Constraining the sub-galactic matter-power spectrum on 1-10 kpc scales would make it possible to distinguish between the concordance $Lambda$CDM model and various alternative dark-matter models due to the significantly different levels of predicted mass structure. Here, we demonstrate a novel approach to observationally constrain the population of overall law-mass density fluctuations in the inner regions of massive elliptical lens galaxies, based on the power spectrum of the associated surface-brightness perturbations observable in highly magnified galaxy-scale Einstein rings and gravitational arcs. The application of our method to the SLACS lens system SDSS J0252+0039 results in the following limits (at the 99 per cent confidence level) on the dimensionless convergence-power spectrum (and the associated standard deviation in aperture mass): $Delta^{2}_{deltakappa}<1$ ($sigma_{AM}< 0.8 times 10^8 M_odot$) on 0.5-kpc scale, $Delta^{2}_{deltakappa}<0.1$ ($sigma_{AM}< 1 times 10^8 M_odot$) on 1-kpc scale and $Delta^{2}_{deltakappa}<0.01$ ($sigma_{AM}< 3 times 10^8 M_odot$) on 3-kpc scale. The estimated effect of CDM sub-haloes lies considerably below these first observational upper-limit constraints on the level of inhomogeneities in the projected total mass distribution of galactic haloes. Future analysis for a larger sample of galaxy-galaxy strong lens systems will narrow down these constraints and rule out all cosmological models predicting a significantly larger level of clumpiness on these critical sub-galactic scales.
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