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An accurate phase unwrapping algorithm is presented for reconstructing the true phase field for deformation interferograms. This algorithm is a combination of reliability sorting and residue mask, while introducing more reliable unwrapping fiducial information. In tests conducted with a pyramidal phase image, a complex simulated interferogram, and a real deformation interferogram, the proposed algorithm successfully unwraps the images with perfect precision. This algorithm is also shown to be superior to the prevailing improved Goldstein's residue-cut algorithm in terms of precision.