东南大学工程力学系陈凡秀

Department of Engineering Mechanics, Southeast University, Nanjing,Jiangsu 210096 China Application of Wavelet Transform for Analyzing Instantaneous Contour of Continual Deformation Object 东南大学工程力学系陈凡秀

Method of 3D profilometry • Moire topography: Proposed by Meadows and Takasaki in the early 1970’s

Fourier transform Fourier transform Filter Inverse Fourier transform Phase Unwrapping

Phase shifting method Limited to surface contouring of static object only • Temporal phase-analysis and temporal phase-unwrapping techniques(late 1990’s) The Fourier-transform method become a popular method • Wavelet transform method (Continuous wavelet transform, CWT)

Continuous wavelet transform (CWT) CWT: (1) Morlet wavelet: (2)

d CCD camera Light source L α γ p Grating α′ γ′ h (x, y) Object (x, y) Fig. 1 Optical geometry Theoretical analysis

(3) (4) (5)

ζ=ω0 / a (6) (7) (8)

Simulation

High-Speed CCD camera White-light source Z X Grating Object Computer Mobile Stage Fig. 3 Experimental setup Experiment and Results

Sample and parameters Fig. 4 Typical moiré fringe patterns of cantilever beam k=22.347 P= 5 lines/mm

Conclusion Fig. 5 The instantaneous contour of T1=0.0025 s and T2=0.047 s.

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东南大学工程力学系 陈凡秀