J. Phys. D: Appl. Phys. 29 (1996) 3009–3016. Printed in the UK An iterative projection-space reconstruction algorithm for tomography systems with irregular coverage L C Ingesson† and V V Pickalov‡ FOM-Instituut voor Plasmafysica ‘Rijnhuizen’, Associatie Euratom–FOM, PO Box 1207, 3430 BE Nieuwegein, The Netherlands Received 3 June 1996 Abstract. Most standard tomographic inversion methods require many measurements with a regular coverage of the object studied. A new method has been developed to obtain tomographic reconstructions from measurements by systems with a small number of detectors and an irregular coverage. The method reconstructs values on a regular grid in projection space from the measurements on an irregular grid by an iterative interpolation scheme. It applies a priori information and smoothing between the iterations. Furthermore, consistency of the results is obtained by an iteration between projection space and actual space. The tomographic reconstructions required in this iteration are made by a filtered-back-projection (FBP) method for the regular grid. The algorithm has been tested on assumed emission profiles. For a fan-beam system with a limited number of views the method has been compared with an FBP method for fan-beam systems; it was found to perform equally well. The method has also been applied to the visible-light tomography system on the RTP tokamak, which has only 80 channels and a very irregular coverage. Satisfactory results were obtained both for simulations and for reconstructions of actual measurements. The method appears to be a promising new approach to tomographic reconstructions of measurements by systems with irregular coverage and a small number of detectors. 1. Introduction In many fields, for example in high-temperature nuclear fusion research, tomography systems have a small number of detectors, which, due to limited access, view the object under consideration in an asymmetrical way. Many standard tomographic reconstruction algorithms require a symmetrical coverage. Other algorithms, that can cope with asymmetrical coverage, do not work well for systems with a small number of detectors and gaps in the coverage. To allow tomographic reconstructions with the sparse, asymmetrical coverage of such systems, an iterative scheme for reconstructing the projection space has been developed. The reconstruction of projection space is obtained by applying interpolation and smoothing to obtain values on a regular grid in projection space, corresponding to parallel beams, from the measurements on the irregular grid, given by the viewing directions of the detectors. A different method to reconstruct in projection space has been † Present address: JET Joint Undertaking, Abingdon, Oxon OX14 3EA, UK. ‡ Permanent address: Institute of Theoretical and Applied Mechanics, Novosibirsk 630090, Russia. described by Prince and Willsky [1, 2]. Other techniques (for example by Akima [3]) which interpolate from an irregular to a regular grid have been considered as well, but were not used because a priori information that is known for the system under consideration and smoothing could not be implemented easily. The reconstructed signals on the regular grid can be tomographically inverted by standard techniques for parallel beams. The method is suitable for straight-line tomography with systems that have few detectors and an irregular coverage of projection space without large gaps. In this article the capabilities of the method are demonstrated by means of simulations and it is applied to the visible-light tomography system on the RTP tokamak. A tokamak is a device for thermonuclear fusion research in which a plasma is confined by magnetic fields. The visible- light tomography diagnostic on RTP, which has a total of 80 detectors distributed asymmetrically over five viewing directions, was used to study the two-dimensional emission distribution in a cross section of the plasma. This article is divided as follows. In section 2 some concepts of tomography are introduced and the algorithm is presented. Section 3 shows numerical simulations both 0022-3727/96/123009+08$19.50 c  1996 IOP Publishing Ltd 3009