Comparison of multiple viewing direction shearography with multiple illumination direction shearography D Francis, S W James and R P Tatam Engineering Photonics Group, Centre for Engineering Photonics, School of Engineering, Cranfield University, Cranfield, Bedford, MK43 0AL, UK. Corresponding email address: [email protected] Abstract. This paper describes the development of a multiple channel shearography system. The system consists of four views remotely ported to the shearing interferometer by fibre optic imaging bundles. The system has been used to determine the six components of displacement gradient that are necessary to fully characterize the surface strain of the object under test. The development of the system and the required image processing is described. Results obtained from a flat perspex plate using the multiple viewing system are presented and compared to results generated previously using and existing system incorporating multiple illumination directions. 1. Introduction Shearography  is a speckle interferometric technique that is sensitive to changes in displacement gradient of a test object’s surface. Speckle patterns are formed illuminating the target’s surface with light from a coherent source, such as a laser. Two speckle images of the surface are combined using a Michelson interferometer with one imaged displaced (sheared) relative to the other. Shearing is applied by tilting one of the mirrors in the interferometer. Combination of speckle patterns results in an interferometric speckle pattern that is imaged onto the surface of the detector of a CCD camera. Light at each point on the detector surface is a superposition of light scattered from two points on the object surface. Any subsequent deformation of the scattering surface will result in a change in the relative phase of the light scattered from the two points. This results in a change in the intensity of the light at on the detector surface. Subtraction of speckle patterns recorded before and after object deformation result in speckle correlation fringes, which contour regions of equal displacement gradient. In order to make a quantitative measurement using shearography, it is first necessary to determine unambiguously the optical phase difference between the reference and signal frames recorded by the camera. This is commonly done using temporal phase stepping techniques . This involves recording a series of frames with a known phase shift between them. The frames are then combined using a phase stepping algorithm resulting in an image of the optical phase distribution. The phase calculated in this manner is bounded between the values of 0 and 2π and is known as a wrapped phase map. To obtain a continuous phase measurement it is necessary to employ phase unwrapping techniques . The component of displacement gradient that a shearography measurement is sensitive to is determined by the sensitivity vector. The sensitivity vector is defined as the bisector of the illumination and viewing directions. To fully characterize the surface strain of an object using shearography, it is necessary to determine six components of displacement gradient. This can be done by making measurements with three different sensitivity vectors, in conjunction with two orthogonal directions of applied shear. Different sensitivity vectors can be obtained by using multiple measurement channels. This can take the form of multiple illumination directions or multiple viewing directions [4-7]. 2. Principles of quantitative shearography Shearography systems incorporating three illumination directions have previously been used to characterize surface strain [4-6]. The locations of the measurement channels in each of these systems were located at three of the four corners of a square, as had previously been determined to be the optimum configuration . The calculated phase determined by a single shearography channel is given by v w u k x ky kz .dx x x x (1) for shear applied horizontally and by u v w k x ky kz .dy y y y (2) for shear applied vertically. In these equations ∂u/∂x, ∂v/∂x, ∂u/∂y and ∂v/∂y represent the in-plane displacement gradients and ∂w/∂x and ∂w/∂y represent the out-of-plane displacement gradients. The components of the sensitivity in the x, y and z directions are represented by kx, ky and kz respectively and dx and dy give the magnitude of the applied shear. In order to determine the orthogonal displacement gradients from the phase measurements from three channels, a coordinate transformation is required. This is achieved using the equation u x k x1 v k x x 2 k x 3 w x k y1 ky2 k y3 k z1 kz 2 k z 3 1 1 1 2 dx 3 (3) for displacement gradients in the x direction. The numbers in the subscripts refer to the particular measurement channel. The addition of a fourth measurement channel offers further advantages. For example, if one measurement channel is blocked for a particular measurement application, the system can still be used. Also, four separate measurements of the displacement gradient components can be made which can lead to an increased confidence in the measurement obtained . 3. Experimental Arrangements of the System 3.1. Shearography system incorporating multiple illumination directions The configuration of this system is shown in figure 1. The system consists of three diode lasers with an operational wavelength of 810 nm and a maximum output power of 100 mW. Light from the diodes is transferred to the illuminating lenses via single mode optical fibres. The laser wavelength is stabilized by using the reflection from fibre Bragg gratings fabricated within the illuminating fibres. Light from each direction is then expanded to illuminate a region of interest on the test surface. Light scattered from the object is imaged via a shearing Michelson interferometer onto the surface of an 8-bit Dalsa CA-D4-0512A CCD camera. The CCD chip consists of a square array of 512x512, 24 μm2 pixels. The interferometer consists of a mirror mounted on a piezo electric transducer, MP, a shearing mirror MS and a beamsplitter BS. The piezoelectric mirror is used to shift the phase of the light by a known amount in order to determine the wrapped phase maps. Phase maps are obtained for each channel by illuminating the surface with each laser sequentially. The phase can then be unwrapped and, along with a measurement of the sensitivity vectors and the shear magnitude, the orthogonal displacement gradient components can be determined using equation (3). Image acquisition, phase stepping and shutter control is controlled by a PC running software written in LabVIEW. Figure 1. Experimental configuration for the shearography system employing multiple illumination directions. MP is the mirror mounted on a piezoelectric transducer, MS is the shearing mirror and BS is the beamsplitter. 3.2. Shearography system incorporating multiple viewing directions The light source used with this system is a custom built Continuum® Nd:YAG laser. A continuous wave diode pumped Nd:YAG laser with an operational wavelength of 1064 nm and maximum output power of 700 mW is sliced into the desired shape using a Kentech pulse shaper. This seed pulse is then amplified through a pair of double-pass 6 mm Nd:YAG rod amplifiers and a pair of single-pass 9 mm Nd:YAG rod amplifiers to achieve a high power. Peak infra-red power of 3000 mJ is frequency doubled, producing pulses of energy up to 1500 mJ. The achievable pulse width varies from 10 ns to 150 ns. The output from the laser is expanded to illuminate the target by a negative lens housed in the centre of a tripod mounted cross structure. In each of the arms of the cross is a camera lens held in a custom made lens holder that offers two orthogonal rotation directions to enable accurate positioning of the lenses. Images from the four camera lenses are then relayed to a remotely located shearing interferometer via fibre optic imaging bundles. The imaging bundles consist of a rectangular matrix of 600x500 optical fibres, each with a core diameter of 8 μm. At the output end the four imaging bundles are joined together so that each forms a quadrant of a composite 1200x1000 array. Light from the output end of the composite bundle is then imaged through a shearing Michelson interferometer and imaged onto the surface of a 12 bit LaVision FlowMaster 3 CCD camera. The CCD chip consists of a rectangular array of 1280x1064, 6.7 μm2 pixels. Image capture is controlled using a PC running LaVisions proprietary DaVis software. Synchronization of frame grabbing with the laser pulsing was achieved using a Berkeley Nucleonics Corporation model 555 dual channel pulse generator. A diagram showing the system layout is shown in figure 2. In order to generate phase maps one of the mirrors in the interferometer was replaced by a mirror mounted on a piezoelectric transducer. A GPIB card housed in the instrumentation PC was used to communicate with a Keithley 230 programmable voltage source which transmitted the voltage to the piezoelectric transducer. The voltage causes the transducer to expand, thereby translating the mirror. The phase was then determined using a 5-step phase stepping algorithm given by 2 I2 I4 2 I3 I5 I1 tan 1 (4) where I is the intensity value for each pixel in the array. The relative phase difference between the frames is π/2. Phase steps of this size were obtained with voltage increments of 0.54 V. The number in the subscript refers to the particular frame. Phase stepping was applied to both the reference and signal frames and the phase difference was then obtained by subtraction of signal and reference phases. Figure 2. Experimental configuration for the shearography system incorporating multiple viewing directions. The camera lenses are labelled CL 1-4 and the negative lens is labelled NL. Since each of the views is oriented at an angle to target surface normal each of the views possesses perspective distortion. This can be corrected for by use of a dewarping algorithm. A target with a black background and an array of white dots with a known separation is attached to the surface of the target. A reference dot is selected and the algorithm determines the location of the other dots using a correlation process. Using the knowledge of the dot separation a mapping function is computed from which the corrected image can be calculated. The image from the first view is dewarped and the subsequent views are dewarped and mapped to the first image based on the location of the reference dot. 4. Results and Discussion In order to calculate the sensitivity vectors for each of the measurement channels in the multiple viewing direction configuration, it is necessary to determine the view vectors for each pixel in the CCD array. To do this, a method that exploits the mapping functions generated previously in the dewarping process was used to calculate the direction cosines of the view vectors . The signs of the direction cosines were then found by using a Sobel filter to determine the local partial derivative in the unsigned map. The illumination vectors were modeled by assuming a point source diverging from the centre of the negative lens. The sensitivity vectors were then calculated by subtracting the illumination vectors from the observation vectors. The object used was a flat perspex plate with dimensions 300x150x10 mm3. The plate had a 10mm wide horizontal slot cut out of it and was loaded by turning a screw located vertically through the slot. Phase maps were generated for both an x and y shear of 12 mm and filtered to remove noise. Filtering was done by applying a low pass filter to the sine and cosine terms twenty times with an intermediate phase calculation between each step . Unwrapping was done using ISTRA software (Dantec- Ettemeyer). The wrapped phase maps obtained from the multiple viewing direction system are shown on the right of in figure 3. On the left are wrapped phase maps obtained previously  using the multiple illumination direction system. The field of view for each measurement channel was approximately 62 mm x 73 mm. Figure 3. Wrapped phase maps taken for both x and y shear using multiple illumination directions (left)  and using multiple viewing directions (right). The unwrapped phase maps and sensitivity vector images were combined using equation (3) to determine the displacement gradient components. The displacement gradients are shown in figure 4. The results in the top row were obtained previously using the multiple illumination direction system and those on the bottom row were obtained with the multiple viewing direction system. The out-ofplane components are similar for each system but the in-plane components show some differences. The reasons for these differences will require some further investigation. Figure 4. Displacement gradient components calculated from phase measurements and sensitivity vectors using multiple illumination directions (top)  and multiple viewing directions (bottom). 5. Discussion The six components of displacement gradient necessary for full analysis of the surface strain of an object have been calculated using shearography instrumentation incorporating multiple viewing directions and multiple illumination directions. The shearography instrumentation incorporating multiple viewing directions is being developed for the application of measuring strain distributions from rotating objects. This application will require the use of high power, pulsed lasers to effectively freeze the motion of the rotating surface. Using multiple illumination directions for this is preferable because only one illumination direction is required. The problem with using multiple illumination directions with pulsed lasers lies in the guiding of the light to the correct positions. The use of single mode fibre as a light guide, as was used in the system presented here, may not be suitable due to the high peak energies contained within the pulses. The relative advantages and disadvantages are summarized in the table below. Table 1: Relative advantages and disadvantages of the two techniques Advantages Multiple illumination direction Compatibility with standard single mode fibre. Suitable for static measurements. Disadvantages Not straightforward to guide light from pulsed lasers. Difficult with surfaces in transient or rotational motion. No additional image dewarping required. Only low laser power required. Greater stability Multiple viewing direction Suitable for use with pulsed lasers Less stable due to disturbances in fibre bundles between frames. Suitable for measuring in transient or rotational motion. Dewarping required to correct for perspective distortion. 6. Summary Shearography systems incorporating multiple illumination directions and multiple viewing directions have been presented. 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