Multipole Expansion Model in Gravitional Lensing

Nontransparent models of the multipole expansion model and the two point-mass model are analyzed from the catastrophe theory. Singularity behaviours of 2n-pole moments are discussed. We apply these models to the triple quasar PG1115+080 and compare with the typical transparent model, softened power law spheroids. The multipole expansion model gives the best fit among them.