Preliminary error analysis of the general cone-beam reconstruction algorithm

An x-ray microscope system for microtomography is under development at SUNY/Buffalo, New York. Considering the characteristics of the x-ray microscope system and the limitations of current cone-beam reconstruction algorithms, a general cone-beam image reconstruction algorithm has been developed at AMIL-ARTS. In order to study the reconstruction error characteristics of the general cone-beam algorithm, a preliminary error analysis on the algorithm is performed in this paper. The most important error source in cone-beam reconstruction is the theoretical precision limitation. Like many cone-beam reconstruction algorithms, the general cone-beam algorithm is not exact in nature. Thus, an analytic reconstruction error formula is derived which relates the error to the specimen structure and various imaging parameters. Approximately, the reconstruction error is proportional to either the distance from a voxel to the midplane or the pitch of a helix-like scanning locus, and inversely proportional to the size of the scanning locus. The reconstruction error also depends on the specimen structure. The faster the structure varies along the z direction, the larger the reconstruction error will be. Specimens are modeled as stochastic fields. Typical simulation results are then depicted and discussed.