We derive a free-form mass distribution for the massive cluster AS1063 (z=0.348) using the completed optical imaging from the Hubble Frontier Fields programme. Based on a subset of 11 multiply lensed systems with spectroscopic redshift we produce a lens model that is accurate enough to unveil new multiply lensed systems, totalling over a 100 arclets, and to estimate their redshifts geometrically. Consistency is found between this precise model and that obtained using only the subset of lensed sources with spectroscopically measured redshifts.Although a relatively large elongation of the mass distribution is apparent relative to the X-ray map, no significant offset is found between the centroid of our mass distribution and that of the X-ray emission map, suggesting a relatively relaxed state for this cluster. For the well resolved lensed images we provide detailed model comparisons to illustrate the precision of our model and hence the reliability of our de-lensed sources. A clear linear structure is associated with one such source extending 23 kpc in length, that could be an example of jet-induced star formation, at redshift z ≈ 3.1.

We present an iterative method to construct a freeform lens model that self-consistently reproduces the sky positions, geometrically inferred redshifts, and relative brightnesses of all multiply lensed images toward a galaxy cluster. This method is applied to the cluster RXC J2248.7−4431 (z = 0.348) from the Hubble Frontier Fields program, toward which 10 multiply lensed sources with accurate spectroscopic redshifts and 6 others with inexact photometric redshifts have been identified. Using the spectroscopically secure systems to define an initial lens model, we compute the geometric redshifts of the photometric systems. We then iterate the lens model by incorporating the photometric systems at redshifts shifted by incremental amounts toward their geometric redshifts inferred from the previous step; on convergence, we find geometric redshifts in good agreement with the spectroscopically determined redshifts, but they can depart significantly from the photometrically determined redshifts. In the final lens model, all 16 lensed sources tightly follow the cosmological form of the angular diameter distance relation. Furthermore, although they are not used as model constraints, our lens model predicts relative brightnesses between image pairs for a given set of multiply lensed images in reasonable agreement with observations, thus providing independent validation of this model. Our method for inferring the redshifts and intrinsic brightnesses of multiply lensed sources will become especially important in the era of the James Webb Space Telescope, when deep infrared detections will typically be unmatched optically such that photometric redshifts will be very uncertain.