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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 3 — Feb. 29, 2012
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Enhancement of photoacoustic image quality by sound speed correction: ex vivo evaluation

Changhan Yoon, Jeeun Kang, Seunghee Han, Yangmo Yoo, Tai-Kyong Song, and Jin Ho Chang  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 3082-3090 (2012)
http://dx.doi.org/10.1364/OE.20.003082


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Abstract

Real-time photoacoustic (PA) imaging involves beamforming methods using an assumed fixed sound speed, typically 1540 m/s in soft tissue. This leads to degradation of PA image quality because the true sound speed changes as PA signal propagates through different types of soft tissues: the range from 1450 m/s to 1600 m/s. This paper proposes a new method for estimating an optimal sound speed to enhance the cross-sectional PA image quality. The optimal sound speed is determined when coherent factor with the sound speed is maximized. The proposed method was validated through simulation and ex vivo experiments with microcalcification-contained breast cancer specimen. The experimental results demonstrated that the best lateral resolution of PA images of microcalcifications can be achieved when the optimal sound speed is utilized.

© 2012 OSA

1. Introduction

Photoacoustic (PA) imaging is an emerging technology that takes advantages of an optical contrast and ultrasonic resolution and provides functional information such as hemoglobin concentration and oxygen saturation under some conditions [1

1. H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24(7), 848–851 (2006). [CrossRef] [PubMed]

3

3. M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 0411011 (2006). [CrossRef]

]. The acoustic waves (i.e., PA signals) are generated only inside the targets absorbing incident laser pulses due to thermoelastic expansion. The PA signals are detected by an ultrasound (US) transducer. Depending on the detection scheme, various image reconstruction techniques can be applied such as PA microscopy (PAM), PA tomography (PAT), and cross-sectional PA imaging [3

3. M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 0411011 (2006). [CrossRef]

5

5. X. Wang, J. B. Fowlkes, J. M. Cannata, C. Hu, and P. L. Carson, “Photoacoustic imaging with a commercial ultrasound system and a custom probe,” Ultrasound Med. Biol. 37(3), 484–492 (2011). [CrossRef] [PubMed]

]. Among them, the cross-sectional PA imaging is capable of real-time imaging after minimal modification of a current commercial US scanner [5

5. X. Wang, J. B. Fowlkes, J. M. Cannata, C. Hu, and P. L. Carson, “Photoacoustic imaging with a commercial ultrasound system and a custom probe,” Ultrasound Med. Biol. 37(3), 484–492 (2011). [CrossRef] [PubMed]

, 6

6. T. Harrison and R. J. Zemp, “The applicability of ultrasound dynamic receive beamformers to photoacoustic imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58(10), 2259–2263 (2011). [CrossRef] [PubMed]

]. Furthermore, this is a dual-modality imaging method combining PA and US images, thus simultaneously providing anatomical and functional information, both of which are important in the diagnosis of disease.

The real-time PA imaging involves beamformation in which the received PA signals are coherently summed by compensating for their different traveling distances (or phase differences) to reconstruct an image of initial pressure distribution. Delay-and-sum beamforming (DAS-BF) and adaptive beamformings based on coherence factor (CF) and minimum variance (MV) have been used [7

7. C.-K. Liao, M.-L. Li, and P.-C. Li, “Optoacoustic imaging with synthetic aperture focusing and coherence weighting,” Opt. Lett. 29(21), 2506–2508 (2004). [CrossRef] [PubMed]

, 8

8. S. Park, A. B. Karpiouk, S. R. Aglyamov, and S. Y. Emelianov, “Adaptive beamforming for photoacoustic imaging,” Opt. Lett. 33(12), 1291–1293 (2008). [CrossRef] [PubMed]

]. These beamforming algorithms generally assume a fixed sound speed (e.g., 1540 m/s) in calculating time delays for the receive focusing. However, the true sound speed changes as PA signal propagates through different types of soft tissues: the range from 1450 m/s in fat to 1600 m/s in muscle. The disparity between an assumed constant sound speed and the true value leads to defocusing and consequently degradation of image quality in both US and PA imaging [9

9. C. Yoon, Y. Lee, J. H. Chang, T.-K. Song, and Y. Yoo, “In vitro estimation of mean sound speed based on minimum average phase variance in medical ultrasound imaging,” Ultrasonics 51(7), 795–802 (2011). [CrossRef] [PubMed]

]. To mitigate the problem in PA imaging, the sound speed estimation methods have been proposed, which are suitable for PAM and PAT [10

10. B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, and P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011). [CrossRef] [PubMed]

, 11

11. R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “Reflection mode photoacoustic measurement of speed of sound,” Opt. Express 15(6), 3291–3300 (2007). [CrossRef] [PubMed]

]. In these methods, the sound speed in a propagating medium was estimated by finding the maximal sharpness of prominent features in image domain with gradient based methods or by fitting the analytic expression of cross-correlation with received radio-frequency (RF) channel data from an annular array transducer. The gradient based method employed a Fourier-transform-based reconstruction algorithm that less suffers from image artifacts (e.g., sidelobe) than the beamforming algorithms [12

12. K. P. Köstli and P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt. 42(10), 1899–1908 (2003). [CrossRef] [PubMed]

]. However, the gradient based method is inappropriate for cross-sectional PA images reconstructed by the beamforming algorithms. This is so because the beamformation with a wrong sound speed leads to severely increasing sidelobe levels that are regarded as edges (or high sharpness) in the gradient based method. Also, the slopes of mainlobe and sidelobes vary depending on imaging depth due to the diffraction of ultrasound and the change in slice thickness. These characteristics of the cross-sectional PA imaging may cause degrading the performance of the gradient based method.

This paper proposes a new method for estimating an optimal sound speed to enhance the cross-sectional PA image quality, e.g., lateral resolution. In the method, the optimal sound speed is determined when a CF value with the sound speed is maximized. Note that the CF value is utilized not only as a focusing quality factor in estimating the optimal sound speed, but also for the adaptive beamforming based on CF to suppress the sidelobe levels [7

7. C.-K. Liao, M.-L. Li, and P.-C. Li, “Optoacoustic imaging with synthetic aperture focusing and coherence weighting,” Opt. Lett. 29(21), 2506–2508 (2004). [CrossRef] [PubMed]

, 8

8. S. Park, A. B. Karpiouk, S. R. Aglyamov, and S. Y. Emelianov, “Adaptive beamforming for photoacoustic imaging,” Opt. Lett. 33(12), 1291–1293 (2008). [CrossRef] [PubMed]

]. In addition, the estimated sound speed is not the true value but the one providing the highest spatial resolution in the region of interest (ROI). To ascertain the performances of the proposed method, ex vivo experiments were conducted with the microcalcification-contained breast cancer specimen of a volunteer patient.

2. Method

2.1 Optimal sound speed estimation

As shown in Fig. 1(a)
Fig. 1 (a) Illustration of PA signal generated from a point-like reflector and received by an US array transducer when the assumed sound speed is equal to or (b) different from the true one.
, PA signals generated from a point-like absorber are propagated toward the US array transducer and received by each element at different time. In DAS-BF, the receive focusing is dynamically conducted to form an image. To focus the PA signals at an imaging point at (x,z), the time delay for the nth element located at (xn,zn) is calculated by
τn=(xxn)2+(zzn)2Rc,
(1)
where R is the distance between the center of the transducer and the focal point; c is the speed of sound in soft tissues, which is generally assumed to be a constant of 1540 m/s. As indicated in Eq. (1), the time delays for the dynamic receive focusing are a function of the sound speed and applied to compensate for phase differences of PA signals received at each channel. If the sound speed is incorrectly assumed, therefore, the PA signals at each channel will have still phase differences after the compensation as shown in Fig. 1(b).

In the proposed estimation, the pre-beamformed RF data in ROI are first captured. With an initial sound speed, the time delays for receive focusing are calculated using Eq. (1). The time delays are used to compensate for the phase differences of the captured RF data, which are also used in computing the CF in Eq. (2). As indicated in Eq. (3), the CF values are iteratively computed with the RF data in the ROI while changing the sound speed. Finally, the sound speed providing the maximal CF is determined as an optimal sound speed.

2.2 Experiment setup

To evaluate the performance of the proposed method, simulation and ex vivo experiments were conducted. In the simulation, PA signals were generated by using a k-wave toolbox [13

13. B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010). [CrossRef] [PubMed]

]; an absorber with the size of 0.09 mm was placed at the depth of 20 mm and scanned by a 5-MHz ultrasound linear array with 128 elements. The element pitch was 0.3 mm. The generated PA signals propagated through a medium with a sound speed of 1500 m/s and received by the array of which fraction bandwidth was 80%.

3. Results and discussion

Figure 3(a)
Fig. 3 (a) PA image obtained by the simulation. The image was logarithmically compressed with a dynamic range of 30 dB. The diameter of absorber was 0.09 mm. (b) Normalized maximal CF values as a function of sound speed. The maximal CF was found at sound speed of 1500 m/s. (c) the −6 dB lateral resolution as a function of sound speed.
shows a PA image obtained by the simulation; ROI for estimating sound speed was indicated. As shown in Fig. 3(b), the maximum of the CF in the ROI was achieved at the sound speed of 1500 m/s. This sound speed is equal to the true value used in the simulation. The −6 dB lateral resolution of the absorber image was measured as a function of sound speed and the minimum beam width of 0.3 mm was obtained at the true sound speed of 1500 m/s as shown in Fig. 3(c). The −6 dB lateral beam width was gradually broadened as the difference between sound speed and the true one was increased. The simulation results indicate that the proposed method is capable of estimating the true sound speed and improving lateral resolution of PA images.

Figure 4
Fig. 4 (a) Normalized maximal CF values as a function of sound speed. The maximal CF was found at sound speed of 1496 m/s. PA images registered on US images were reconstructed with the sound speed of (b) 1540 m/s and (c) 1496 m/s. The dynamic ranges were 30 dB and 60 dB for PA and US imaging, respectively.
presents the ex vivo experimental results; normalized maximal CF values corresponding to each sound speed are plotted in Fig. 4(a) and the ROI for estimating optimal sound speed is indicated by a white box in Fig. 4(b). As shown in Fig. 4(a), the maximal CF was found at a sound speed of 1496 m/s, which is similar to the simulation result. Although the medium contained fat (or soft tissue) in the specimen, the main composition was saline. Therefore, the optimal sound speed came close to the sound speed in saline solution, which can be computed by [15

15. C. R. Hill, J. C. Bamber, and G. Haar, “Physical principles of medical ultrasonics (John Wiley and Sons, 2004), Chap. 5.

]
csaline=1449.05+45.7T5.21T2+0.23T3+(1.3330.126T+0.009T2)(10S35),
(4)
where T=T/10 (Tin Celsius) and S is the salt concentration in g dry salt per 100 ml water. From Eq. (4), the sound speed in 0.9% saline solution was calculated to be 1503.8 m/s when T = 24 þC. This was similar to the estimated sound speed, i.e., 1496 m/s. Figures 4(b) and (c) show the reconstructed PA images registered on US images with the commonly used sound speed (i.e.,1540 m/s) and the estimated one (i.e., 1496 m/s), respectively. The dynamic ranges were 30 dB and 60 dB for the PA and the US images, respectively. Under visual assessment, it is easily recognized that the sound speed of 1496 m/s (Fig. 4(b)) provides higher distinction of individual microcalcifications than the one of 1540 m/s.

The lateral beam profiles of the microcalcification (indicated by an arrow in Fig. 4(b)) were measured from the PA images and presented in Fig. 5(a)
Fig. 5 (a) Lateral beam profile of the microcalcification indicated by an arrow in Fig. 3(b) and (b) the corresponding CF values at each location.
. The image formed with the sound speed of 1496 m/s provided narrower lateral beam width than that with 1540 m/s; the −6 dB lateral beam width was 0.62 mm in the case of the sound speed of 1496 m/s, while it was 1.40 mm in the case of 1540 m/s. These results can be explained with the fact that the image reconstruction with the optimal sound speed allows for a stark difference between CFs for the main lobe and sidelobes as shown in Fig. 5(b), compared to that with the wrong sound speed.

When the −6 dB lateral beam widths from the same microcalcification were measured as a function of sound speeds (see Fig. 6
Fig. 6 The −6 dB lateral resolution as a function of sound speed.
), it was learned that the lateral resolution was deteriorated more and more as the sound speed went away from the optimal one. In addition, the signal-to-noise ratio (SNR), defined as a ratio of the maximum intensity from 1496 m/s to that from 1540 m/s, was improved by 3.7 dB due to higher efficacy in beamforming and CF weighting.

Phase distortion (i.e., phase aberration) due to the variation of sound speed is a function of imaging depth. Therefore, the accurate compensation for the phase distortion may be conducted by measuring phase aberration or sound speed variation along imaging depth. This can be done by computing cross-correlation between RF data at each channel, which requires considerable computational cost [16

16. S. W. Flax and M. O’Donnell, “Phase-aberration correction using signals from point reflector and diffuse scatterers: basic principles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35(6), 758–767 (1988). [CrossRef]

]. Although the proposed method is not for measuring accurate sound speed along imaging depth, it can provide an optimal sound speed with which the best spatial resolution is achieved in the ROI. The proposed method may be more useful in combined PA/US imaging because the ROI for PA imaging is usually confined over a large area of US imaging.

In the calculation of CF for ultrasound imaging, there are two possible error sources that under- or over-estimate the value: low input SNR and strong reflectors positioned outside ROI [17

17. C. I. Nilsen and S. Holm, “Wiener beamforming and the coherence factor in ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(6), 1329–1346 (2010). [CrossRef] [PubMed]

]. The low input SNR is generally problematic in ultrasound imaging when CF is calculated for point scatterers and anechoic cysts of which amplitude is either similar to or a few times higher than noise level. Also, the sidelobes from strong reflectors outside ROI may affect the accuracy of CF when the ROI contains only weak reflectors. However, the proposed method is robust against those error sources because the sound speed estimation is conducted using PA signals from strong absorbers; in particular, this is true in the PA imaging for microcalcifications. The amplitude of PA signals is generally 30 dB higher than noise level, so that the low input SNR is no longer any issue. Since strong absorbers are the main concern in PA imaging, furthermore, ROI should contain the strong absorbers.

4. Conclusions

In this paper, we proposed the method for an optimal sound speed estimation, which was based on maximizing CF in ROI for PA imaging. The proposed method was verified through the simulation and the ex vivo experiments with the microcalcification-contained breast specimen. The results demonstrated that proposed method can enhance PA image quality, and is useful in observation of breast microcalcifications.

Acknowledgment

This work was supported by International Collaborative R&D Program (2010-TD-500409-001) funded by the Ministry of Knowledge Economy (MKE), South Korea.

References and links

1.

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24(7), 848–851 (2006). [CrossRef] [PubMed]

2.

R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, and W. Steenbergen, “Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis,” Opt. Express 13(1), 89–95 (2005). [CrossRef] [PubMed]

3.

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 0411011 (2006). [CrossRef]

4.

T. N. Erpelding, C. Kim, M. Pramanik, L. Jankovic, K. Maslov, Z. Guo, J. A. Margenthaler, M. D. Pashley, and L. V. Wang, “Sentinel lymph nodes in the rat: noninvasive photoacoustic and US imaging with a clinical US system,” Radiology 256(1), 102–110 (2010). [CrossRef] [PubMed]

5.

X. Wang, J. B. Fowlkes, J. M. Cannata, C. Hu, and P. L. Carson, “Photoacoustic imaging with a commercial ultrasound system and a custom probe,” Ultrasound Med. Biol. 37(3), 484–492 (2011). [CrossRef] [PubMed]

6.

T. Harrison and R. J. Zemp, “The applicability of ultrasound dynamic receive beamformers to photoacoustic imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58(10), 2259–2263 (2011). [CrossRef] [PubMed]

7.

C.-K. Liao, M.-L. Li, and P.-C. Li, “Optoacoustic imaging with synthetic aperture focusing and coherence weighting,” Opt. Lett. 29(21), 2506–2508 (2004). [CrossRef] [PubMed]

8.

S. Park, A. B. Karpiouk, S. R. Aglyamov, and S. Y. Emelianov, “Adaptive beamforming for photoacoustic imaging,” Opt. Lett. 33(12), 1291–1293 (2008). [CrossRef] [PubMed]

9.

C. Yoon, Y. Lee, J. H. Chang, T.-K. Song, and Y. Yoo, “In vitro estimation of mean sound speed based on minimum average phase variance in medical ultrasound imaging,” Ultrasonics 51(7), 795–802 (2011). [CrossRef] [PubMed]

10.

B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, and P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt. 16(9), 090501 (2011). [CrossRef] [PubMed]

11.

R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “Reflection mode photoacoustic measurement of speed of sound,” Opt. Express 15(6), 3291–3300 (2007). [CrossRef] [PubMed]

12.

K. P. Köstli and P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt. 42(10), 1899–1908 (2003). [CrossRef] [PubMed]

13.

B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. 15(2), 021314 (2010). [CrossRef] [PubMed]

14.

J. Kang, E. K. Kim, J. Y. Kwak, Y. Yoo, T.-K. Song, and J. H. Chang, “Optimal laser wavelength for photoacoustic imaging of breast microcalcification,” Appl. Phys. Lett. 99(15), 153702 (2011). [CrossRef]

15.

C. R. Hill, J. C. Bamber, and G. Haar, “Physical principles of medical ultrasonics (John Wiley and Sons, 2004), Chap. 5.

16.

S. W. Flax and M. O’Donnell, “Phase-aberration correction using signals from point reflector and diffuse scatterers: basic principles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 35(6), 758–767 (1988). [CrossRef]

17.

C. I. Nilsen and S. Holm, “Wiener beamforming and the coherence factor in ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(6), 1329–1346 (2010). [CrossRef] [PubMed]

OCIS Codes
(110.7170) Imaging systems : Ultrasound
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.5120) Medical optics and biotechnology : Photoacoustic imaging

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: December 2, 2011
Revised Manuscript: January 17, 2012
Manuscript Accepted: January 18, 2012
Published: January 25, 2012

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Changhan Yoon, Jeeun Kang, Seunghee Han, Yangmo Yoo, Tai-Kyong Song, and Jin Ho Chang, "Enhancement of photoacoustic image quality by sound speed correction: ex vivo evaluation," Opt. Express 20, 3082-3090 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-3-3082


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References

  1. H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol.24(7), 848–851 (2006). [CrossRef] [PubMed]
  2. R. I. Siphanto, K. K. Thumma, R. G. M. Kolkman, T. G. van Leeuwen, F. F. M. de Mul, J. W. van Neck, L. N. A. van Adrichem, and W. Steenbergen, “Serial noninvasive photoacoustic imaging of neovascularization in tumor angiogenesis,” Opt. Express13(1), 89–95 (2005). [CrossRef] [PubMed]
  3. M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum.77(4), 0411011 (2006). [CrossRef]
  4. T. N. Erpelding, C. Kim, M. Pramanik, L. Jankovic, K. Maslov, Z. Guo, J. A. Margenthaler, M. D. Pashley, and L. V. Wang, “Sentinel lymph nodes in the rat: noninvasive photoacoustic and US imaging with a clinical US system,” Radiology256(1), 102–110 (2010). [CrossRef] [PubMed]
  5. X. Wang, J. B. Fowlkes, J. M. Cannata, C. Hu, and P. L. Carson, “Photoacoustic imaging with a commercial ultrasound system and a custom probe,” Ultrasound Med. Biol.37(3), 484–492 (2011). [CrossRef] [PubMed]
  6. T. Harrison and R. J. Zemp, “The applicability of ultrasound dynamic receive beamformers to photoacoustic imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control58(10), 2259–2263 (2011). [CrossRef] [PubMed]
  7. C.-K. Liao, M.-L. Li, and P.-C. Li, “Optoacoustic imaging with synthetic aperture focusing and coherence weighting,” Opt. Lett.29(21), 2506–2508 (2004). [CrossRef] [PubMed]
  8. S. Park, A. B. Karpiouk, S. R. Aglyamov, and S. Y. Emelianov, “Adaptive beamforming for photoacoustic imaging,” Opt. Lett.33(12), 1291–1293 (2008). [CrossRef] [PubMed]
  9. C. Yoon, Y. Lee, J. H. Chang, T.-K. Song, and Y. Yoo, “In vitro estimation of mean sound speed based on minimum average phase variance in medical ultrasound imaging,” Ultrasonics51(7), 795–802 (2011). [CrossRef] [PubMed]
  10. B. E. Treeby, T. K. Varslot, E. Z. Zhang, J. G. Laufer, and P. C. Beard, “Automatic sound speed selection in photoacoustic image reconstruction using an autofocus approach,” J. Biomed. Opt.16(9), 090501 (2011). [CrossRef] [PubMed]
  11. R. G. M. Kolkman, W. Steenbergen, and T. G. van Leeuwen, “Reflection mode photoacoustic measurement of speed of sound,” Opt. Express15(6), 3291–3300 (2007). [CrossRef] [PubMed]
  12. K. P. Köstli and P. C. Beard, “Two-dimensional photoacoustic imaging by use of Fourier-transform image reconstruction and a detector with an anisotropic response,” Appl. Opt.42(10), 1899–1908 (2003). [CrossRef] [PubMed]
  13. B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt.15(2), 021314 (2010). [CrossRef] [PubMed]
  14. J. Kang, E. K. Kim, J. Y. Kwak, Y. Yoo, T.-K. Song, and J. H. Chang, “Optimal laser wavelength for photoacoustic imaging of breast microcalcification,” Appl. Phys. Lett.99(15), 153702 (2011). [CrossRef]
  15. C. R. Hill, J. C. Bamber, and G. Haar, “Physical principles of medical ultrasonics (John Wiley and Sons, 2004), Chap. 5.
  16. S. W. Flax and M. O’Donnell, “Phase-aberration correction using signals from point reflector and diffuse scatterers: basic principles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control35(6), 758–767 (1988). [CrossRef]
  17. C. I. Nilsen and S. Holm, “Wiener beamforming and the coherence factor in ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control57(6), 1329–1346 (2010). [CrossRef] [PubMed]

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