Recent experimental work has shown that the contrast of near-field optical images depends on the path followed by the tip during the scan. This artifact may misguide the interpretation of the images and the estimation of the optical resolution. We provide a rigorous theoretical study of this effect based on three-dimensional perturbation theory and two-dimensional exact numerical calculations. We quantitatively study the dependence of the artifact on the illumination/detection conditions and on the scattering potential of the sample. This study should provide guidelines for future experimental work.