  The newly developed X-ray visibility forward fitting technique is applied to
Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) data of a limb
flare to investigate the energy and height dependence on sizes, shapes, and
position of hard X-ray chromospheric footpoint sources. This provides
information about the electron transport and chromospheric density structure.
The spatial distribution of two footpoint X-ray sources is analyzed using
PIXON, Maximum Entropy Method, CLEAN and visibility forward fit algorithms at
nonthermal energies from $\sim 20$ to $\sim 200$ keV. We report, for the first
time, the vertical extents and widths of hard X-ray chromospheric sources
measured as a function of energy for a limb event. Our observations suggest
that both the vertical and horizontal sizes of footpoints are decreasing with
energy. Higher energy emission originates progressively deeper in the
chromosphere consistent with downward flare accelerated streaming electrons.
The ellipticity of the footpoints grows with energy from $\sim 0.5$ at $ \sim
20$ keV to $\sim 0.9$ at $\sim 150$ keV. The positions of X-ray emission are in
agreement with an exponential density profile of scale height $\sim 150$~km.
The characteristic size of the hard X-ray footpoint source along the limb is
decreasing with energy suggesting a converging magnetic field in the footpoint.
The vertical sizes of X-ray sources are inconsistent with simple collisional
transport in a single density scale height but can be explained using a
multi-threaded density structure in the chromosphere.

Solar and Stellar Astrophysics