ETC

The way the different spectra are convolved is taking in consideration only the spectral binning size, by convolving with a constant averaging kernel with this size. This calculation is not enough for the source spectrum. In this case the kernel should not be constant but it should follow the spatial distribution (the PSF for point sources or the convolution of the PSF with the surface brightness profile for extended sources).

Note that this problem exist only for per spectral pixel calculations and not for per spectral resolution element calculations, because for at second case there is only one calculation done for each spectral binning, which makes the averaging kernel calculation valid.