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Chapter 3.5 Digital Speckle Shearography Applied to
Artefacts Claas Falldorf, Reiner Klattenhoff, Christoph
von Kopylow, Werner Jüptner BIAS - Bremer Institut für angewandte
Strahltechnik, Klagenfurter Straße 2, 28359 Bremen, Germany
Contents 3.5.8.2
Providers and Useful Websites Digital speckle shearography is a field wise, non contact and non invasive laser based diagnostic technique which is mainly used to determine structural imperfections such as inclusions and delaminations which are hidden under the surface [1,2]. An important prerequisite to the digital speckle shearography is that those hidden defects cause a local deformation of the surface if the object is mechanically or thermally loaded. A typical thermal loading regime for example consists of an IR-lamp which is used to increase the temperature of the investigated surface by some few Kelvin. The resulting magnitudes of the corresponding surface deformations are in the range of few microns and thus can not be recognized by the human eye. However, speckle shearography uses the coherent properties of laser light to make the small displacements visible and therefore can be used to detect the underlying defects. The size of the measurement area depends on both the power of the light source and the reflectance of the investigated object. Typical measurement systems provide investigation areas beginning from several cm² up to square meters. Due to the field wise nature of the method, the measurement process takes just a few seconds including all necessary steps like loading, data acquisition and evaluation. Since the defect hidden within the material must cause a local deformation of the surface due to the loading regime [3], the applicability of digital speckle shearography depends on both, the type of the material and texture of the investigated surface. Although this important prerequisite is valid to most of the technical surfaces [4], it must be verified for materials which are typical to artworks and items of cultural heritage. This chapter gives a short introduction to the
technical and physical background of digital speckle shearography. A
typical setup is presented and the investigation procedure is discussed
in detail. Finally, to prove the suitability of speckle shearography,
different types of surface materials common to cultural heritage such
as fresco, wood and marble are investigated. The samples under
investigation feature inclusions and delaminations hidden behind the
surface. From the results, these structural imperfections are shown to
be detected.
Digital speckle shearography is used to determine deformation gradients of an objects surface under load. It belongs to the so called whole field measurement techniques, which means that the result of the measurement corresponds to a whole area of the investigated object usually being recorded by a digital camera. Fig. 3.5.1 illustrates the principle of the digital speckle shearography. The object on the left side is being illuminated by an expanded laser beam. One mirror of the Michelson Interferometer on the right side is tilted by α. Together with the lens objective, this configuration produces two laterally shifted images Ia(x,y) and Ib(x,y) of the same surface on the camera target. The spacing between the two correlated areas of the surface is called shear s = (Δu,Δv). Both intensity distributions feature a noisy appearance called speckle effect. This statistical effect is based on multiple interferences in the image plane and occurs if rough surfaces are illuminated by coherent light. Since it is coherent, laser light originating
from surface positions P1=(u1,v1) and P2=(u2,v2) separated by the shear interferes at the same
position on the camera target P’=(x,y). The recorded
intensity I(x,y) is given by:
In Eq. 1 the phase value φ(x,y) is the data of interest. It provides information about the difference δs(x,y) between the two paths along which the interfering light travels. There exist numerous phase sampling techniques [5,6] to extract the argument of the cosine in Eq. 1. Most of them deal with taking several images while inserting known phase steps by shifting one mirror of the setup as shown in Fig. 3.5.1. A simple phase sampling technique uses four frames I1 to I4 with the phase being shifted by π/2 for consecutive frames. In this case, the phase value is obviously obtained modulo 2π by:
Repeating this procedure with the object being deformed yields the corresponding phase value φD(x,y). Thus in a good approximation the gradient of the deformation along the shear δd/δs can be derived from the phase difference Δφ(x,y) [7]:
In Eq. 3 b(x,y) denotes the direction of illumination, r(x,y) is the direction of observation, λ is the wavelength and s is the absolute value of the shear. It should be mentioned that this approximation is only valid, if the shear is small compared to the lateral dimension of the surface area under test.
From Eq. 3 it is seen that the sensitivity depends on the direction and the magnitude of the shear. Due to the ambiguity of the tan-1 in Eq. 2, the result of the phase evaluation remains ambiguous. Thus the calculated phase difference Δφ(x,y) always performs a modulo step when it exceeds 2π. Because of the small differences in the relative path lengths of the light, digital speckle shearography has rather low demands regarding the stability of the setup. This is one of its major benefits compared to other interferometric techniques. Since the gradient of deformation is measured, the method is rather insensitive to rigid body movements.
The outline of a compact shearographic setup is shown in Fig. 3.5.2a. An F-Mount objective was chosen as the imaging system. The F-Mount standard provides approx. 46.5 mm of space between the mount of the objective lens and the image plane. This area is used to place the optical components needed to build up a shearographic system providing a variable shear. Furthermore, this makes it feasible to change the focal length or the zoom factor by just choosing a suitable objective. In order to avoid averaging effects on the camera target, the spatial frequency of the speckle effect can be adapted by selecting a suitable aperture. Additionally, to overcome problems caused by reflections, a polarization filter can be mounted to the objective. The interference filter ensures the wavelength of the laser to be selected, enabling the sensor head to be used in broad daylight. In order to produce the shear, one of the mirrors allows the beam to be tilted along the optical axis. The corresponding mirror is attached to a Piezo stack which is used to apply phase sampling techniques. Due to the geometry of the F-Mount standard, the overall light path should yield 1,832” (approx. 46.5 mm) to have the CCD target being situated in the focal plane. However, regarding the refractive index (nnBK7 = 1.41) and the dimensions of the beam splitting cube, the light path in the sensor head extends to 58.1 mm.
Fig. 3.5.2b shows the ready assembled
shearographic sensor mounted on a tripod. The inner structure of the
device is shown, revealing its compact nature due to the limited space
between the objective lens and the camera target. The sensor is
designed to work with an external laser source providing coherent light.
A typical investigation scheme of the digital speckle shearography is displayed in Fig. 3.5.3. It is divided into five steps beginning with the setting of the operational parameters of the system. The focal length of the zoom objective has to be selected according to the desired field of view. The shear has to be set in order to adjust the sensitivity. The aperture is set to adjust the spatial frequency of the speckle effect. In the second step, the first measurement is done. Therefore, four images are taken with the phase being shifted by π/2 for consecutive frames and the phase value is evaluated modulo 2π following Eq. 2. The next step regards the loading of the object under test. Mechanical loading regimes such as screws or air pressure invoking stress into the material are typical to technical objects. In art conservation thermal loading seems to be a reasonable approach, because in this case there is no mechanical contact necessary to investigate the items. A typical thermal loading regime gently increases the surface temperature of the object by approx. ΔT=5 K. After the loading has been applied, the second measurement is done by taking another set of four phase shifted images. Finally, the distribution of the deformation gradients can be calculated from the two measurements following Eq. 3 and diagnostic techniques can be used to identify inclusions or delaminations. Structural imperfections are usually indicated by a distinct change of the deformation gradient for example.
In Fig. 3.5.4a measurement example is shown. The membrane in Fig. 4a has a rough surface of 80 mm in diameter. The configuration allows for loading it centrally from the backside by a micrometer screw. Fig. 3.5.4b shows the intensity distribution as it is seen by the camera. It comprises two laterally shifted images both featuring speckle noise. The magnitude of the shear is approx. s = 8 mm. Fig. 3.5.4c presents the phase difference calculated from both phase measurements each corresponding to a particular object state. Because of the ambiguity of the phase evaluation following Eq. 2, the phase difference always performs a step when it exceeds 2π. Fig. 3.5.4d illustrates the deformation gradients obtained by inserting the phase difference into Eq. 3. The mod 2π steps have been eliminated by means of image processing. This procedure is usually referred to as demodulation or phase unwrapping [8-10]. The range of values denoted in the diagram reveals the high sensitivity of this approach. The maximum deformation gradient for example is given by (δd/δs)max ≈ 4·10-5 mm/mm.
For structural imperfections to be measured by the digital speckle shearography, those defects must cause a local deformation of the objects surface when being loaded. This important prerequisite must be verified for materials which are common to artworks and items of cultural heritage. Therefore, the following section investigates different types of surface materials such as sandstone, fresco, wood inlays and marble in order to prove the suitability of this approach.
The sculpture shown in Fig. 3.5.5a is made from sandstone. It has a rough, opaque surface with crust on it. The layer of crust has a thickness of approx. 1 mm covering nearly the whole sculpture. The conservator was interested in finding the exact position and the size of possible delaminations covered by the crust. The sandstone was exemplarily investigated at the position denoted by the red square in Fig. 3.5.5a. Adjusting the shear to 15 mm an IR lamp was used to invoke a temperature difference of ΔT= 4 K. Fig. 5b shows the measurement result. Denoted by the green rectangles it is seen from the phase difference, that there are delaminations which have been well detected by the digital speckle shearography.
The surface of a fresco consists of various
layers of plaster. The topmost layer is named Intonaco and the second
one is referred to as Arriccio.
Fig. 3.5.6a shows a sample with textured surfaces and purposely
inserted inclusions in both layers Intonaco
and Arriccio.
The inclusion within the Arriccio
layer is marked by the dashed line whereas the inclusion within the Intonaco layer is
denoted by the continuous line.
Wood inlays consist of a wooden plate with thin inlays being glued to it. The sample shown in Fig.7a has been prepared with purposely delaminated inlays within the marked regions.
In Fig. 3.5.7b the result of the shearographic measurement is shown. The thickness of the inlay is 0.3 mm. The shear was adjusted to 3 mm and the loading was done by invoking a temperature difference of ΔT = 15 K to the objects surface. It is seen from the phase distribution that the delaminated regions are well detected.
The following example demonstrates the limits of the digital speckle shearography and illustrates its strong dependency on the properties of the surface material. Fig. 3.5.8a shows a sculpture made of marble
featuring a large surface crack of approx. 80 mm in length which is
even visible to the naked eye. Fig. 3.5.8b shows the result of the
measurement. The crack was hardly detected, considering it residing
directly at the surface and the fact that the temperature difference
induced to load the material was approx. ΔT
= 50 K. The reason for the bad response is the surface material itself.
Due to its crystalline structure, marble features transmittance as well
as reflectance. This causes local speckle decorrelation because of
multiple reflections within the surface and polarization effects.
Concluding the measurement results presented in the preceding paragraphs, Tab. 3.5.1 shows the investigation parameters magnitude of shear and excitation temperature with respect to the tested types of artworks and defects. Tab. 3.5.1: Investigation parameters with respect to the tested types of artworks.
A remarkable result is, that the stone like items are best investigated using a shear of s = 20 - 30 mm on the objects surface and a rather low temperature gradient of ΔT = 2 - 4 K. In contrast, wood samples are best investigated using a shear of s = 3 - 5 mm and a rather high temperature gradient of ΔT = 15 K.
In the preceding paragraphs the principles of digital speckle shearography were explained. It was shown that this measurement technique is well suited to investigate typical items of cultural heritage. Moreover, the successful detection of defects hidden within the material shows the big potential of the digital speckle shearography regarding the fields of conservation science. A flexible and compact sensor head was presented and measurement results were obtained in laboratory conditions as well as on-field. It was shown that the optimum investigation parameters such as the magnitude of the shear and the temperature of the thermal loading depend on the surface material. However, current limits to this technique arise from translucent surface materials like marble as well as from the size and the position of the defect. The latter is especially true because in order to be detected, a defect must cause a local deformation of the surface material due to the thermal heating. Therefore the maximum depth and the minimum size of detectable defects is mainly a function of material properties like the thermal conductivity. Since the method proofed to be applicable in on-field conditions, an important and remaining task is to standardize it in regards to materials common to items of artwork and cultural heritage.
Part of this work was performed within the
project LaserAct supported by the European Union under the grant
EVK4-CT-2002-00096.
[1] Y. Y. Hung, “Image-shearing camera for direct measurement of strains”, Appl. Opt. Vol.18, (1979) 1046-1051. [2] A. R. Ganesan, D. K. Sharma, M. P. Kothiyal, “Universal Digital Speckle Shearing Interferometer”, Appl. Opt., Vol.27, (1988) 4731-4734. [3] Y. Y. Hung, ”Electronic Shearography versus ESPI for Nondestructive Evaluation”, in F.P. Chiang, ed., Moire Techniques, Holographic Interferometry, Optical NDT and Applications to Fluid Mechanics, Proc. of Soc, Photo-Opt. Instr. Eng., Vol. 1554B, (1991) 692-700. [4] Osten, W., Kalms, M., Jüptner, W., Tober, G., Bisle, D., Scherling, D., “A shearography system for the testing of large scale aircraft components taking into account non-cooperative surfaces”, Proc. SPIE Vol. 4101B, (2000) 432-438. [5] W. Jüptner, T. Kreis, H. Kreitlow, „Automatic Evaluation of Holographic Interferometry by Reference Beam Phase Shifting. Industrial Applications of Laser Technology”, W. Fagan, ed., Proc. SPIE, Vol. 398, (1983) 22-29. [6] K. Creath, “Phase-Shifting Holographic Interferometry”, in P. K. Rastogi, ed., Holographic Interferometry, Springer Series in Optical Sciences, Vol.68, (1994) 109-150. [7] Th. Kreis, “Holographic Interferometry”, Akademie Verlag, Berlin, 1996, p. 263. [8] J.M. Huntley,
„Noise-immune phase unwrapping algorithm“, Appl.
Opt. 28, (1989) 3268-3270 . [9] H. Brug, „Temporal Phase Unwrapping and its Application in Shearography Systems“, Appl. Opt., Vol.37, (1998) 6701-6706. [10] M. Rivera,
J. L. Marroquin, “Half-Quadratic Cost Functions for Phase
Unwrapping”, Opt. Letter, Vol.29, (2004) 504-506.
3.5.8.2
Providers and Useful Addresses BIAS – Bremer Institut für
angewandte Strahltechnik
Claas
Falldorf Reiner
Klattenhoff Christoph
von Kopylow Werner
Jüptner BIAS
- Bremer Institut für angewandte Strahltechnik |
(Eq. 1) 
