For a real industrial CT system

it is very difficult to meet the rigorous aligned relations among the X-ray focus

the rotation center of turntable and the linear detector

which is required by the conventional image reconstruction formula.Misalignment will result in geometric artifacts in the image reconstructed by the conventional image reconstruction formula.In this paper

we first introduce a set of geometric parameters which fully describe general CT scanning configuration

and then propose an indirect method to estimate the set of parameters from the projection data of a metal silk.We also propose a generalized filtered back-projection (FBP) reconstruction formula based on such set of parameters.In this paper

we assume that the rotation axis of the CT turntable is vertical to the fan-beam formed by the X-ray focus and the linear detector array

but do not require that the CT scanning system satisfies other alignment relations.For a misaligned scanning system

we can first estimate the parameters by our method

and then reconstruct the image correctly using our reconstruction formula with the estimated parameters.