Scattering and simulation geometry used throughout this work. The third dimension is neglected. The path of protons traveling inside an object is determined by a multitude of individual scattering events leading to a zigzag path (red). Both the position and direction of entry and exit proton are registered. Given the boundary of the reconstruction region, the intersecting points and of a proton with the object can be obtained assuming there is no scattering medium between registration planes and reconstruction boundaries. While the intersecting points are sufficient to estimate the straight line path (black) of the proton, additional knowledge of the entry and exit directions permits estimation of the most likely path (blue line).
Examples of MLPs for protons in water entering the - plane at and with two different exit displacements and several different exit angles . The depth coordinate is given as a fraction of the exit depth. Note that the same SLP applies to each group of MLPs.
Elliptical phantom consisting of an outer shell with bone density (1), an elliptical interior of water density (2), and two sets of strip patterns with either bone density (white) or air density (black). The strip densities of the patterns (listed by number) are: (3, 11), (4, 12), (5, 13), (6, 14), (7, 15), (8, 16), (9, 17), and (10, 18).
Three examples of MC-simulated proton paths in water and their estimated SLP, MLP, and CSP.
Comparison of the RMS deviation of the lateral displacement in the projection plane between each path estimate and the MC-simulated internal path as a function of depth in a 20-cm water layer
Reconstructions of the elliptical phantom by the ART algorithm using SLP (top) CSP (bottom left) and MLP (bottom right) estimates.
Average profiles through the top pattern of the reconstructed elliptical phantom of Fig. 3 for the three different path estimates.
Convergence speed and squared residual error for the three different path estimates.
Entry and exit positions and directions of three arbitrarily selected proton events ( initial energy), of which the simulated paths and estimated paths are plotted in Fig. 4.
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