Gravitational Lens MG J0414+0534

Gravitational lenses MG J0414+0534, B0218+357, B0957+561, BI422+231, and PKS B1830-211were observed at 5 GHz with the VLBA. MG0414+0534 revealed substructure not seen at lower resolutions: four subcomponents in each lensed image AI, A2, B, and C, with clear, consistent mapping between subcompo-nents. This provides more flux and position constraints for deflector modeling than other lenses provide. Lens modeling requires both source and deflector models. By treating subcomponents as pointlike, analytic expressions are given for model source flux and position parameters, reducing the parameter search space dimensionality. Image centroid may not correspond to source centroid for non-pointlike subcomponents; a correction for this was derived. The deflector potential was multipole-expanded in angle; each multipole component's radial dependence was Taylor-expanded in distance from the Einstein ring radius. Slightly regrouping the expansion terms, their coefficientsgive the multipole moments of mass ex-terior to, interior to, and at the ring radius. The dominant terms ' coefficients parameteriz