LAUSR

This paper analyses the properties of minimal solutions for the reconstruction of the lens potential in the singular perturbative approach. These minimal solutions corresponds to an expansion with a minimal degree in Fourier expansion of the perturbative fields. Using these minimal solutions prevent spurious physically meaningless terms in the reconstruction of the fields. In effect a perturbative analysis indicates that a small change in the source model will corresponds to the higher order terms in the expansion of the fields. The results of the perturbative analysis are valid not only for slightly non-circular sources but also for more distorted sources to order two. It is thus of crucial importance to minimize the number of terms used in the modelling of the lens. Another important asset of the minimal solutions is that they offers a de-coupling between the source and lens model and thus help to break the source lens degeneracy issue. The possible drawback of minimal solutions is to under-estimate the higher order terms in the solution. However this bias has its merit since the detection of higher order terms using this method will ensure that these terms are real. This type of analysis using minimal solutions will be of particular interest when considering the statistical analysis of a large number of lenses, especially in light of the incoming satellite surveys.