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The galaxy-scale gravitational lens B0128+437 generates a quadrupole-imageconfiguration of a background quasar that shows milli-arcsecond-scalesubcomponents in the multiple images observed with VLBI. As this multiple-imageconfiguration including the subcomponents has eluded a parametric lens-modelcharacterisation so far, we determine local lens properties at the positions ofthe multiple images with our model-independent approach. Using PixeLens, wealso succeed in setting up a global free-form mass density reconstructionincluding all subcomponents as constraints. We compare the model-independentlocal lens properties with those obtained by PixeLens and those obtained by theparametric modelling algorithm Lensmodel. A comparison of all three approachesand a model-free analysis based on the relative polar angles of the multipleimages corroborate the hypothesis that elliptically symmetric models are toosimplistic to characterise the asymmetric mass density distribution of thislenticular or late-type galaxy. In addition, the model-independent approachefficiently determines local lens properties on the scale of the quasarsubcomponents, which are computationally intensive to obtain by free-formmodel-based approaches. As only 40% of the small-scale subcomponent local lensproperties overlap within the 1-$\sigma$ confidence bounds, mass densitygradients on milli-arcsecond scales cannot be excluded. Hence, aiming at aglobal reconstruction of the deflecting mass density distribution, increasinglydetailed observations require flexible free-form models that allow for densityfluctuations on milli-arcsecond scale to replace parametric ones, especiallyfor asymmetric lenses or lenses with localised inhomogeneities like B0128.

Model-independent and model-based local lensing properties of B0128+437 from resolved quasar images