Development of a lifting wavelet representation for surface characterization

This paper reviews the existing numerical analysis methods and their problems in surface metrology. Based on the requirements of functional analysis of surfaces, this paper proposes a lifting wavelet representation for extraction of di¬erent compo-nents of a surface. The theory of the lifting wavelet is introduced and a fast algo-rithm is developed. Di¬erent frequency components of the surface can be separated, extracted and then reconstructed according the intended requirements of functional analysis. The surface textures can be highlighted and multi-scalar topographical fea-tures can be identi ed and clearly recovered. In order to verify the behaviour of the new model, a computer simulation based on sinusoidal and triangular waveforms is used. Case studies are conducted using a series of typical surfaces of engineering and bioengineering, such as planes, cylinders and curves, measured by contact (stylus) and non-contact (phase-shifting interferometry) instruments, to demonstrate the fea-sibility and applicability of using the lifting wavelet model in the analysis of these surfaces