Power spectrum of the residual surface-brightness fluctuations remaining in the lensed images of SDSS J0252 + 0039 after the smooth lens modelling. The lens modelling is performed alternatively with the highest source-grid resolution (n = 1), using either an adaptive (magenta line) or a non-adaptive (yellow line) source-grid regularization, or with a lower source-grid resolution (n = 3; blue line) chosen for this study to prevent overfitting. As an alternative solution, the red line shows the effect of using a larger mask in the smooth lens modelling combined with n = 1 and a non-adaptive source-grid regularization (for consistency reasons, the power spectrum is calculated within the original tight mask). The sky-background power spectrum (black line) is estimated based on a sample of 20 blank-sky regions (overlaid with the original tight mask) in the proximity to the lens. The estimated total noise power spectrum (green line) accounts for the additional flux-dependent (Poisson) shot noise in the science image.