In optical scanning holography, holographic information of an object is generated by 2D active optical scanning. The optical scanning beam can be a time-dependent Gaussian apodized Fresnel zone plate. We first derive the resolution achievable with such a scanning beam. We then show through computer simulation that the use of a larger Fresnel zone plate for holographic recording leads to a noisier twin-image reconstruction in the near field, thereby degrading the resolution. This is particularly noticeable with objects of more complicated structures.