Construction of a Map from Sampled Points.
10 October 1988
A two-dimensional version of the sampling theorem, first discussed by Bracewell in 1962, is cast in a form which can be implemented as a computer program. Consider a scalar function of two dimensions, the distribution of brightness in an image. If this function is fully-sampled by an instrument having finite spatial-frequency bandwidth, then it is possible to calculate exactly what that instrument would observe at any arbitrary point between the samples. Thus, a band-limited map can be constructed from finite samples.