Discrete Estimation of Data Completeness for 3D Scan Trajectories with Detector Offset

The sequence of source and detector positions in a CT scan determines reconstructable volume and data completeness. Commonly this is regarded already in the design phase of a scanner. Modern flatpanel scanners, however, allow to acquire a broad range of positions. This enables many possibilities for different scan paths. However, every new path or trajectory implies different data completeness. Analytic solutions are either designed for special trajectories like the Tam-window for helical CT scans or do not incorporate the actual detector size such as Tuy’s condition. In this paper, we describe a method to determine the voxelwise data completeness in percent for discretely sampled trajectories. Doing so, we are able to model any sequence of source and detector positions. Using this method, we are able to confirm known theory such as Tuy’s condition and data completeness of trajectories using detector offset to increase the field-of-view. As we do not require an analytic formulation of the trajectory, the algorithm will also be applicable to any other source-detector-path or set of source-detector-path segments.