Enhancing reconstruction precision of zonal methods under low sampling density in non-uniform meshes

The fringe reflection method is widely used to determine the three-dimensional shape of mirror objects. The three-dimensional shape is produced by integrating local gradient data. Notably, the loss of middle- or high-frequency information often leads to the appearance of error in surface reconstruction. It is necessary to make full use of gradient data if we want to reconstruct the surface accurately. After reconstruction under low sampling density by existing algorithms, some high-frequency information will inevitably be lost. Considering the unequally spaced or non-uniform sampling, this paper proposes a new algorithm based on zonal methods that are applicable to non-uniform meshes. The key to obtaining improvement in precision is that our algorithm introduces surface compensation. On the basis of simulation results, we conclude that the proposed algorithm has stronger applicability and higher reconstruction precision under low sampling density.