Abstract
Abstract
Ultra-precision machined micro-structures are widely used in optical components. Surface waviness, as a key indicator of surface quality, can affect the optical performance of these components. However, after the nominal form of the micro-structures are removed by filtering, existing non-differentiable boundaries and abnormal outliers can still significantly affect surface waviness evaluation. Therefore, this study proposes a surface waviness evaluation method for ultra-precision machined micro-structures by combining a geometric parameter regression network with probability-distribution-based parameterization. First, a geometric parameter regression network is established for nominal-form removal. A low-frequency proxy of the measured topography is used as the network input to estimate structural parameters and alignment parameters. These estimates are introduced into an analytical micro-structure model to reconstruct the reference surface, followed by multi-scale alternating optimization to refine the structural and alignment parameters and generate the residual topography. Second, direction-dependent cut-off wavelengths are selected from the residual topography using directional power spectral density analysis and multi-criterion evaluation. Finally, probability-distribution-based weighted moments and weighted quantiles are used to parameterize surface waviness evaluation and reduce the influence of outliers. Results show that the proposed method improves nominal-form removal and provides a reliable residual topography for direction-dependent surface waviness extraction. The probability-distribution-based parameterization reduces the influence of boundary-contaminated samples and local abnormal extrema while preserving the main surface waviness trend. Therefore, the study provides an effective approach for surface waviness parameterization of ultra-precision machined micro-structures with non-differentiable boundaries and local abnormal extrema.