## Photoacoustic Doppler measurement of flow using tone burst excitation

Optics Express, Vol. 18, Issue 5, pp. 4212-4221 (2010)

http://dx.doi.org/10.1364/OE.18.004212

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### Abstract

In this paper a novel technique for flow measurement which is based on the photoacoustic (PA) Doppler effect is described. A significant feature of the proposed approach is that it can be implemented using tone burst optical excitation thus enabling simultaneous measurement of both velocity and position. The technique, which is based on external modulation and heterodyne detection, was experimentally demonstrated by measurement of the flow of a suspension of carbon particles in a silicon tube and successfully determined the particles mean velocity up to values of 130 mm/sec, which is about 10 times higher than previously reported PA Doppler setups. In the theoretical part a rigorous derivation of the PA response of a flowing medium is described and some important simplifying approximations are highlighted.

© 2010 OSA

## 1. Introduction

2. M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” R. Sci. Inst. **77**(4), 041101 (2006). [CrossRef]

3. H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. **99**(18), 184501 (2007). [CrossRef] [PubMed]

5. H. Fang and L. V. Wang, “M-mode photoacoustic particle flow imaging,” Opt. Lett. **34**(5), 671–673 (2009). [CrossRef] [PubMed]

3. H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. **99**(18), 184501 (2007). [CrossRef] [PubMed]

4. H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. **91**(26), 264103 (2007). [CrossRef]

5. H. Fang and L. V. Wang, “M-mode photoacoustic particle flow imaging,” Opt. Lett. **34**(5), 671–673 (2009). [CrossRef] [PubMed]

## 2. Theory

6. Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. **49**(14), 3117–3124 (2004). [CrossRef] [PubMed]

*c*in the surrounding medium. At zero flow rate

*v*. The absorber is represented by a 3-dimentional delta function,

*a*is the PA efficiency coefficient of the particle,

**v**is the absorber’s velocity vector and

7. S. M. Blinder, “Delta functions in spherical coordinates and how to avoid losing them: fields of point charges and dipoles,” Am. J. Phys. **71**(8), 816–818 (2003). [CrossRef]

*θ*and

*ϕ*. Equation (3) can be easily integrated yielding:The complex PA response for continuous sinusoidal excitation at frequency

**v**. This result, which reproduces the expression for the PA Doppler frequency given by Fang

*et al.*[3

3. H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. **99**(18), 184501 (2007). [CrossRef] [PubMed]

8. W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. **21**(3), 183–192 (1974). [CrossRef] [PubMed]

9. G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. **26**(5), 853–862 (2000). [CrossRef]

*d*is the characteristic length of the spatial inhomogeneities of the optical beam or the dimension of the beam in the direction of the flow if the beam is homogenous. Another homogeneous broadening factor stems from the finite size of the ultrasound detector. This leads to a range of angles

*r*is the radial distance from the tube axis,

*R*is the tube radius,

*F*is the flow rate,

*A*is the tube cross-section area and

## 3. Experimental setup

10. A. Sheinfeld, E. Bergman, S. Gilead, and A. Eyal, “The use of pulse synthesis for optimization of photoacoustic measurements,” Opt. Express **17**(9), 7328–7338 (2009). [CrossRef] [PubMed]

_{2}O) with volume fraction

_{2}O was due to its relatively low absorption (around 1 cm

^{−1}) in the relevant spectral range. The absorption of the suspension was estimated to be around 5 cm

^{−1}by measuring its PA response and using the PA response of double distilled water for calibration.

## 4. Experimental results

## 5. Conclusions

## Appendix

## Acknowledgement

## References and links

1. | L. V. Wang, |

2. | M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” R. Sci. Inst. |

3. | H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. |

4. | H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. |

5. | H. Fang and L. V. Wang, “M-mode photoacoustic particle flow imaging,” Opt. Lett. |

6. | Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. |

7. | S. M. Blinder, “Delta functions in spherical coordinates and how to avoid losing them: fields of point charges and dipoles,” Am. J. Phys. |

8. | W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. |

9. | G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. |

10. | A. Sheinfeld, E. Bergman, S. Gilead, and A. Eyal, “The use of pulse synthesis for optimization of photoacoustic measurements,” Opt. Express |

**OCIS Codes**

(170.5120) Medical optics and biotechnology : Photoacoustic imaging

(280.2490) Remote sensing and sensors : Flow diagnostics

(110.4153) Imaging systems : Motion estimation and optical flow

(110.5125) Imaging systems : Photoacoustics

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: November 16, 2009

Revised Manuscript: January 17, 2010

Manuscript Accepted: January 19, 2010

Published: February 17, 2010

**Virtual Issues**

Vol. 5, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Adi Sheinfeld, Sharon Gilead, and Avishay Eyal, "Photoacoustic Doppler measurement of flow using tone burst excitation," Opt. Express **18**, 4212-4221 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4212

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### References

- L. V. Wang, Photoacoustic imaging and spectroscopy (CRC Press, 2009).
- M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006). [CrossRef]
- H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. 99(18), 184501 (2007). [CrossRef] [PubMed]
- H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. 91(26), 264103 (2007). [CrossRef]
- H. Fang and L. V. Wang, “M-mode photoacoustic particle flow imaging,” Opt. Lett. 34(5), 671–673 (2009). [CrossRef] [PubMed]
- Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004). [CrossRef] [PubMed]
- S. M. Blinder, “Delta functions in spherical coordinates and how to avoid losing them: fields of point charges and dipoles,” Am. J. Phys. 71(8), 816–818 (2003). [CrossRef]
- W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. 21(3), 183–192 (1974). [CrossRef] [PubMed]
- G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. 26(5), 853–862 (2000). [CrossRef]
- A. Sheinfeld, E. Bergman, S. Gilead, and A. Eyal, “The use of pulse synthesis for optimization of photoacoustic measurements,” Opt. Express 17(9), 7328–7338 (2009). [CrossRef] [PubMed]

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