Image reconstruction methods for the PBX-M pinhole camera

We describe two methods that have been used to reconstruct the soft x-ray emission profile of the PBX-M tokamak from the projected images recorded by the PBX-M pinhole camera [Proc. Soc. Photo-Opt. Instrum. Eng. 691, 111 (1986)]. Both methods must accurately represent the shape of the reconstructed profile while also providing a degree of immunity to noise in the data. The first method is a simple least-squares fit to the data. This has the advantage of being fast and small and thus easily implemented on the PDP-11 computer used to control the video digitizer for the pinhole camera. The second method involves the application of a maximum entropy algorithm to an overdetermined system. This has the advantage of allowing the use of a default profile. This profile contains additional knowledge about the plasma shape that can be obtained from equilibrium fits to the external magnetic measurements. Additionally the reconstruction is guaranteed positive, and the fit to the data can be relaxed by specifying both the amount and distribution of noise in the image. The algorithm described has the advantage of being considerably faster for an overdetermined system than the usual Lagrange multiplier approach to finding the maximum entropy solution [J. Opt. Soc. Am. 62, 511 (1972); Rev. Sci. Instrum. 57, 1557 (1986)].