Using active thermography to inspect pin-hole defects in anti-reflective coating with k-mean clustering

NDT&E International 76 (2015) 66–72

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NDT&E International journal homepage: www.elsevier.com/locate/ndteint

Using active thermography to inspect pin-hole defects in anti-reflective coating with k-mean clustering Hongjin Wang a, Sheng-Jen Hsieh a,b,n, Xunfei Zhou a, Bo Peng a, Bhavana Singh a a b

Department of Mechanical Engineering, Texas A&M university, College Station, TX, United States Department of Engineering Technology & Industrial Distribution, Texas A&M University, College Station, TX, United States

art ic l e i nf o

a b s t r a c t

Article history: Received 30 April 2015 Received in revised form 29 August 2015 Accepted 31 August 2015 Available online 9 September 2015

The study here demonstrates the capability of thermography to detect and characterize pinhole defects in a visually transparent anti-reflection (AR) film. The diameter of the pin-holes varies from 0.03 mm to 4 mm. Each inspected area was unevenly heated for 65 s. Thermal images were processed by the following steps: de-trend processing, primary edge detection based on Sobel approximation, and further edge separation based on k-means clustering. Then, the diameter of pinholes was directly measured from binary images. The proposed image processing enables thermography to detect 86 of 90 inspected areas correctly in position. & 2015 Elsevier Ltd. All rights reserved.

Keywords: NDT Thermography k-means clustering Anti-reflection films for display screen

1. Introduction The size of a pin-hole defect is one of the dominant factors in the quality control of an anti-reflection coating because the presence of pinholes lowers the usability, degrades the functionality and negatively impacts the user satisfaction. To the best of authors' knowledge, many manufacturers of AR coatings used for viewing applications have set limits on the maximum tolerable pinholes size [1–4]. A commonly acceptable pinhole size for such applications is 0.08–0.1 mm [1–4]. Nowadays, the visual inspection of AR films is still performed manually despite the fact that machine vision technology has existed for several years; furthermore, the manual inspection of defects is tedious and may cause a hazardous working environment [1–7]. Separately, other technologies [8–13] such as atomic force microscopy (AFM) [8], functionalized near-field scanning optical microscopy [9], and photo-thermal related technologies [10,11] have been developed for the detection of small defects in other fields. Their cost efficiency should be considered from the viewpoint of use for AR films for viewing application. Automatic visual inspection using a charge coupled device (CCD) camera provides a much quicker and convenient method to detect defects. In this approach [14], an illumination system and a CCD camera are used to obtain multiple images. Defects are then detected based on the intensity changes caused by them. However, the n

Corresponding author. +1 979 845 4985. E-mail address: [email protected] (S.-J. Hsieh).

http://dx.doi.org/10.1016/j.ndteint.2015.08.006 0963-8695/& 2015 Elsevier Ltd. All rights reserved.

images captured using the CCD camera strongly depend on the viewing angles of the illumination source as the brightness differences caused by pinholes are large enough for the CCD method to capture only within certain view angles [5–7]. The viewing angle is the largest source of error when analyzing images. To improve the inspection capabilities, Tsai [15] and Kim [16] developed two methods to enhance the contrast between the defective and the non-defective areas. To overcome the problems faced with CCDs, thermography, which detects defects based on changes in infrared radiation caused by them, has been proposed [17–20]. The attenuation coefficient of many visually transparent materials, such as PETs [4,21–23], is large in long-wave infrared radiation [24,25]. In other words, the IR radiation intensity through the surface of such a film may change rapidly with the film thickness. The observed IR intensity through the film combines the emitted radiance, which is related to the heat conduction, and transmitted intensity, which is related to the intensity of the illumination source. The larger the attenuation coefficient, the more significant is the emitted radiance due to heat diffusion. This study discusses the possibility of using a thermal image to detect the defects in AR coatings for a flat panel display and proposes image processing methods to measure the diameter of defects from the millimeter to sub-pixel scales. A de-trend process is established based on statics principles behind the infrared image measurement and on heat conduction theories behind thermography testing process. k-mean clustering [26–29] is used to distinguish the edge pixel of a defective and a non-defective area. This study shows that proposed image processing method

H. Wang et al. / NDT&E International 76 (2015) 66–72

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can recognize pinhole defects with sizes from 0.03 to 4 mm and predict their diameters within 0.23 mm.

2. Experimental setup Multilayer AR coatings for a flat panel display (Dexerials Corporation) were used as the sample. The films had an average thickness of 160 μm, and they were designed to be anti-reflective to light with wavelength of 450–670 nm [4]. The emissivity of the AR film had a value of 0.88 when tested under an ASTM code [30]. The overall transmittance of the AR film within a wavelength of 7– 14 μm is 0.22 according to the ASTM code E1897–14 [31]. The samples were cut using a PLS6.120D carbon-dioxide laser system (Universal Laser Systems). The size of the pinholes varied from 0.03 to 4 mm, as presented in Table 1. The pinholes were 130-μmdeep blind holes rather than through holes. All experiments were conducted using the setup shown in Fig. 1. A Compix 222 infrared camera (Compix Inc.) with microbolometer focal plane arrays with a size of 160
120 pixels was set 3.8 cm above the surface of the tested samples. The detectors sensed light ranging from 7 to 14 μm. As a result, a 0.106 mm by 0.106 mm instantaneous field of view (IFOV) was obtained. The camera was calibrated to achieve a noise equivalent temperature difference (NETD) at 0.1 K and accuracy at 72 °C or 2%, whichever is larger. A 60-W incandescent lamp was used as a heating source for the thermography testing. The lamp was located about 5 cm below the sample. The center of the lamp was not held strictly right under the defect. In fact, in all 90 tests, the lamp’s location varied from 0 to 3 cm away from the defect. If the detection results were to show the same quality under such a design, one can conclude that the heating source may not have a dominant effect on thermography detection using the above-described image processing technique. The lamp was kept on for 65 s. During this time, thermal images were captured at a rate of one frame per second.

3. Background and methodology 3.1. Heat conduction theories behind thermography and image processing

Fig. 1. Experimental setup of the test, (1) Compix 222 Infrared Camera, (2) Antireflection film, (3) heating source, (4) Heating source controller, (5) Data center with WINTES2 software.

to radiation can be written as: S ¼ gðrÞf ðdÞuðt Þ  Sem þ Sab

ð2Þ

where g ðx; yÞf ðdÞuðt Þ represents the heat absorbed from the bubble across the surface at different times; Se the emitted heat from the film; and Sab the energy absorbed from the ambient. According to the Beer–Lambert law, the volumetric heat absorption in attenuated media can be expressed as [32]     Z   βe λ i I 0 λ exp  β e d dλ ð3Þ f ðdÞ ¼ 2ke where βe is defined as the effective absorption coefficient for the Anti-reflective film with thickness at d. βe is tested based on total attenuation reflective Fourier transform Infrared spectroscope (ATR-FTIR)   ε2hc2 I0 λ ¼ 5

λ

1   exp κB λðθhcs þ θ Þ  1 0

ð4Þ

Where h and Κ B are Planck’s constant and Boltzmann's constant respectively; c is the speed of light in vacuum; λ is the wave length; and the θ0 is the reference temperature that is equal to the initial temperature of the film. It also equals to the ambient temperature. Under the experimental conditions used in this study, the heat source is a step function of time:  1 t Z0 uðt Þ ¼ 0 t o0 The heat gain from the bottom side of the film can be expressed as:

The pinhole defects in an AR film have different optical properties and thickness from the AR film itself. As the temperature variance over the horizontal direction is far larger than that across the depth, a lumped temperature across depth is considered. Furthermore, as the system is radially symmetric if there is no defect, the heat conduction model is reduced to one dimension: ∂θ ∂ θ α ∂θ S ¼α 2þ þ ∂t r ∂r ke ∂r 2

ð1Þ

where θ is the temperature increment from the initial temperature of the film to the current film temperature θf ðtÞ; α the thermal diffusive coefficient of the film; and ke , the thermal conductivity of the AR film. And the S is the heat source due to light absorption and emission. If the heat source caused by chemical reaction, heat convection, or phase change at surface can be neglected, the heat source due Table 1 Dimension of pinholes. Diameter (mm) No.

4 10

3 10

2 10

1 10

0.7 10

0.4 10

0.2 10

0.08 10

0.03 10

Sem ¼ F b ðx; yÞεe σ Sab ¼ F b ðx; yÞεe σ





θ þ θ0

4 

θab þ θ0

4 

ð5Þ ð6Þ

where F b is the view factor. During heating, although the temperature of the AR film increases by 20 °C, the heat loss due to radiation is smaller than the heat gain. The lumped temperature of the AR film can be solved by applying the Fourier transform temporally and the Hankel transform spatially to Eq. (1): " # rffiffiffiffiffiffi ! Z Z 1  βe I 0  i iω θ¼ exp  βe d dλ  K r  g ðr Þ eiωt dω; 2ke ω 0 α 1 ð7Þ where K 0 ðxÞ is a modified Bessel function of the second kind at zero order: Z 1 cos ðxtÞ pffiffiffiffiffiffiffiffiffiffiffiffi dt; K 0 ðxÞ ¼ 0 t2 þ 1

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H. Wang et al. / NDT&E International 76 (2015) 66–72

K0

qffiffiffiffi  iω α r is the convolution of the function and g(r) over the

radius. The temperature of the AR film is observed to increase as the film thickness decreases. The temperature readings θreading from a bolometer infrared camera depend on both the surface temperature and the transparent radiance from an incident source for a semi-transparent film at a pixel, since the energy sensed by a single bolometer cell M is the sum of emitted radiance and transparent radiance:

θreading ¼ Δθr þ θreference þ εr

ð8Þ

Δθr ¼ M U G

ð9Þ





G ¼ F b εe σ θ  θab þ 4

4

Z

    F b Τ λ I 0 λ dλ

ð10Þ

where   Τ λ ¼ 10  βe d

ð11Þ

εr is the random error introduced by the characteristics of microbolometer cell. By substituting Eqs. (7) and (9)–(11) into Eq. (8), one can find that the bolometer readings increases as the film thickness d decreases owing to the increase in both the temperature and the transmitted radiance; in contrast, visual inspection can only detect defects based on the change in transmittance at the defect area. Moreover, the transmittance of visual light is affected little by the film thickness as AR films with thickness of the order of 100 μm are usually transparent to visual light. IR camera readings θreading described in Eq. (8) is smooth if there is no random errors. In other words, a harsh change in the spatial gradient of the temperature indicates the boundary of a defective area or noise at this location. However, if an uneven heating source is applied, IR camera readings θreading is uneven even though there is no random errors. Under this condition, IR camera readings θreading bends spatially following a certain curve described by Eqs. (7)–(11) for non-defective areas. The unevenness of infrared readings causes a problem [36–38]. When using spatial derivations, which were used to detect the edge of defective areas [33–35], to detect defects in the film: once the main trend of the derivations of the thermal image is close to the level of the change caused by a defect, the defect edge may become blurred based on derivations. The contrast of thermal images is affected by nonhomogenous heating (Eq. (7)) [36–38], this occurs frequently for small-sized defects. Therefore, a method to reduce the impact of non-homogenous heating on the image should be applied. The phase image is commonly used for this purpose [36–38]. However, recent numerical simulations have shown that the phase image has limited capability to eliminate the effect of a temporal stepwise non-homogenous heating source [39]. According to an analysis of thermography processing, the trend of the thermal image can be estimated. Based on the definition of 1 P xn the exponential function: expðxÞ ¼ limn-1 n! , the temperature n¼1

at a given time t can always be approximated by a high-order twodimensional polynomial equation within a given area as n limn-1 xn! -0. In other words, the general trend of the Infrared camera reading can be approximated by a high-order polynomial equation. If the order of polynomial equation is high enough, the fitted model θðx; yÞvf should be able to represent the Infrared camera readings θreading ðx; yÞ [40,41]. The value of random noises should take a large portion of the residuals between the thermal readings and the fitted values: 

εr ðx; yÞ  θ ði; jÞ ¼ θðx; yÞvf  θreading ðx; yÞ 

θ ði; jÞ also refers to the de-trended temperature in the following paragraphs.

That is to say, the residuals from a good fitting model should follow normal distribution [40–42]. In this research, the average of ninth order polynomial fittings along x and y direction separately was selected to fit the image based on least square regression:  1 θðx; yÞvf ¼ θj ðyÞvf þ θi ðxÞhf 2

θi ðxÞhf ¼

9 X

bk xk :

k¼1

θj ðyÞvf ¼

9 X

ak yk ;

k¼1

with constrains:   2   j ¼ 1; 2; …:N; J j ϕ ¼ min SUMð θði; jÞMeasured  θj ðiÞvf Þ   2   i ¼ 1; 2; …:M: J i ϕ ¼ min SUMð θði; jÞMeasured  θi ðjÞhf Þ The order of the model is determined by F-test [40,41]. The sum of squares due to error (SSE) is calculated to evaluate the goodness n  2 P wi yi  y^i . For all fittings for 90 tested of each fitting: SSE ¼ i¼1

areas in this study, the maximum SSE is 0.271. The residuals of each fittings from non-defective area are randomly positive and negative based on runs tests [40,41]. The distribution residuals of the model were tested with Shapiro–Wilk test [42–44]. Test results show that the residuals from the non-defective area follow normal distribution as expected. The proposed curve fitting models fit each images well. The above process is also called de-trend filter. After detrending, the defective pixel should be separated from the background so that the size of the pinhole can be calculated. Sobel edge detection is commonly used to extract a defective feature from inspection images. Sobel edge detection for each thermal image can be expressed as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gi ¼ G2x;i þ G2y;i i ¼ 1; 2; 3…65 Gx;i ¼ hx  Ai ; Gy;i ¼ hy  Ai ; where Gi stands for the edge detection image based on Sobel approximation for de-trended images derived at each data point, and hx ; hy are so called Sobel kernels. Ai is the de-trended image derived at each data point. For each single image, the Sobel edge detection algorithm detects the boundaries of defects as well as, occasionally, some noise. However, as white noise does not appear at the same pixels along time, the defect edges take heavy weights in the sum of binary images over time while the noise will be eliminated automatically. Thus, a new binary Gcredit ðx; yÞ image is generated for each pinhole with the equation below: Gcredit ðx; y Þ ¼

65 X

Gi ðx; yÞ

i¼1

k-means clustering is a widely used centroid-based clustering algorithm [30–39,45–47]. It aims to separate all n observations (x1 ; x2 ; x3 ; …xn ) into k (k on) clusters, {S1 ; S2 ; S3 …Sk }, in such a way that each observation belongs to the cluster with the nearest mean. In other words, in k-means clustering, the square sum within one cluster is minimized: argmin S

k X X i ¼ 1 x A Si

‖x  μi ‖2 ;

H. Wang et al. / NDT&E International 76 (2015) 66–72

where μi are the mean points of Si . To achieve this minimization objective, several general steps should be followed [36].

69

4. Data processing and results 4.1. Image-streams based defect recognition

3.2. Methodology of image processing In general, several steps are applied to identify, extract, and estimate the diameter of the pinhole area, as shown in Fig. 2. The trend of original images was estimated using high-order polynomial curves based on the thermal response under thermography by the method described in Section 3.1. The de-trend images were prepared. Then, edge detection based on Sobel approximation was applied to extract the boundary of the defective area. Taking into account the noise in the thermal images, the Sobel edge detection method was applied to each de-trended image. As the algorithm was implanted in MATLAB, the threshold for Sobel edge detection was determined by MATLAB automatically [47,48]. Then, the binary images of edges based on Sobel approximation were convoluted over each image sampled at each second after heating began. The new images were used as the input of k-means clustering. Then, the diameter of the defective area was measured based on the method described in Hsieh's study [49]. k-means clustering returned defective and non-defective clusters as results. The coordinates of the pixels in defective clusters were stored for diameter calculation.

Fig. 2. Data processing.

The original image is shown in the left-hand side of Fig. 3. Obviously, the background area was not uniform owing to nonhomogenous heating. By applying the de-trend filter described in Section 3, the background was flattened (uniform with noise), as shown in the right-hand side of Fig. 3. We noted that when the defective area was relative large (in Fig. 3, the diameter of the defective area is around one-third the width of the image), the polynomial curve may followed the trend inside the defective area. However, owing to the sharp spatial change in temperature, the polynomial curves did not follow the trend at the boundaries between defective and non-defective areas. After de-trending, the edge of the defect area becomes extremely clear. The edge of the defect (dark circle in the righthand side of Fig. 3) differed significantly from the average readings of all pixels. The de-trend filter is essential for detecting small-sized pinholes. The top figure in Fig. 4 compares the horizontal thermal profile of pinholes with 0.08-mm diameter and the estimated trend based on polynomial curves. The polynomial curves well approximated the trend of the surface temperature. By subtracting the estimated trend from the thermal image, the de-trended thermal profile (residuals of the model) was obtained as shown in the middle figure of Fig. 4. The difference in the de-trended temperature between the defective pixels and the average of the non-defective pixels was significant larger than that between nondefective pixels in the de-trended thermal image (Fig. 4 middle). Our study found that binary edge images based on the de-trended temperature (Fig. 4 bottom right) showed the boundary of a defect clearly whereas those based on the original image (Fig. 4 bottom left) failed to indicate the position of a defect. Fig. 5 shows a set of pictures obtained based on the image processing method described in Fig. 2. The proposed algorithm extracted the features of defects with little noise. The circles with solid gray lines in Fig. 5 indicate the designed defect position and their diameters. The thermography image detected pinholes located at the margin area. All tests were reported as responding correctly. For pinholes with diameters of 0.2, 0.08, and 0.03 mm, 10 tests were conducted for each size. No false negatives or positives were reported for diameters greater than 0.03 mm. For pinholes with 0.03-mm diameter, two false positives and two false negatives were reported (as presented in Table 2). This indicates that the position of the heat source relative to the pinhole does not seem to play a significant rule in the detection of pinholes with

Fig. 3. Original thermal image vs. de-trended image.

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H. Wang et al. / NDT&E International 76 (2015) 66–72

Table 2 False negative error and false positive error for each pinhole diameter. Diameter (mm)

4

3

2

1

0.7

0.4

0.2

0.08

0.03

Tested times False positive False negative

10 0 0

10 0 0

10 0 0

10 0 0

10 0 0

10 0 0

10 0 0

10 0 0

10 2 2

Table 3 Estimated diameter (Est. dia.), standard deviation (Std. of est. dia.), and average estimation bias based on algorithm.

Fig. 4. Thermal profile, top – original thermal profile with estimated base trend, middle – de-trended thermal profile; bottom – edge detection result for Pin hole with 0.08 mm without (left) and with (right) de-trending.

Pinhole dia. (mm)

Est. dia. (mm)

Std. of est. dia. (mm)

Average bias (%)

4 3 2 1 0.7 0.4 0.2 0.08 0.03

3.91 2.96 2.17 1.16 0.89 0.53 0.25 0.26 0.27

0.25 0.06 0.27 0.13 0.07 0.05 0.02 0.02 0.00

 2.17  1.48 8.67 15.91 26.50 33.32 26.42 227.59 801.25

Table 3 presents the calculated pinhole diameter based on thermography. Obviously, the diameters estimated by the proposed method responded to the variance of the pinhole diameter for diameters exceeding 0.2 mm. However, pinholes with diameters less than 0.2 mm were detectable but not recognizable based on the proposed method as they were smaller than one pixel in size. For pinholes with diameters less than 0.2 mm, the infrared camera identified them as 0.2-mm diameter holes with a predicted diameter of 0.27 mm. Simultaneously, the estimated size of pinholes with diameter greater than 0.2 mm approximates the named defect size. The difference between the average estimated diameter and the named diameter for pinholes with 0.03-mm diameter can be as large as 700%. However, this number decreases to 3% for pinholes with 4-mm diameter. For pinholes with diameters of 0.2–1 mm, the estimated diameter is always 25–33.3% larger than the named diameter on average. Furthermore, in all 90 tests, the proposed method predicted pinhole diameters that were greater than the actual size. The standard deviation for an estimated pinhole diameter of 0.03 mm was 0.004 mm; that for a pinhole diameter of 0.08 mm was 0.0165 mm; and that for a pinhole diameter of 0.2 mm was 0.015 mm. The algorithm estimates multiple-pixel defects with acceptable accuracy. However, it overestimates the diameter of sub-pixel defects. Therefore, an algorithm to recognize subpixel defects should be developed. 4.2. Discussion about the dimension of sub-pixel defect recognition algorithm

Fig. 5. Binary images for a set of detected areas.

diameters exceeding 0.08 mm as all ten areas inspected for each pinhole size were detectable.

The sub-pixel defect can just irradiate part of a pixel or irradiate a 2
2 pixel partially. Therefore, the temperature measured using the infrared camera will be underestimated. For a sub-pixel defect to be recognized from a thermal image, the temperature change caused by the defect should be greater than the noise equivalent temperature. An interesting phenomenon was observed in the experiment. The pinhole area did not illuminate the FPA detectors as soon as the heating source was turned on. Instead, even the largest defect took about 10 s to become recognizable from the thermal image. The time required for sub-pixel defects may be longer than that required for large defects. The image below compares the time required to show 0.2-mm-diameter pinholes (larger than IFOV)

H. Wang et al. / NDT&E International 76 (2015) 66–72

71

Fig. 6. Time sequence for appearance of defect boundary in thermal image.

and that for 0.08-mm-diameter pinholes and 0.03-mm-diameter pinholes (smaller than IFOV). The tests were conducted nine times each on pinholes with diameters of 0.03, 0.08, and 0.2 mm. The yaxis showed the time after the heating source had been turned on. After the defects were recognized according to the abovedescribed method, the significance of the defect at each sampling point was determined by the Sobel edge detection algorithm. The brightness in Fig. 6 shows what percentage of the defect boundaries was detected by the Sobel operator at each sampling point for each sample. In other words, if a pure white bar was seen in a trial at some sampling point, it meant that a complete boundary was shown at that time in that trial. A concept called critical time is introduced here. It is defined as the first time at which 70% of a defect edge can be observed continuously for 5 s. This study shows that the critical time for edges of a 0.2-mmdiameter pinhole could be detected no later than 20 s. For 0.08mm-diameter pinholes, 25–35 s were required for 70% of their edges to be continuously detectable in the thermal image. However, the edges of 0.03-mm-diameter pinholes may appear earlier than those of 0.08-mm-diameter pinholes but later than those of 0.2-mm-diameter pinholes.

5. Conclusion This study shows the possibility of using a thermal image to detect the defects in AR coatings for a flat panel display and proposes corresponding image processing methods to measure the diameter of defects from the millimeter to the sub-pixel scales with speeds of 17 mm
13 mm/min. With de-trending, the proposed algorithm can recognize pinhole defects in the AR film with diameters as small as 0.03 mm. The proposed method suffers from a false positive and false negative rate of 2.2% each in all the 90 tested areas. It also indicates that the position of the heat source relative to the pinhole does not seem to play a significant role in the detection of pinholes with diameters exceeding 0.08 mm as all the ten areas inspected for each pinhole diameter are detectable. This study shows that the proposed image processing method can detect pinhole defects with diameters of 0.03–4 mm and predict their diameters. For large pinholes with diameters of 1–4 mm, the algorithm can predict the diameter with 3% bias. However, for pinhole diameters of 0.03 mm, the algorithm predicts the diameter with 700% bias although it recognizes such sub-pixel defects. The thermal images show that there is a difference between the critical time when the defect can be recognized from the thermal images after heating begins among all tested sub-pixel

defects. However, the accurate correlation between the defect diameter and the critical time requires further study.

Acknowledgments The authors sincerely thank Dexerials Corporation for providing the AR 1.5 thin films that were used as the inspected samples. The authors also thank Texas A&M University Laboratory for allowing the use of their facilities for the synthetic-biologic interactions. Finally, the authors would like to thank Mr. Richen Li.

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