Optical interferometry plays an important role in the topographical surface measurement and characterization in precision/ultra-precision manufacturing. An appropriate surface reconstruction algorithm is essential in obtaining accurate topography information from the digitized interferograms. However, the performance of a surface reconstruction algorithm in interferometric measurements is influenced by environmental disturbances and system noise. This paper presents a comparative analysis of three algorithms commonly used for coherence envelope detection in vertical scanning interferometry, including the centroid method, fast Fourier transform (FFT), and Hilbert transform (HT). Numerical analysis and experimental studies were carried out to evaluate the performance of different envelope detection algorithms in terms of measurement accuracy, speed, and noise resistance. Step height standards were measured using a developed interferometer and the step profiles were reconstructed by different algorithms. The results show that the centroid method has a higher measurement speed than the FFT and HT methods, but it can only provide acceptable measurement accuracy at a low noise level. The FFT and HT methods outperform the centroid method in terms of noise immunity and measurement accuracy. Even if the FFT and HT methods provide similar measurement accuracy, the HT method has a superior measurement speed compared to the FFT method.

Real-time parametric interpolation plays a crucial role in achieving high-speed and high-precision multi-axis CNC machining. In the interpolation cycle, the position of the next interpolation point is required to be calculated in real-time to guide the action of the machining process. Due to the existence of the positioning error of the interpolation point, it is extremely difficult to eliminate the feedrate fluctuation, which may lead to dramatic decreases in machining quality and the driving capabilities’ saturation of each axis. A computationally efficient and precise feedrate fluctuation minimization method is proposed for the NURBS tool path interpolation in the CNC milling process. The model for the arc length and curvature, with respect to the parameter of the NURBS tool path, is established to reduce the calculation amount required by interpolation points determination. The deviation between the theoretical and actual interpolation step length is decreased by the proposed arc length compensation method to minimize the feedrate fluctuation. In addition, the interpolation points derived from the arc length compensation process are further corrected by performing the Newton iteration to restrict the feedrate fluctuation within the preset accuracy threshold. The effectiveness and superiorities of the proposed feedrate fluctuation minimization method are verified by simulation and milling experiments.