Noise analysis and correction on carrier phase in coherence scanning interferometry for high accuracy surface topography measurements

•A new surface recovery approach for coherent scanning interferometry, which can offer high-accuracy surface topography for nanostructure characterization and industrial inspection applications.•The noise transmission from the correlogram to the carrier phase is theoretically analyzed and modeled and the impacts to measurement accuracy are investigated.•Both envelope and phase information are comprehensively utilized to enhance measurement accuracy, while preserving the high efficiency advantages of carrier-based method. Coherence scanning interferometry is a widely used technique for surface evaluation. This paper proposes a novel surface recovery approach, which can improve the measurement accuracy and robustness by attenuating the impact of noise in carrier phase distribution. The noise transmission from the interference signal to the carrier phase is firstly investigated. Afterwards, a more refined relationship between carrier phase and scan position is established, where the phase noise in carrier is estimated. To evaluate the similarity between the distribution of the estimated noise and the theoretical one, a likelihood function is defined. When the function reaches maximum, most carrier phase noises can be removed and the corrected surface is then recovered. Simulations indicate that this method reduces reconstruction error by at least 27 % compared with several common carrier-based methods under various intensity noises and scan position errors. In experiments, a step height standard (9.5 nm ± 1.0 nm), a nested square microstructure and an aeroengine sliding oil nozzle are measured to investigate the accuracy of the proposed method, where the mean height of repeated step measurements is 9.33 nm with repeatability 2.17 %. The measurement comparisons with commercial white light profiler and atomic force microscope are also provided.