ACOUSTICS UNPACKED A General Guide for Deriving Abundance Estimates from Hydroacoustic Data

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### Acoustic transducers

Transducers transmit a sound wave that varies in intensity in different directions because of constructive and destructive interference patterns – the beam pattern (Fig. 1 below).  Due to the directivity of a transducer, the echo level from an organism will be greater on-axis than off-axis.  To measure the TS of the organism, the echo level must be compensated for the location in the acoustic beam.  This can be done with statistical analysis of single beam data, and directly from the phase deviation and beam pattern in split beam transducers.

### Beam pattern

All transducers should have a measured beam pattern, showing the magnitude of the main lobe and associated side lobes.  Performed by the manufacturer, these transducer-specific measurements also provide measures for Ψ (equivalent beam angle) and the 3-dB angle used in data collection and processing.  The active radius (a) of a circular transducer, the half-intensity beam angle (θ3dB) and the equivalent beam angle (Ψ) are related and can be calculated from each other through the following equations (when ka>10):

 [14]

where:

θ3dB is the half power beam angle (º)
k is the wave number [k=2π/λ] and λ is the wavelength (m).

and,

 [15.1]

 [15.2]

Figure 1. Schematic image of transducer beam pattern (scaled in dB and reproduced from Johannesson and Mitson (1983)). The full angle is the 3dB beam angle, which is defined as the angle between the lines that represent the half-intensity direction on either side of the main axis.