Synchrotron radiation computed laminography (CL) was developed to complement the conventional computed tomography as a non-destructive 3D imaging method for the inspection of flat thin objects. Recent progress in hardware at synchrotron sources allows one to record internal evolution of specimens at the micrometer scale and sub-second range but also requires increased reconstruction speed to follow structural changes online. A 3D image of the sample interior is usually reconstructed by the well-established filtered backprojection (FBP) approach. Despite of a great success in the reduction of reconstruction time via parallel computations, the FBP algorithm still remains a time-consuming procedure. A promising way to significantly shorten computation time is to directly perform backprojection in frequency domain (a direct Fourier inversion approach). The corresponding algorithms are rarely considered in the literature because of a poor performance or inferior reconstruction quality resulted from inaccurate interpolation in Fourier domain. In this paper, we derive a Fourier-based reconstruction equation designed for the CL scanning geometry. Furthermore, we outline the translation of the continuous solution to a discrete version, which utilizes 3D sinc interpolation. A projection resampling technique allowing for the reduction of the expensive interpolation to its 1D version is proposed. A series of numerical experiments confirms that the resulting image quality is well comparable with the FBP approach while reconstruction time is drastically reduced.

Computed laminography (CL) was developed to use X-rays from synchrotron sources for high-resolution imaging of the internal structure of a flat specimen from a series of 2-D projection images. The projections are acquired by irradiation of the sample under different rotation angles where the object rotation axis is inclined with respect to the beam direction. This yields for laterally extended objects a more uniform average transmitted intensity during sample rotation compared with computed tomography (CT). The reconstruction problem of CL cannot be reduced to a data-efficient 2-D case (as for parallel-beam CT) since each single slice perpendicular to the rotation axis requires a 2-D region on the detector as input data for all projection directions. This paper describes a computationally efficient reconstruction procedure based on filtered backprojection (FBP) adapted to the CL acquisition geometry. From the Fourier slice theorem, we derive a framework for analytic image reconstruction and outline implementation details of the generic FBP algorithm. Different approaches reducing the reconstruction time by means of parallel and distributed computations are considered and evaluated.