Development of a Lifting Wavelet Representation for Surface Characterization

X. Q. Jiang, Liam Blunt, K. J. Stout

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64 Citations (Scopus)

Abstract

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 different components of a surface. The theory of the lifting wavelet is introduced and a fast algorithm is developed. Different 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 features can be identified 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 feasibility and applicability of using the lifting wavelet model in the analysis of these surfaces.

LanguageEnglish
Pages2283-2313
Number of pages31
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume456
Issue number2001
DOIs
Publication statusPublished - 8 Sep 2000

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Wavelets
functional analysis
Functional Analysis
Functional analysis
Surface Texture
bioengineering
Phase Shifting
Non-contact
Requirements
requirements
Interferometry
Metrology
Waveform
Fast Algorithm
Numerical Analysis
Triangular
metrology
Computer Simulation
numerical analysis
Numerical analysis

Cite this

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abstract = "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 different components of a surface. The theory of the lifting wavelet is introduced and a fast algorithm is developed. Different 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 features can be identified 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 feasibility and applicability of using the lifting wavelet model in the analysis of these surfaces.",
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