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Proton computed tomography (pCT) has the potential to improve the accuracy of dose calculations for proton treatment planning, and will also be useful for pretreatment verification of patient positioning relative to the proton beam. A design study was performed to define the optimal approach to a pCT system based on specifications for applications in proton therapy. Conceptual and detailed design of a pCT system is presented consisting of a silicon-based particle tracking system and a crystal calorimeter to measure energy loss of individual protons. We discuss the formation of pCT images based on the reconstruction of volume electron density maps and the suitability of analytic and statistical algorithms for image reconstruction.