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The defectoscopy of visualized transparent polymeric foils.

Abstract: The contribution treats the topic of statistical properties of image of transparent polymeric foils obtained by the Schlieren optical visualization method applied under laboratory conditions. Experimental results obtained from different types of polymeric foil serve as an evidence of applicability of statistical approach in the defectoscopy of transparent polymeric foils are presented as well.

Key words: schlieren, optical visualization, polymeric foil, defectoscopy.


Optical visualization methods offer numerous advantages in studies of hydrodynamic properties of fluids, but they can provide useful information on the visually inaccessible objects such as optically transparent polymers and, especially, polymeric foils as well (Bolf, et al, 1993). The most common means of visualizing transparent materials is to record the refractive behavior when illuminated by a beam of visible light. The material density is a function of the refractive index of tested foil representing now, in optical terms, a phase object. A light beam transmitted through the tested foil is affected with respect to its optical phase, but the density or amplitude of the light remains unchanged after passage. Optical methods, which are sensitive to changes of the index of refraction in the tested object can provide information on the density distribution and from the so-determined density values further information on properties of tested material can be deduced. The intensity and direction of optical beam leaving the tested object depends on the material depth. The main advantage of these methods is that they provide information that can be used for further processing after photographic or digital recording.

From many optical visualization methods (shadowgraph, interferometric method) we have chosen the schlieren method. In the fundamental arrangement, mostly referred to as the Toepler system (Smith & Lim, 2000), a parallel light beam traverses the test object and is focused thereafter by means of a lens or spherical mirror, named the schlieren head. A knife edge is placed in the plane of the light source image to cut off part of the transmitted light. An optical apparatus constructed after J.Bolf utilizes a modified schlieren head in form of the small circular diaphragm. Light is deviated along the optical path from its nominal course in the absence of refractive--index variations. The amount of light deflection generated by a transparent optical phase is measured. (Castle, et al, 1994). In fig.1 is the fundamental optical arrangement of the schlieren system. The apparatus consists of the light source located at the focal point of the condenser lens K.


Beyond this lens there is on the optical axis focal point D as the common point of the lens K and the objective O1. The collimated light passes through the test object [O.sub.o] (polymeric foil) and enters the objective [O.sub.2], that focuses the light to form an image of the light source. The diaphragm D2 (a knife edge in the original arrangement, mostly referred to as the Toepler system) is located at the focal point of the second objective. A camera lens is positioned beyond the diaphragm and located to form an image of the light source. The camera objective focuses the test object onto the recording plane, where a reduced intensity of light, depending on the amount of light cut off by the carefully adjusted diaphragm, can be observed. Without any disturbances in the optical path, the original light source will have uniform reduction in intensity due to the light cutoff by the diaphragm. When there is a disturbance in the optical path, the light rays will be deflected.


For image processing it is necessary to correct influence of light source inhomogeneity, influence of the optical string and the sensing device for evaluation of images gained by the optical visualization of polymeric foils.

The brightness disturbances can be caused by the inhomogeneity of the light source, by impurities in the optical path and by the noncollinearity of optical axes of objectives O1 and O2 (fig.1). Experiments showed, that the last factor has the substantial influence on the homogeneity of the image obtained by the schlieren apparatus (fig.2).

In order to rectify this error a useful tool consisting of four square areas one another 900 turned round was produced. Areas were carved out of the suitable choice perspex. Sense of areas direction is such adjusted, that the change of brightness of respective area marks direction of adjustment of optical axis of the objective O2 in the schlieren apparatus.

For image processing it is necessary to correct influence of light source inhomogeneity, influence of the optical string and the sensing device for evaluation of images gained by the optical visualization of polymeric foils. One of the possibilities is to use reference image picked up without presence of test object.



The reference image can be taken as an image of errors of the whole optical system on the assumption that we have used a virtual light source (Sonka, et al, 1998). Correction of brightness errors is necessary for the further image processing by the statistical methods. The brightness correction can be evaluated from

g(i, j) = c / [f.sub.c](i, j). f(i, j) (1)

where f(i,j) are values of brightness of tested foil (fig.3.b), [f.sub.c](i,j) are values of reference image brightness in the same point (fig. 3.a), c is a suitable chosen constant and g(i,j) is the grey level of resulting image (fig.3.c).

In an ideal image of visualized foils the changes of brightness reflect changes of refractive index of transparent foil. The refractive index depends on the density of material through which light beams traverse. One of the possibility how to describe character of foils images is to use the statistical characteristics (Haralick & Shapiro, 1992). The attributes of histograms can be numerically characterized using moments of distribution as the mean value of grey level

m = [L.summation over (i=1)] [x.sub.1]p([x.sub.i]) (2)

central moments of the distribution of the kth order

[[mu].sub.k](x) = [L.summation over (i=1)] [([x.sub.i] - m).sup.k]xp([x.sub.i]) (3)

and normalized moments of the distribution of the kth order

[[mu].sub.kN](x) = [[mu].sub.k](x) / [[[[mu].sub.2](x)].sup.k/2] (4)

for k>2, where [x.sub.i] is the value of i-th grey level, p([x.sub.i]) is the relative occurrence of this grey level, which can be taken as the probability of occurrence of grey level, and L is the number of grey levels in the image.


The main problem of defectoscopy is to detect, or to localize areas in the tested object, in our case in the polymeric foils or in the images of foils, which correspond to disturbances or inhomogeneities that are present in the tested material. Images of the foils without defects are characterized by the regularity of stochastic character of the structure. In the case of images with defects the damaged areas will be characterized by the different structure. One of the possibilities of detection of defects is the visual comparison of images of foils with and without defect. In order to increase effectiveness of comparison it is possible to use other tools of image processing as are sharpening or equalization of histogram. These structures can be described by the numerical characteristics calculated from the histogram of grey level occurrence. From the tested characteristics the best results have been achieved using the even order central moments of distribution. To verify the possibilities of inhomogeneities we detected foils images of 16 foil samples from which 6 had defects.


Statistical characteristics calculated for the whole foil image and for their four parts created by division of foil image into four parts have been compared. Graph in fig. 4 demonstrates values of the normalized moment of 6th order for all tested foils and for their parts. Variance of calculated moment values depends on the homogeneity of foils images.

The experiments showed that detection of anomalous parts of foil image using normalized central moments of even order is suitable for more extensive defects (comparable with dimension of image). For smaller anomalies it is suitable to use central moments according to the formula (4). For detection of more extensive defects it is possible to compare statistical characteristics calculated from the whole image, what is especially marked while comparing values for foils KX30, KX40 and ON30 (e.g. foils without defects) with the corresponding values for foils with defects (KX30D, KX40D and ON30D). The values of normalized central moment are for KX40D maximum, after that follow foils KX30D and ON30D. In all mentioned cases values are considerably distinct from values corresponding to the foils without defects.


Presented results show that visual quality assessment by the schlieren visualization method is suitable for on-line evaluation of foils in their production, because it allows localization the places with elastic strains by means of variations in the level brightness (grade of level). The completion of the method with suitable statistical characteristics calculated from the pre-processed image has found the application in the area of defectoscopy, identification and classification of polymeric foils as well.


Bolf, J.; Bajcsy, J. & Bolf, P. (1993). Methods of the Properties Testing of Optically Transparent Materials. Journal of Electrical Engineering, Vol. 44, No. 8, pp. 244-247.

Smith, A. J. & Lim, T. T. (2000). Flow Visualization, Imperial College Press, ISBN 1-86094-193-1, London

Castle, D. A.; Gibbins, B. & Hamer, P. S. (1994). Physical Methods for Examining and Comparing Transparent Plastic Bags and Cling Films, Journal of Forensic Science Society, Vol. 34, pp. 61-68.

Sonka, M.; Hlavac, V. & Boyle, R. (1998). Image Processing, Analysis and Machine Vision. Brooks/Cole Publishing Company, ISBN 0-534-95393-X, Pacific Grove

Haralick, R. M. & Shapiro, L. G. (1992). Computer and Robot Vision, Addison-Wesley Publishing Company, ISBN 0-201-10877-1, New York
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Author:Syrova, Livia; Ravas, Rudolf; Grman, Jan
Publication:Annals of DAAAM & Proceedings
Geographic Code:4EUAU
Date:Jan 1, 2007
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