Parallel unambiguous generalized phase-shifting and T-spline fitting algorithms for optical micro-structured surface 3D topography metrology.

3D topography metrology of optical micro-structured surfaces is critical for controlled manufacturing and evaluation of optical properties. Coherence scanning interferometry technology has significant advantages for measuring optical micro-structured surfaces. However, the current research faces difficulties of designing high accuracy and efficient phase shifting, and characterization algorithms for optical micro-structured surface 3D topography metrology. In this paper, parallel unambiguous generalized phase-shifting and T-spline fitting algorithms are proposed. To avoid phase ambiguity and improve the accuracy of the phase-shifting algorithm, the zero-order fringe is determined by the iterative envelope fitting with Newton's method, and the accurate zero optical path difference is determined by a generalized phase-shifting algorithm. In particular, the calculation procedures of the multithreading iterative envelope fitting with Newton's method and generalized phase shifting are optimized with the graphics processing unit-Compute Unified Device Architecture kernel function. Additionally, to fit the base form of optical micro-structured surfaces and characterize the surface texture and roughness, an effective T-spline fitting algorithm is proposed by optimizing the preimage of the T-mesh with image quadtree decomposition. Experimental results show that the surface reconstruction of optical micro-structured surfaces using the proposed algorithm is more accurate, and the efficiency is 10 times higher than that of current algorithms; the time of the surface reconstruction is less than 1 s. Compared with the current B-spline method, the accuracy of roughness characterization using the proposed T-spline algorithm is improved by more than 10%.