Half‐scan cone‐beam X‐ray microtomography formula

An x‐ray shadow projection microtomographic system using a scannable point source is under development at AMIL‐ARTS, SUNY at Buffalo. To overcome the limitations of the commonly used Feldkamp's cone‐beam reconstruction formula, we have developed a generalized Feldkamp‐type cone‐beam reconstruction formula. In the generalized Feldkamp‐type cone‐beam reconstruction, a scanning locus can be either planar or helix‐like, and a transaxial slice is reconstructed using projection data collected from a 360° angular range (full scan). In this paper, the full‐scan cone‐beam formula is modified to require only projection data of approximate 180° plus two fan‐angles (half scan). First, a half‐scan derivative‐free noncircular fan‐beam reconstruction formula is formulated. Then, a half‐scan cone‐beam reconstruction formula is derived as an extension of the half‐scan fan‐beam reconstruction formula using Feldkamp's procedure. Typical numerical simulation results are given for both half‐scan formulae. Compared with the full‐scan cone‐beam formula, the half‐scan cone‐beam formula reduces the involved angular range of projection data and allows better longitudinal/temporal resolution.