A look-up table (LUT) method for solving the problem of phase unwrapping is presented. Considering the effect of noise on the unwrapping process, a concept called “tolerance” is advanced, and an associated algorithm called the “equipartition of tolerance” algorithm is proposed. The proposed algorithm eliminates the need for a high signal-to-noise ratio while retaining the LUT method’s advantages of extended measurement range and high precision. Further, it improves the tolerance of the LUT method and enables reconstruction of discontinuous objects. In simulations and experiments conducted, the proposed algorithm successfully unwrapped the absolute phase of a slope model and a three-step model. The proposed algorithm is significantly more accurate and has better stability and sensitivity than the heterodyne algorithm.