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Latin America Optics and Photonics Conference (LAOP) © OSA 2014
Two-wavelength electronic speckle pattern interferometry for simultaneous measurement of two in-plane displacement fields Amalia Martínez-García1, Raúl Cordero2 J. A. Rayas1,2 1
Centro de Investigaciones en Óptica, Loma del Bosque 115, Lomas del Campestre, C. P. 37150, León Guanajuato México 2 Departamento de Física,Universidad de Santiago de Chile, Avenida Ecuador 3493, Estación Central, Santiago, Chile
[email protected],
[email protected],
[email protected]
Abstract: We present the simultaneous measurement of bidimensional displacements by electronic speckle pattern interferometry by using of two dual illumination systems mutually perpendicular and with two different colors for each one them. OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (120.5050) Phase measurement; (120.6160) Speckle interferometry
1. Introduction Speckle interferometry systems can measure out-of-plane and/or in-plane displacements of a surface. Methods for recording speckle images in a non-simultaneous manner for static deformations in three dimensions have been implemented with optics arranged for multiple sensitivity vectors [1-3]. However, simultaneous collection of data is required for observation of phenomena that occur on the order of nanoseconds or microseconds. In order, a method was implemented to simultaneous measurement of three-dimensional deformation by using of three wavelengths to differentiate data from interferometers with three mutually orthogonal sensitivity vectors. Each color is collected by a different CCD camera [4]. In this work, an example of simultaneous measurements of displacement fields u and v is presented by using two dual in-plane electronic speckle pattern interferometer (ESPI) system. Each one of interferometer ESPI use illumination at different wavelength which avoid crossed talk. One advantage of the system presented is the use of only one CCD camera. The method can be extend to measure three displacement vector components by using three wavelength and one camera. 2. In-Plane Electronic Speckle Pattern Interferometry As with all ESPI techniques, the interference that takes place between the two speckle patterns is imaged by a CCD camera and displayed. When the object is being deformed, all subsequent interference patterns are subtracted from the initial pattern, producing a fringe pattern. The theory of fringe formation is well documented [5]. The fringes represent contours of equal displacement. The fringe spacing is inversely proportional to the gradient of the displacement, and the fringes are aligned perpendicularly to the direction of the displacements. The most common technique for interferogram interpretation is the phase-shifting method [6]. Phase shifting is used to obtain a fringe pattern that depicts the − π and π range phase change that occurred between the two speckle patterns. A procedure called phase unwrapping must be carried out to restore the unknown multiple of 2π to each pixel. The displacement d of the fringes in an in-plane system is related to phase change ∆φ by the following expression ∆φ =
4π
λ
d senθ
(1)
where θ is the angle between the illumination beam and the viewing direction and λ is the wavelength of the laser. Use of this expression allows the phase map to be converted into accurate displacement data. The displacement d will correspond to u and v fields respectively in our experiment. 3. Experimental demonstration Figure 1 depicts the object illumination. Two dual-illumination interferometers collect in-plane displacement information in orthogonal directions. In each dual-illumination interferometer, a laser beam is split into two arms, and both illuminate the surface at equal angles from the surface normal. These dual-illumination configurations make these interferometers insensitive to out of plane displacement. Incidence angles of 140 and 40 are used for x-
LM1A.3.pdf
Latin America Optics and Photonics Conference (LAOP) © OSA 2014
axis and y-axis respectively. He-Ne ( λ = .633µm ) and Verdi Lasers λ = .532 µm are utilized to avoid cross talk between the orthogonal illuminations. As with all ESPI techniques, the interference that takes place between two speckle patterns is imaged by a CCD camera and displayed. When the object is being deformed, all subsequent interference patterns are substracted from the initial pattern, producing a fringe pattern. Speckle patterns due to both illuminations over the sample were captured by one shot by means a CCD color camera of 1280x1024 pixels, and 8 bits by channel (RGB). The information is separated and processed for each color channel. The figure 2 shows: A) initial speckle patterns, and B) speckle patterns after the applied mechanical stress to sample. In figure a) and b) are showed the reference speckle patterns obtained from each channel which make possible to measure the displacements along the x and y axis respectively. The speckle patter ns showed in figure 2 c) and d), obtained after deformation, correspond to x and y sensitivity respectively. The fringe pattern showed in figure 2 e) is obtained from the substraction between the speckle patterns of a) and c) while that f) is the result of the substraction between the speckle patterns of b) and d). The test specimen was mounted on an INSTROM® machine to tensión test. The parameters of the universal machine were programmed at 0.5 mm/min. In figure 3 and 4 are showed the u and v displacement fields respectively for one measurement. PZT
CCD
Sample
Láser He-Ne
Láser Verdi Instron
Fig. 1. Double dual illumination for simultaneous measurement of in-plane displacements. A)
a)
B)
b)
e)
c)
d)
f)
Fig. 2. Intensity patterns: A) Before the deformation, B) After the deformation. Fringe patterns: e) obtained from the substraction between a) and c) when is used λ = .633µm . f) substraction between b) and d) and λ = .532 µm .
4. Conclusions The system described here is a reliable and robust, double dual in-plane ESPI system which use two wavelengths. Interference fringes are obtained when speckle patterns are correlated, which are obtained in a single shot to each one of reference and deformation states. The ESPI systems use only one color CCD camera which permits measure both the x and the y plane components simultaneously, have a distinct advantage. The technique can be extend to simultaneous measurement of three displacement components when an out-of-plane system and a third wavelength are considered.
LM1A.3.pdf
Latin America Optics and Photonics Conference (LAOP) © OSA 2014
14.8 a) 7.4 b) e)
y (mm)
0
c) -7.4
d) -14.8
-14.8 -7.4
0
7.4
14.8
x (mm) Fig. 3. a) In-plane displacement fringes (u component, λ = .633µm ), b) Filtered fringes, c) Wrapped phase map, d) Unwrapped phase map, e) Measured in-plane displacement component. 14.8 a) 7.4 b) e)
0
y (mm)
c) -7.4
d) -14.8
-14.8 -7.4
0
7.4
14.8
x (mm) Fig. 4. a) In-plane displacement fringes (v component, λ = .532 µm ), b) Filtered fringes, c) Wrapped phase map, d) Unwrapped phase map, e) Measured in-plane displacement component.
5. References [1] Amalia Martínez, J. A. Rayas, R. Rodríguez-Vera, and H. J. Puga, " Three-dimensional deformation measurement from the combination of inplane and out-of-plane electronic speckle pattern interferometers," Appl. Opt. 43, 4652-4658 (2004). [2] S. Winther, “3D strain measurements using ESPI,” Opt. Lasers Eng. 8, 45-57 (1988). [3] L. S. Wang, K. Jambunathan, B. N. Dobbins, and S. P. He, “Measurement of three-dimensional surface shape and deformations using pkase stepping speckle interferometry,” Opt. Eng. 35, 2333-2340 (1996). [4] Eric B. Flynn, Lori C. Bassman, Timothy P. Smith, Zamir Lalji, Laurel H. Fullerton, Tommy C. Leung, Scott R. Greenfield, and Aaron C. Koskelo, “Three-wavelength electronic speckle pattern interferometry with the Fourier-transform method for simultaneous measurement of microstructure-scale deformations in three dimensions,”Appl. Opt. 45, 3218-3225 (2006). [5] R. Jones and C. Wykes, Holographic and Speckle Interferometry, (Cambridge University Press, Cambridge, UK, 1989), Chap. 4. [6] K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053-3058 (1985).
