Beam patterns and Directivity
The beam pattern of a transducer contain information about the transducer’s spatial response i.e. how it transmits or receives in different directions. Transducers that are very small compared to the wavelength have omni directional beams, which means that the energy is not concentrated in any particular direction. Transducers that are large compared to the wavelength have a very directive beam pattern, which means that their energy is concentrated in a specific direction.
The beam width, which is the angle subtended by the points where the intensity has dropped 3dB below the maximum on-axis response, is often used as indicators of how concentrated the energy is for a specific transducer in a given cross section.
The directivity index of a transmitter describes how concentrated the transmitted energy is at the maximum response point and for receivers the directivity index indicates the ability to discriminate a signal from an ambient background noise, both cases relative to an omni directional transducer.
Table 1: Approximations to far-field beam width and directivity index for various sources. Formulas for finding beam widths assume that the speed of sound is c≈1500m/s (c=λ•f). Notice that the beam width of a transducer is the same whether it is transmitting or receiving.
The nearfield (or Fresnel field) of a transducer is characterized by irregularity and changes due to refraction effects leading the fact that the interference pattern (the beam) has not yet been fully formed. The Rayleigh distance r0 can approximate the nearfield extension:
Aactive is the active area of the transducer’s face. For line arrays, cylindrical arrays and the like it is often better to use Aactive=(Lmax)2 where Lmax is the longest dimension found on the active face of the transducer. The farfield (Fraunhofer field) precedes the nearfield after a transition region and is characterized by spherical spreading and regular beam patterns.
