Shape reconstruction based on zero-curl gradient field estimation in a fringe reflection technique

A novel shape reconstruction method based on zero-curl gradient field estimation is presented in this paper. Zero-curl field estimation makes the most of curl information to obtain the ideal gradient data, and achieves the reconstruction with the quality map path integration method. In the estimation process, an algebraic approach is adopted to enforce integrability, which maintains the local information well. Moreover, we use the residual gradients of surface obtained from the Southwell zonal reconstruction algorithm as the raw gradient data in zero-curl field estimation, which has a stable tradeoff between smoothness and local shape confinement. The performance of the proposed method over antinoise capability is discussed and demonstrated by the simulations. The measurement experiment of an ultraprecision sphere mirror identifies the validity over general shapes, and the reconstruction results of hyperbolic surface with a local shape map demonstrate the better performance on local details retention. Therefore, this method performs well in handling complex objects with local mutation regions and high accuracy requirement of local information in practical measurement.