We reconstruct spectra of secondary x-rays generated from a 500 MeV - 2 GeV laser plasma electron accelerator. A compact (7.5 $times$ 7.5 $times$ 15 cm), modular x-ray calorimeter made of alternating layers of absorbing materials and imaging plates records the single-shot x-ray depth-energy distribution. X-rays range from few-MeV inverse Compton scattered x-rays to $sim$100 MeV average bremsstrahlung energies and are characterized individually by the same calorimeter detector. Geant4 simulations of energy deposition from mono-energetic x-rays in the stack generate an energy-vs-depth response matrix for the given stack configuration. A fast, iterative reconstruction algorithm based on analytic models of inverse Compton scattering and bremsstrahlung photon energy distributions then unfolds x-ray spectra in $sim10$ seconds.
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