  Modelling the acoustic scattering response due to penetrable objects of
arbitrary shapes, such as those of many marine organisms, can be
computationally intensive, often requiring high-performance computing equipment
when considering a completely general situation. However, when the physical
properties (sound speed and density) of the scatterer object under
consideration are similar to those of the surrounding medium, the Born
approximation provides a computationally efficient way to calculate the
scattering. For simple geometrical shapes like spheres and spheroids, the
acoustic scattering in the far field can be evaluated through the Born
approximation recipe as a formula which has been historically employed to
predict the response of weakly scattering organisms, such as zooplankton.
Moreover, the Born approximation has been extended to bodies whose geometry can
be described as a collection of non-circular rings centred on a smooth curve.
In this work, we have developed a numerical approach to calculate the far-field
backscattering by arbitrary 3D objects under the Born approximation. The
object's geometry is represented by a volumetric mesh composed of tetrahedrons,
and the computation is efficiently performed through analytical 3D integration,
yielding a solution expressed in terms of elementary functions for each
tetrahedron. The method's correctness has been successfully validated against
benchmark solutions. Additionally, we present acoustic scattering results for
species with complex shapes. To enable other researchers to use and validate
the method a computational package named tetrascatt implemented in the R
programming language was developed and published in the CRAN (Comprehensive R
Archive Network).
