Least-Squares Phase Unwrapping Based on Hermite Interpolation of the Southwell Regional Wavefront Method

Phase unwrapping is a fundamental procedure in optical metrology and image processing. The least-squares (LS) method has been widely adopted in phase unwrapping (PU) tasks due to its computational efficiency and mathematical elegance.Since PU-LS issues can be formulated as a two-dimensional integration, modal wavefront (MW) integration techniques have been extensively employed for the numerical solution. Although regional wavefront (RW) integration methods preserve the independence of measurement points through a distinctive geometric structure and offer improved robustness in the presence of incomplete data, they have not yet been applied to PU-LS issues. Therefore, this study introduces a Southwell RW integration approach based on Hermite interpolation and applies it to the PU-LS framework.Compared with existing MW and discrete cosine transform (DCT) methods, the proposed RW approach achieves a reduction of approximately 50% in peak-to-valley (PV) error. It exhibits superior robustness to phase occlusion. Experimental results validate the practical feasibility and effectiveness of the RW-based strategy for PU-LS applications.