Reconstruction of multidirectional interferometric data using an isoparametric finite-element method

The spatial resolution of tomographic reconstructions is critical when the object field contains large- and small-scale features. Simply increasing the number of elements used in the reconstruction process throughout the domain is generally an unsatisfactory method to achieve higher resolution because additional multiview data are required. Here a new series-expansion reconstruction procedure, based on isoparametric finite-element concepts, is described. This procedure permits the shape and size of the reconstruction elements to be arbitrarily specified. The method is demonstrated by the use of an analytic function and is directly compared with results obtained from other series-expansion methods on a uniform grid. Given identical input data and reconstruction grids, the absolute error of reconstruction is improved by the use of the new method. The advantages of performing the reconstruction of a complex field on a nonuniform grid is also demonstrated.