Local polynomial phase identification and wrapped phase recovery from circular harmonic integrals

Local polynomial phase modeling is a powerful scheme for fringe analysis. This paper develops an algebraic equation relating the polynomial phase coefficients to the circular harmonic integrals of the fringe signal, enabling accurate identification of the local phase field. By transforming the circular harmonic integrals into 2D kernel convolutions, we derive a system of equations that estimates the local polynomial coefficients across the entire observed phase field. This yields an efficient denoising and recovery algorithm for the wrapped phase field. Experiments confirm that the proposed algorithm achieves model identification accuracy comparable to the Cramér-Rao lower bound and demonstrate preferred parameter settings and adaptability across various phase fields.