Statistical and systematic uncertainties in pixel-based source reconstruction algorithms for gravitational lensing

Gravitational lens modelling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixelbased source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularization, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the lens mapping but is irregular, and an adaptive Cartesian grid.We also consider regularization schemes that minimize derivatives of the source (using two finite difference methods) and introduce a scheme that minimizes deviations from an analytic source profile. Careful choice of gridding and regularization can reduce 'discreteness noise' in the χ² surface that is inherent in the pixel-based methodology.With a gridded source, some degree of interpolation is unavoidable, and errors due to interpolation need to be taken into account (especially for high signal-to-noise data). Different realizations of the noise and telescope pointing lead to slightly different values for lens model parameters, and the scatter between different 'observations' can be comparable to or larger than the model uncertainties themselves. The same effects create scatter in the lensing magnification at the level of a few per cent for a peak signal-to-noise ratio of 10, which decreases as the data quality improves.