Ultrasound is a cyclic acoustic pressure wave that has a frequency above that of human hearing.  Most signal generators output signals in electrical form because this is the most convenient way to modify and output the signal.  A device such as a piezoelectric crystal or a ceramic is needed to convert the electrical power into acoustic power.  Piezoelectric materials have the ability to generate an electrical potential to an applied mechanical stress and vice versa.  Ultrasound uses the latter.  Lead zirconate titanate (PZT) is the most commonly used piezoelectric material in ultrasound transducers.  The piezoelectric property of PZT allows it to change an electrical excitation into motion and pressure, the two necessary elements of acoustic waves. 

Besides PZT, there are other piezoelectric materials that can be used for transducers.  Each piezoelectric material has its own unique properties as shown in Table 1.  Among all the piezoelectric materials, PZT has the highest piezoelectric stress coefficient which yields higher acoustic power with the same electrical power input.

Table 1.  Values for some piezoelectric transducer materials.

The resonant frequency of the transducer depends on the thickness and speed of sound in the transducer.  The transducer will be resonant for a wavelength equal to twice the thickness, which translates to a frequency equal to the speed of sound divided by twice the thickness. 

A basic transducer is composed of three parts, the backing, the piezoelectric crystal, and a matching layer, as shown in figure 1. 

Figure 1.  Drawing of a basic transducer.

The crystal length is chosen as half the wavelength of the pulse.  This is referred to as “thickness” mode.  There is a mismatch between the high acoustic impedance (Z) of the crystal (approximately 30-36 Mrayl) and low acoustic impedance of the tissue (approximately 1.5 Mrayl).  There would be very little transmission from the crystal to the tissue if a matching layer were not present.  A matching layer is required to optimize the power transfer between the piezoelectric crystal and the tissue. 

From basic wave physics, it is known that the ratio of the transmitted pressure (pt) to the incident pressure (pi) is equal to the twice the impedance of the receiving medium (Z2) divided by the sum of the impedance of the receiving medium and the incident medium (Z1).  This relationship is shown in equation 1.

The ratio of the transmitted intensity (It) to the incident intensity (Ii) is equal to four times the product of the impedances of the two layers divided by the square of the sum of the two impedances.  This relationship is shown in equation 2.

With equations 1 and 2, the impedance required for the matching layer can be calculated.  A diagram of the transducer and the calculations are shown in figure 2.  .

Figure 2.  Calculation of the impedance of the matching layer.

This optimizes the transfer between the piezoelectric crystal and the tissue. 

Transducer Characterization

The transducer must be characterized to ensure that it is functioning correctly.  For this, a beam plot and a Schlieren image can be performed. 

Beam Plot

For this test, the ultrasound transducer is submerged in a water tank lined with acoustic absorbers to reduce ultrasound reflections from the side of the tank.  A hydrophone attached to a robotic arm is placed facing the transducer in the tank. Using LabVIEW (National Instruments, Austin, Texas) or other comparable software, the hydrophone can be used to record pressure caused by the ultrasound from a specified volume at specified intervals.  From this a plot of the transducer ultrasound wave can be formed. 

Schlieren Imaging

A detailed description of Schlieren imaging can be found in Gary S. Settles’ book titled Schlieren & Shadowgraph Techniques.  In a Schlieren imaging system, a collimated beam of light is passed through a water tank, containing an ultrasound field, and focused onto blank sheet.  This collimated beam is produced by using a laser to generate the light, an expanding lens to expand the light and then a collimating lens to collimate the light.  The ultrasound transducer is placed orthogonally to the light propagation.  The light then passes though degassed water which is compressed and decompressed because of the sound waves generated by the transducer.  The light is then focused using a focusing lens and the zero order light is blocked using a needle.  The ultrasound changes the refractive index of the water.  The light that passes through these disturbances are not limited to passing through the blocked zero order focal spot.  The variation in brightness caused by the stray light can be projected onto the blank sheet.  In this fashion the ultrasound beam can be visualized.