Convolution and the first detection

One can show (Irwin1985) that the optimal filter to detect point sources of weak flux on an image is related to spreading out of the point sources of the image considered: its own PSF.

The subtraction is the result of the difference of the image of better seeing brought to the resolution of the second. The seeing of the subtraction is thus equal to the seeing of the image of less good seeing.

A Gaussian profile of width equal to the seeing is a good approximation (Irwin1985) profile of stars. It is thus proceeded to a convolution of the image by this profile.

One calculates then the variance of the convoluted image. The pixels corresponding to a signal on noise higher than the threshold are selected (the threshold is typically between 2 and 3 $\sigma$ of the convoluted image).

We have after the first stage of a list candidates whose majority are Poissonnian fluctuations. For a cut in signal on noise of $3 \sigma$, one awaits on average 3000 candidates on a CCD of the CFH12K.