  Megabar (1 Mbar = 100 GPa) laser shocks on precompressed samples allow
reaching unprecedented high densities and moderately high 10000-100000K
temperatures. We describe here a complete analysis framework for the
velocimetry (VISAR) and pyrometry (SOP) data produced in these experiments.
Since the precompression increases the initial density of both the sample of
interest and the quartz reference for pressure-density, reflectivity and
temperature measurements, we describe analytical corrections based on available
experimental data on warm dense silica and density-functional-theory based
molecular dynamics computer simulations. Using our improved analysis framework
we report a re-analysis of previously published data on warm dense hydrogen and
helium, compare the newly inferred pressure, density and temperature data with
most advanced equation of state models and provide updated reflectivity values.
