A ray-length-based ROI-correction for computed laminography
Computed tomography (CT) is a well-established and widely used non-destractive inspection method for the analysis of the interior structure of objects. Applying Standard reconstruction methods for circular or helical sampling to planar objects, two fundamental problems arise; impenetrability in longitudinal direction and collision risks between X-ray source and object at high magnifications. During a CT, the object is rotated by 360 degrees while being irradiated. Planar objects are challenging since they exhibit very different Irradiation lengths. In normal direction to the surface absorption is very much lower than in longitudinal direction. Tiying to compensate for this by increasing the energy of the X-rays, one automatically reduces contrast and geometrical resolution, thereby possibly rendering the reconstruction useless. The opening angle of the X-ray source allows for a Variation of magnification by changing the distance between X-ray source and object. Small object features can be inspected in detail this way. Especially planar objects with very fine structures can require such a high magnification, that the required source-detector distance gets too small to permit a full 360° rotation without risking a collision between source and object. Circumventing this problem by increasing both source-object and source-detector distances while keeping the desired magnification ratio results in a severely limited opening angle which in tum restricts the field of view making multiple scans necessary to cover the entire area of interest. Computed laminography (CL) can solve these problems. In contrast to Standard CT geometries where X-ray source and detector are perpendicular to each other and the axis of rotation and a füll 360° coverage is necessary  , CL can also work with a limited angular range of less than 90° (Swing laminography) or completely dispense with the traditional Set-up and use linear translational (translation CL), planar rotational (classic CL) or tilted geometries (CLARA (Computed Laminography And RAdiography)) [4,5,6]. The advantage of all these trajectories lies in their possibility to place the object close enough to the source to achieve the desired resolution without colliding with the X-ray tube. Additionally most of these geometries permit a constant oblique Irradiation angle throughout the entire measurement. This eliminates the problem of widely differing object thicknesses with all the drawbacks mentioned above.