  We present and demonstrate a method for optical homodyne tomography based on
the inverse Radon transform. Different from the usual filtered back-projection
algorithm, this method uses an appropriate polynomial series to expand the
Wigner function and the marginal distribution and discretize Fourier space. We
show that this technique solves most technical difficulties encountered with
kernel deconvolution based methods and reconstructs overall better and smoother
Wigner functions. We also give estimators of the reconstruction errors for both
methods and show improvement in noise handling properties and resilience to
statistical errors.
