Assume we have a heterogeneous array with N antennas, of diameters . The r.m.s. visibility rms on baseline ij is:
In the least square analysis one should then weigh each baseline by where (assuming the system temperatures equal). One may normalize the weights by
Now the least squares analysis gives:
which may be rewritten:
We define
Then
after multiplying by and summation over i one may compute :
where
and obtain a closed form for :
For the r.m.s. fluctuations we get:
However if we note the flux sensitivity of a baseline connecting antenna i with an identical antenna:
Then
Now if N is large enough, and . Neglecting all terms in 1/N:
which shows than when the number of elements N is large, the precision of the gain measurement for one element is only determined by the size of this element and the total collecting area.