Transducers ultrasonic field

In Doppler echography, the object is not to use a plain longitudinal wave, but rather an ultrasonic beam that is as thin as possible throughout the measurement depth. The geometry of the acoustic field is governed by the diameter D of the emitter and the wavelength of the ultrasonic waves l, which is equal to the ratio of the sound velocity in the analyzed medium and the emitting frequency. The typical shape of the ultrasonic field is illustrated on the two figures, which show two particular zones.

The near field

The region located near the transducer surface is called the near field. In the near field, the acoustic field is basically cylindrical, with a diameter slightly less than the diameter of the emitter, and the intensity of the acoustic waves oscillates along the axis of the transducer. As the characteristic distances of these oscillations are much smaller than the dimensions of the measured volumes, they do not significantly affect Doppler information collected in this region. The length of the near field, Z, is determined by the position of the last maximum of the acoustic intensity.

The far field

The zone lying beyond Z is called the far field. In the far field, the intensity of the acoustic waves along the axis varies as the inverse of the square of the distance from the transducer and small oscillations appear in the radial direction. Most of the acoustic energy is contained in a cone of which the half angle d is characterized by the wavelength and the diameter of the emitter.

How small are the measured volumes

In Doppler echography, the axial dimension of the measured volumes is defined by the instrument that analyzes the Doppler echoes and their lateral size by the amount of acoustic energy reflected by the particles. Due to the spatial dependence of the acoustic intensity, the lateral dimension of the measured volumes depends on their position as represented by the disks in the figure above.

How much the beam diverges

The divergence of the ultrasonic beam depends on the diameter of the emitter and the wavelength. Most of the time, a compromise between these two parameters has to be established in order to achieve the thinnest beam possible at a defined distance. The chart below gives the theoretical value of the half angle d in relation to the diameter and the frequency of the transducer for a sound velocity of 1500 m/s (water). Note that a higher frequency gives a better axial resolution but also often induces higher attenuation of the ultrasonic waves.

Some practical aspects

The equation and curves presented above are issued from the computation of the acoustic pressure that can be measured at a particular point in the acoustic field. But Ultrasonic Doppler Velocimetry analyzes reflected or backscattered energy. This means that the acoustic pressure measured at particular point is not enough to characterize the dimensions of the sampling volume. The width of the sampling volume can be determined by measuring the intensity of an echo generated by a small spherical target. Such measurements are available here