The galaxy-scale gravitational lens B0128+437 generates a quadrupole-image configuration of a background quasar that shows milli-arcsecond-scale subcomponents in the multiple images observed with VLBI. As this multiple-image configuration including the subcomponents has eluded a simple parametric lens-model characterisation so far, we determined local lens properties at the positions of the multiple images with our model-independent approach. Using PixeLens, we also succeeded in setting up a global free-form mass density reconstruction, including all subcomponents as constraints. We compared the model-independent local lens properties with those obtained by PixeLens and those obtained by the parametric modelling algorithm Lensmodel. A comparison of all three approaches and a model-free analysis based on the relative polar angles of the multiple images corroborate the hypothesis that elliptically symmetric models are too simplistic to characterise the asymmetric mass density distribution of this lenticular or late-type galaxy. Determining the local lens properties independently of a model, the sparsity and the strong alignment of the subcomponents yield broad 1-σ confidence intervals ranging from 8% to over 1000% of the local lens property values. The lens model approaches yield comparably broad confidence intervals. Within these intervals, there is a high degree of agreement between the model-independent local lens properties of our approach based on the subcomponent positions and the local lens properties obtained by PixeLens. In addition, the model-independent approach efficiently determines local lens properties on the scale of the quasar subcomponents, which are computationally intensive to obtain by free-form model-based approaches. Relying on the quadrupole moment of each subcomponent, these small-scale local lens properties show tighter 1-σ confidence bounds by at least one order of magnitude on the average with a range of 9% to 535% of the of the local lens property values. As only 40% of the small-scale subcomponent local lens properties overlap within the confidence bounds, mass density gradients on milli-arcsecond scales cannot be excluded. Hence, aiming at a global reconstruction of the deflecting mass density distribution, increasingly detailed observations require flexible free-form models that allow for density fluctuations on milli-arcsecond scale to replace parametric ones, especially for such lenses as B0128, which have an asymmetric mass density distribution that may include localised inhomogeneities.
Measuring the Autocorrelation Function of Nanoscale Three-Dimensional Density Distribution in Individual Cells Using Scanning Transmission Electron Microscopy, Atomic Force Microscopy, and a New Deconvolution Algorithm
