# Sonic split-beam beam compensation

The Sonic split-beam method works by determining the angular position of a single target within the beam, and calculating the beam compensation from that position.

### Beam compensation equation

In split-beam systems the beam compensation equation can be written as a function of beam position as follows: Where:

 α is the minor-axis angle of the single target+ (degrees) β is the major-axis angle of the single target+ (degrees) TS(0,0) is the TS derived from received power measurements - valid at α=0, β=0 (dB re 1 m2) - see uncompensated_TS TS(α,β) is the TS predicted for a target at position α, β in the beam (dB re 1 m2) - see compensated_TS B(α,β) is the beam compensation function (dB).

+Single target angles passed on by a Single target detection split beam method virtual variable.

Assuming the transducer face is a circular disk, the theoretical beam shape may be expressed using the first order Bessel function J1. The Sonic beam compensation function is given by: where:

 θ This is the off-axis angle of the single target with respect to the beam axis expressed in terms of minor and major axis angles, α and β respectively.   θ = tan-1((tan(α)2 + tan(β)2)1/2)   Refer to KFC-6000/KSE-300 Major and minor axis angles for further details about θ. SonicTransducerRadiusCoefficient This is a Sonic coefficient that expresses the relationship of the transducer radius to the wavelength.   It can be read from the data file and appears as the calibration setting SonicTransducerRadiusCoefficient on the Calibration page of the single target detection variable. J1(x) The first order Bessel function J1 evaluated numerically for the argument (2π SonicTransducerRadiusCoefficient sin θ).