Displacement and Strain Measurement Using Gratings

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Presentation at CSC015 Chung Yuan Christian University March 0-1 Grating, Moire, and Speckle Methods for Measuring Displacement, Shape, Slope, and Curvature Fu-pen Chiang SUNY Distinguished Professor

1 Presentation at CSC015 Chung Yuan Christian University March 0-1 Grating, Moire, and Speckle Methods for Measuring Displacement, Shape, Slope, and Curvature Fu-pen Chiang SUNY Distinguished Professor & Chair Department of Mechanical Engineering Member, Dept of Biomedical Engineering Graduate Program Member, Institute of Molecular Cardiology Stony Brook University And Chair Professor Dept of Mechanical Engineering National Taiwan University Displacement and Strain Measurement Using Gratings 1

2 Displacement and Strain Measurement Using Gratings 3 The Need For Higher Density Grating Leads to the Invention of the Moiré Method 4

3 Moiré Patterns 5 Field Equation for In-plane Moiré Fringes Recording the grating before and after deformation. Two fringes pattern are needed for strain analysis U=Np, V=N p P: Pith of the grating, or grating constant N, N = 0,1,,3 fringes orders 6 3

4 Strain Measurement Using Moiré Fringes 7 Displacement and Strain Measurement Using Moire Crack Tip Deformation 8 4

Displacement and Strain Measurement Using Moiré Fringes Moiré fringe pattern with crossed gratings of different pitch on the master and the specimen 9 Shadow Moiré

5 Displacement and Strain Measurement Using Moiré Fringes Moiré fringe pattern with crossed gratings of different pitch on the master and the specimen 9 Shadow Moiré and Projection Moiré Shadow- Moiré method with point illumination and point receiving Np w ; when 0 tan tan Schematic of the single-projection arrangement w Np tan 10 5

6 Shadow Moiré for Measuring Shape Takasaki 11 Deflection and Depth Moiré Fringes Shadow Moiré Projection Moiré Moving-grating fringes Stationary-grating fringes 1 6

Speckle Photography White Light Camera Surface with attached

7 Laser Speckle Photography Laser Light Camera Optically Rough Surface Recording of a laser speckle pattern 13 Laser Speckle Photography White Light Camera Surface with attached or natural speckles Recording of a white light speckle pattern 14 7

indicator y λ : wavelength of laser light N,N = 0, 1,, 3 fringe nodes 15

8 Speckle Methods for Displacement, Shape, and Slope Measurement For In-plane Speckle Fringes U u V u y NL r N'L r y r r, r spatial frequency indicator y λ : wavelength of laser light N,N = 0, 1,, 3 fringe nodes 15 Displacement Measurement by Speckle U field V field Moiré Fringes Speckle Fringes 16 8

Projection Speckle Method for Mapping Depth or Deflection NL w mr tan m =

Measurement by Laser Speckle G. K. Jaisingh and F.P.

Optics A technique is presented to determine surface contours of 3-D objects by

A double eposure specklegram is recorded by giving the object a small tilt

9 Projection Speckle Method for Mapping Depth or Deflection NL w mr tan m = magnification λ = wavelength N = 0,1,,3 r = Fourier Filtering distance 17 Shape Measurement by Laser Speckle G. K. Jaisingh and F.P. Chiang, 1 October 1981/ Vol. 0, No. 19/ App. Optics A technique is presented to determine surface contours of 3-D objects by laser speckle interferometry. A double eposure specklegram is recorded by giving the object a small tilt between eposures. Surface contours are obtained by Fourier filtering of the specklegram. Schematic of eperimental setup Surface contours of a 5-cm diam sphere Surface contours of a light bulb 18 9

Reflection Laser Speckle Methods are Equivalent N P (moiré)

10 Slope Measurement by Laser Speckle or Reflection Moire w w y N D N, D, L r L r y 19 Thus the Reflection Moiré and Reflection Laser Speckle Methods are Equivalent N P (moiré) (speckle) r Slope Fringe by Moiré Slope Fringe by Laser Speckle 0 10

Versatilities of Speckle Method I Displacement or slope contours along different directions Partial slope contours of a clamped centrally loaded

Different patterns are obtained by placing the filtering aperture at different angles at the transform plane as shown at top figure 1 Versatilities of

11 Versatilities of Speckle Method I Displacement or slope contours along different directions Partial slope contours of a clamped centrally loaded triangular plate. Different patterns are obtained by placing the filtering aperture at different angles at the transform plane as shown at top figure 1 Versatilities of Speckle Method II Displacement or slope contours with Different sensitivity Fringe patterns of partial slope contours with different sensitivity of a clamped circular plate under concentrated central load Circles at top of figure depict the position of filtering aperture at transform plane 11

12 Versatilities of Speckle Methods III Time Average Fringes with different sensitivity with different orientations 3 Projection Grating Methond for Measuring Shape Phase-shifting Method Huang et al -D photo I 1 (-3p/) I (0) I 3 (3p/) Wrapped phase map 3-D model 4 1

A Piece of Rabbit Hair of above 0 micron as Mapped by the Digital Projection Grating Technique 5 An optical method of generating slope and curvature contours of bent

13 A Piece of Rabbit Hair of above 0 micron as Mapped by the Digital Projection Grating Technique 5 An optical method of generating slope and curvature contours of bent plates Chiang, F.P. and Kao, T.Y., 1979 An Optical Method of Generating Slope, and Curvature Contours of Bent Plates. Int. J. of Splids and Structures, V.15. pp

14 Optical arrangement of the method 0 ξ ξ ξ f t an α β f t an α f t an sec α 1 t an α t an 7 0 ξ ξ ξ f t an α β f t an α f t an sec α 1 t an α t an (1) cos ξ cos f ξ α or α f () w w n n p 0 Np cos α cos α or f f (3) 8 14

15 Image shifting due to diffraction 9 u z t an β θ t an β z sec t an β t an θ β t an θ (4) u p λz 3 cos β (5) 1 I u 0 1 cos n u π 1 I u 1 γ 1 cos n 1 u u π 1 I u 1 γ 1 cos n 1 u u π (6) (7) (8) 30 15

16 1 I u 1 γ 1 cos nπ γ 1 cos n n π cos n n π T 1 1 γ 1 cos nπ 1 γ1 cos n π (9) Assume γ I u cos nπ T 1 cos n π For n 0, 1,,, Eq. (10) reduces to (10) T 1 cos I u nπ (11) 31 cos u u u n u u n u p α u u u f 3 np cos α cos β (1) fzλ Noting that z b 1 f And the magnification M b 1 w b 1 Eq. 1 is reduced to u u b a (13) N ' p cos α cos β 3 w λf N ' n The new order of the enveloping fringes (14) 3 16

17 If the field lens has a long focal length and small aperture the angle β may be approimated by α 5 w N ' p cos α λf (15) w w w w csc δ cos δ si n δ y s y (16) w Np w N ' p and (17) f λf 33 Slope contours of a cantilever beam under tip load and comparison between theory and eperiment 34 17

18 Slope contours of a clamped circular plate under centrally applied concentrated load and comparison between theory and eperiment 35 Curvature contours of a cantilever beam under tip load and comparison between theory and eperiment 36 18

19 Curvature contours of a clamped circular plate under centrally applied concentrated load and comparison between theory and eperiment 37 Slope and curvature contours along and y directions of a clamped triangular plate under uniform pressure 38 19

20 Propagating slope contours of a square cantilever beam under impact (numbers in sec) 39 Propagating curvature contours of a square cantilever beam under impact (numbers in sec) 40 0

21 Partial List of Relevant References 1. Chiang, F.P., and Sciammarella, C.A., Moiré method applied to three-dimensional elastic problems, Eperimental Mechanics, 4(11), pp Chiang, F.P., and Sciammarella, C.A., Gap effect on moiré fringe, Zeitschrift fur Angewandte Mathmatik und Phsik, 19(), pp Chiang, F.P., and Ranganayakamma, B., Some eperimental evidence for the validity of moiré gap equation, Eperimental Mechanics, 10(7), pp Chiang, F.P., Treibser, J., A note on Ligtenberg s reflective moiré method, Eperimental Mechanics, 10(1), pp Chiang, F.P., Faber, C., et al., Two dimensional stress measurement in permalloy thin films by moiré method, J. Applied Physics, 4(4), pp Chiang, F.P., and Ranganayakamma, B., Deflection measurements using moiré gap effect, Eperimental Mechanics, 11(7), pp Chiang, F.P., 197. On a moiré method applied to the determination of two-dimensional dynamic strain distribution, J. Applied Mechanics, Trans. of the ASME, 39(3), Series E., pp Chiang, F.P., and Jaisingh, G., Dynamic moiré methods for the bending of plates, Eperimental Mechanics, 1(4), pp Chiang, F.P., Lin, C.J., A time average reflection moiré method for vibration analysis of plates, Applied Optics, 18(9), pp Chiang, F.P., Halioua, M., et al., Projection moiré with moving gratings for automated 3D topography, Appl. Opt., (6), pp Chiang, F.P., and Khetan, R.P., Strain analysis by one-beam laser speckle interferometry I: single aperture method, Applied Optics, 15(9), pp Chiang, F.P., Laser speckle interferometry for plate bending problems, Applied Optics, 15(9), pp Partial List of Relevant References 13. Chiang, F.P., and Juang, H., Vibration analysis of plates and shells by laser speckle interferometry, Optica Acta, 3(1), pp Chiang, F.P., Dynamic laser speckle interferometry applied to transient fleure problems, Applied Optics, 15, pp Chiang, F.P., and Lin, C.J., A Ligtenberg method for plate bending studies using laser speckles, Mechanics Research Communications, 7(4), pp Chiang, F.P., and Lin, C.J., Stress analysis of in-plane vibration of D structure by a laser speckle method, Applied Optics, 19(16), pp Chiang, F.P., and Lin, C.J., Laser speckle method for the analysis of steady-state in-plane vibrations of plates, J. of Acoustic Soc. of Am., 69(), pp Chiang, F.P., and Jaisingh, G., Contouring by laser speckle, Appl. Opt., 0(7), pp Chiang, F.P., and Bailangadi, M.N., General analysis of the projection speckle method, Applied Optics, 0(9), pp. A Chiang, F.P., and Kin, C.C., 198. Strain Determination on curved surfaces using far-field objective laser speckles, Opt. Eng., 1(3), pp Chiang, F.P., and Kin, C.C., Objective laser speckle method for 3D displacement measurement on curved surfaces, Opt. Engrg., (1), pp Chiang, F.P., and Gupta, P.K., Laser speckle interferometry applied to studying transient vibrations of a cantilever beam, J. Of Sound and Vibration, 133(), Chiang, F.P A family of D and 3D eperimental stress analysis techniques using laser speckles, Solid Mechanics Archives 3(1), pp Chiang, F.P Optical stress analysis using moiré fringe and laser speckles, Optical Engineering, 18(9), pp

22 Partial List of Relevant References 5. Chiang, F.P Random (speckle) patterns for displacement and strain measurement: some recent advances, Optical Engineering, 4 (6), pp Chiang, F.P Some recent advances in speckle techniques for photomechanics and optical metrology, Invited paper, SPIE Proc. Vol. 661, pp Some Recent Advancement in Fringe Projection Techniques for 3-D Shape Measurement, (with P.S. Huang), Invited paper, SPIE conference on Optical Diagnostics for Fluids/Heat/Combustion and Photomechanics for solids. The Int. Sym. On Optical Science, Engrg & Instrumentation, Denver, Co, 7/18-3, Chiang, F.P. Some New Developments in Eperimental Mechanics Using Random Particles and Fractal Dimension, (Keynote paper), Proc. SPIE, vol 4317, nd International Conference on Eperimental Mechanics, June 1-6, Chiang, F.P., and Asundi, A., Interior displacement and strain measurement using white light speckles, Applied Optics, 19(4), pp Chiang, F.P., and Bailangadi, M.N., White light projection speckle method for generating deflection contours, Applied Optics, 19(15), pp Chiang, F.P., Liu, B.C., and Lin, S.T., Multi-aperture white light speckle method applied to the strain analysis of cylinders with holes under compression, Optics and Lasers in Engineering, (3), pp Chiang, F.P., and Asundi, A., 198. Measurement of large deformation using the white light speckle method, Mechanics Research Communication, 9(5), pp Asundi, A., and Chiang, F.P., 198. Theory and application of white light speckle methods, Optical Engineering, 1(4), pp Chiang, F.P., and Chen, D.J., 199. Optimal sampling resolution and range of measurement in digital speckle correlation 1: laser speckle method, Ep. Mech., 3(6), pp Chen, D.J., Chiang, F.P., Tan, Y.S., and Don, H.S., Digital speckle displacement measurement using comple spectrum method, Applied Optics, 3, pp Chiang, F.P. and Kao, T.Y., 1979 An Optical Method of Generating Slope, and Curvature Contours of Bent Plates. Int. J. of Splids and Structures, V.15. pp Acknowledgement Many thanks to funding agencies: National Science Foundation Office of Naval Research Air Force Office of Scientific Research Army Research Office National Institute of Health Department of Transportation Thanks also to many graduate students, postdoctoral fellows, visiting scholars from all over the world: China, Taiwan, Japan, Singapore, Switzerland, England, Kuwait, Germany, Italy, Canada, Israel, and USA 44

23 THANK YOU for Your Attention 45 3

Comparative Measurement in Speckle Interferometry using Fourier Transform

Egypt. J. Solids, Vol. (30), No. (2), (2007) 253 Comparative Measurement in Speckle Interferometry using Fourier Transform Nasser A. Moustafa Physics Department, Faculty of Science, Helwan University,