  We present new necessary and sufficient conditions for a function on
$\partial\Omega\times S^1$ to be in the range of the attenuated Radon transform
of a sufficiently smooth function support in the convex set
$\bar\Omega\subset\mathbb{R}^2$. The approach is based on an explicit Hilbert
transform associated with traces of the boundary of A-analytic functions in the
sense of Bukhgeim.
