We present a systematic study, where effects of the illumination probe design on ptychography reconstruction quality are evaluated under well-controlled conditions. The illumination probe was created using Fresnel zone-plate (FZP) optics with locally displaced zones to provide a fine control over perturbations of the illumination wavefront. We show that optimally designed wavefront modulations not only reduce bias and variance in the reconstruction of the lowest spatial frequencies but also lead to improved imaging resolution and reduction of artefacts compared to a conventional FZP. Both these factors are important for quantitative accuracy and resolution of ptychographic tomography. Our work furthers the understanding of the important characteristics of an optimal illumination for high-resolution X-ray ptychography and how to design optimal FZP wavefront modulations for different applications of ptychographic imaging. These findings are applicable and relevant for ptychography using optical, EUV, and X-ray photons as well as electrons.