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1 WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT Optical Metrology and NDT ME-593L, C 2018 Introduction: Fringe Skeletonization February 2018
2 Quantitative analysis Fringe skeletonization Recording o intererograms Identiication o boundary area (AOI) Preprocessing, e.g., iltering Identiication o ringe centers Numbering o intererence ringes: ringe ordering Reconstruction o phase using interpolation Review reerence papers (list is on next page)
3 Reerence papers: Quantitative analysis Fringe skeletonization J. Novak, Techniques or automatic identiication and numbering o intererence ringes using MATLAB. T. Merz, D. Paulus, and H. Niemann, Line segmentation or intererograms o continuously deorming objects. L. Z. Cai, Q. Liu, and X. L. Yang, A simple method o contrast enhancement and extremum extraction or intererence ringes. J. Budzinski, SNOP: a method or skeletonization o a ringe pattern along the ringe direction.
4 Recording o intererograms Classic intererometry Michelson Mach-Zehnder Sagnac Holographic intererometry Digital holographic intererometry Speckle pattern intererometry White-light intererometry
5 Identiication o boundary area Identiication o area o interest (AOI) Area o operation Selection o convolution Kernel Minimization o power leakage
6 Pre-processing, e.g., iltering: convolution Application o digital spatial convolution to the pixel located at the (m,n) image plane position Image convolution: m Q D ( m, n) H Q' ( m, n) kl D m 1 m m+1 n 1 n * (0,0) = n n+1 ( m, n) Q D H kl ( m, n) Q ' D Original image Kernel Convolved image
7 Pre-processing, e.g., iltering: convolution Digital spatial convolution by scanning the convolution kernel line by line over the entire image plane m n Kernel (3 x 3, in this case)
8 Pre-processing, e.g., iltering: convolution Low-pass iltering Image convolution: ' 1 Q D ( m, n) QD ( m k, n l) ( 2r 1) ( 2r 1) r k r r l r Weighting actors: H kl 1 ( 2r 1) ( 2r 1)
9 Pre-processing, e.g., iltering: convolution Median iltering Digital spatial convolution to median iltering the pixel value located at the (m,n) image plane position Original image Convolved image m m n n (a) (b) Kernel (3 x 3, in this case) Sorted list
10 Fringe skeletonization Pre-processing, e.g., iltering: convolution Fourier iltering Fourier transormation: )}, ( { ), ( n m Q Q D v u D Convolution in the requency domain: ), ( ), ( ), ( v u v u D v u T D W Q Q ), ( v W u is the weighting unction Inverse Fourier transormation: )}, ( { ), ( 1 v u D ' D Q m n Q T
11 Pre-processing, e.g., iltering: convolution Fourier iltering Fourier transormation: Q D (, ) { Q ( m, n)} u v D Original intererogram Original intererogram: requency domain
12 Weighting actor Fringe skeletonization Pre-processing, e.g., iltering: convolution Fourier iltering W (, v) u, weighting unction: Gaussian unction 2D representation 3D representation
13 Pre-processing, e.g., iltering: convolution Fourier iltering Convolution in the requency domain: QT D( u, v ) QD ( u, v ) W ( u, v ) ' 1 T Inverse Fourier transormation: Q D ( m, n) { QD( u, v)} Original intererogram Filtered intererogram
14 Pre-processing: thinning Multiple algorithms exist, e.g., contrast enhancement, edge detection, etc. Original intererogram Thinned ringes: contrast enhancement
15 Identiication o ringe centers Fringe centers Thinned ringes: contrast enhancement
16 Semi-quantitative analysis 1 ringe is 2/: ringe ordering and counting Intererogram o a turbine blade: contouring Intererogram o a turbine blade: vibrations Fringe-locus unction (ringe localization): ( x, y, z) K L ( x, y, z) 2 n n = is the ringe order A ringe represents a contour o constant phase n is the ringe order or number o waves
17 Sample: identiication o ringe centers Closed ringe pattern and continuous deormations:
18 Fringe ordering: n-th order Identiy zero-order: understanding o the physical phenomena Use sequential ordering Fringe orders: n Zero order
19 Fringe ordering Opened ringe pattern and continuous deormations: A A Intensity line: A-A Fringe ordering:
20 Phase reconstruction Fringe interpolation, e.g., Lagrange, Zernike polynomials, etc. Lagrange polynomials o degree n-1 x o
21 Phase reconstruction Fringe interpolation, e.g., Lagrange, Zernike polynomials, etc. Lagrange polynomials o degree n-1 x o. x 2
22 Phase reconstruction: 1-ringe = /2 Reconstruction along speciic lines: Interpolation along speciic lines:
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