next up previous contents
Next: Further Reading Up: Mapping II Previous: Time Average Smearing   Contents


Zero-spacing Problem

Since visibility and the brightness distribution are related via a Fourier transform, $V(0,0)$ measures the total flux from the sky. However, since the difference between the antenna positions is always finite, $V(0,0)$ is never measured by an interferometer. For a point source, it is easy to estimate this value by extrapolation from the smallest $u$ and $v$ for which a measurement exist, since $V$ 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 $(u,v)=(0,0)$ 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 $I$ from $I^d$ or $V$, 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.


next up previous contents
Next: Further Reading Up: Mapping II Previous: Time Average Smearing   Contents
NCRA-TIFR