Wavelets and their applications for surface metrology

This paper presents three generations of wavelet representations that are designed for micro/nano-scale surfaces. These wavelets include a basic biorthogonal wavelet (for the establishment of a surface filtering equation), an evolutionary lifting wavelet (for surface oriented frequency analysis, surface recognition and reconstruction with nano-scale accuracy) and a complex wavelet (for surface morphological feature extraction). The benefits of using these wavelets in the subject area will be demonstrated throughout as follows (1) their metrology properties: the linear phase, finite impulse filtering, simplicity and naturalness, shift-invariance and direction sensitivity; (2) practical applications in surface measurement denoising, feature extraction for engineering and bioengineering surfaces.