Direct Fourier Inversion Reconstruction Algorithm for Computed Laminography

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.