Top three panels: an artificial He⁺ VDF as a function of the He⁺ angle of incidence β and relative velocity w_sw. Centre three panels: the same distribution convolved with a complex angular response function. Bottom three panels: reconstruction of the reduced He⁺ VDF (RVDF) with the proposed analysis technique based on data from the centre three panels. The RVDF representation of the VDF is only able to reconstruct structures that systematically change with the orientation of B (Gaussian feature at w_sw = 1.1). Structures that stay constant over different orientations of B (Gaussian feature at w_sw = 0.6) are not resolved.