Application of Mathematical Theories of Approximation to Aerial Smoothing in Radio Astronomy

Abstract

An aerial rarely provides a perfect image of a radio brightness distribution. If we consider an array as a filter of "spatial harmonics", the image function is a trigonometric sum approximating the object function. An application of mathematical theories shows the influence of the length and the shape of the array on the difference between object and image. Whatever the array, the image contrasts are bounded. The results provided by various arrays of the same length may be reduced by linear transforms. Inaccuracies of measurement, especially those due to the receiver noise, add to the systematic error due to the finite length of the antenna. We may try to get a compromise between these various causes of uncertainty.