Tomography and reliable information

Principles of tomography are developed and applied to the problem of two-view interferometry on a tokamak plasma. It is shown that M equispaced views, or projections, of a two-dimensional object yield precisely M 2 + M numbers characterizing the object. This result is an extension of the previous work of Niland [J. Opt. Soc. Am. 72, 1677 (1982)], who proved that M2 generalized Fourier coefficients, or moments of the object, could be retrieved by M-view tomography. Furthermore it is shown that only half of the alias-free numbers are useful in reconstructing a uniform image of the unknown object. Questions of sampling within a view are addressed and the aliasing contaminants explicitly identified. An algorithm using an orthogonal expansion in the frequency domain is used to examine the attributes of the image reconstructed using various subsets of the available Fourier coefficients.