Series-expansion methods for interferometric tomography of continuous flow fields are discussed. The techniques are based on series expansion by orthogonal polynomials and circular harmonics multiplied by an envelope function. These methods employing continuous basis functions are appropriate for reflecting the peculiar characteristics of interferometric tomography of fluid flow fields, namely, continuity, data sparsity, and nonuniform sampling. The high approximating power of the methods allows accurate representation of fields with a small number of series terms. This generates enough redundancy for a given number of data points in setting up a system of linear algebraic equations. The data redundancy thus generated yields accurate reconstruction even under ill-posed conditions including limited view angle, incomplete projections, and high noise level.
"Interferometric Tomography For Three-Dimensional Flow Fields Via Envelope Function And Orthogonal Series Decomposition," Optical Engineering 27(7), 277557 (1 July 1988). http://dx.doi.org/10.1117/12.7976722