title: Improved method for rapid shape recovery of large specular surfaces based on phase measuring deflectometry.
abstract: Incorporating the modal and zonal estimation approaches into a unifying scheme, we introduce an improved three-dimensional shape reconstruction version of specular surfaces based on phase measuring deflectometry in this paper. The modal estimation is first implemented to derive the coarse height information of the measured surface as initial iteration values. Then the real shape can be recovered utilizing a modified zonal wavefront reconstruction algorithm to simultaneously achieve consistently high accuracy and dramatically rapid convergence. Moreover, the iterative process based on an advanced successive over-relaxation technique shows a consistent rejection of measurement errors, guaranteeing the stability and robustness in practical applications. The reconstruction results of numerical examples of the sphere, hyperbolic, and arbitrary surfaces, as well as an experimentally measured sphere mirror demonstrate the validity and efficiency of the proposed improved method. In the simulations, the proposed method increases the rate of convergence by fourfold compared with the existing zonal approach and realizes three orders of magnitude improvement in reconstruction accuracy compared with the modal technique when handling the sample points of 401×401  pixels of a sphere surface. Furthermore, the computation time decreases approximately 74.92% in contrast to the zonal estimation, and the surface error is about 6.68 μm with reconstruction points of 391×529  pixels of an experimentally measured sphere mirror. In general, this new method can be conducted with fast convergence speed and high accuracy, providing an efficient, stable, and real-time approach for shape reconstruction in practical situations.
authors.forename: Tian
authors.initials: T
authors.lastname: Zhou
authors.forename: Kun
authors.initials: K
authors.lastname: Chen
authors.forename: Haoyun
authors.initials: H
authors.lastname: Wei
authors.forename: Yan
authors.initials: Y
authors.lastname: Li