Furuno FCV-38 power, Sv, TS and angular position equations

Furuno FCV-38 power, Sv, TS and angular position equations are derived from equations provided by Furuno and based on The SONAR-netCDF4 convention for sonar data, version 2.0. Echoview does not support some variables in the original Furuno equations. Contact Furuno Electric Co., Ltd, for further details.

Beams and quadrants

The FCV-38 transducer is configured according to the split beam arrangement of case A in Figure 3 of section 6.2.1 of The SONAR-netCDF4 convention for sonar data, version 2.0.

Complex backscatter signals are recorded as 4 beams in the data file. Each beam (beam 0, 1, 2, 3) records complex data (in the form of z = a +bi) for a pair of quadrants.

Figure 1: The split beam configuration for A with quadrants 1, 2, 3 and 4. Each beam (beam 0, 1, 2, 3) records complex data (z0, z1, z2, z3) for each pair of respective quadrants. The diagram on the left shows the quadrant pairs for z0 and z1 outlined in blue and orange. The diagram on the right shows the quadrant pairs for z2 and z3 outlined in blue and orange.

Let z = a + bi be the complex expression for each beam.

The complex expression for each beam is:

where:

backscatter_r[ping_time, beam_n] is the real part of the raw backscatter measurements for beam n (0, 1, 2, 3), read from the data file.

backscatter_i[ping_time, beam_n] is the imaginary part of the raw backscatter measurements for beam n, read from the data file.

i is the imaginary number, the square root of -1.

The quadrants that contribute to each beam (beam 0, 1, 2, 3) are:

where yn is the complex signal from quadrant n.

Calculation of power, Sv and TS

Equations based on the content in Section 4.6 Type 6 of The SONAR-netCDF4 convention for sonar data, version 2.0.

Power

Echoview derives received power:

where:

Pr	is the received power (dB)
A	is the amplitude of the received voltage signal. where: Re(zn) is the real component of zn. Refer to the complex expression for beam 0 and beam 1. Im(zn) is the imaginary component of zn. Refer to the complex expression for each beam 0 and beam 1.
ΔG	is the system gain (dB) read from the data file. It is displayed on the Calibration page of the Variable Properties dialog box as GainCorrection and can be modified via an ECS file.
TR	is the transmit-receive coefficient (dB) is read from the data file.

The TS and Sv equations are calculated from power as follows:

TS

where:

TS	is the Target strength (dB).
Pr	is the received power (dB).
r	is the range (m) from the transducer to the ping sample. where: c is the sound speed (ms-1) read from the data file. dt is the time (s) between recorded samples read from the data file. i is the sample number i, where samples range from [0, n-1], with n being the number of samples in a ping. t0 is the sample time offset (s) read from the data file.
α	is the absorption coefficient (dB/m) read from the data file.

Sv

where:

Sv	is the mean volume backscattering strength (dB)
Pr	is the received power (dB)
r	is the range (m) from the transducer to the ping sample. See the TS description for more details
α	is the absorption coefficient (dB/m) read from the data file
c	is the sound speed (ms-1) read from the data file
τe	is the effective pulse duration (seconds) read from the file.
ψ	is the TwoWayBeamAngle (Steradian) read from the data file.

Angular position

Angular position data is derived from complex data recorded under beams that are associated with pairs of quadrants. The equations are based section 6.2.1 in SONAR-netCDF4 convention for sonar data, version 2.0.

where:

θ	is the minor axis angle in degrees.
φ	is the major axis angle in degrees.
yθ	is the complex signal for the minor axis, where yθ = z0 x z1*. Refer to the complex expression for beam 0 and beam 1. * is the complex conjugate. Given z = a + bi then z* = a - bi Im(yθ) is the imaginary part of yθ. Re(yθ) is the real part of yθ.
yφ	is the complex signal for the major axis, where yφ = z3 x z2*. Refer to the complex expression for beam 3 and beam 2. * is the complex conjugate. Im(yφ) is the imaginary part of yφ. Re(yφ) is the real part of yφ.
ηθ	is the angle sensitivity for the minor axis, read from the data file.
ηφ	is the angle sensitivity for the major axis, read from the data file.

Note:

This page documents equations used for Furuno FCV-38 version 2 (.nc) files. Furuno FCV-38 version 1 files are not supported.

See also

Furuno FCV-38 file format
Raw variables derived from Furuno data files
Calibration settings for Furuno FCV-38 data