Background of UDV

Functioning principles of pulsed Doppler ultrasound

Doppler ultrasonic technique

Doppler ultrasound technique, was originally applied in the medical field and dates back more then 30 years. The use of pulsed emissions has extended this technique to other fields and has open the way to new measuring techniques in fluid dynamics.

The term "Doppler ultrasound velocimetry" implies that the velocity is measured by finding the Doppler frequency in the received signal, as it is the case in Laser Doppler velocimetry. In fact, in ultrasonic pulsed Doppler velocimetry, this is never the case. Velocities are derived from shifts in positions between pulses, and the Doppler effect plays a minor role. Unfortunately, many publications, even recent ones, fails to make this distinction, resulting in erroneous system description and fallacious interpretation of the influence from various physical effects.

The pulsed Doppler method

In pulsed Doppler ultrasound, instead of emitting continuous ultrasonic waves, an emitter sends periodically a short ultrasonic burst and a receiver collects continuously echoes issues from targets that may be present in the path of the ultrasonic beam. By sampling the incoming echoes at the same time relative to the emission of the bursts, the velocity of the particles can be computed.

How the velocity is measured

Let's assume a situation, as illustrated in the figure beside, where only one particle is present along the path of the ultrasonic beam.

At time T1, a burst is emitted. This burst propagates inside the liquid. At time T2, the burst touches the particle. If the sizes of the particle are much smaller than the wave length, only a very small echo is generated (scattering effect) This echoes goes back in direction to the transducer, while the main energy continues its propagation.

At time T3, the echo reaches the transducer. The depth of the particle can be determined from the traveling time (T3-T1):

where C is the sound velocity of the acoustic wave in the liquid.

In pulsed ultrasonic velocimetry burst are emitted periodicaly. Following each emission, the echo signal is sampled at a fixed delay after the emission. From the above equation, this delay defines the depth.

If the particle moves between the successive emissions the sampled values taken at time Ts will change over the time. Depending of the shape of the emitted signal, these values may form a sinusoidal signal.

The main equation

The frequency, Fd, of this sinusoidal signal, which is named Doppler frequency, is directly connected to the velocity of the particle, which is given by the Doppler equation.

where C is the sound velocity of the acoustic wave in the liquid and Fe the frequency of the emitted burst.

In the real world, there are many particles and these particles are randomly distributed inside the ultrasonic beam. The echoes issue from each particle are therefore combined together in a random fashion, and gives a random echo signal. Hopefully, a high degree of correlation exists between the different emissions. The algorithms we developed to extract the velocity information are based on this correlation.

Advantages and limitations

Pulsed Doppler ultrasound offers instantaneously a complete velocity profile. Unfortunately, as the information is available only periodically, this technique suffers from the Nyquist theorem. This means that a maximum velocity exists for each pulse repetition frequency (Fprf):

The maximum measurable depth is also defined by the pulsed repetition frequency:

Therefore the product of Pmax and Vmax is constant, and is given by:

Ultrasound scattering

The ultrasonic waves generated by the transducer are more or less confined in a narrow cone. As they travel in this cone they may be reflected or scattered when they touch a particle having a different acoustic impedance.

The acoustic impedance is defined by the product of the density of the material of the particle and its sound velocity.

If the size of the particle is bigger than the wave length, the ultrasonic waves are reflected and refracted by the particle. In such a case the direction of propagation and the intensity of the ultrasonic waves are affected. But if the size of the particle is much smaller than the wave length an other phenomena appears, which is named scattering. In such a case, a very small amount of the ultrasonic energy is reflected back to the transducer (backward scattering). The intensity and the direction of propagation of the incoming waves are practically not affected by the scattering phenomena. Ultrasonic Doppler velocimetry needs therefore particles smaller than the wave length.