verified [*a posteriori*]{} that with this condition our algorithm is able to detect extended sources down to a flux level much lower than that required to characterize them as extended. Therefore, this step does not significantly affect the final flux limit for extended source detection. The filter was applied not only to the final source list, but also [*on the run*]{} to the temporary source list to avoid applying the extension criterion to unreliable sources and thus to reduce the computation time.

![Curves in the net photons-background photons plane corresponding to a probability $p$ of $10^{-3}$ or $10^{-4}$ of being a random fluctuation (red lines), compared with those corresponding to $S/N$ of $3$ or $4$ (blue lines). Curves for $S/N=4$, $p=10^{-4}$ and $S/N=3$, $p=10^{-3}$ are shown with solid and dashed lines, respectively.[]{data-label="poisson"}](poisson_snr.eps){width="\linewidth"}

\[0cm\]\[0cm\][![image](example_kstest.ps){width="40.00000%"}]{} ![image](kstest.eps){width="65.00000%"}

To classify all sources according to their extent, we drew a circle centered on the position of each source after masking all surrounding detected sources. The radius was chosen to enclose $60\%\sim70\%$ energy (slightly larger than $HEW/2$ of the PSF). For the sources that survived the reliability filter, we produced a normalized cumulative profile in the core circle by sorting each pixel according to the distance 