The underlying assumption for the derivation of Eq.(1) was that the variation in m was due to Poisson fluctuations in the number of stars projected in front of the source. In order to test this, we have investigated the correlation between m and the actual number of stars (N) projected in front of the source. The results are shown in Fig. 2, where we have plotted the correlation coefficient as a function of , for three different values of with . We see that the correlation increases with increasing source size and is larger than 0.9 already for , confirming very well the underlying assumption.
The standard deviation and the analytical approximation given by Eq. (1), are plotted as a function of for and .
It is generally found that also when shear terms are included, represents an upper limit for . Except for a narrow interval around , we even find that the value of is smaller than for . For a large range of -values we see however that the effect of the shear is rather small. An obvious exception is of course the "forbidden" intervals around where the amplification again gets very large and approaches zero. Eqs.(1) and (2) can therefore still be used to estimate an upper limit of the source size if is available from observations:
© European Southern Observatory (ESO) 1997
Online publication: April 28, 1998