Gravitational lensing potential reconstruction in quadruply imaged systems

We develop a semi-analytical method to reconstruct the lensing potential in quadruply imaged gravitational lens systems. Assuming that the potential belongs to a broad class of boxy non elliptical models, we show how it is possible to write down a system of equations which can be numerically solved to recover the potential parameters directly from image positions and using physical constraints. We also describe a code developed to search for solutions of the system previously found and test it on simulated cases. Finally, we apply the method to the quadruple lens PG1115+080 which allows us to get also an estimate of the Hubble constant H0 from the measured time delay as H0 = 50 +18 −16 km s −1 Mpc.