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• This paper proposes an efficient high-order harmonics correction method for phase measuring profilometry. • The addition of the ideal phase and the residual harmonics is converted to the multiplication based on Hilbert transform. • Simulations and experiments have validated the proposed method compared with conventional methods. Gamma nonlinearity severely affects the accuracy of phase measuring profilometry (PMP). Through averaging two phase maps with inverse errors, conventional methods including double phase-shifting (DPS) and Hilbert transform (HT) only compensate the fundamental harmonic while leaving high-order harmonics. To address this issue, this paper presents an efficient high-order harmonics correction (HHC) method. The averaged phase is encoded into factitious fringes on the computer. Then we directly apply HT on these factitious fringes to generate transformed fringes, while the addition of the ideal phase and residual harmonics is converted to multiplication. Finally, the residual high-order harmonics are suppressed, and the corrected phase is calculated using the phase-shifting algorithm. In comparison to conventional DPS and HT methods, the proposed HHC method can efficiently correct the residual high-order harmonics, thereby enhancing the measuring accuracy. [ABSTRACT FROM AUTHOR]