Maximum-likelihood absorption tomography

– Maximum-likelihood methods are applied to the problem of absorption tomography. The reconstruction is done with the help of an iterative algorithm. We show how the statistics of the illuminating beam can be incorporated into the reconstruction. The proposed reconstruction method can be considered as a useful alternative in the extreme cases where the standard ill-posed direct-inversion methods fail. Introduction. – The standard reconstruction method in present computerized tomographic (CT) imaging is the filtered back-projection (FBP) algorithm which is based on the Radon transformation [1]. Unfortunately FBP fails in case of missing projections and/or if strong statistical fluctuations of the counting numbers are present in the small detector pixels. The latter situation occurs e.g. in neutron tomography [2–5], if monochromatic neutron beams are applied in order to avoid beam artifacts [6] or at the investigation of strong absorbing materials. The cases of missing projections and incomplete data sets for monochromatic neutron beams have been already investigated in the past in detail by means of algebraic reconstruction technique [7–9]. Scattering data from a double crystal diffractometer have been used to reconstruct 2D scattering pattern and the results were compared with the standard FBP. With this algebraic approach one could reconstruct 2D pattern in spite of the lack of nearly 90 degrees of the scanning angle, whereas in such cases the FBP method entirely failed. The computing time, however, was extremely long (up to several hours), so that this method is useful for rather small 2D arrays (100× 100 pixels) only. The new reconstruction method proposed in this paper can improve several tomographic applications in neutron optics which in many cases are limited by the weak intensity and the poor detector resolution. The use of well collimated pencil beams which are scanned across the sample surface could dramatically enhance the spatial image resolution but this method is only rarely used due the long measurement times [10]. An improved reconstruction method can encourage new applications in neutron optics which often suffer from the low counting (∗) Email: [email protected]