Composite Phase-Shifting and Height Fusion Algorithm With Vibration-Robust in White Light Interferometry

White light interferometry is commonly illuminated using stable and long-lasting white light emitting diodes (LEDs). The measurement process is, however, susceptible to the spectral effects of LEDs and environmental vibrations, which will reduce its reconstruction accuracy. This article proposes a composite phase-shifting and height fusion algorithm to rectify the spectral distortions caused by LED light sources and minimize vibration impact by correcting errors arising from the special spectral effects in phase-shifting interferometry. Through the composite phase-shifting algorithm, this article constructs a composite Gaussian phase-shift model based on the dual-peak spectral characteristics of LED light sources to extract phase information. Then, a height fusion algorithm is presented to suppress the impact of vibration in the measuring process. This algorithm proves that the height error of the phase-shifting method has the characteristic of normal distribution, and thus, lays a theoretical basis for its average calculation of random error suppression. Through plane measurement simulations and standard step height measurement experiments, the proposed method was validated consistently with high measurement accuracy and stability under various degrees of vibration interference. Compared with other methods, the proposed method can reduce the impact of LED dual-peak spectral and dynamic vibration interference on the measurements, and thus, significantly enhance 3-D reconstruction accuracy for white light interferometric measurement.