4 A Digital Laser Speckle Technique for Generating Slope, Curvature, and Deflection Contours of Bent Plates 45 Fig. 4.2 Algorithm by which CASI operates 4.3 Principle of the Method Fringes are formed when coherent waves interfere. When the number of point sources increases, the interference pattern takes the form of randomly distributed light and dark spots of varying size. These light and dark spots are speckles. The speckles in space will move when the specimen surface is moved. Under the classical assumptions of the thin plate theory, the stress field can be determined once the surface curvature is obtained. The present technique produces slope contours from which curvature can be calculated. By selecting an arbitrary plane in space parallel to the surface of the plate, the speckles contained in the plane will move according to the local surface tilt. The displacement of the speckles d can be related to the surface slope φ. From Fig. 4.1b it can be shown that [2] d = A[tan(2φ+α) −tan(α)] tan2φ(1+tan2α) 1−tan(α)tan(2φ) . (4.1) From Eq. (4.1), we can obtain the slope contours as follows depending on which direction we select to display the result: ∂w ∂x =φx = U 2A . (4.2) When the input for d is the U-displacement. ∂w ∂y =φy = V 2A . (4.3) When the input for d is the V-displacement. Using the slope data curvature can be obtained via numerical differentiation. From Eq. (4.2) we can obtain the x-curvature contour as follows: κx = ∂ ∂x ∂w ∂x . (4.4)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==