The traditional white-light interferometer is highly sensitive to vibrations, causing scanning step errors and reducing measurement accuracy. To address this, a three-point arcsine (3P-Asin) algorithm is proposed. This method divides WLI interferograms into groups of three adjacent frames, with overlap between groups. By analyzing fringe movement, the phase shift deviation and exact scanning step are determined. Using this step, a least-squares method calculates phase and modulation for non-equal step scanning to reconstruct surface height. The 3P-Asin algorithm detects fast and large scanning step errors using only three interferograms, with no approximation. Simulations and experiments show it achieves an accuracy of 0.5% for a 10 μm step height and adapts to various surfaces in mechanical machining. Both theoretical and experimental results demonstrate that the 3P-Asin algorithm effectively attenuates scanning step errors across a wide frequency range, making it suitable for WLI in vibrating environments.