To achieve good image quality for computed tomography, it is important to accurately know the geometrical relationship between the X-ray source, the axis of rotation, and all of the detector channels. This usually involves knowing gross parameters such as iso-ray coordinate, detector pixel pitch, and source-to-detector distance, but for some detector types such as distorted arrays, polygonal or tiled arrays, or arrays of irregularly placed sparse detectors, it is beneficial to measure a more detailed description of the individual channel locations. Typically, geometric calibration and distortion
calibration are performed using specialized phantoms, such as a pin, an array of pellets, or a wire grid, but these can have
their practical downsides for certain applications. A promising recent alternative is to calibrate geometry in a way that
requires no particular phantom or a priori knowledge of the scanned object -- these approaches are particularly helpful for high magnifications, large heavy objects, frequent calibration, and retrospective calibration. However, until now these approaches have only addressed gross geometry. In this paper, a framework is given which allows one to calibrate both gross and fine geometry from unknown objects. Example images demonstrate the success of the proposed methods on both real and simulated data.