Zero-spacing Problem

Since visibility and the brightness distribution are related via a Fourier transform, measures the total flux from the sky. However, since the difference between the antenna positions is always finite, is never measured by an interferometer. For a point source, it is easy to estimate this value by extrapolation from the smallest and for which a measurement exist, since as a function of baseline length is constant. However for an extended source, this value remains unknown and extrapolation is difficult.

For the purpose of understanding the effect of missing zero-spacings,
we can multiply the visibility in Eq. 11.3.6 by a rectangular
function which is 0 around and 1 elsewhere. In the map
domain then, the *Dirty Map* gets convolved with the Fourier
transform of this function, which has a central negative lobe. As a
result, extended sources will appear to be surrounded by negative
brightness in the map which cannot be removed by any processing. This
can only be removed by either estimating the zero-spacing flux while
restoring from or , or by supplying the zero-spacing flux
as an external input to the mapping/deconvolution programs. The
Maximum Entropy class of image restoration algorithms attempt to
estimate the zero-spacing flux, while the CLEAN class of image
restoration algorithms needs to be supplied this number externally.
Both these will be discussed in the later lectures.