  Ramp compression experiment are used to deduce the relation between
compression and normal stress in a material, by measuring how a compression
wave evolves as it propagates through different thicknesses of the sample
material. The compression wave is generally measured by Doppler velocimetry
from a surface that can be observed with optical or near-optical photons. For
high-pressure ramp loading, the reflectivity of a free surface often decreases
as it is accelerated by the ramp wave, and window materials transparent to the
probing photons are used to keep the surface flatter and preserve its
reflectivity. We previously described a method of analyzing ramp-wave data
measured at the free surface which did not require numerical iteration.
However, this method breaks down when the pressure at the surface changes and
hence cannot be used for data taken with a finite-impedance window. We have now
generalized this non-iterative analysis method to apply to measurements taken
through a window. Free surfaces can be treated seamlessly, and the need for
sampling at uniform intervals of velocity has been removed. These calculations
require interpolation of partially-released states using the
partially-constructed stress-compression relation, making them slower than the
previous free-surface scheme, but they are still much more robust and fast than
iterative analysis.
