Far-field directivity measurements require sampling the sound field over a sphere. A high angular resolution isusually attained either by sequentially scanning the sphererotating an half-circle antenna of microphone, or by placinga high number of microphones to cover the full sphereat once. The first method assumes repeatability of thesource under study. This is not applicable to most naturalsources, e.g. the human voice. The second approachrequires a high number of microphones located on thesurface of a sphere. Low cost Mems microphones allowto design microphone arrays with a large number of elements.However, it is cumbersome to precisely placethese sensors on a sphere. The method proposed in thisstudy allows to estimate far-field directivity from pressuremeasurements performed on a non-spherical surface, viaa spherical wave propagation model. The robustness ofthe proposed method to experimental uncertainties (measurementnoise and uncertainty on microphones location)is tested numerically using simulated sound fields. Arraydesign guidelines are proposed after comparison ofthe quality of reconstruction for different array geometriesand numbers of microphones.