Fast and analytical exact reconstruction of large CT-volumes.

Computed Tomography (CT) has become very important for industrial applications. The fields of application are ranging from highly specialized tasks in CT inline inspection to universal X-ray systems, metrology and highresolution CT, for example in microelectronics. For high-energy scans of high quality fan-beam CT using linear detector arrays (LDA) is the right choice due to the bigger field of view and the superior collimation reducing scatter artefacts compared to flat panel detectors, which are used for cone-beam CT. The conventional filtered back projection (FBP) as reconstruction algorithm requires equally spaced X-rays, i.e. it was designed for parallel beam geometry. Its computational effort depends mainly on the size of the reconstructed volume. In this article we will introduce a fast and analytical exact reconstruction algorithm, based on the orthogonal polynomial expansion on the disk (OPED). Its numerical complexity only depends on the amount of the input data (projections). OPED is designed to overcome aliasing artefacts and streaks. It needs no special filtering, i.e. it can be easily parameterized. The alignment of the sample grid is very well suited for fan beam geometry with its non-equally spaced X-rays. As result, we will compare the performance of the OPED and FBP algorithm