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Laser sheet scattered light method for industrial measurement of thickness residual stress distribution in flat tempered glass
Optics and Lasers in Engineering 50 (2012) 787–795
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Laser sheet scattered light method for industrial measurement of thickness residual stress distribution in flat tempered glass P. Castellini, L. Stroppa, N. Paone n Universita Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy
a r t i c l e i n f o
abstract
Article history: Received 1 August 2011 Received in revised form 15 December 2011 Accepted 18 December 2011 Available online 5 January 2012
The paper presents the laser sheet scattered light technique, a fast optical non contact method for measuring internal stress distribution over a cross section of flat glass specimens, designed for closed loop control of glass tempering furnaces. The technique is an evolution of the scattered light method for flat glass residual stress analysis and allows a full thickness stress profile to be measured with a single shot acquisition across a glass plate without any contact. A linearly polarized laser sheet, shaped into a thin plane of parallel light beams, enters orthogonally to the side of the flat glass illuminating its full thickness. Light sheet is orthogonal to the glass surface and travels parallel to it. Stress induced birefringence through the glass affects light polarization, thus scattered light intensity detected at 901 with respect to the polarization of the incident light appears spatially modulated in intensity. A camera aligned orthogonal to the laser light polarization collects an image of fringes whose shape is digitally analyzed to measure the thickness stress state. The paper describes the development of this technique by recalling the scattered light method, then describing its automation by scanning a collimated beam across the glass thickness and finally by showing that the scan method can be substituted by the light sheet method. Light sheet method provides a full field non contact stress measurement across the glass thickness, thus allowing for a fast inspection method, suitable for industrial use. Flat glass items for industrial use have bevelled edges; this does not allow measurements close to glass surface. To solve this limit, experimental data are extrapolated by a symmetrical polynomial fitting and imposing a zero integral to the stress profile. Results on surface stress measured by the laser sheet scattered method are in agreement with those of the automated light scattered method and show a fair agreement with measurement by an epibiascope, thus proving the applicability of the method for fast and contact-less detection of residual thickness stress; the industrial application of the method is outlined, so that a tempering furnace could be controlled using feed-back data from thickness stress measurements on flat glass. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Residual stress measurement Scattered light method Flat glass tempering Furnaces control
1. Introduction Float glass is used for the production of a large variety of glass items; examples are glass components for the furniture industry, for the building industry, etc. The industrial realization of components made of float glass takes place through thermal and mechanical processes; for safety reasons, glass items have then to be toughened or tempered before they can be brought to the market, while mechanical processing can be done only on annealed glass plates, otherwise they would break during the machining process. Thermal treatment allows for toughening and tempering and it is achieved by specially designed tempering furnaces, which make use of air jets to cool the heated glass plate
n
Corresponding author. E-mail address: [email protected] (N. Paone).
0143-8166/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2011.12.008
from the two sides; the proper control of the tempering process guarantees the final result, i.e. the presence of an adequate residual stress. Even if in production systems of glass items the tempering process is of utmost importance, its control is still critical, mostly because the measurement of residual stress state in glass is complex, often requires off-line laboratory measurements, and does not allow to close control loops in real time. The main characteristic that differentiates a tempered glass from a standard glass is its internal residual stress profile; if we consider a section of the tempered plate, its surface is in compression, while the inner part is in tension and the stress state is practically two-dimensional, being stress normal to the plate negligible. The internal stress state inside a glass plate is indeed the superposition of membrane stress and thickness stress. Membrane stress is constant throughout the thickness; it is a uniform compression stress if we consider the borders of the glass plate. Thickness stress has instead a variable profile through
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the thickness, with a classical U shape, usually modeled as polynomial curves of 2nd or 4th order, and its integral is zero. At the surface the sum results in a compressive stress, which may reach several tens of megapascal; the glass plate therefore becomes much more resistant to bending and, if the glass breaks, the internal tensional state determines a fragmentation in small pieces. These two effects make the glass item safe, because of its increased mechanical resistance to bending loads and to the fact that in case of breakage the mass of the sharp and edgy fragments is small. Several standards prescribe the characteristics that tempered glass should have in order to be classified a safe glass; for glass used in buildings the reference standards in Europe are EN-12150-1 and 12150-2, [1,2]. According to these standards, one parameter that indicates a good tempered glass for buildings is its fragmentation characteristic; the test is destructive. This standard has been developed for certification purposes, i.e. it is prescribed to glass manufacturers to periodically sample the production, perform a fragmentation test on the sample and use the output information for certification of all the production population, which is being produced under similar and stable conditions of the tempering furnace. It is evident that the use of such a standard may also provide information for controlling the tempering process, even if this is not precisely the scope of it. Indeed, state-of-art industrial practice shows that personnel operating the tempering furnace often use it to keep the process under control. This is mostly due to the simplicity of a fragmentation test, if compared to the complexity of existing techniques for residual stress measurement. Actually, several methods are available for residual stress measurement in glass and a vast literature exists; most of them are optical methods based on the observation of stress induced birefringence of glass. A comprehensive overview of the fundamentals of photoelastic methods applied to residual stress measurement in glass can be found in [3] and in a number of following papers, for example [6,7]. Residual stress in flat glass plates can vary significantly in three-dimensional space; therefore literature reports also relevant progress in a variety of photoelastic techniques capable of mapping spatial stress distributions [8–10]. These techniques can, in principle, be implemented on samples taken from the production process and provide feed-back information on residual stress useful for quality control of production and for furnace control; the interest for such an approach is recently confirmed for example in [11]. In any case, when dealing with measurement techniques to be applied at industrial level, one should consider that manufacturers of glass items, especially for building and furniture industry, are often small-medium enterprises, with limited technical and economical resources, which therefore tend to minimize investments in complex measurement systems, which require expert operators and which they would manage with difficulty. Even considering these limits, at least two optical techniques, amongst the many others reported in literature, have met some favor amongst operators and can be found in such an industrial context: the epibiascope and the scattered light method. Epibiascope [3] exploits light beams traveling through the outermost superficial layers of a glass plate; they change in polarization due to stress and distance and when observed emerging from the surface through an analyzer, the fringe pattern allows measuring the surface stress. Such a technique requires the operator to put the instrument over the surface, which should be flat, and perform a manual observation of the fringe pattern. In order to have light guided through the superficial layer of the glass, a refractive index matching liquid should be used between the instrument optics and the glass and the method is effective on the tin side of the float glass.
The scattered light method provides information about the whole stress profile in specimens of virtually any dimension. A vast literature presents its fundamentals and applications [3–6]; recently interest on it is rising again, thanks to the advances in imaging technology and vision systems suited for industrial application. This optical technique consists in sending a linearly polarized laser beam traveling either parallel to the glass plate surface or at an oblique incidence [11] and observing the spatial modulation of scattered light intensity or phase. The method can be implemented with a traversing system, so that the whole stress profile can be measured over a grid of points across the glass plate thickness. In its implementation presented in [11], this instrument named SCALP is proposed as a portable device, which is a substantial step for its industrial application. Nevertheless, the device still requires special care in sending light into the glass and collecting it out, which make it necessary for the use of coupling optics (prisms) and refractive index matching fluids. Both the epibiascope and the scattered light methods can provide quantitative information on internal stress profile; this is useful to set up correctly the tempering process parameters and to keep the process under control by periodic sampling. The main idea is to run the furnace, which performs the tempering process on the glass products, and to introduce test specimens in the product flow at regular time intervals and to measure their stress states periodically. Test specimens should be made of the same type of glass, with the same thickness of the product, which is being processed, so that the internal stress profile in the test specimen would build up similarly to what happens in the product being processed. The information on stress profile of the specimen is then used to update the furnace parameters to obtain a good quality tempered glass. But both methods have draw-backs, which limit their applicability: they require a manual operation, special care in optical coupling and are rather slow and complex techniques, which require expert operators and do not allow automation. Therefore there is still an industrial need for a fast, automated and possibly fully non-contact measurement method. Hereafter is discussed a possible way to proceed in such a direction.
2. Theoretical background: the scattered light method Light scattering in glass is caused by local and microscopic fluctuations of index of refraction. If linearly polarized light travels through the glass material Rayleigh scattering occurs. Scattered light intensity Isc observed in a plane orthogonal to the light beam direction of propagation depends on the angle y, which is the angle between the polarization vector of the incoming beam and the direction of observation, as reported in the Fig. 1. The following Eq. (1) applies: Isc ¼ Io
8p4 N a2
l4 R2
ð1cos2 yÞ
ð1Þ
where I0 is the incoming light intensity, N is number of scatters, a is an ability of polarization, R is distance from scatter to observer, l is wavelength of light beam and y is the angle between the polarization vector and the direction of observation. Replacing some terms with a constant k the formula above becomes Isc ¼ kI0 ð1cos2 yÞ
ð2Þ
The constant k depends on glass characteristics and is proportional to l 4. Clearly Isc depends on observation angle y, and it is equal to 0 for y ¼01, and has its maximum value for y ¼901, in a direction perpendicular to the direction of polarization of incoming light.
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The classical scattered light instrument is briefly recalled hereafter; it consists of a linearly polarized laser, which is used to shine light through the edge of a glass sample, so that the collimated beam travels parallel to the glass surfaces. The beam is aligned orthogonal to the glass plate edge. Following geometrical and symmetry considerations, the principal stress directions within the glass plate are normal to the plate surface and to the plate edge (the glass plate is a parallelepiped); therefore the beam is orthogonal to the plane formed by s1 and s3 and travels along the direction of s2. The laser beam polarization vector is set at 451 relative to the glass surface (see Fig. 2). As the beam enters the tempered glass, which is birefringent, it splits into two perpendicular components of polarization, traveling at different velocities; one component is orthogonal to the glass surface and parallel to the principal stress s1 while the other is parallel to the glass surface and to the principal stress s3. The two wave components along stresses s1 and s3 have phase retardation to each other because of the two different refractive indexes. Therefore as the light propagates through the sample the two beam components alternate between being in-phase and outof-phase and periodically the resulting light vector is linearly polarized along the initial direction, i.e. at 451 relative to the glass surface. Now, when looking at the scattered light observed at y ¼451 relative to the surface of the glass, when the components are exactly in-phase with one another, there is a maximum intensity of scattered light, while when the components are opposite in phase, no light will be scattered. The consequence is that the intensity of the scattered light is spatially modulated as it goes through the glass along y direction. By analyzing the modulation pattern it is possible to calculate the absolute value of the stress in that point. If the period of
Fig. 1. Light scattering angular distribution.
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modulation is the distance y¼a, it can be written:
s1 s3 ¼
l Ca
ð3Þ
where s1 and s3 are the principal stresses perpendicular to the light beam, C is the photoelastic constant of glass and l is the wavelength of laser beam. The stress s3 can be ignored since we are dealing with a plane stress state, where s1 b s3, because of the relative small thickness of the glass plate in comparison with its lateral. Eq. (3) can therefore be rewritten as
s1 ¼
l Ca
ð4Þ
In order to take a measurement using the scattered light technique the observer looks at 901 with respect to incident beam polarization; the image of the spatially modulated line produced is analyzed and its spatial period is measured, then Eq. (4) allows determining local stress It must be pointed out the thickness stress s1 is a function of vertical coordinate across the glass plate so the beam spot must be as small as possible to have sufficient spatial resolution across the glass thickness. Therefore, if we scan the whole thickness of the specimen we can measure the total stress profile; parallel scan is shown in Fig. 2. Sign of stress can be determined by imposing an equilibrium condition across the plate thickness, i.e. a zero integral of the stress profile.
3. Automated scattered light method If the method has to be applied to industrial environments, it should be automated, in particular for beam scanning, and image and data processing. Automated scanning was already shown in [3] and [5]. An automated version of the measuring process is presented hereafter. The system that we have developed can operate on square flat glass plates having 300 mm side and variable thickness up to 25 mm, which can be periodically processed through the tempering furnace as test samples. The measurement system (see Fig. 2) is made by a He–Ne laser which projects light into the glass specimen. The collimating optics allow for a thin parallel collimated beam, about 0.1 mm diameter, so to have adequate spatial resolution across the glass thickness. The light is polarized at 451 with respect to the glass surface. The laser beam, before reaching the specimen, passes through a deflecting system that can displace the light to scan the entire thickness of the glass. The deflecting system is made by a thick flat optical glass coupled with a stepper motor; its rotation produces a parallel displacement of the beam. In this way, the laser beam can be translated with steps of 0.2 mm just by rotating the flat. The geometry of the flat glass allows for an accurate
Fig. 2. Optical scheme for laser light scattering method with automated parallel beam scanning. From this figure we can observe also the relevant directions for scattered light method.
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parallel scan of the laser beam across the glass plate, once initially aligned parallel to the glass plate surface. Than the laser beam enters the specimen and an image of the spatially modulated laser beam is recorded with a camera placed at 451 with the glass surface, which is 901 in respect to the laser polarization vector of the incoming laser beam. Fig. 3 reports a typical image taken on a 12 mm float glass sample. A second camera (not shown on the figure) takes an image of the light beam entering the side of the glass plate: this image provides information on the position of the beam along the glass plate thickness and is used to control it. In most industrial applications, the edges of a glass plate are bevelled, so to avoid sharp edges which are dangerous. Bevelling cannot be performed on tempered glass, therefore, very frequently, glass plates entering a tempering furnace have already bevelled edges. This means that the laser beam in real world application cannot be shone close to the outer surface of the glass plate. This limit will be evident in the stress profiles presented later in this paper, which lack data close to the glass plate surface. Fig. 4 shows a cross section of a bevelled glass plate as observed from the side, where the regions, which are not optically accessible from the edges, are highlighted. Hereafter the main steps for the measurement of the thickness stress profile are explained. Once the laser beam has been aligned to the glass plate surface, the beam is automatically displaced to the desired position inside the plate by rotating the flat plate by the stepper motor. Beam position is acquired as the coordinate of the centroid of the beam spot image, which forms on the edge of the glass plate. The whole test bench is digitally controlled, so to automate the measurement. The camera records scattered light pattern in a Region-ofInterest, which is schematically depicted in Fig. 4; therefore images similar to Fig. 3 are available at each position across the glass thickness. The camera is aligned so that the laser beam appears to travel parallel to the horizontal lines of the image, the y axis in Fig. 2. In order to increase signal-to-noise ratio, several images are averaged. Each average image is low pass filtered for noise attenuation and then a one-dimensional compression of the image is achieved by summing data by columns in a rectangular region-of-interest which contains the scattered light pattern. The
one-dimensional compression has the effect to increase signal-tonoise ratio. Fig. 5 reports on top the fringe image; it can be observed that scattered light intensity decreases along the laser beam direction of propagation y, due to light scattering and absorption, which reduce the incident light intensity as long as the beam penetrates the glass. This determines a visible average trend in the second plot of the Fig. 5, which represents the one-dimensional compressed data; superimposed to the average negative trend the periodicity of the signal clearly emerges, even if noise is present on the data. Therefore it is applied a de-trending filter, so to remove the negative trend in the data; the third plot in Fig. 5 reports the result of de-trending. Now the data are ready for the measurement of the period of the spatial modulation, hence for the indirect measurement of residual stress, using Eq. (4) and imposing a zero integral to the stress profile. The period a of the modulation, needed to use Eq. (4), is extracted by a least square sinusoidal fitting on the de-trended signal from the image. The use of a sinusoidal function for data fitting relies on the assumption that the principal stress s1(y) is constant along the direction y. This hypothesis holds if the length over which the measurement is taken is limited with respect to the scale of variation of stress along y. In our case the image length is 45 mm; each fitting takes place over a distance of 20 mm, so to guarantee for a sufficient spatial resolution when measuring over a glass plate having lateral dimensions larger than 300 mm. Fig. 6 reports real data and the fitting sinusoidal function. The data in this paper report results obtained from a 12 mm thick tempered glass. Then the absolute stress value is computed for every step of the process, which is repeated at different positions z through the glass plate thickness. Fig. 7 shows the stress versus a nondimensional position; tin side is at a normalized thickness equal to 1. It should be recalled that, due to the bevelled shape of the glass plate edges of real glass plates of industrial interest, no data can be collected close to the surface. As it can be seen in Fig. 7 physically meaningful stress data are present only in the central part of the thickness and exhibit a typical U shape. The reliable data are selected by considering only the interval in which sinusoidal fitting of the fringe image provides residuals below a given threshold and in which data are consistent with the physics
Fig. 3. Typical scattered light image in a tempered float glass plate.
Fig. 4. Cross section of a bevelled glass plate; regions which are not optically accessible from the edges are highlighted.
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Original image of scattered light pattern One-dimensional compressed data
Detrended data.
Fig. 5. Steps in image processing.
Fig. 6. Sinusoidal fitting of the laser beam intensity modulation (mean value of intensity has been subtracted); these data were taken in the center plane of the glass plate.
In order to determine the absolute values and the sign of stresses, it is then imposed the condition that the integral of the stress profile across the thickness should be zero and that stresses in the core are positive (tensile), while they are negative (compressive) at the surface. In order to compare the measured values with a proven measurement method of industrial use, an epibiascope (GASP from Strainoptics) is used as a reference instrument. On the tin side a value of 80 MPa is observed by the epibiascope, while the extrapolated superficial stress measured by the automated scattered light technique are about 84 MPa; we may notice that there is a fair agreement between the two methods, given also their rather large uncertainty.
4. Laser sheet scattered light method Fig. 7. Evaluation of the whole stress profile in the thickness from measured data using a symmetric 4th order polynomial fit, under the conditions of zero integral.
of the stress distribution. Outside this region, data diverge from the expected U shape, therefore they are rejected, as shown in Fig. 7. Anyway the available information is enough for data interpolation in the central region which can be used to reconstruct the stress profile across the whole thickness by fitting a polynomial curve to the data. Least square fitting has been done with a fourth order symmetrical polynomial curve, chosen in agreement to existing stress models used in literature (see for example [11]). Surface stress, which is known to be the most relevant information for tempered glass, can be therefore computed by extrapolation of the measured information through the fitting process.
This paragraph introduces the evolution of the scattered light method, into a full field measurement technique of stress profile across the glass plate thickness. Its use is intended to be the same as the scanning method described above, i.e. it is designed to be a measurement technique in support of furnace control. The main goal in developing the scattered light sheet method is to eliminate the scanning device, so to realize a fast measurement of the whole thickness stress profile, thus overcoming the main limitation to industrial use of the conventional scattered light method. Laser sheet method could also be implemented with a pulsed illumination; this in principle would open the possibility to measure on glass plates moving on the transport line. Even if this perspective would be appealing, we did not perform experiments for its validation. The basic theoretical principle of this technique is the same already explained in the previous sections and in literature
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(for example [3,6]). The difference is related to the fact the illumination is obtained with a light sheet that allows illuminating the whole section of the flat glass and therefore collecting information on stress distribution in one single image. Fig. 8 shows schematically the scattered light sheet method that we have realized. The light sheet optics is made of cylindrical lenses which are put downstream of a beam collimator; therefore a thin parallel laser light sheet is formed. The light sheet enters orthogonal to the plate edge and orthogonal to the plate surface. The light sheet is formed so to have its polarization vector at 451 with respect to the plane of the laser sheet. Polarization vector has two orthogonal components lying along the directions of the principal stresses that are expected in a glass plate. The camera is aligned so to collect light scattered at 901 with respect to polarization direction. The use of a powerful laser source is necessary in order to compensate the low spatial density of light in a laser sheet. An Ar þ ion gas laser is used to form the light sheet; it is operated on its green line, at l ¼514 nm. This choice is made because the green line is the most powerful in Ar þ lasers (in our case up to 1 W are available) and the use of a shorter wavelength with respect to He–Ne laser allows for a much higher scattering efficiency of the Rayleigh phenomenon as shown in Eq. (1). Indeed, also a pulsed light source could be used; a candidate for this application could be Nd-YAG solid state laser, having a l ¼532 nm at its second harmonic. The light sheet method suffers from the low intensity of scattered light. Our realization makes use of a high resolution (3008 2000 pixels) CCD sensor, which acquires 12 bit images. Sensor sensitivity is high, with respect to standard; furthermore exposure time can be set to allow for a sufficient collection of light, if the glass plate is not moving. The system is operated in a dark environment. In particular, the 12 bit resolution is necessary for this application, due to the low signal amplitude. A macro objective (f¼60 mm) with an f-number f/2.8 has been used, to improve image quality in terms of spatial distortion and maximize quantity of collected light. All these choices allow for an image acquisition which achieves a sufficient signal-to-noise ratio. The camera acquires a single, high resolution image of the whole section illuminated by the laser sheet, as shown in Fig. 9. The light enters parallel to the glass surface, across the whole thickness of the plate, with exception of the surface layers; this again is due to the bevelled edges of glass plates of industrial use, which are of interest in this application. A curved fringe pattern forms clearly on the image. The figure reports two yellow lines parallel to the plate surface, corresponding to the end of the bevelled parts of the plate edge. Outside these lines only noise is present in the form of bright spots due to the light scattering by dust particle on the glass surface.
The image is acquired over the glass thickness (12 mm) and is 37 mm long. Along this distance the stress can vary. The acquired fringe image is processed so to extract the spatial frequency, or the fringe period a, along the direction of light propagation. Spatial frequency can be variable along the y direction; fitting therefore is done taking into account this possibility, with a sinusoidal function of linearly variable period. Therefore both the variations of the frequency along the y and z directions (thickness) are considered, in order to obtain the stress distribution in the two-dimensional section. Once the fringe image has been processed, the stress distribution can be measured. The main limitation of the laser sheet method is the reduced signalto-noise ratio of the fringe image compared with single beam scattered light method. This requires special efforts in image processing. On the other hand, spatial resolution is in general much better. In fact, using the laser sheet the spatial resolution is in the order of the pixel, while using the scanning beam it is limited by the scanning system resolution, which is generally coarser being it obtained with a mechanical device, and by the laser beam diameter. This better resolution can be exploited to have more information or to improve SNR in the fringe image by averaging, interpolation or line comparison. Noise spikes in the image are rejected applying a Median filter on the image. A Region-of-Interest (RoI) is selected in the central part of the image in Fig. 9, where SNR is the largest; residual stress can be measured only within this RoI. The selection of the RoI is very important to guarantee good quality in the data. In fact if very noisy data are considered, the fitting process could diverge and output unrealistic values, in particular at the edge. Therefore data fitting by the polynomial curve has been done on a filtered subset of data. Filtering is based on criteria for fringe image quality and it is aimed to remove all unreliable data from the data set. In particular a fringe image is considered to have a good quality if: (a) image intensity I is above a minimum threshold, (b) fringe visibility Vis (or contrast) is above a fixed threshold. This filtering
Fig. 9. Image of the scattered light fringe pattern across the whole thickness of a glass plate; the yellow lines are the limits outside which the bevelled edges do not allow light sheet illumination (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
Fig. 8. Scheme of the laser sheet scattered light method.
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procedure improves the confidence level of the data fitting process. Fig. 10 reports a plot of fringe image intensity along a line across the glass plate thickness; it can be seen that image intensity is fading to zero close to the two surfaces of the glass plate, while it is larger in the central core of the glass, where one can observe also the intensity modulation produced by the fringes. Only in the regions where this modulation is present one can process the fringe pattern and determine its period reliably. This region is characterized by a high fringe visibility, which can be computed according to the following formula: Vis ¼
IMAX Imin IMAX þ Imin
ð5Þ
Therefore the selection criterion of the points on which the curve fitting procedure is applied is based on fringe visibility, which in physical terms means large signal-to-noise ratio in the image. The threshold on fringe visibility is fixed and was set initially to select regions with adequate contrast. This criterion can be applied to glasses having different thickness or different material composition without affecting its performance. Fig. 11 reports a typical set of data and their fitting within the interval determined as described above vs. normalized thickness; tin side is at a normalized thickness equal to 1. Raw data derive
Fig. 10. Image intensity profile across the thickness; fringe visibility and image intensity are above fixed thresholds only within part of the thickness, the ‘‘fitting interval’’ put in evidence.
Fig. 11. Data fitting with a symmetrical 4th order polynomial curve; fitting is done only on the data (reported in green), which satisfy specific criteria for quality. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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from the measurement of the fringe pattern frequency; the subset of data coming from the region of the image which satisfies the image quality criteria are highlighted in green color in Fig. 11. Polynomial interpolation will use only this subset of filtered data. A large number of raw data are discarded when applying the image quality criteria. Again data fitting is done by a 4th order symmetrical polynomial curve and a zero value is imposed to the integral of the thickness stress distribution. Surface stress can be determined after extrapolation using the polynomial model. The surface stress values obtained by the polynomial curve (about 81 MPa) are compatible to those obtained with the automated scattered light method described in paragraph 3 and with the GASP system, which were shown previously. In Fig. 12a it is shown the result of the processing of the whole fringe image of Fig. 9; it provides the two dimensional residual stress distribution over the flat glass cross section (stress values are coded by colors). Positions 0 and 37 are in mm; the 0 mm position is not at the edge of the plate, but it is offset by 10 mm. The inner core of the flat glass is under tension, while the outer layers are compressed. Surface stress can be determined only by extrapolating data to the surface, due to the absence of information caused by bevelled edges. The two dimensional stress distribution can be further processed, so to extract stress profiles across the flat glass in different sections; the high spatial density of available information would allow to observe the spatial distribution with great detail. In Fig. 12b and c two stress profiles taken at 17 mm away from each other are plotted. The residual stress profile changes along the flat glass can be highlighted comparing single profiles at different y positions across the thickness. An analysis of the stress distribution in the plate is out of scope in this paper, specifically devoted to present the measurement method, rather than to analyze stress in specific glass plates. The scattered light sheet method, which has been discussed presents some significant advantages with respect to the classical scattered light method, even if considering the case of automatic scanning. All information is collected on one single image. The full field nature of the method allows the measurement to be obtained in a fraction of second in a whole cross section of the flat glass; this makes the method simpler than others, because it reduces the interaction to a minimum, which is required to the operator and simplifies the optical set-up. In particular, the absence of moving parts determines a significant improvement in reliability and, in an industrial environment, could provide a significant advantage on measurement uncertainty. The method is fully non-contact, which is a further advantage in industrial applications. On the other hand, some limitations are present; indeed the technique suffers from a low signal-to-noise ratio because the image intensity and fringe visibility can be very low in some parts of the images. Solving this problem requires on one side an intense illumination and on the other side a very sensitive imaging sensor. High sensitivity cameras are now available on the market; their use improves image quality in laser sheet method. Furthermore, image quality is enhanced by longer exposure time, if the test is performed in a dark environment and on a static glass plate. This option is not ideal for an industrial application. Increasing laser power would also improve the image but, on the other side, special care has to be taken in preventing eye safety problems, which for an industrial application have to be carefully considered.
5. Concluding remarks In order to realize a full-field, non-contact and fast method for residual stress measurement in flat glass, necessary to meet
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60
40
Stress [MPa]
20
0
0
0.2
0.4
0.6
0.8
1
Normalised Thickness
-20
-40
-60
-80 50 40 30
Stress [MPa]
20 10 0 0 -10
0.2
0.4
0.6
0.8
1
Normalised Thickness
-20 -30 -40 -50 Fig. 12. (a) Stress distribution in the glass plate section. (b) Stress distribution in the glass plate, section A at 3 mm of (a). (c) Stress distribution in the glass plate, section B at 20 mm of (a).
industrial requirements, we have presented the scattered light sheet method developed employing a parallel sheet of polarized laser light. The main advantage of such a device is that it realizes a full field and non contact technique, which allows a full stress profile to be acquired by a single shot in a two-dimensional cross section of a flat glass plate. From a theoretical point of view this technique is an evolution of the scattered light method for flat glass residual stress analysis. Indeed the paper details at first how an automated scattered light method is implemented, then it describes the implementation of a light sheet to improve system performance. In the light sheet
method no moving parts are present and no scanning of beams is necessary, therefore system reliability is intrinsically high and suitable for industrial application. The paper presents a realization of this concept. A high resolution 12 bit CCD sensor is used for the scope, with a macro objective f/2.8. Illumination was by an Ar þ ion laser operated in its green line 532 nm, having a power of 1 W. It presents the typical fringe image, which is formed and the main steps for its processing are discussed in depth. The output is a residual stress map across the glass thickness, obtained after filtering and interpolation of available raw data. It should be
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noted that no data can be taken close to the two surfaces of the glass plate, because the glass plate edges are bevelled for safe manipulation. This is a constraint imposed by the industrial use, to which the measurement method should be applied. Fringe images have low intensity, low visibility and contrast; this imposes the use of very sensitive image acquisition devices. The method could be implemented also using pulsed lasers, but the authors did not try it. Indeed the use of high power lasers should be considered with care in developing measurement systems, because it raises the issue of laser safety, which is a concern in any industrial application. Stress data at the surface on bevelled plates, which are known to be the most relevant data in tempering process control, can only be derived by extrapolation of data with fitting polynomials; results in fair agreement with epibiascope data and with the automated light scatter method are obtained by fitting data with a symmetrical 4th order polynomial curve having a zero integral. If bevels were not present, the light sheet method would allow measurements up to the surface. The paper provides hints for the possible use of the scattered light sheet method for process control of tempering furnaces for glass specimens. Indeed, in industrial applications, an optical method for measuring internal stress state in flat glass specimens can be used for closing control loops of furnaces for glass tempering, but for a wide acceptance it should be a fast noncontact measurement technique, such as the light sheet scattered method. What presented allows one to conclude that the proposed method could meet the industrial needs for tempering furnace control.
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Acknowledgments Part of the research has been supported by the company Tornati Forni, with the co-financing of the Marche Region (POR MARCHE 2007–2013). The authors thank Dr. Vladimir Abaskin for his precious suggestions during the work and his support in setting up the hardware and performing part of the experiments.
References [1] EN 12150-1, Glass in building—Thermally toughened soda lime silicate safety glass-Definition and description, 2001. [2] EN 12150-2, Glass in building—Thermally toughened soda lime silicate safety glass-Part 2: Evaluation of conformity/Product standard, 2004. [3] Aben H, Guillemet C. Photoelasticity of glass. Ed. Springer; 1993. [4] Ascough J. A review of the scattered-light method in photoelasticity. Opt Lasers Eng 1981;2(3):215–28. [5] R Weissmann, D Durkop, A novel method for measuring stresses in flat glass. In: Proceedings XV International Congress on Glass. Leningrad, 3b, 1989, p. 217–20. [6] Hundhammer I, Lenhart A, Pontesch D. Stress measurement in transparent materials using scattered laser light. Glass Sci Technol 2002;75:236–42. [7] Aben H, Anton J, Errapart A. Modern photoelasticity for residual stress measurement in glass. Strain 2008;44:40–8, doi:10.1111/j.1475-1305.2008.00422.x. [8] Kihara T. Phase unwrapping method for three-dimensional stress analysis by scattered-light photoelasticity with unpolarized light. Appl Opt 2006;45:8848–54. [9] D Lochegnies, E Romero, J Anton, A Errapart, H Aben, Measurement of complete residual stress fields in tempered glass plates. In: Proceedings of the Nineth International Conference, Glass Processing Days, 2005. [10] Aben H, Errapart A, Ainola L, Anton J. Photoelastic tomography for residual stress measurement in glass. Opt Eng 2005;44:093601. [11] Aben H, Anton J, Errapart A, Hodemann S, Kilas J, Klassen H, Lamp M. On nondestructive residual stress measurement in glass panels. Est J Eng 2010; 16(2):150–6. doi:103176/eng2010.2.04.
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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Laser sheet scattered light method for industrial measurement of thickness residual stress distribution in flat tempered glass P. Castellini, L. Stroppa, N. Paone n Universita Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy
a r t i c l e i n f o
abstract
Article history: Received 1 August 2011 Received in revised form 15 December 2011 Accepted 18 December 2011 Available online 5 January 2012
The paper presents the laser sheet scattered light technique, a fast optical non contact method for measuring internal stress distribution over a cross section of flat glass specimens, designed for closed loop control of glass tempering furnaces. The technique is an evolution of the scattered light method for flat glass residual stress analysis and allows a full thickness stress profile to be measured with a single shot acquisition across a glass plate without any contact. A linearly polarized laser sheet, shaped into a thin plane of parallel light beams, enters orthogonally to the side of the flat glass illuminating its full thickness. Light sheet is orthogonal to the glass surface and travels parallel to it. Stress induced birefringence through the glass affects light polarization, thus scattered light intensity detected at 901 with respect to the polarization of the incident light appears spatially modulated in intensity. A camera aligned orthogonal to the laser light polarization collects an image of fringes whose shape is digitally analyzed to measure the thickness stress state. The paper describes the development of this technique by recalling the scattered light method, then describing its automation by scanning a collimated beam across the glass thickness and finally by showing that the scan method can be substituted by the light sheet method. Light sheet method provides a full field non contact stress measurement across the glass thickness, thus allowing for a fast inspection method, suitable for industrial use. Flat glass items for industrial use have bevelled edges; this does not allow measurements close to glass surface. To solve this limit, experimental data are extrapolated by a symmetrical polynomial fitting and imposing a zero integral to the stress profile. Results on surface stress measured by the laser sheet scattered method are in agreement with those of the automated light scattered method and show a fair agreement with measurement by an epibiascope, thus proving the applicability of the method for fast and contact-less detection of residual thickness stress; the industrial application of the method is outlined, so that a tempering furnace could be controlled using feed-back data from thickness stress measurements on flat glass. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Residual stress measurement Scattered light method Flat glass tempering Furnaces control
1. Introduction Float glass is used for the production of a large variety of glass items; examples are glass components for the furniture industry, for the building industry, etc. The industrial realization of components made of float glass takes place through thermal and mechanical processes; for safety reasons, glass items have then to be toughened or tempered before they can be brought to the market, while mechanical processing can be done only on annealed glass plates, otherwise they would break during the machining process. Thermal treatment allows for toughening and tempering and it is achieved by specially designed tempering furnaces, which make use of air jets to cool the heated glass plate
n
Corresponding author. E-mail address: [email protected] (N. Paone).
0143-8166/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2011.12.008
from the two sides; the proper control of the tempering process guarantees the final result, i.e. the presence of an adequate residual stress. Even if in production systems of glass items the tempering process is of utmost importance, its control is still critical, mostly because the measurement of residual stress state in glass is complex, often requires off-line laboratory measurements, and does not allow to close control loops in real time. The main characteristic that differentiates a tempered glass from a standard glass is its internal residual stress profile; if we consider a section of the tempered plate, its surface is in compression, while the inner part is in tension and the stress state is practically two-dimensional, being stress normal to the plate negligible. The internal stress state inside a glass plate is indeed the superposition of membrane stress and thickness stress. Membrane stress is constant throughout the thickness; it is a uniform compression stress if we consider the borders of the glass plate. Thickness stress has instead a variable profile through
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the thickness, with a classical U shape, usually modeled as polynomial curves of 2nd or 4th order, and its integral is zero. At the surface the sum results in a compressive stress, which may reach several tens of megapascal; the glass plate therefore becomes much more resistant to bending and, if the glass breaks, the internal tensional state determines a fragmentation in small pieces. These two effects make the glass item safe, because of its increased mechanical resistance to bending loads and to the fact that in case of breakage the mass of the sharp and edgy fragments is small. Several standards prescribe the characteristics that tempered glass should have in order to be classified a safe glass; for glass used in buildings the reference standards in Europe are EN-12150-1 and 12150-2, [1,2]. According to these standards, one parameter that indicates a good tempered glass for buildings is its fragmentation characteristic; the test is destructive. This standard has been developed for certification purposes, i.e. it is prescribed to glass manufacturers to periodically sample the production, perform a fragmentation test on the sample and use the output information for certification of all the production population, which is being produced under similar and stable conditions of the tempering furnace. It is evident that the use of such a standard may also provide information for controlling the tempering process, even if this is not precisely the scope of it. Indeed, state-of-art industrial practice shows that personnel operating the tempering furnace often use it to keep the process under control. This is mostly due to the simplicity of a fragmentation test, if compared to the complexity of existing techniques for residual stress measurement. Actually, several methods are available for residual stress measurement in glass and a vast literature exists; most of them are optical methods based on the observation of stress induced birefringence of glass. A comprehensive overview of the fundamentals of photoelastic methods applied to residual stress measurement in glass can be found in [3] and in a number of following papers, for example [6,7]. Residual stress in flat glass plates can vary significantly in three-dimensional space; therefore literature reports also relevant progress in a variety of photoelastic techniques capable of mapping spatial stress distributions [8–10]. These techniques can, in principle, be implemented on samples taken from the production process and provide feed-back information on residual stress useful for quality control of production and for furnace control; the interest for such an approach is recently confirmed for example in [11]. In any case, when dealing with measurement techniques to be applied at industrial level, one should consider that manufacturers of glass items, especially for building and furniture industry, are often small-medium enterprises, with limited technical and economical resources, which therefore tend to minimize investments in complex measurement systems, which require expert operators and which they would manage with difficulty. Even considering these limits, at least two optical techniques, amongst the many others reported in literature, have met some favor amongst operators and can be found in such an industrial context: the epibiascope and the scattered light method. Epibiascope [3] exploits light beams traveling through the outermost superficial layers of a glass plate; they change in polarization due to stress and distance and when observed emerging from the surface through an analyzer, the fringe pattern allows measuring the surface stress. Such a technique requires the operator to put the instrument over the surface, which should be flat, and perform a manual observation of the fringe pattern. In order to have light guided through the superficial layer of the glass, a refractive index matching liquid should be used between the instrument optics and the glass and the method is effective on the tin side of the float glass.
The scattered light method provides information about the whole stress profile in specimens of virtually any dimension. A vast literature presents its fundamentals and applications [3–6]; recently interest on it is rising again, thanks to the advances in imaging technology and vision systems suited for industrial application. This optical technique consists in sending a linearly polarized laser beam traveling either parallel to the glass plate surface or at an oblique incidence [11] and observing the spatial modulation of scattered light intensity or phase. The method can be implemented with a traversing system, so that the whole stress profile can be measured over a grid of points across the glass plate thickness. In its implementation presented in [11], this instrument named SCALP is proposed as a portable device, which is a substantial step for its industrial application. Nevertheless, the device still requires special care in sending light into the glass and collecting it out, which make it necessary for the use of coupling optics (prisms) and refractive index matching fluids. Both the epibiascope and the scattered light methods can provide quantitative information on internal stress profile; this is useful to set up correctly the tempering process parameters and to keep the process under control by periodic sampling. The main idea is to run the furnace, which performs the tempering process on the glass products, and to introduce test specimens in the product flow at regular time intervals and to measure their stress states periodically. Test specimens should be made of the same type of glass, with the same thickness of the product, which is being processed, so that the internal stress profile in the test specimen would build up similarly to what happens in the product being processed. The information on stress profile of the specimen is then used to update the furnace parameters to obtain a good quality tempered glass. But both methods have draw-backs, which limit their applicability: they require a manual operation, special care in optical coupling and are rather slow and complex techniques, which require expert operators and do not allow automation. Therefore there is still an industrial need for a fast, automated and possibly fully non-contact measurement method. Hereafter is discussed a possible way to proceed in such a direction.
2. Theoretical background: the scattered light method Light scattering in glass is caused by local and microscopic fluctuations of index of refraction. If linearly polarized light travels through the glass material Rayleigh scattering occurs. Scattered light intensity Isc observed in a plane orthogonal to the light beam direction of propagation depends on the angle y, which is the angle between the polarization vector of the incoming beam and the direction of observation, as reported in the Fig. 1. The following Eq. (1) applies: Isc ¼ Io
8p4 N a2
l4 R2
ð1cos2 yÞ
ð1Þ
where I0 is the incoming light intensity, N is number of scatters, a is an ability of polarization, R is distance from scatter to observer, l is wavelength of light beam and y is the angle between the polarization vector and the direction of observation. Replacing some terms with a constant k the formula above becomes Isc ¼ kI0 ð1cos2 yÞ
ð2Þ
The constant k depends on glass characteristics and is proportional to l 4. Clearly Isc depends on observation angle y, and it is equal to 0 for y ¼01, and has its maximum value for y ¼901, in a direction perpendicular to the direction of polarization of incoming light.
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The classical scattered light instrument is briefly recalled hereafter; it consists of a linearly polarized laser, which is used to shine light through the edge of a glass sample, so that the collimated beam travels parallel to the glass surfaces. The beam is aligned orthogonal to the glass plate edge. Following geometrical and symmetry considerations, the principal stress directions within the glass plate are normal to the plate surface and to the plate edge (the glass plate is a parallelepiped); therefore the beam is orthogonal to the plane formed by s1 and s3 and travels along the direction of s2. The laser beam polarization vector is set at 451 relative to the glass surface (see Fig. 2). As the beam enters the tempered glass, which is birefringent, it splits into two perpendicular components of polarization, traveling at different velocities; one component is orthogonal to the glass surface and parallel to the principal stress s1 while the other is parallel to the glass surface and to the principal stress s3. The two wave components along stresses s1 and s3 have phase retardation to each other because of the two different refractive indexes. Therefore as the light propagates through the sample the two beam components alternate between being in-phase and outof-phase and periodically the resulting light vector is linearly polarized along the initial direction, i.e. at 451 relative to the glass surface. Now, when looking at the scattered light observed at y ¼451 relative to the surface of the glass, when the components are exactly in-phase with one another, there is a maximum intensity of scattered light, while when the components are opposite in phase, no light will be scattered. The consequence is that the intensity of the scattered light is spatially modulated as it goes through the glass along y direction. By analyzing the modulation pattern it is possible to calculate the absolute value of the stress in that point. If the period of
Fig. 1. Light scattering angular distribution.
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modulation is the distance y¼a, it can be written:
s1 s3 ¼
l Ca
ð3Þ
where s1 and s3 are the principal stresses perpendicular to the light beam, C is the photoelastic constant of glass and l is the wavelength of laser beam. The stress s3 can be ignored since we are dealing with a plane stress state, where s1 b s3, because of the relative small thickness of the glass plate in comparison with its lateral. Eq. (3) can therefore be rewritten as
s1 ¼
l Ca
ð4Þ
In order to take a measurement using the scattered light technique the observer looks at 901 with respect to incident beam polarization; the image of the spatially modulated line produced is analyzed and its spatial period is measured, then Eq. (4) allows determining local stress It must be pointed out the thickness stress s1 is a function of vertical coordinate across the glass plate so the beam spot must be as small as possible to have sufficient spatial resolution across the glass thickness. Therefore, if we scan the whole thickness of the specimen we can measure the total stress profile; parallel scan is shown in Fig. 2. Sign of stress can be determined by imposing an equilibrium condition across the plate thickness, i.e. a zero integral of the stress profile.
3. Automated scattered light method If the method has to be applied to industrial environments, it should be automated, in particular for beam scanning, and image and data processing. Automated scanning was already shown in [3] and [5]. An automated version of the measuring process is presented hereafter. The system that we have developed can operate on square flat glass plates having 300 mm side and variable thickness up to 25 mm, which can be periodically processed through the tempering furnace as test samples. The measurement system (see Fig. 2) is made by a He–Ne laser which projects light into the glass specimen. The collimating optics allow for a thin parallel collimated beam, about 0.1 mm diameter, so to have adequate spatial resolution across the glass thickness. The light is polarized at 451 with respect to the glass surface. The laser beam, before reaching the specimen, passes through a deflecting system that can displace the light to scan the entire thickness of the glass. The deflecting system is made by a thick flat optical glass coupled with a stepper motor; its rotation produces a parallel displacement of the beam. In this way, the laser beam can be translated with steps of 0.2 mm just by rotating the flat. The geometry of the flat glass allows for an accurate
Fig. 2. Optical scheme for laser light scattering method with automated parallel beam scanning. From this figure we can observe also the relevant directions for scattered light method.
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parallel scan of the laser beam across the glass plate, once initially aligned parallel to the glass plate surface. Than the laser beam enters the specimen and an image of the spatially modulated laser beam is recorded with a camera placed at 451 with the glass surface, which is 901 in respect to the laser polarization vector of the incoming laser beam. Fig. 3 reports a typical image taken on a 12 mm float glass sample. A second camera (not shown on the figure) takes an image of the light beam entering the side of the glass plate: this image provides information on the position of the beam along the glass plate thickness and is used to control it. In most industrial applications, the edges of a glass plate are bevelled, so to avoid sharp edges which are dangerous. Bevelling cannot be performed on tempered glass, therefore, very frequently, glass plates entering a tempering furnace have already bevelled edges. This means that the laser beam in real world application cannot be shone close to the outer surface of the glass plate. This limit will be evident in the stress profiles presented later in this paper, which lack data close to the glass plate surface. Fig. 4 shows a cross section of a bevelled glass plate as observed from the side, where the regions, which are not optically accessible from the edges, are highlighted. Hereafter the main steps for the measurement of the thickness stress profile are explained. Once the laser beam has been aligned to the glass plate surface, the beam is automatically displaced to the desired position inside the plate by rotating the flat plate by the stepper motor. Beam position is acquired as the coordinate of the centroid of the beam spot image, which forms on the edge of the glass plate. The whole test bench is digitally controlled, so to automate the measurement. The camera records scattered light pattern in a Region-ofInterest, which is schematically depicted in Fig. 4; therefore images similar to Fig. 3 are available at each position across the glass thickness. The camera is aligned so that the laser beam appears to travel parallel to the horizontal lines of the image, the y axis in Fig. 2. In order to increase signal-to-noise ratio, several images are averaged. Each average image is low pass filtered for noise attenuation and then a one-dimensional compression of the image is achieved by summing data by columns in a rectangular region-of-interest which contains the scattered light pattern. The
one-dimensional compression has the effect to increase signal-tonoise ratio. Fig. 5 reports on top the fringe image; it can be observed that scattered light intensity decreases along the laser beam direction of propagation y, due to light scattering and absorption, which reduce the incident light intensity as long as the beam penetrates the glass. This determines a visible average trend in the second plot of the Fig. 5, which represents the one-dimensional compressed data; superimposed to the average negative trend the periodicity of the signal clearly emerges, even if noise is present on the data. Therefore it is applied a de-trending filter, so to remove the negative trend in the data; the third plot in Fig. 5 reports the result of de-trending. Now the data are ready for the measurement of the period of the spatial modulation, hence for the indirect measurement of residual stress, using Eq. (4) and imposing a zero integral to the stress profile. The period a of the modulation, needed to use Eq. (4), is extracted by a least square sinusoidal fitting on the de-trended signal from the image. The use of a sinusoidal function for data fitting relies on the assumption that the principal stress s1(y) is constant along the direction y. This hypothesis holds if the length over which the measurement is taken is limited with respect to the scale of variation of stress along y. In our case the image length is 45 mm; each fitting takes place over a distance of 20 mm, so to guarantee for a sufficient spatial resolution when measuring over a glass plate having lateral dimensions larger than 300 mm. Fig. 6 reports real data and the fitting sinusoidal function. The data in this paper report results obtained from a 12 mm thick tempered glass. Then the absolute stress value is computed for every step of the process, which is repeated at different positions z through the glass plate thickness. Fig. 7 shows the stress versus a nondimensional position; tin side is at a normalized thickness equal to 1. It should be recalled that, due to the bevelled shape of the glass plate edges of real glass plates of industrial interest, no data can be collected close to the surface. As it can be seen in Fig. 7 physically meaningful stress data are present only in the central part of the thickness and exhibit a typical U shape. The reliable data are selected by considering only the interval in which sinusoidal fitting of the fringe image provides residuals below a given threshold and in which data are consistent with the physics
Fig. 3. Typical scattered light image in a tempered float glass plate.
Fig. 4. Cross section of a bevelled glass plate; regions which are not optically accessible from the edges are highlighted.
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Original image of scattered light pattern One-dimensional compressed data
Detrended data.
Fig. 5. Steps in image processing.
Fig. 6. Sinusoidal fitting of the laser beam intensity modulation (mean value of intensity has been subtracted); these data were taken in the center plane of the glass plate.
In order to determine the absolute values and the sign of stresses, it is then imposed the condition that the integral of the stress profile across the thickness should be zero and that stresses in the core are positive (tensile), while they are negative (compressive) at the surface. In order to compare the measured values with a proven measurement method of industrial use, an epibiascope (GASP from Strainoptics) is used as a reference instrument. On the tin side a value of 80 MPa is observed by the epibiascope, while the extrapolated superficial stress measured by the automated scattered light technique are about 84 MPa; we may notice that there is a fair agreement between the two methods, given also their rather large uncertainty.
4. Laser sheet scattered light method Fig. 7. Evaluation of the whole stress profile in the thickness from measured data using a symmetric 4th order polynomial fit, under the conditions of zero integral.
of the stress distribution. Outside this region, data diverge from the expected U shape, therefore they are rejected, as shown in Fig. 7. Anyway the available information is enough for data interpolation in the central region which can be used to reconstruct the stress profile across the whole thickness by fitting a polynomial curve to the data. Least square fitting has been done with a fourth order symmetrical polynomial curve, chosen in agreement to existing stress models used in literature (see for example [11]). Surface stress, which is known to be the most relevant information for tempered glass, can be therefore computed by extrapolation of the measured information through the fitting process.
This paragraph introduces the evolution of the scattered light method, into a full field measurement technique of stress profile across the glass plate thickness. Its use is intended to be the same as the scanning method described above, i.e. it is designed to be a measurement technique in support of furnace control. The main goal in developing the scattered light sheet method is to eliminate the scanning device, so to realize a fast measurement of the whole thickness stress profile, thus overcoming the main limitation to industrial use of the conventional scattered light method. Laser sheet method could also be implemented with a pulsed illumination; this in principle would open the possibility to measure on glass plates moving on the transport line. Even if this perspective would be appealing, we did not perform experiments for its validation. The basic theoretical principle of this technique is the same already explained in the previous sections and in literature
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(for example [3,6]). The difference is related to the fact the illumination is obtained with a light sheet that allows illuminating the whole section of the flat glass and therefore collecting information on stress distribution in one single image. Fig. 8 shows schematically the scattered light sheet method that we have realized. The light sheet optics is made of cylindrical lenses which are put downstream of a beam collimator; therefore a thin parallel laser light sheet is formed. The light sheet enters orthogonal to the plate edge and orthogonal to the plate surface. The light sheet is formed so to have its polarization vector at 451 with respect to the plane of the laser sheet. Polarization vector has two orthogonal components lying along the directions of the principal stresses that are expected in a glass plate. The camera is aligned so to collect light scattered at 901 with respect to polarization direction. The use of a powerful laser source is necessary in order to compensate the low spatial density of light in a laser sheet. An Ar þ ion gas laser is used to form the light sheet; it is operated on its green line, at l ¼514 nm. This choice is made because the green line is the most powerful in Ar þ lasers (in our case up to 1 W are available) and the use of a shorter wavelength with respect to He–Ne laser allows for a much higher scattering efficiency of the Rayleigh phenomenon as shown in Eq. (1). Indeed, also a pulsed light source could be used; a candidate for this application could be Nd-YAG solid state laser, having a l ¼532 nm at its second harmonic. The light sheet method suffers from the low intensity of scattered light. Our realization makes use of a high resolution (3008 2000 pixels) CCD sensor, which acquires 12 bit images. Sensor sensitivity is high, with respect to standard; furthermore exposure time can be set to allow for a sufficient collection of light, if the glass plate is not moving. The system is operated in a dark environment. In particular, the 12 bit resolution is necessary for this application, due to the low signal amplitude. A macro objective (f¼60 mm) with an f-number f/2.8 has been used, to improve image quality in terms of spatial distortion and maximize quantity of collected light. All these choices allow for an image acquisition which achieves a sufficient signal-to-noise ratio. The camera acquires a single, high resolution image of the whole section illuminated by the laser sheet, as shown in Fig. 9. The light enters parallel to the glass surface, across the whole thickness of the plate, with exception of the surface layers; this again is due to the bevelled edges of glass plates of industrial use, which are of interest in this application. A curved fringe pattern forms clearly on the image. The figure reports two yellow lines parallel to the plate surface, corresponding to the end of the bevelled parts of the plate edge. Outside these lines only noise is present in the form of bright spots due to the light scattering by dust particle on the glass surface.
The image is acquired over the glass thickness (12 mm) and is 37 mm long. Along this distance the stress can vary. The acquired fringe image is processed so to extract the spatial frequency, or the fringe period a, along the direction of light propagation. Spatial frequency can be variable along the y direction; fitting therefore is done taking into account this possibility, with a sinusoidal function of linearly variable period. Therefore both the variations of the frequency along the y and z directions (thickness) are considered, in order to obtain the stress distribution in the two-dimensional section. Once the fringe image has been processed, the stress distribution can be measured. The main limitation of the laser sheet method is the reduced signalto-noise ratio of the fringe image compared with single beam scattered light method. This requires special efforts in image processing. On the other hand, spatial resolution is in general much better. In fact, using the laser sheet the spatial resolution is in the order of the pixel, while using the scanning beam it is limited by the scanning system resolution, which is generally coarser being it obtained with a mechanical device, and by the laser beam diameter. This better resolution can be exploited to have more information or to improve SNR in the fringe image by averaging, interpolation or line comparison. Noise spikes in the image are rejected applying a Median filter on the image. A Region-of-Interest (RoI) is selected in the central part of the image in Fig. 9, where SNR is the largest; residual stress can be measured only within this RoI. The selection of the RoI is very important to guarantee good quality in the data. In fact if very noisy data are considered, the fitting process could diverge and output unrealistic values, in particular at the edge. Therefore data fitting by the polynomial curve has been done on a filtered subset of data. Filtering is based on criteria for fringe image quality and it is aimed to remove all unreliable data from the data set. In particular a fringe image is considered to have a good quality if: (a) image intensity I is above a minimum threshold, (b) fringe visibility Vis (or contrast) is above a fixed threshold. This filtering
Fig. 9. Image of the scattered light fringe pattern across the whole thickness of a glass plate; the yellow lines are the limits outside which the bevelled edges do not allow light sheet illumination (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
Fig. 8. Scheme of the laser sheet scattered light method.
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procedure improves the confidence level of the data fitting process. Fig. 10 reports a plot of fringe image intensity along a line across the glass plate thickness; it can be seen that image intensity is fading to zero close to the two surfaces of the glass plate, while it is larger in the central core of the glass, where one can observe also the intensity modulation produced by the fringes. Only in the regions where this modulation is present one can process the fringe pattern and determine its period reliably. This region is characterized by a high fringe visibility, which can be computed according to the following formula: Vis ¼
IMAX Imin IMAX þ Imin
ð5Þ
Therefore the selection criterion of the points on which the curve fitting procedure is applied is based on fringe visibility, which in physical terms means large signal-to-noise ratio in the image. The threshold on fringe visibility is fixed and was set initially to select regions with adequate contrast. This criterion can be applied to glasses having different thickness or different material composition without affecting its performance. Fig. 11 reports a typical set of data and their fitting within the interval determined as described above vs. normalized thickness; tin side is at a normalized thickness equal to 1. Raw data derive
Fig. 10. Image intensity profile across the thickness; fringe visibility and image intensity are above fixed thresholds only within part of the thickness, the ‘‘fitting interval’’ put in evidence.
Fig. 11. Data fitting with a symmetrical 4th order polynomial curve; fitting is done only on the data (reported in green), which satisfy specific criteria for quality. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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from the measurement of the fringe pattern frequency; the subset of data coming from the region of the image which satisfies the image quality criteria are highlighted in green color in Fig. 11. Polynomial interpolation will use only this subset of filtered data. A large number of raw data are discarded when applying the image quality criteria. Again data fitting is done by a 4th order symmetrical polynomial curve and a zero value is imposed to the integral of the thickness stress distribution. Surface stress can be determined after extrapolation using the polynomial model. The surface stress values obtained by the polynomial curve (about 81 MPa) are compatible to those obtained with the automated scattered light method described in paragraph 3 and with the GASP system, which were shown previously. In Fig. 12a it is shown the result of the processing of the whole fringe image of Fig. 9; it provides the two dimensional residual stress distribution over the flat glass cross section (stress values are coded by colors). Positions 0 and 37 are in mm; the 0 mm position is not at the edge of the plate, but it is offset by 10 mm. The inner core of the flat glass is under tension, while the outer layers are compressed. Surface stress can be determined only by extrapolating data to the surface, due to the absence of information caused by bevelled edges. The two dimensional stress distribution can be further processed, so to extract stress profiles across the flat glass in different sections; the high spatial density of available information would allow to observe the spatial distribution with great detail. In Fig. 12b and c two stress profiles taken at 17 mm away from each other are plotted. The residual stress profile changes along the flat glass can be highlighted comparing single profiles at different y positions across the thickness. An analysis of the stress distribution in the plate is out of scope in this paper, specifically devoted to present the measurement method, rather than to analyze stress in specific glass plates. The scattered light sheet method, which has been discussed presents some significant advantages with respect to the classical scattered light method, even if considering the case of automatic scanning. All information is collected on one single image. The full field nature of the method allows the measurement to be obtained in a fraction of second in a whole cross section of the flat glass; this makes the method simpler than others, because it reduces the interaction to a minimum, which is required to the operator and simplifies the optical set-up. In particular, the absence of moving parts determines a significant improvement in reliability and, in an industrial environment, could provide a significant advantage on measurement uncertainty. The method is fully non-contact, which is a further advantage in industrial applications. On the other hand, some limitations are present; indeed the technique suffers from a low signal-to-noise ratio because the image intensity and fringe visibility can be very low in some parts of the images. Solving this problem requires on one side an intense illumination and on the other side a very sensitive imaging sensor. High sensitivity cameras are now available on the market; their use improves image quality in laser sheet method. Furthermore, image quality is enhanced by longer exposure time, if the test is performed in a dark environment and on a static glass plate. This option is not ideal for an industrial application. Increasing laser power would also improve the image but, on the other side, special care has to be taken in preventing eye safety problems, which for an industrial application have to be carefully considered.
5. Concluding remarks In order to realize a full-field, non-contact and fast method for residual stress measurement in flat glass, necessary to meet
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-20 -30 -40 -50 Fig. 12. (a) Stress distribution in the glass plate section. (b) Stress distribution in the glass plate, section A at 3 mm of (a). (c) Stress distribution in the glass plate, section B at 20 mm of (a).
industrial requirements, we have presented the scattered light sheet method developed employing a parallel sheet of polarized laser light. The main advantage of such a device is that it realizes a full field and non contact technique, which allows a full stress profile to be acquired by a single shot in a two-dimensional cross section of a flat glass plate. From a theoretical point of view this technique is an evolution of the scattered light method for flat glass residual stress analysis. Indeed the paper details at first how an automated scattered light method is implemented, then it describes the implementation of a light sheet to improve system performance. In the light sheet
method no moving parts are present and no scanning of beams is necessary, therefore system reliability is intrinsically high and suitable for industrial application. The paper presents a realization of this concept. A high resolution 12 bit CCD sensor is used for the scope, with a macro objective f/2.8. Illumination was by an Ar þ ion laser operated in its green line 532 nm, having a power of 1 W. It presents the typical fringe image, which is formed and the main steps for its processing are discussed in depth. The output is a residual stress map across the glass thickness, obtained after filtering and interpolation of available raw data. It should be
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noted that no data can be taken close to the two surfaces of the glass plate, because the glass plate edges are bevelled for safe manipulation. This is a constraint imposed by the industrial use, to which the measurement method should be applied. Fringe images have low intensity, low visibility and contrast; this imposes the use of very sensitive image acquisition devices. The method could be implemented also using pulsed lasers, but the authors did not try it. Indeed the use of high power lasers should be considered with care in developing measurement systems, because it raises the issue of laser safety, which is a concern in any industrial application. Stress data at the surface on bevelled plates, which are known to be the most relevant data in tempering process control, can only be derived by extrapolation of data with fitting polynomials; results in fair agreement with epibiascope data and with the automated light scatter method are obtained by fitting data with a symmetrical 4th order polynomial curve having a zero integral. If bevels were not present, the light sheet method would allow measurements up to the surface. The paper provides hints for the possible use of the scattered light sheet method for process control of tempering furnaces for glass specimens. Indeed, in industrial applications, an optical method for measuring internal stress state in flat glass specimens can be used for closing control loops of furnaces for glass tempering, but for a wide acceptance it should be a fast noncontact measurement technique, such as the light sheet scattered method. What presented allows one to conclude that the proposed method could meet the industrial needs for tempering furnace control.
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Acknowledgments Part of the research has been supported by the company Tornati Forni, with the co-financing of the Marche Region (POR MARCHE 2007–2013). The authors thank Dr. Vladimir Abaskin for his precious suggestions during the work and his support in setting up the hardware and performing part of the experiments.
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