## 1 Introduction
The algorithm proposed in this paper can be used to segment three-frame binary deformation maps with a duty ratio of 1/3 and relative displacement of a 1/3 period. Three sinusoidal deformation modes with 2\(\pi\)/3 shift phase can be obtained by extracting the fundamental frequencies of the three binary deformation modes, and the 3D shape of the object can be reconstructed by using PMP methodology. [PERSON] et al. [13] achieved a multi-wavelength digital phase-shifting moire by determining multiple moire wavelengths through system calibration over the full operating depth range. In this methodology, the extended noise phase diagram is used as reference, and the phase diagram is expanded at a shorter wavelength to obtain a continuous phase diagram with lower noise and more accuracy moire wavelength calibration determines the relationship between moire wavelength and height, allowing pixel-level refinement of moire wavelength and height during 3D reconstruction. Only one mode needs to be projected, so only one image needs to be captured to calculate each phase map with different wavelengths to perform a digital phase-shift moire time phase unrolling. Two-wavelength phase unwrapping requires only two capture images, and three-wavelength phase unwrapping requires only three capture images. This methodology has been verified in the 3D surface shape measurement of objects with surface discontinuity and space isolation. However, the accuracy of moire in this methodology is too high for experiment. [PERSON] et al. [14] proposed a square-root volume Kalman filtering phase unwrapped (SCKFU) procedure. By combining SCKF algorithm with phase gradient estimator, a phase unwrapping method for discrete Markov jump systems is proposed for tracking maneuvering targets. The phase quality estimation function is designed and the optimal path tracking strategy is proposed. This strategy ensures that the SCKFU method performs both noise suppression and InSAR image expansion along pixel points, and has highly dependent and low-dependence pixels in the image. However, this procedure has many steps and increases the computational burden. [PERSON] et al. [15] calculate the bar based on the heterodyne principle. The fractional part of the grain series, and then the actual value of the current fractional part is calculated from the phase principal value of the raster fringe of the frequency corresponding to the fringe series. Then, according to the phased master, the error of the value itself sets the judgment threshold, and the threshold is used to judge the difference between the calculated value and the actual value. Finally, according to the judgment results, the period of the intermediate parameters. The number of times is adjusted to add or subtract to correct the absolute phase. However, there are still some jump points. According to the above problems, a phase unwrapping correction procedure based on multi-frequency heterodyne procedure is proposed to solve the jumping error in phase unwrapping. Firstly, the phase principal values under three different frequencies are obtained by the four-step phase shifting method. Then, the dual-frequency heterodyne phase unwrapping method is used to obtain the phase principal values of the two adjacent frequencies, and the two lower frequency wrapped phases are obtained. Then the threshold is set for the absolute difference between the actual value of the decimal part with certain error calculated from the phase principal value and the theoretical value of the decimal part derived from the three-frequency heterodyne phase principle, so that the number of cycles for phase unwrapping can be added by one, subtracted by one, or the original value may be left unchanged to realize absolute phase correction. The experimental results show that this procedure can correct the jumping error effectively and has high noise resistance.