Progress in High-Speed and High-Precision Laser Interferometric Surface-Figure Analysis

High-speed and high-precision laser interferometric surface-form analysis must balance acquisition speed, phase accuracy, spatial resolution, and systematic-error control. With interferogram acquisition, phase extraction, and phase unwrapping as the main thread, this article reviews high-speed measurement approaches, including two-frame phase shifting, simultaneous phase shifting, and spatial carrier, and discusses the application of deep learning to phase recovery. Unified numerical simulations are used to compare the error characteristics of representative two-frame phase-shifting and spatial-carrier algorithms. The analysis shows that two-frame phase shifting can shorten the acquisition sequence but is relatively sensitive to noise, the phase-shift value, and preprocessing; simultaneous phase shifting can acquire multiple phase-shift states in a single exposure; and spatial carrier enables single-frame demodulation but is constrained by spatial bandwidth and retrace error. Deep learning provides new approaches to phase extraction, phase unwrapping, and end-to-end recovery, but still depends on consistency between the training data and actual measurement conditions. This article aims to clarify the implementation principles and applicable conditions of different technical approaches and to provide a reference for method selection in dynamic testing and in-line surface-form measurement.