We propose the synthetic aperture wavefront sensing approach. It is based on acquiring several sets of measurements of the wavefront slopes by displacing sequentially the microlens array with respect to the unknown wavefront. These measurements are stacked together and processed as if obtained with a single-sampling array with an effective number of subpupils equal to the product of the number of microlenses by the number of displacements. We analyze and compare the performance of this approach with the method of modal coefficient averaging. The comparison is made in terms of the squared wavefront reconstruction error, spatially averaged over the pupil and statistically averaged over the noise and the aberrations of the population. We focused our attention on its applications to eye aberrometry. Our numerical results were obtained for a population statistics consistent with a wide sample of young adult eyes using different sampling grids and with several signal-to-noise ratios. They indicate that the synthetic aperture wavefront sensing is affected by less bias and noise propagation than the averaging method, providing smaller mean-squared estimation error. The number of complete Zernike radial orders that can be estimated using the synthetic aperture approach is consistently higher than that allowed by the conventional method.