In the macrolensing regime, corresponding to Einstein radii of the order of arcseconds, the overall mass distribution (including the dark matter halo and the stellar and gaseous disks and bulges) is responsible for the image separation of the multiple images and their multiplicity. Gravitational lensing observations combined with velocity dispersion measurements (Warren et al. 2003ApJ590(2003)673, Sand et al. 2003astro-ph/0309465, Sand et al. 2004ApJ604(2004)88, Sand et al. 2008ApJ674(2008)711) can be used to image the dark matter halo in the baryon dominated cores. Gravitation imaging of the small-scale structure (highly magnified Einstein rings and arcs) seen in the Hubble Space Telescope (HST) imaging data, requires lensing models that go beyond the singular isothermal ellipse (SIE) of Kormann et al. 1994A&A284(1994)285 or the light traces mass (LTM) model.
With the availability of high-resolution, high signal-to noise Hubble Space Telescope (HST) CCD (pixelized) images of galaxy-galaxy gravitational lenses, the mass distribution of the lens galaxy (or lens potential through the two-dimensional Poisson equation) can be computed simultaneously with the surface brightness distribution of the source galaxy, by inverting the lensed image.
According to Treu 2010arXiv:1003.5567, a number of groups are in the process of developing grid-based lensing models (e.g. Warren et al. 2003ApJ590(2003)673, Treu et al. 2004ApJ611(2004)739, Dye et al. 2005ApJ623(2005)31, Koopmans 2005MNRAS363(2005)1136, Brewer et al. 2006ApJ637(2006)608, Suyu et al. 2006MNRAS371(2006)983), "where the potential (or surface mass density) of the deflector and/or the surface brightness of the source are described by a set of pixels on regular or irregular grids using regularization schemes to suppress spurious features due to noise." Vegetti et al. 2009MNRAS392(2009)945 introduced a new adaptive grid-based lensing method, mapping a regular grid on the lens plane cast back to the source plane through the lens equations, to model strong galaxy-galaxy lenses with extended images incorporating a fully Bayesian inversion method designed to limit the number of free parameters.