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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 8126–8135
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Microfiber interferometric acoustic transducers

Xiuxin Wang, Long Jin, Jie Li, Yang Ran, and Bai-Ou Guan  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 8126-8135 (2014)
http://dx.doi.org/10.1364/OE.22.008126


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Abstract

Acoustic and ultrasonic transducers are key components in biomedical information technology, which has been applied in medical diagnosis, photoacoustic endoscopy and photoacoustic imaging. In this paper, an acoustic transducer based on Fabry-Perot interferometer (FPI) fabricated in a microscaled optical fiber is demonstrated. The transducer is fabricated by forming two wavelength-matched Bragg gratings into the microfiber by means of side illumination with a 193nm excimer laser. When placing the transducer in water, the applied acoustic signal periodically changes the refractive index (RI) of the surrounding liquid and modulates the transmission of the FPI based on the evanescent-field interaction between the liquid and the transmitting light. As a result, the acoustic signal can be constructed with a tunable laser whose output wavelength is located at the slope of the inteferometric fringes. The transducer presents a sensitivity of 10 times higher than the counterparts fabricated in conventional singlemode fibers and has great potential to achieve higher resolution for photoacoustic imaging due to its reduced diameter.

© 2014 Optical Society of America

1. Introduction

Acoustic/ultrasonic transducer is a device which converts mechanical energy into ultrasound or electrical signals. The transducers have been applied in biomedical information technology, including medical diagnosis, photoacoustic endoscopy and imaging. For photoacoustic imaging, bulk transducers, e.g., piezoelectric and optical ones have been used for acquiring photoacoustic signals [1

1. E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009). [CrossRef] [PubMed]

]. The spatial resolution of imaging is limited by dimensions of the transducers. In 2004, Haltmeier et al presented the theory of integrating transducers [2

2. M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltuaf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004). [CrossRef]

], which indicates that photoacoustic imaging can be realized with a line-profile transducer [3

3. T. Berer, H. Grün, C. Hofer, and P. Burgholzer, “Photoacoustic microscopy with large integrating optical annular detectors,” Proc. SPIE 7371, 73710X (2009). [CrossRef]

5

5. P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005). [CrossRef] [PubMed]

]. Such integrating line transducers can be implemented by use of optical fiber interferometers due to the small fiber diameter [6

6. H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography using a fiber based fabry-perot interferometer as an integrating line detector and image reconstruction by model-based time reversal method,” Proc. SPIE 6631, 663107 (2007). [CrossRef]

,7

7. R. Nuster, S. Gratt, K. Passler, H. Grün, Th. Berer, P. Burgholzer, and G. Paltauf, “Comparison of optical and piezoelectric integrating line detectors,” Proc. SPIE 7177, 71770T (2009). [CrossRef]

]. For the optical fiber transducers, the main limitation of sensitivity lies on the high stiffness of the silica glass. The high Young’s modulus means that the optical phase variation is difficult to change by applied acoustic wave. Polymer fiber has been employed to implement an interferometric transducer with a Mach-Zehnder and a Fabry-Perot interferometer, respectively [8

8. H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, “Fiber-based detectors for photoacoustic imaging,” Proc. SPIE 7371, 73710T (2009). [CrossRef]

]. The sensitivity was enhanced by 5 times using a Fabry-Perot interferometer due to the lower Young’s modulus. However, the integration between the polymer and the existing silica fibers can introduce significant insertion loss.

In this paper, we present our preliminary result on interferometric transducers in a silica optical microfiber. The microfiber is tapered from the conventional singlemode fiber and has a diameter that is comparable with optical wavelength. The transducer is fabricated by forming a grating based Fabry-Perot cavity with a 193 nm excimer laser. When immersed in water, the applied acoustic field can vary the water density shift the interferometric fringes in the transmission spectrum and can effectively change the phase variation within the F-P cavity. As a result, with a laser source whose output wavelength is located at the slope of the fringes, the applied signal can be constructed in the recorded transmitting light. Compared with the counterpart in singlemode fibers, the sensitivity is enhanced by 10 times, due to the strong evanescent field interaction. In addition, the diameter of the transducer is only 5.2 μm, which can significantly enhance the spatial resolution for photoacoustic imaging applications.

2. Principle

The Fabry-Perot cavity can be formed by cascading two wavelength-matched FBGs. The lengths and reflectivities of the two FBGs are l1,2 and R1,2, respectively. Due to the multi-beam interference, periodic narrow transmission peaks can be produced within the reflection band of the gratings. The transmission maxima correspond to the resonance condition:
φ=2k0neffLeff=2mπ
(1)
where φ denotes the round trip phase variation, k0=2π/λ represents the wave number in vacuum, m is an integer denoting the order of resonance. Leff = l0 + leff1 + leff2 is the effective cavity length, where l0 is the grating spacing, leff1,2 is the effective length that a single grating contribute to the cavity [9

9. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef] [PubMed]

].

The working principle of the transducer is described as follows: When the transducer is immersed into water, the fundamental guided mode of the microfiber partially spread into the water in the form of evanescent field. The transverse mode field and the corresponding effective index neff can be changed by varying the refractive index or density of water, based on the evanescent-field interaction. When applying an acoustic field, the refractive index of water can be expressed by [10

10. C. Wurster, J. Staudenraus, and W. Eisenmenger, “The fiber optic probe hydrophone,” IEEE Ultrason. Symp.2(3), 941–944 (1994). [CrossRef]

]
nw(p)=1+(nw,01)(1+pp0p0+Q)1r
(2)
where p is the applied acoustic pressure, r = 7.44, p0 = 100 kPa andQ = 295.5 MPa are the Tait parameters, nw,0 = 1.33 is the refractive index of water at static condition. The index change can be approximately considered linear considering the acoustic pressure is weak. By performing the first-order Taylor’s expansion, the relation between the refractive index and the acoustic pressure can be simplified as
nw(p)=nw,0+k(pp0)
(3)
where k = 1.5 × 10−10 Pa−1. For the F-P cavity, the acoustic signal can be considered as a weak perturbation, which changes the round-trip phase within the cavity and thus spectrally shift the fringes. By launching a laser into the F-P cavity and adjusting the lasing wavelength to λp (corresponding to a round-trip phase φp) at the slope of the interferometric fringes, the transmitting light can be modulated by the acoustic signal and therefore the signal can be reconstructed by monitoring the transmitting intensity. The transmitting intensity of the tunable laser involves a convolution process with the transmission of the F-P cavity, as a photonic filter. However, considering the laser has a linewidth of only ~100 MHz in our experiment, the transmitting intensity can be approximately considered proportional to the transmission of the filter.

The relation between the transmission T of the F-P cavity and the round-trip phase φ can be expressed by [11

11. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition (Oxford University Press, 2006).

]
T=(1-R1)(1-R2)(1R1R2)2+4R1R2sin2φ
(4)
For simplicity, we assume R1 = R2 = R and Eq. (4) can be simplified as
T=(1-R)2(1R)2+4Rsin2φ
(5)
Figure 2 (a) shows the calculated transmission as a function of φ for different reflectivities.
Fig. 2 Calculated transmission of the F-P cavity and dT/dφ as a function of round-trip phase.
For φ = 2mπ, T = 1 corresponds to the transmission maxima. For φ = (2m + 1)π, T = (1-R)2/(1 + R)2, represents the transmission minima, and can be close to zero with high grating reflectivity R.

When applying acoustic signal, the acoustic pressure p changes the round trip phase and therefore changes the transmission at λp. The dependence of the transmission change on acoustic pressure can be expressed by
dTdp=dTdφdφdp
(6)
Derived from Eq. (5),
dTdφ=1(1+4R(1R)2sin2φ)28R(1R)2sinφcosφ
(7)
Figure 2(b) shows the calculated variation of dT/dp with round trip phase φ. It has maximum at the sharp slopes near the transmission maxima, and becomes zero at φ = 2mπ and (2m + 1)π. The calculated result suggests that one can achieve high sensitivity by locating the lasing wavelength at around the transmission maxima as well as increasing the grating reflectivities.

On the other hand, the dependence of phase change on acoustic signal can be expressed by
dφdP=φ(1LeffdLeffdP+1neffdneffdP)
(8)
The first term in the bracket denotes the induced elongation of the cavity and the second term represents the induced effective-index change. In this work, the acoustic wavelength is much larger than fiber diameters and shorter than the length of optical fiber. As described in [12

12. R. D. Paula, J. Cole, and J. Bucaro, “Broad-band ultrasonic sensor based on induced optical phase shifts in single-mode fibers,” J. Lightwave Technol. 1(2), 390–393 (1983). [CrossRef]

], the fiber behaves axially constrained, which means that the axial elongation is zero. Therefore, only the index change contributes to the phase change.

3. Experimental result

In the experiment, the microfiber is tapered from a standard 62.5/125 multimode fiber (Corning Company). The fiber is spliced to singlemode fibers at both ends and then tapered down to 5.2 μm with the assistance of a scanning flame [13

13. J. J. Zhang, Q. Z. Sun, R. B. Liang, J. H. Wo, D. M. Liu, and P. Shum, “Microfiber Fabry-Perot interferometer fabricated by taper-drawing technique and its application as a radio frequency interrogated refractive index sensor,” Opt. Lett. 37(14), 2925–2927 (2012). [CrossRef] [PubMed]

]. The multimode fiber is used because it has a larger Ge-doped photosensitive region, which enables highly efficient grating inscription without hydrogen loading or other photosensitization treatment [14

14. Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics Journal. 4(1), 181–186 (2012). [CrossRef]

]. The F-P cavity is formed by inscribing two wavelength-matched Bragg gratings with a 193nm ArF excimer laser and a phase mask. The single-pulse energy and repetition rate are 3mJ and 200 Hz, respectively. The phase mask has a period of 1070nm. The lengths of the gratings are 3 mm and the grating spacing is 5 mm. After illumination for a duration of 180 seconds, a F-P cavity can be fabricated with a transmission depth of 24.2 dB.

Light propagation in the microfiber relies on the index step between the silica glass and the surrounding medium (air or water). When the fiber is immersed into water, the mode field partially penetrates the water as the form of evanescent field. We numerically calculated the mode field and found that 1.75% of the mode energy resides in water for the 5.2 μm microfiber. Figure 3 shows transmission spectrum of the F-P cavity placed in water measured by an optical spectrum analyzer with a resolution of 0.02 nm.
Fig. 3 Measured transmission spectra of the FPIs fabricated in microfiber and conventional singlemode fibers, respectively. The blue fine line denotes the output wavelength of the incident laser.
The transmission depth decreases to 21.2 dB when the F-P cavity is immersed into water, because the mode field partially spread into water, which lowers the transverse overlap between the optical mode with the grating. Another F-P cavity is fabricated in conventional singlemode fiber with almost identical exposure parameters for comparison. Its transmission is also exhibited in Fig. 3.

Figure 4 shows the experimental setup to transduce the acoustic signal into optical and then electrical signals.
Fig. 4 Experimental setup to test the performance of the transducer.
A tunable laser is used to illuminate the FPI whose output wavelength is adjusted to 1538.33 nm, at the slope of the interferometric fringes. The other end is connected to a photodetector and an oscilloscope. The acoustic waves in the water are generated by pulse generator (Olympus 5072PR). The microfiber FPI is placed in front of the generator head orthogonally to the direction of the propagation of the acoustic wave. The distance between the generator head and transducer is 2 cm. The acoustic field can be approximately considered uniform over the transducer for simplicity before the acoustic wave diverges. The water tank was equipped with sonic absorbent rubber over the inner walls to weaken the reflections of acoustic waves.

Figure 5(a) shows the waveform of a single pulse generated by the pulse generator, whose peak amplitude is 25mV and dip amplitude is −31.25mV, respectively.
Fig. 5 (a) Waveform from the generator; (b) Transduced signal. Inset: Pulse series with a repetition of 5 kHz.
The peak-peak amplitude corresponds to an acoustic pressure of 10.03 kPa. Figure 5(b) shows the transduced signal recorded by the oscilloscope. The measured peak and dip amplitudes are 17.43mV and −26.77mV, respectively. As can be seen from Fig. 5, the detected signal almost remains the original signal waveform. Figure 5(b) inset shows a series of pulses with a repetition of 5 kHz. The background noise is mainly caused by the electrical noise of the photodetector. The noise level is about 0.1 mV, corresponding to a pressure of 0.54 kPa. This can be considered as the minimum acoustic pressure that can be transduced. We increased the incident power of the laser and observed the background noise level over the range from 500 Hz to 10 kHz by use of the electrical spectrum analyzer and did not see obvious raise, which indicates that the photon shot noise is not the dominate factor. The deviation of profiles between the original and regenerated signals in Fig. 5(a) and 5(b) is probably caused because the applied acoustic wave is not a perfect plane wave. Figures 2 and 3 indicate that the spectral slope is not linear with wavelength (or round trip phase), which may also possibly contribute to the distortion. However, the applied acoustic pressure is only of kPa order and the resultant phase change is extremely small, considering the high stiffness of silica glass. This is not likely the reason for the distortion. Note that the fringes shift with ambient temperature with a rate of ~8 pm/°C. The fluctuation in temperature may cause significant change in transducing sensitivity. Therefore, we prefer to locate the incident lasing wavelength at smooth slope for better stability.

We replot the transduced waveform in Fig. 6(a) and the result is compared with the measured result for the interferometric transducer in singlemode fiber under the same testing conditions.
Fig. 6 (a) Transduced signals for the interferometric transducers fabricated in microfiber and siglemode fiber. (b) Measured output voltages as a function of applied acoustic pressure for both transducers. (c) Power spectra of transduced signals. The applied acoustic pressure is 10.03 kPa and the repetition frequency is 5 kHz.
The peak and dip voltages for the singlemode transducer is 1.69 and −2.67 mV, respectively, much lower than the present transducer. Figure 6(b) shows the measured peak-peak voltage as a function of applied acoustic pressure for both transducers. The sensitivities are 1.845 and 0.184 mV/kPa, respectively. Figure 6(c) shows the power spectrum of the transduced signals for both transducers when the applied acoustic pressure is 10.03 kPa. The microfiber transducer present a signal-to-noise ratio of over 40 dB and the power is 10.8 dB higher than the singlemode fiber transducer. The transducer in singlemode fiber has a low sensitivity due to the high stiffness of silica glass. In contrast, the microfiber transducer presents much higher sensitivity, as a result of the higher acoustically induced index change arising from the evanescent-field interaction.

Figure 7 shows the measured frequency response of the microfiber and singlemode fiber interferometric transducers from 100 Hz to 5 kHz.
Fig. 7 Measured frequency responses for the microfiber and singlemode-fiber transducers when the applied acoustic pressure is 10.03 kPa.
The responses are quite uniform and the fluctuations are no more than 0.002 dB. The flat response curves are a result of the small transverse diameters of the transducers compared with the acoustic wavelength. It has been demonstrated in [12

12. R. D. Paula, J. Cole, and J. Bucaro, “Broad-band ultrasonic sensor based on induced optical phase shifts in single-mode fibers,” J. Lightwave Technol. 1(2), 390–393 (1983). [CrossRef]

] and [15

15. Th. Berer, I. A. Veres, H. Grün, J. Bauer-Marschallinger, K. Felbermayer, and P. Burgholzer, “Characterization of broadband fiber optic line detectors for photoacoustic tomography,” J Biophotonics 5(7), 518–528 (2012). [CrossRef] [PubMed]

] that the acoustically induced phase shift in an optical fiber is dependant on kar, where ka = 2π/Λa is the wavenumber of the acoustic wave and r denotes the radius of the fiber. The response curve is relatively flat when the acoustic frequency is as low as kHz order. The induced birefringence change can be ignored over the low-frequency range for the present transducer. As the acoustic frequency is increased to MHz order, the induced birefringence becomes higher, and the polarization alignment of the incident laser is required to avoid the effect of birefringence.

The directivity is investigated by varying the alignment angle as shown in Fig. 8(a).
Fig. 8 (a) schematic for the incident angle when testing the directivity of the transducer. (b) Measured normalized sensitivities as a function of alignment angle for both transducers.
The distance between the center of the F-P cavity and the acoustic generator is kept constant while varying the angle. Figure 8(b) shows the measured direction-dependant normalized sensitivities for both transducers. The maximum sensitivities are obtained when the propagation of incident acoustic waves are orthogonal to the fiber. The sensitivity quickly dropped with alignment angle and becomes close to zero when the angle is 80°. The evolutions for the microfiber and singlemode fiber transducers are close. The strong directivity is mainly a result of the line profile of the transducers. Maximum phase shift can be achieved when θ = 0, since the acoustic pressure is identical over the whole F-P cavity, considering the transverse diameter of the transducer is significantly smaller than the acoustic wavelength. In contrast, when the acoustic waves are incident with an angle, the acoustic pressure are nonuniform and the phase changes at different positions can compensate with each other, because the length of the cavity is comparable with the acoustic wavelength.

4. Discussion

5. Conclusion

In conclusion, an acoustic transducer with a F-P cavity structure fabricated in a microscaled optical fiber has been demonstrated. The input wavelength of the tunable laser is located at the slope of the interferometric fringes. When acoustic signal is applied, the transmission is modulated, mainly due to the strong evanescent-field interaction. The sensitivity is about 10 times higher than its counterparts in conventional singlemode fiber and the spatial resolution has been improved due to the small diameter of the transducer.

Acknowledgments

This work was supported by the National Science Foundation for Distinguished Young Scholars of China (Grant No. 61225023), the National Natural Science Foundation of China (Grant No. 11374129), the Research Fund for the Doctoral Program of Higher Education (Grant No. 20114401110006), the Guangdong Natural Science Foundation (Grant No. S2013030013302), and the Planned Science and Technology Project of Guangzhou (Grant No. 2012J5100028).

References and links

1.

E. Z. Zhang, J. G. Laufer, R. B. Pedley, and P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009). [CrossRef] [PubMed]

2.

M. Haltmeier, O. Scherzer, P. Burgholzer, and G. Paltuaf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004). [CrossRef]

3.

T. Berer, H. Grün, C. Hofer, and P. Burgholzer, “Photoacoustic microscopy with large integrating optical annular detectors,” Proc. SPIE 7371, 73710X (2009). [CrossRef]

4.

G. Zangerl, O. Scherzer, and M. Haltmeier, “Circular integrating detectors in photo and themoacoustic tomgraphy,” Inverse Probl. Sci. Eng. 17(1), 133–142 (2009). [CrossRef]

5.

P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005). [CrossRef] [PubMed]

6.

H. Grün, G. Paltauf, M. Haltmeier, and P. Burgholzer, “Photoacoustic tomography using a fiber based fabry-perot interferometer as an integrating line detector and image reconstruction by model-based time reversal method,” Proc. SPIE 6631, 663107 (2007). [CrossRef]

7.

R. Nuster, S. Gratt, K. Passler, H. Grün, Th. Berer, P. Burgholzer, and G. Paltauf, “Comparison of optical and piezoelectric integrating line detectors,” Proc. SPIE 7177, 71770T (2009). [CrossRef]

8.

H. Grün, T. Berer, R. Nuster, G. Paltauf, and P. Burgholzer, “Fiber-based detectors for photoacoustic imaging,” Proc. SPIE 7371, 73710T (2009). [CrossRef]

9.

Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef] [PubMed]

10.

C. Wurster, J. Staudenraus, and W. Eisenmenger, “The fiber optic probe hydrophone,” IEEE Ultrason. Symp.2(3), 941–944 (1994). [CrossRef]

11.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition (Oxford University Press, 2006).

12.

R. D. Paula, J. Cole, and J. Bucaro, “Broad-band ultrasonic sensor based on induced optical phase shifts in single-mode fibers,” J. Lightwave Technol. 1(2), 390–393 (1983). [CrossRef]

13.

J. J. Zhang, Q. Z. Sun, R. B. Liang, J. H. Wo, D. M. Liu, and P. Shum, “Microfiber Fabry-Perot interferometer fabricated by taper-drawing technique and its application as a radio frequency interrogated refractive index sensor,” Opt. Lett. 37(14), 2925–2927 (2012). [CrossRef] [PubMed]

14.

Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, and B. O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics Journal. 4(1), 181–186 (2012). [CrossRef]

15.

Th. Berer, I. A. Veres, H. Grün, J. Bauer-Marschallinger, K. Felbermayer, and P. Burgholzer, “Characterization of broadband fiber optic line detectors for photoacoustic tomography,” J Biophotonics 5(7), 518–528 (2012). [CrossRef] [PubMed]

16.

J. Li, X. Shen, L. P. Sun, and B. O. Guan, “Characteristics of microfiber Fabry-Perot resonators fabricated by UV exposure,” Opt. Express 21(10), 12111–12121 (2013). [CrossRef] [PubMed]

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Fiber Optics

History
Original Manuscript: January 30, 2014
Revised Manuscript: March 23, 2014
Manuscript Accepted: March 23, 2014
Published: March 31, 2014

Virtual Issues
Vol. 9, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Xiuxin Wang, Long Jin, Jie Li, Yang Ran, and Bai-Ou Guan, "Microfiber interferometric acoustic transducers," Opt. Express 22, 8126-8135 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8126


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References

  1. E. Z. Zhang, J. G. Laufer, R. B. Pedley, P. C. Beard, “In vivo high-resolution 3D photoacoustic imaging of superficial vascular anatomy,” Phys. Med. Biol. 54(4), 1035–1046 (2009). [CrossRef] [PubMed]
  2. M. Haltmeier, O. Scherzer, P. Burgholzer, G. Paltuaf, “Thermoacoustic computed tomography with large planar receivers,” Inverse Probl. 20(5), 1663–1673 (2004). [CrossRef]
  3. T. Berer, H. Grün, C. Hofer, P. Burgholzer, “Photoacoustic microscopy with large integrating optical annular detectors,” Proc. SPIE 7371, 73710X (2009). [CrossRef]
  4. G. Zangerl, O. Scherzer, M. Haltmeier, “Circular integrating detectors in photo and themoacoustic tomgraphy,” Inverse Probl. Sci. Eng. 17(1), 133–142 (2009). [CrossRef]
  5. P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, O. Scherzer, “Thermoacoustic tomography with integrating area and line detectors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(9), 1577–1583 (2005). [CrossRef] [PubMed]
  6. H. Grün, G. Paltauf, M. Haltmeier, P. Burgholzer, “Photoacoustic tomography using a fiber based fabry-perot interferometer as an integrating line detector and image reconstruction by model-based time reversal method,” Proc. SPIE 6631, 663107 (2007). [CrossRef]
  7. R. Nuster, S. Gratt, K. Passler, H. Grün, Th. Berer, P. Burgholzer, G. Paltauf, “Comparison of optical and piezoelectric integrating line detectors,” Proc. SPIE 7177, 71770T (2009). [CrossRef]
  8. H. Grün, T. Berer, R. Nuster, G. Paltauf, P. Burgholzer, “Fiber-based detectors for photoacoustic imaging,” Proc. SPIE 7371, 73710T (2009). [CrossRef]
  9. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef] [PubMed]
  10. C. Wurster, J. Staudenraus, W. Eisenmenger, “The fiber optic probe hydrophone,” IEEE Ultrason. Symp.2(3), 941–944 (1994). [CrossRef]
  11. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition (Oxford University Press, 2006).
  12. R. D. Paula, J. Cole, J. Bucaro, “Broad-band ultrasonic sensor based on induced optical phase shifts in single-mode fibers,” J. Lightwave Technol. 1(2), 390–393 (1983). [CrossRef]
  13. J. J. Zhang, Q. Z. Sun, R. B. Liang, J. H. Wo, D. M. Liu, P. Shum, “Microfiber Fabry-Perot interferometer fabricated by taper-drawing technique and its application as a radio frequency interrogated refractive index sensor,” Opt. Lett. 37(14), 2925–2927 (2012). [CrossRef] [PubMed]
  14. Y. Ran, L. Jin, Y. N. Tan, L. P. Sun, J. Li, B. O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics Journal. 4(1), 181–186 (2012). [CrossRef]
  15. Th. Berer, I. A. Veres, H. Grün, J. Bauer-Marschallinger, K. Felbermayer, P. Burgholzer, “Characterization of broadband fiber optic line detectors for photoacoustic tomography,” J Biophotonics 5(7), 518–528 (2012). [CrossRef] [PubMed]
  16. J. Li, X. Shen, L. P. Sun, B. O. Guan, “Characteristics of microfiber Fabry-Perot resonators fabricated by UV exposure,” Opt. Express 21(10), 12111–12121 (2013). [CrossRef] [PubMed]

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