  In this article we study the fan-beam Radon transform ${\cal D}_m $ of
symmetrical solenoidal 2D tensor fields of arbitrary rank $m$ in a unit disc
$\mathbb D$ as the operator, acting from the object space ${\mathbf
L}_{2}(\mathbb D; {\bf S}_m)$ to the data space $L_2([0,2\pi)\times[0,2\pi)).$
The orthogonal polynomial basis ${\bf s}^{(\pm m)}_{n,k}$ of solenoidal tensor
fields on the disc $\mathbb D$ was built with the help of Zernike polynomials
and then a singular value decomposition (SVD) for the operator ${\cal D}_m $
was obtained. The inversion formula for the fan-beam tensor transform ${\cal
D}_m $ follows from this decomposition. Thus obtained inversion formula can be
used as a tomographic filter for splitting a known tensor field into potential
and solenoidal parts. Numerical results are presented.
