  The key to using a strong gravitational lens system to measure the Hubble
constant is to obtain an accurate model of the lens potential. In this paper,
we investigate the properties of gravitational lens B1608+656, a
quadruply-imaged lens system with an extended source intensity distribution.
Our analysis is valid for generic quadruply-lensed systems. Limit curves and
isophotal separatrices are defined for such systems, and we show that the
isophotal separatrices must intersect at the critical curves and the satellite
isophotes must be tangent to the limit curves. The current model of B1608+656
(Koopmans et al. 2003) satisfies these criteria for some, but not all, of the
isophotal separatrices within the observational uncertainty. We study a
non-parametric method of potential reconstruction proposed by Blandford, Surpi
& Kundic (2001) and demonstrate that although the method works in principle and
elucidates image formation, the initial potential only converges to the true
model when it is within ~ 1 percent of the true model.
