### Abstract

We describe the theoretical principles of a new Doppler method, which uses the acoustic response of a moving object to a highly localized dynamic radiation force of the ultrasound field to calculate the velocity of the moving object according to Doppler frequency shift. This method, named vibro-acoustic Doppler (VAD), employs two ultrasound beams separated by a slight frequency difference, f, transmitting in an X-focal configuration. Both ultrasound beams experience a frequency shift because of the moving objects and their interaction at the joint focal zone produces an acoustic frequency shift occurring around the low-frequency (f) acoustic emission signal. The acoustic emission field resulting from the vibration of the moving object is detected and used to calculate its velocity. We report the formula that describes the relation between Doppler frequency shift of the emitted acoustic field and the velocity of the moving object. To verify the theory, we used a string phantom. We also tested our method by measuring fluid velocity in a tube. The results show that the error calculated for both string and fluid velocities is less than 9.1%. Our theory shows that in the worst case, the error is 0.54% for a 25 angle variation for the VAD method compared with an error of -82.6% for a 25 angle variation for a conventional continuous wave Doppler method. An advantage of this method is that, unlike conventional Doppler, it is not sensitive to angles between the ultrasound beams and direction of motion.

Original language | English (US) |
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Article number | 6189182 |

Pages (from-to) | 752-765 |

Number of pages | 14 |

Journal | IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control |

Volume | 59 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2012 |

### ASJC Scopus subject areas

- Instrumentation
- Acoustics and Ultrasonics
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control*,

*59*(4), 752-765. [6189182]. https://doi.org/10.1109/TUFFC.2012.2253