Fourier transformation of fringe visibility measurements in Earth-rotation synthesis can be performed directly from the sampling loci for limited amounts of data, but with most major instruments, consideration of computing time requires the use of the algorithm for the fast Fourier transform in its two-dimensional form. With this powerful technique the computation of the transform becomes a relatively minor task. The required reordering of the input data into values at points in a rectangular array is more time consuming. How best to interpolate the array-point values a practical question that merits investigation. Radial interpolation, an exact method, and Lagrangian interpolation, a simplified version of it, require that the sampling points be distributed on concentric, equally spaced elliptical loci in the (u, V )-plane, as occurs with east-west arrays. Cell summing and cell averaging are simpler approximate methods, and Gaussian convolution and averaging are variations which can give improved accuracy but require somewhat more computation. The approximate nature of the methods, which involve smoothing of fine detail in the visibility function and shifting of values on the (u', V `)-plane, results in various forms of distortion. Choice between the methods depends upon considerations of computing time, accuracy, and the response to sources outside the synthesized field. Examples discussed illustrate how the suitability of the method can depend upon the nature of the astronomical problem concerned. No single interpolation technique is recommended for all circumstances, and the conclusions given are intended to provide a guide in considering possible options.
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Thompson et al. (1974) studied this question.