and p12 = 0.252. Figure 3(b) additively plots the calculated frequency response, which is in good agreement with the measured results. The measured response at 39 MHz is much weaker than the calculated result, which may be caused by absorption loss in water. Figure 3(c) shows the acoustically induced deformation over the fiber cross section at different acoustic frequencies. We use (l, n) to denote the azimuthal and radial order numbers of the in-plane vibration modes. The two peaks in the frequency response curve correspond to the (2, 1) and (2, 2) vibration modes, respectively. As shown in Fig. 3(c), the (2, 1) mode is analogous to compression of the fiber along the incident direction of the ultrasound wave. The (2, 2) mode corresponds to the case of compressing the inner region while stretching the outer region of the fiber along the same direction. Note that the ultrasound waves can also excite other azimuthal orders but only l = 2 azimuthal modes can effectively induce birefringence changes.
To measure the spherical-wave response, a 532-nm pulsed laser (SPOT-10-200-532, Elforlight) is focused on a black tape with a spot size of 3.2 µm (objective lens N. A., 0.1). The laser spot can be approximately considered as a broadband point source. The excitation light has a repetition rate of 1 kHz and a pulse width of 1.8 ns. The sample holder was submerged in deionized water for acoustic propagation. The sensor can be rotated with two fiber holders for sensitivity maximization. Figure 4(a) shows the recorded temporal signal and frequency response to PA signals. Here the acoustic source S is facing the middle region of the laser cavity. The sensor presents a maximum at 22 MHz, with a bandwidth of about 18 MHz. Compared with the planar-wave response, the 39-MHz response is significantly reduced, as a result of a short Leq. The spherical-wave response has been calculated based on Eq. (4) and the result is superimposed in Fig. 4(b). The shape of the 22-MHz peak is also modified and has a broader bandwidth. The shape difference between the planar- and spherical-wave responses is due to self-cancellation among different acoustic phases.
Fig. 4 (a) Recorded signals in response to spherical ultrasound waves. (b) Measured and calculated frequency responses.
3.2 Spatial sensitivity
We characterize the spatial distribution of sensitivity, i.e., how the acoustic response varies with source position (r, θ, z) [32]. The knowledge of spatial sensitivity helps on maximizing the imaging contrast of PAM. Figure 5(a) shows the measured longitudinal profiles of acoustic sensitivities. The responses have been measured for sensors with different cavity lengths Ls, which is approximately the length of the grating separation. The results are obtained by plotting the PA amplitude while scanning the source along the fiber length. The source-to-fiber distance keeps at d = 250 μm. The 3-mm and 5-mm sensors present flat-top profiles. At the two edges, the intracavity light is reflected by the distributed grating reflector, and the sensitivity decreases towards outward directions over the grating regions. In contrast, the 2-mm one presents a Gaussian-like profile which approximates to the distributed feedback (DFB) lasers. The beat frequency fluctuations over the top regions in the response curves arise from the power instability of excitation light. Based on Eq. (4), the optical response is weighted by the intracavity intensity density (strictly speaking, the average density over the length Leq). The measured sensitivity curves are in accordance with the profiles of laser modes, considering the interaction length Leq is much shorter than the laser cavity. The full width at half maximum (FWHM) of these sensors are 2.2mm, 3.5mm and 4.6 mm, respectively. The 2-mm one presents higher sensitivity than others due to the more confined laser mode. Figure 5(b) shows the measured responses with increasing source-sensor distance d. This result characterizes the sensitivity along the radial direction. The acoustically induced response half weakens when moving the source moves from d = 0.25 mm to 1.0 mm. The response variation follows d-1/2 dependence, which is in accordance with the theoretical analysis in Sec. 2. Figure 5(c) shows the measured azimuthal variation of the acoustic sensitivity. This is measured by rotating the sensor with a step of 10 degrees while fixing the acoustic source. The variation exhibits a |cos(2θ)| dependency, which is a result of core asymmetry. The acoustically induced deformation is analogous to the case of laterally squeezing the fiber. When the fiber is squeezed along the principle axis, the induced phase difference change is maximized. In contrast, squeezing the fiber at 45 degree induce a nearly equal phase changes for both polarization modes, thus the beat signal makes nearly zero responses. As a result, the sensor offers a 60-degree full angle at half maximum (FAHM) along the azimuthal direction.
Ultrasound detection bandwidth determines the axial resolution of PAM. To quantify the bandwidth, PA signals were recorded while scanning the acoustic source in a plane at a distance d = 1mm, as shown in Fig. 6(a). Figures 6(b) and 6(c) demonstrate the measured frequency responses along the x and z axis, respectively. The signals were recorded with step sizes of 46 μm along the x axis and 6.5 μm along the z axis. Each frequency curve is normalized to its maximal response at 22 MHz and presented in color map. The measured profile over 1 to 30 MHz, where the (2, 1) mode is excited, hardly changed with different source positions, and the bandwidth was almost unchanged. Based on Eq. (4), the frequency response is determined by the product of . Over the short effective interaction region, the intracavity intensity can be considered as constant. Therefore, the effective length Leq is almost unchanged for different source positions. In addition, the amplitude of the 39-MHz peak reduces when the source moves away from the fiber sensor due to the increased absorption loss.
Fig. 6 (a) Schematic of scanning acoustic source to measure the spatial distribution of the fiber sensor bandwidth. (b) and (c) Measured frequency responses with scanning source along x and z axis, respectively.
4. OR-PAM
OR-PAM of a resolution target (R1DS1P, Thorlabs) is carried out by raster scanning it with a 2-D linear stage. The target is normal to the incident excitation light. A fiber laser sensor is placed 1.25-mm above the sample. Two fiber laser sensors with cavity lengths Ls = 5 and 2 mm are used to compare their imaging performances. The maximum intensity projection (MIP) images are shown in Figs. 7(a) and 7(b). The 2-mm one provides better imaging contrast than the 5-mm one, as a result of its higher acoustic sensitivity. Figures 7(c) and 7(d) shows the recorded PA signals at the same scanning position for comparison. The 2-mm sensor presents a signal-to-noise ratio of 16.7 dB, much higher than the 6.22 dB of the 5-mm one. The 6th elements of the group 7 can be resolved in both images. The lateral resolution is estimated as 3.5 μm, which is determined by the laser spot size.
Fig. 7 Record PA signals by the 5-mm (a) and 2-mm (b) fiber laser detector. PAM results of the same target with the 5-mm (c) and 2-mm (d) fiber laser.
Two human hairs which embedded in chicken breast tissue were imaged with the same setup. The scanning region is 2.4 × 1.4 mm2. The diameter of the hair is about 78 μm. The single-pulse excitation energy is 80 nJ. The light intensity at the tissue surface was ~20 mJ/cm2 in accordance with the American National Standards Institute (ANSI) safety limit. Figure 8 shows the reconstructed 3-D PAM images acquired with the 5-mm and 2-mm sensors, respectively. The 2-mm one provides a deeper penetration depth (940 μm) than that the 5-mm one (460 μm). The 5-mm sensor can hardly visualize one of the hairs due to the low SNR. It looks like the 5-mm one offers higher resolution, which is actually because the photoacoustic signal is partially lost in noise.
Fig. 8 Reconstructed images of two human hairs embedded in the chicken breast by using the Ls = 5 mm (a) and Ls = 2 mm (b) sensors. (c) and (d) show the side views of the sample. The white dashed lines represent the tissue surface.
5. Conclusion
In this work, we have studied the performance of fiber laser ultrasound sensors, which offers guidance to optimize fiber-optic photoacoustic imaging. The frequency response of the sensor peaks at 22 MHz, which is due to the excitation of the (2, 1) vibration mode of the fiber. With a 100-MHz sampling rate, the sensor exhibits a NEP of 45 Pa. We also characterized the spatial response and found that the sensor presents highest sensitivity at the principle axis facing the middle region of the laser cavity. The acoustic sensitivity can be enhanced by shortening the laser cavity to achieve a more confined laser mode. In a comparative study, a phantom of human hairs inserted into chicken breast tissue was imaged with two sensors having different cavity lengths. Results show that the short one enables higher contrast and deeper penetration. The comprehensive characterization of the fiber sensor provides useful information for its application in photoacoustic imaging.
Funding
National Natural Science Foundation of China (NSFC) (61235005); Guangdong Natural Science Foundation (S2013030013302); Research Grants Council of the Hong Kong Special Administrative Region (Early Career Scheme) (21205016); City University of Hong Kong startup grant (7200474, 9610339); and Shenzhen (China) Basic Research Project (JCYJ20160329150236426).
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