Digital Image Correlation combined with Electronic Speckle Pattern Interferometery for 3D Deformation Measurement in Small Samples

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1 Digital Image Correlation combined with Electronic Speckle Pattern Interferometery for 3D Deformation Measurement in Small Samples Phillip L. Reu * and Bruce D. Hansche Sandia National Laboratories, PO Box 5800, Albuquerque, NM ABSTRACT The small size of meso- and microelectromechanical systems (MEMS) devices presents several challenges for full-field deformation measurements. A hybrid system combining Digital Image Correlation (DIC) for in-plane deformation and Electronic Speckle Pattern Interferometry (ESPI) for out-of-plane deformation measurements has been developed for working with these small size scales. Measurement of the full-field 3D deformation is useful for material characterization including tensile and performance testing of the samples. The combination of the two techniques yields a 3D deformation field of the component under test. For this paper, simple tensile test specimens of 0.76 mm 10 mm were deformed to create simultaneous in-plane and out-of-plane deformations. The experimental system will be described in detail with a discussion of the results. A comparison between ESPI and DIC results will be briefly discussed, and compared to a conventional point-to-point shadowgraph measurement. Keywords: Digital Image Correlation (DIC), Electronic Speckle Pattern Interferometry (ESPI), MEMS, LIGA. 1. INTRODUCTION Research into microelectromechanical system (MEMS) component properties and performance has expanded over the last decade. As a part of the research into these micro-machines, diagnostic measurement techniques have also been developed. These are typically optical in nature, as the small scale of the components (tens of microns to millimeters) requires a non-contacting measurement method. Silicon MEMS made with lithographic methods have a specular surface. This leads naturally to the use of classical interferometry or possibly holography for out-of-plane measurements, while in-plane measurements are via image analysis techniques. The in-plane measurements are typically point-to-point with fiducials, edges, or other tracking points utilized to measure displacement. Laser Doppler vibrometry has also been successfully utilized on these components to measure out-of-plane velocity and displacement, but is limited to single point measurements, with full field measurements built up by scanning techniques. LIGA (lithographie galvanoformung abformung) [1] components are made from electroplatable metals/alloys rather than semiconductor materials, and may have optically diffuse surfaces. Even for those components with naturally specular surfaces, artificial roughening via etching or painting allows full-field deformation measurements to be made by DIC or ESPI. Both techniques can be used independently to yield full 3D deformation data, and are used in this experiment in this way for checking one technique against the other. Application of these techniques at the sub-mm scale presents a number of challenges; chief of which are the illumination and viewing angle requirements which are difficult to implement in close quarters. ESPI has the additional problem of speckle decorrelation, which becomes more significant at high magnifications. DIC typically has lower displacement resolution than ESPI, especially in the out-of-plane direction. (Theoretical out-of-plane resolution for DIC for the experimental setup used is 80 nm and for ESPI is.5 nm.) This paper examines some of the challenges, compares ESPI and DIC in-plane strain measurement capability, and presents a hybrid solution which combines the best features of ESPI and DIC to perform 3D strain measurements. The hybrid method measures full-field 3D displacement data using ESPI for out-of-plane (z-direction) measurements and DIC to measure in-plane deformation (x- and y-directions). * plreu@sandia.gov

2 1.1 ESPI background and equations Figure 1 is a schematic of typical ESPI configurations. Camera Camera Beam 1 Ref. Beam 1 Beam kˆ 1 K kˆ ˆ kˆ k 1 Object L L Object (a) (b) Figure 1. (a) In-plane and (b) out-of-plane ESPI schematic. K For both the in-plane and out-of-plane ESPI configurations shown in Figure 1, the following equation can be derived to describe the light intensity measured by the camera []: I( A( 1 cos(( ( n ( ) ) (1) Where I is the intensity of the imaged speckle field, A is the speckle intensity locally a constant related to the intensities of the two beams is the random speckle phase, is the change in phase due to the motion of the object, is the fringe visibility, and is a user controlled phase-shifting parameter. Using the Carré algorithm, which requires that four frames be taken with different phase shifts, the following equation can be used to find the total phase shift of the object being measured: 1 (I1 I4 ) (I I3 ) 3(I I3 ) (I1 I4 ) n( y ) ( y ) n ( y ) tan () (I I3 ) (I1 I4 ) Where I 1 through I 4 are four images taken as is varied in steps of / increments. Of course, the absolute shape measurement is not available with this arrangement, only the change in shape. Typically for many testing procedures, such as strain measurement, this is not a drawback. The incremental change in phase can then be calculated using the following equation, which yields the total phase change ( ) between any two sets of four frames taken before and after deformation. Tot ( y ) 1( y ) ( y ) 1 ( y ) ( y ) (3) The phase is wrapped in increments, and must be unwrapped to yield the total displacement across the field of view [3]. Depending on the arrangement of the ESPI system, complete 3D information can be calculated using two in-plane laser inputs and an out-of-plane reference beam. The sensitivity of the ESPI arrangement is defined by the following sensitivity vector equation (as illustrated in Figure 1): K ( k 1 k ), (4) where is the wavelength of the laser illumination used, and k defines the vectors of the illumination beams. The motion can be calculated using a matrix approach to get the 3D deformation with the following equation, where L is the calculated motion based on the unwrapped phase. 1 L( K ( (5) For the case of 1D deformation as used in this paper, two equations can be simplified from the previous equation. For the in-plane case, the deformation is calculated using: ( L x ( (6) 4 sin

3 Where is the angle between the two illumination beams (or the two sensitivity vectors). For the out-of-plane deformation, where the angle between the reference and object beams is small, the z-deformation may be simply calculated using: ( (. (7) L z Both arrangements were used for this experiment: with the in-plane arrangement used for comparing the results of the DIC and ESPI techniques, and then the out-of-plane setup used for the hybrid 3D system. 1. ESPI speckle decorrelation ESPI at the sub-mm scales presents a number of challenges, including speckle decorrelation, and practical difficulty in illumination at the proper angle, especially when a microscope objective is used for imaging. Speckles are created by the interference of a random number of light waves combining at the image plane to create the well known bright and dark pattern of subjective speckle. Decorrelation occurs when the deformation is of the same order as the speckle size, causing the speckle patterns before and after deformation to lose registration. That is, in order for the random phase ( to cancel in equation (3), the two speckle images must be registered. Figure illustrates the decorrelation phenomenon with a simple translation. Strain causes a change in speckle pattern shape, in addition to translation, exacerbating the decorrelation [4]. 4 Before Translation After 130 µm Translation 100 µm. Figure. Subjective speckle decorrelation showing before and after translation speckle fields. There are several possible techniques that can be applied to circumvent the decorrelation problem, including recorrelation of the speckles and summing extremely small intermediate steps. Figure 3 is an example of recorrelation, which is possible if the speckle decorrelation is mainly due to translation of the speckle pattern, as is common for in-plane tensile experiments. Here, the speckle translation is measured with a DIC technique, then one of the images is translated to remove the decorrelation before the standard ESPI analysis techniques (equations 1-3) are applied.

4 Figure 3. ESPI phase (equation 3) before (top) and after (bottom) recorrelation operation. 1.3 DIC overview DIC uses photometric techniques to calculate the shape and displacement of an object. A pattern of unique points, typically random speckles, is attached to the surface of the object. For D image correlation, a camera system is mounted approximately perpendicular to the axis in which the motion will take place. For 3D systems, two cameras view the object from different angles, forming a stereo view. The geometry is calibrated, and the 3D position of all of the object points can subsequently be calculated. An undeformed image is acquired as a reference frame, to which all subsequent frames are compared. The deformed images are then acquired as the object is moved or strained. The surface is then subdivided into discrete subsets which contain a unique pattern. A typical pattern used on the LIGA samples is shown in Figure 4. Each subset is fit with a B-spline curve that is then used with a minimization function to calculate the displacement vector that minimizes the difference between the reference and deformed images. This procedure is thoroughly covered in reference [5] where Cheng and Sutton detail the D correlation mathematics and calculate the expected errors in the method. An important point to make is that laser speckle cannot be used for creating the speckle pattern used for D correlation. The evolution of the speckle field is typically too drastic between the deformed and undeformed states, and the correlation algorithms completely fail after a few frames. For this reason, a painted surface was used for DIC. The paint does not affect the laser speckle used for the out-of-plane ESPI measurements. Figure 4. Speckled DIC sample for tensile testing.

5 . EXPERIMENTS Two series of experiments were performed. First, both the ESPI and DIC techniques were arranged to make inplane measurements, in order to compare the two techniques. Second, a hybrid system was demonstrated, using DIC for in-plane measurements and ESPI for out-of-plane. In all experiments, a shadowgraph (Keyence LS5041) was also used to measure the single-point displacement of the ears..1 Sample and sample preparation These experiments were motivated by the need to measure the material properties of LIGA nickel. The primary samples (Figure 5) were dog-bone tensile samples with a gage area of 0.75 mm width, approximately 6 mm long and 0. mm thick. Within the gage section, four ears were included to provide fiducial points for a shadowgraph extensometer. The ears were 3. mm apart. Ears 3. mm Figure 5. LIGA Nickle tensile sample In order to have enough data points on the surface, the speckles must be sized appropriately to give enough viable subsets on the specimen. Speckling at these small scales is not always a simple process and requires some trial and error to get an optimum speckle pattern. The pattern shown in Figure 4 was obtained using a white spray paint and while the paint was still wet, blowing copier toner powder over the sample. Once dry, the speckle pattern follows the metal surface as it deforms.. Experiment Setup Figure 6 shows both the in-plane and hybrid experiment setup. Figure 6(a) is the in-plane ESPI setup, showing the two illumination fibers at approximately 30 degrees from the sample normal. Figure 6(b) is a closer view of the hybrid setup, showing the nearly normal ESPI illumination fiber, and the white light illumination fiber bundle for DIC. In this case, a 75 mm focal length c-mount lens with 10 mm of extension tube provided sufficient magnification to fill the field of view with the desired gage length. The separate ESPI and DIC images are taken sequentially, as described below. ESPI illumination fiber ESPI illumination fibers White light illumination Sample Keyence Sensor Sample (a) (b) Figure 6. (a) In-plane ESPI experimental setup, (b) hybrid system setup.

6 3. RESULTS 3.1 Comparison of in-plane ESPI and DIC The first stage in the development of the hybrid ESPI-DIC system was to compare the results between the ESPI and DIC calculations. This was done using a simple tensile test method. The sample was clamped between two grips and known loads were applied to the sample and measured with a load cell. Both ESPI and DIC measurements were taken simultaneously for a number of incremental steps. The resulting in-plane deformation could then be compared. The two methods were nearly equal during elastic deformation of the sample. They deviated slightly after the sample yielded, likely due to slightly different gage sections used in the two analysis techniques, or different methods of calculating average strain within the gage section. In all cases, the Keyence sensor gave somewhat different answers from both the ESPI and DIC techniques, even in the elastic region. This was presumably due to rotation of the ears during sample deformation. Figure 7 shows typical results, both as deformation versus time (frame number) and in standard stress-strain format. Percent strain DIC ESPI Shadowgraph Frame number Figure 7. Load (lb) Shadowgraph ESPI DIC Percent strain ESPI and DIC comparison of in-plane deformation showing deformation versus frame number and in standard stress-strain format. 3. Hybrid ESPI-DIC 3D results Both the 3D DIC system and the in-plane ESPI system require illumination and/or viewing of the object at an angle. It can be impractical to provide this off-axis optical path, especially if the object is small enough to require a microscope objective to image it. A natural solution would be a hybrid ESPI/DIC system, since in-plane DIC and out-of-plane ESPI only require normal illumination and viewing. In the case of a microscope, standard axial illumination can be used for both the laser light and the white light for DIC. To demonstrate the hybrid ESPI and DIC system, one of the tensile samples was pre-bent out of plane (compressively buckled), as shown in Figure 8. As the actuator was displaced, the sample straightened out, providing an out-of-plane deformation in addition to the tensile strain. (Note that very little tensile load was applied this geometry was used to supply true 3D deformation, rather than to measure tensile properties). Figure 8. Bent tensile sample, side view.

7 To take the data, the actuator was displaced incrementally, a series of four ESPI speckle frames was taken, then the white light illumination was turned on and a DIC image was taken. This was repeated for 0 to 30 frames of data. The ESPI deformation was analyzed for each step and the deformation summed. The DIC data was analyzed only once, for the final relative to original deformation. The results were combined to provide a full 3D deformation map, as shown in Figure 9. Figure 9. 3D Deformation map. The arrows show in-plane deformation,and the intensity shows out-of-plane. Maximum lateral deformation (largest arrow) is 5.1 micron. 4. CONCLUSIONS This paper presents a proof-of-concept hybrid ESPI-DIC system for use with meso- to microsystem size components. The main advantage to this system compared with 3D arrangements for either type of measurement technique is the use of a single camera and lens arrangement. This is important in small scale measurements, as access to the part is often limited, and there is often not room for positioning the lenses and illumination components. The 1D ESPI and in-plane DIC configurations are each simpler, hence more cost effective, than their 3D counterparts, but it begs the question to claim that the hybrid system is simpler than either single 3D technique. A successful comparison between in-plane ESPI and DIC was conducted with good agreement between the strain measurements on a small tensile specimen. The hybrid 3D system also demonstrated measurement results on a simultaneous in-plane and out-of-plane deformation using a bent tensile specimen. 5. ACKNOWLEDGEMENTS Appreciation is extended to Tom Buchheit for providing the LIGA samples and motivation for this development. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL REFERENCES 1. Buchheit T.E., LaVan D. A., Michael J. R., et al. Microstructural and mechanical properties investigation of electrodeposited and annealed LIGA nickel structures, Metallurgical and Materials Transactions A:-Physical Metallurgy and Materials Science, Vol. 33, No. 3, pp , 00.. Cloud, G., Optical Methods of Engineering Analysis, Cambridge University Press, New York, Ghiglia, D and M Pritt, Two Dimensional Phase Unwrapping Theory, Algorithms, and Software, Wiley, New York, Brillaud, J. and F. Lagattu, Limits and possibilities of laser speckle and white-light image-correlation methods: theory and experiments, Applied Optics, Vol. 41, No. 31, pp , Cheng, P., M.A. Sutton, H.W. Schreier, and S.R. McNeill, Full-field Speckle Pattern Image Correlation with B-Spline Deformation Function, Experimental Mechanics, Vol. 4, No. 3, pp , 00.