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Results of a niobium absorption experiment are presented that represent a major step in the development of techniques necessary for the quantitative characterization of hot, dense matter. The general requirements for performing quantitative analyses of absorption spectra are discussed. Hydrodynamic simulations are used to illustrate the behavior of tamped x-ray-heated matter and to indicate potential two-dimensional problems inherent in the technique. The absorption spectrum of a low-Z material, in this case aluminum, mixed with niobium provides a temperature diagnostic, which together with radiography as a density diagnostic fully characterizes the sample. A discussion is presented of opacity calculations and a comparison to the measurements is given that illustrates the need for experiments to provide a critical test of theory. The experimental technique is placed in context with a review of previous measurements using absorption spectroscopy to probe hot, dense matter. It is shown that the overall experimental concepts, although understood, were not always achieved in previous experiments.