A practical method for measuring the H matrix of digital x-ray and cone beam CT imaging systems

Digital clinical imaging systems designed for radiography or cone-beam computed-tomography are highly shift-variant. The x-ray cone angle of such systems varies between 0 degrees and 15 degrees, resulting in large variations of the focal spot projection across the image field. Additionally, the variable x-ray beam incidence across the detector field creates a location-dependent asymmetric detector response function. In this paper we propose a practical method for the measurement of the angle of incidence dependent two-dimensional presampled detector response function. We also present a method for the measurement of the source radiance at the center of the detector, and provide a geometric transformation for reprojecting given any location in object space. The measurement procedure involves standard, readily available tools such as a focal-spot/pinhole camera, and an edge. Using the measured data and a model based on smooth functions derived from Monte Carlo simulations we obtain the location-dependent detector response function. In this paper we ignore scatter, therefore the resulting location dependent system response is a function of the focal spot and detector response. The system matrix, a representation of the full deterministic point response of the system for all positions in object space, can then be calculated. The eigenvalues and eigenvectors of the system matrix are generated and interpreted.