Effect of an incorrect estimate of the Poisson noise on a very simple fit. A symmetrical Gaussian profile is simulated (red) and fitted for 1000 realizations of the simulation using the correct noise estimate (blue). When the error bars on the pixel values are computed using the (noisy) data themselves, the fit (black) is affected by systematics, meaning that in this case the FWHM of the Gaussian is underestimated.