PICARD, a Sun observing satellite, has produced more than one million images during its 4-year mission. SODISM is one of three instruments on-board, whose main goal is to measure the solar limb and its spectral dependence from the middle ultraviolet to the near infrared. The very high accuracy (a few milli-arcseconds) needed to measure the solar limb with its spatial and temporal variations makes the instrument very sensitive to small aberrations. In this paper, we will present the impact of various parameters on the solar limb measurement, from simple displacements of mirrors to complex mirror deformations and thermal gradients. A complete scenario has been constructed from these simulations, leading to a model that describes the actual limbs obtained with SODISM. All these simulations will help improving future missions, by assessing the critical parameters affecting the measurement accuracies of such instruments.