A technique is described for the tomographic mapping of transverse phase space in beams with space charge. Most prior studies where performed at high energy where space charge was negligible and therefore not considered in the analysis. The tomographic reconstruction process is compared with results of simulations using the particle-in-cell code WARP. The new tomographic technique is tested for beams with different intensities (both emittance and space-charge dominated), and with different initial distributions. Effects of various errors in the data collection process on the reconstructed phase space are discussed. It is shown that the crucial factor is not necessarily the number of projections but the range of angles over which the projections are taken. This study also includes a number of experimental results on tomographic phase space mapping performed on the University of Maryland Electron Ring.

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A tomography algorithm is proposed for the reconstruction of the three-dimensional ͑3D͒ distribution of the real refractive index of a pure phase sample from the projections of cone-beam propagation-based imaging ͑PBI͒. The algorithm first retrieves the integral of the real refractive index based on the formula described in this letter, and then a conventional computed tomography algorithm is performed to reconstruct the 3D distribution of the real refractive index of the sample. The computer simulations show that this method is effective for PBI tomography.