  We previously reported an experimental platform to induce a
spherically-convergent shock in a sample using laser-driven ablation, probed
with time-resolved x-ray radiography, and an analysis method to deduce states
along the principal shock Hugoniot simultaneously with the x-ray opacity. We
have now developed a modified method of analysis that is numerically
better-conditioned and faster, and usually provides a better representation of
the radiograph with correspondingly lower uncertainties. The previous approach
was based on optimizing parameters in a model of the density distribution as a
function of radius and time, warped to follow loci such as the shock and the
outside of the sample. The converging shock configuration can be described more
efficiently in terms of the shocked density and sound speed, expressed as
functions of the shock speed Studies of the Hugoniot from various theoretical
equations of state (EOS) indicate that, in the typical range of states explored
by these experiments, these functions can be described by low-order
polynomials. Similarly, few-parameter functions were found suitable for
representing the variation of x-ray opacity with shock pressure. This approach
was found to perform better in most cases than an alternative method based on
parameterization of the EOS.
