Analysis of signal processing techniques in Pulsed Thermography

Fernando Lopez*a, Clemente Ibarra-Castanedob, Xavier Maldagueb, Vicente de Paulo Niculaua

a Dept. of Mechanical Engineering, Federal University of Santa Catarina, 88040-900, Florianopolis, Brazil. b Electrical and Computing Engineering Dept., Laval University, G1K 704, Quebec City,

Canada

ABSTRACT

Pulsed Thermography (PT) is one of the most widely used approaches for the inspection of composites materials, being its main attraction the deployment in transient regime. However, due to the physical phenomena involved during the inspection, the signals acquired by the infrared camera are nearly always affected by external reflections and local emissivity variations. Furthermore, non-uniform heating at the surface and thermal losses at the edges of the material also represent constraints in the detection capability. For this reason, the thermographics signals should be processed in order to improve – qualitatively and quantitatively – the quality of the thermal images. Signal processing constitutes an important step in the chain of thermal image analysis, especially when defects characterization is required. Several of the signals processing techniques employed nowadays are based on the one-dimensional solution of Fourier’s law of heat conduction. This investigation brings into discussion the three-most used techniques based on the 1D Fourier’s law: Thermographic Signal Reconstruction (TSR), Differential Absolute Contrast (DAC) and Pulsed Phase Thermography (PPT), applied on carbon fiber laminated composites. It is of special interest to determine the detection capabilities of each technique, allowing in this way more reliable results when performing an inspection by PT.

Keywords: thermographic signals processing, thermographic signal reconstruction, differential absolute contrast, pulsed phase thermography, composites materials

1. INTRODUCTION Active Thermography as a Nondestructive Testing (NDT) technique is based on the use on an external stimulation in order to provoke an internal heat flux which will be altered by the presence of internal defects within the material. This variation in the heat diffusion rate will produce in turn a thermal gradient on the surface which can be detected by using an infrared camera. Currently, various mode of external stimulation techniques are available, i.e. mechanical (mechanical vibrations), electromagnetic (Eddy current induction) and thermal/optical excitation (pulsed, lock-in, and long pulse), each one having different physical aspects, advantages and disadvantages. This work in focused on thermal/optical excitation methods, more specifically the inspection by Pulsed Thermography.

PT is one of the most attractive NDT techniques because of its quickness and easiness over other classical methods that use optical/thermal excitation. This NDT method relies on the application of a short thermal stimulation pulse (with duration lasting from a few , , to , depending on the thermal properties and thickness of the material) while observing the temperature evolution during the subsequent cooling regime. Abnormal behavior of cooling curves reveals subsurface defects. As heat sources, high power photographic flashes are typically employed.

Even though the advantages of PT, one of the main constrain is concerned to the non-uniform heating due to the application of the thermal/optical excitation, which is an unavoidable problem in the configuration of the irradiation sources. The negative effects associated to the non-uniformity of the heating considerably limit the results of the inspection. Reduction of the spatial resolution (affecting smaller defects) as well as the limits of detection (affecting deeper defects) are among the most important side-effects. Furthermore, it is almost unlikely to obtain reliable results when performing quantitative analysis (size and depth retrieval) of defects with raw data.

Most of the problems that arise from the non-uniform heating can be considerable reduced through the implementation of signal processing techniques to the raw data obtained from a PT inspection. In this work will be discussed and

*ferlopezr@gmail.com; phone 418 261-1780

Thermosense: Thermal Infrared Applications XXXV, edited by Gregory R. Stockton, Fred P. Colbert, Proc. of SPIE Vol. 8705, 87050W · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2015949

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analyzed three techniques based on the solution of the 1D Fourier equation of heat conduction that have greatly improved the reduction of noise contents in raw data: Thermographic Signal Reconstruction (TSR), Differential Absolute Contrast (DAC) and Pulsed Phase Thermography. An inspection by PT is carried out over an academic carbon fiber reinforced polymeric specimen. The three processing techniques are applied over the thermogram sequence obtained during the experiment. A quantification of signal-to-noise ratio is carried out in order to evaluate the performance of each of the techniques.

2. FUNDAMENTALS OF PULSED THERMOGRAPHY Pulsed Thermography consists on the application – via radiation heat transfer – of a short and high power thermal pulse to the specimen surface. Once this energy is absorbed by the surface, it generates a thermal front which propagates by diffusion through the material. Subsurface defects – characterized by the difference of thermal properties in relation to their surroundings – will affect the heat diffusion rate producing then abnormal temperature patterns (or thermal contrasts) which can be detected with an infrared camera.

The thermal process and the subsequent analysis behind the inspection by PT are depicted in Figure 1. The inspection begins at ambient temperature , from which the thermal excitation is applied at the surface of the material. The absorption of energy produces a rapid increase of the temperature up to ; from which a cooling process takes place induced by the exchange of heat (by convection and radiation) between the material surface and the ambient and also by the diffusion of heat through the material. From the beginning of the cooling process (at time ) is carried out the acquisition of the thermal images with an IR camera until time , at which the presence of convective effects make more difficult the detection of thermal contrasts inherent to internal defects.

(a) (b)

Figure 1. Thermal process involved during the deployment of an inspection by pulsed thermography and temperature evolution curves of defective and sane area when > .

As showed in Figure 1a, the temperature decay curves of both – defective and sound area – behave similarly at the beginning of the cooling process. Once the thermal front reaches the internal defect, the accumulation of heat produced by the defective region originates an increase of temperature over the defective area on the surface. This “breaking point” between and occurs at (see Figure 1b), initiating the temporal detection window, time over which the defect is visible. The occurrence of and depend on the thermal properties of the material and depth of the defects. The determination of constitutes one of the main steps in order to characterize the depth of defects. The experimental approach as well and as characteristics of the specimen used in this work are discussed next.

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3. EXPERIMENTAL APPROACH The experimental approach consists on the employment of an FPA infrared camera (Santa Barbara Focalplane SBF125, 3 to 5 µm, with a 320x256 pixel array) to monitor the temperature of the specimen along the cooling process induced by the application of a thermal excitation pulse. Two high power photographic flashes (Balcar FX 60), giving 6.4 KJ for 15 µm each, are used as a thermal source. The acquisition is performed using a sampling frequency of 157 Hz. Thermographic raw data is analyzed and processed using Matlab® language from the Mathworks, Inc. The geometric configuration of the specimen used in this work along with the position of the Teflon insertions is showed in Figure 2.

Figure 2. Academic CFRP006 specimen with Teflon insertions.

The specimen consists of a 10-plies carbon fiber reinforced polymer with 25 Teflon square insertions at different depths (0.2 < < 1.0 ) and lateral sizes (15 < < 3 ). The inspection was carried out under the reflection mode, where the infrared camera and the heat sources are in the same side of the specimen. A total of 1000 frames were collected to apply then each of the processing techniques under discussion in this work. However, before continue with the thermographic processing techniques, it is important to establish a sampling methodology of signals from defective and non-defective regions. This matter is explained in details in next paragraphs.

3.1 Thermal contrast

In both – qualitative and quantitative analysis – it is crucial to determine a variable with which may be possible to account how strong or how weak is the signature of a defect – or in other words, its visibility –. When dealing when thermal images this variable is the absolute thermal contrast ∆ ( ), which is defined as [1]: ∆ ( ) = ( ) − ( ) ( 1 )

being ( ) and ( ) the temperature evolution of a defective and non-defective region. However, one of the downside of using Eq. (2) is the requirement to establish a reference point (or region) as a sound area. In most cases, the computation of ∆ ( ) will differ as a function of the localization of the non-defective region, mainly because of the effects of non-uniform heating (see for instance [2]). In order to avoid these inconvenient, in this work and are computed as follows:

= ( , ). ( 2 )

= ( , ). ( 3 )

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In Equations ( 2 ) and ( 3 ), and correspond to the signals of the defective and non-defective regions. is computed as the mean value over the entire defective region. In similar manner is computed as the mean value over the surrounding of the defective area. Figure 2 shows the methodology used in this work to calculate and . The area over which the mean value is calculated is based upon the lateral size of the defective region. All the calculation and techniques discussed in this paper are based on Equations ( 2 ) and ( 3 ).

Figure 3. Selection of defective (red square) and non-defective (blue square) regions for different lateral

sizes of defects.

4. SIGNAL PROCESSING TECHNIQUES IN PT This section is dedicated to discuss the basic theory and application of each of the signal processing techniques subject of study in this work.

4.1 Thermographic Signal Reconstruction

As it name implies, TSR is based on the use of a low order polynomial function to reconstruct – or to fit – the temperature evolution curve obtained from an inspection by PT. Assuming that the temperature decay of a free-defect region behave in a similar manner as the solution of the 1D Fourier equation of heat conduction, the temperature evolution of a non-defective area can be written in logarithmic form as: ( − ) = − 12 ln( . ) ( 4 )

In Eq. ( 4 ) is the initial temperature whereas is the variable temperature; is the applied heat energy as external stimulation, is the thermal effusivity of the material [defined as = ( ) / ] and is the time. From Eq. ( 4 ) it is possible to model the temperature evolution of a free-defect region as a fixed and straight line with slope = −0.5. This linear and fixed-slope behavior is independent of the thermal properties and the applied heat flux (see second term of Eq. 4). Obviously, defective regions will diverge from linearity.

Shepard [3] proposed to use an m-degree polynomial function to approximate the logarithmic time dependence of thermographic data. This polynomial function can be written as: ( − ) = + ( ) + ( ) + ⋯+ ( ) ( 5 )

There are significant improvements on the use of synthetic data obtained through the application of TSR, such as: reduction of high frequency noise, data compression (from to m+ 1 images), increasing of temporal and spatial resolution [4]. Furthermore, calculation of first and second time derivatives using synthetic data brings important signal improvement due to the reduction of blurring effect present in temperature raw data (blurring effects are inherent to the lateral heat diffusion at later times). This is because the times at which occur changes in first (rate of cooling) and second time (rate of change in the rate of cooling) derivative are shorter than in raw thermal images.

Figure 3 shows the temperature (column a), first derivative (column b) and second derivative (column c) profiles obtained after the implementation of TSR on the raw data obtained in the PT inspection to the CFRO006 specimen. The plotted profiles correspond to defects located at 0.2 mm (on top) and 0.6 mm (on the bottom) depth, both having 10 mm of lateral size. A 6th degree polynomial was used to fit the experimental data. The corresponding sound area (red lines) for each defect is also plotted together with the contrast evolution (green lines) between the defective and sane region. As mentioned above, the temperature evolution curve in logarithmic scale for a free-defect region behaves linearly doesn’t matter where the sound area is located. It can be also observed that the intensity of the thermal contrast diminishes as the

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depth increases. Furthermore, the time of occurrence of the maximum contrast in first and second derivatives profiles takes place at earlier times than in temperature raw images, reducing then the effects of blurring.

(a) (b) (c)

Figure 4. Temperature (a), first time derivative (b) and second time derivative (c) profiles obtained after the implementation of Thermographic Signal Reconstruction, for defects located at 0.2 mm and 0.6 mm depth.

Notwithstanding the significant reduction of high frequency noise content in thermographic raw data, synthetic raw data is still vulnerable to non-uniform heating. This can be noted in the thermal contrast evolution curve of the defect located at 0.6 mm depth, where an abnormal oscillation of the curve takes place due to the effects of the non-uniform heating.

4.2 Differential Absolute Contrast

Differential absolute contrast (DAC) [1] is one of the first technique developed as an alternative to the classical thermal contrast computations and all the inherent problems that brings with it (non-uniform heating, emissivity variations and environmental reflections). Based on the solution of the 1D Fourier heat equation, DAC looks for a at time which is computed locally assuming that on the first few images all points behave as a sound area [5]. Thus, the thermographic data obtained from a PT experiment can be approximated to the 1D solution of heat equation through following expression [5]:

∆ = ( ) − ∙ ( ) ( 6 )

The first step in the implementation of the DAC method is to define ′ as a given time value between the instant when the thermal excitation is applied , and the precise moment when the first defective spot appears on the thermogram. It is important emphasize that Eq. (6) is a good approximation at earlier times. As time elapses, Eq. (6) will diverge from the semi-infinite case.

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4.3 Pulsed Phase Thermography

Pulsed Phase Thermography (PPT) [6] is a processing technique based on the superposition principle, which states that a time-domain response ( ) may be obtained from a frequency-domain response using Fourier expansion: ( , ) = ( ) ( , , ) ( 7 )

in which ( , , ) is a plane thermal wave of angular frequency propagating in the -direction and ( ) is a measure of the strength of this component in the transient concerned. Physically, the diffusion of heat from the surface into the solid can be understood in terms of the propagation of these thermal waves into the solid away from the surface. The different frequency components will suffer different amounts of attenuation, increasing or decreasing the penetration of each of the thermal waves. It is because of this duality between the transient and harmonic problem that PPT is considered as the link between Pulsed and Lock-in Thermography [7].

In PPT the data is transformed from the time domain to the frequency domain using the one-dimensional discrete Fourier transform (DDT) [8]:

= Δ ( Δ ) = + ( 8 )

where is the imaginary number, designates the frequency increment ( = 0,1, … , ), Δ is the sampling frequency interval, and and are the real and imaginary part of the transform, respectively. Although from Eq. ( 8 ) is possible to obtain amplitude and phase , fast Fourier transform algorithms are available in commercial in packages such as Matlab.

There are two major aspects that make PPT a powerful processing technique having advantages over other routines; one of them is the phase which is less affected than raw thermal images by environmental reflections, emissivity variations and non-uniform heating. The other aspect is concerned to the application to other type of signals that do not follow the solution of the 1D Fourier Equation, increasing its depth probing capabilities to deeper defects. Notwithstanding these advantages, phase data in PPT is very sensitive to high frequency noise. Figure (4) shows the ringing effects when selecting different truncation windows. In Figure 4a, a truncation window of 43.7 s was used to apply the Fourier transform, while in Figure 4b the truncation window was of 68.4 s. Increasing the value of the truncation window will introduce high-frequency thermal waves, producing oscillation especially in deeper defects.

(a) (b)

Figure 5. Phase profiles for defects located at 0.2, 0.6 and 0.8 mm depth. Truncation windows used to apply the FT are: (a) ( ) = 43.7 and, (b) ( ) = 68.4

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-

Besides of interfering in the determination of the blind frequency - which is a crucial step in quantitative analysis of defects - these high-frequency oscillations increase the noise in the phase images. Figure 5 shows two phasegrams corresponding to the lowest frequency available ( ) for two different truncation windows. In 5a the phasegrams correspond to = 0.0457 while in 5b the lowest frequency is = 0.0329 . Along with the phasegrams are profile along the yellow line (on top) and the image histograms (on the bottom).

(a) (b)

Figure 6. Lowest frequency phasegrams obtained for two different truncation windows.

It is important to highlight that although there is a reduction of the frequency resolution when reducing the truncation window, high frequency noises is almost eliminated allowing the better SNR for deeper and smallest defects.

5. PEAK SIGNAL TO NOISE RATIO Signal to Noise Ratio (SNR) is a physical measure of the sensitivity of an imaging system. In this work this variable is used to determine the performance of each of the signal processing techniques previously discussed. From this quantification it is also possible to determine which processing technique is more suitable for a certain situation, based on: thermal properties of the material, defect depth and size. Generally, SNR can be calculated using the following expression: = (7)

being and the amplitude of the signal and noise respectively. The signal can be either thermal or phase contrast, or any of the quantities obtained when performing first and second derivative on synthetic temperature data. Signal amplitude is calculated using Equations (3a) and (3b), while the noise is determined from the variance over the entire defective region (as previously described in Figure 2). Eq. (7) can be also expressed in logarithmic decibels. In decibels, the SNR is defined as [9]: = 10 ∙ = 20 ∙ (8)

In other to calculate the Peak Signal to Noise Ratio (PSNR), either the amplitude of the signal and the noise should be measured at its maximum power . Thus, the PSNR in decibels can be expressed as: = 20 ∙ − 20 ∙ (9)

σ = 0.024 σ = 0.0347

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The selection of is inherent to a particular defect. Depth, size and the method used as a processing technique will determine the time of occurrence of . The results obtained from this analysis are presented in next section.

6. RESULTS AND DISCUSSION Figure 7 shows a comparison between synthetic raw data (first row), first derivative (second row), second derivative (third row) and DACs images (fourth row) at (a) 1.36 and (b) 10.86 s. At the right is also the histogram of each image with a fitted normal function displayed to evaluate the noise content on each image. As it can be observed, there is a considerably reduction of noise when is applied any of the thermographic signal processing technique compared to raw data. Although synthetic data reduce high frequency noise, is still affected by non-uniform heating.

(a) (b)

Figure 7. Comparison between synthetic raw data (first row), first derivative (second row), second derivative (third row) and DACs images (fourth row) at: (a) = 1.36 and, (b) = 10.86 .

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As expected, there is an increase on the overall noise at later times since the approximation of each technique diverge from the 1D Fourier equation. First derivative images provide a good performance over the other techniques in terms of noise reduction in both, at earlier and later times.

Figure 8 shows the comparison of the PSNR calculation using three techniques discussed in this work (TSR, DAC and PPT).

(a) (b)

(c) (d)

(e)

Figure 8. Comparative results of PSNR of all three techniques (TSR, DAC and PPT) showing the PSNR for defects located at: (a) 0.2mm, (b) 0.4 mm, (c) 0.6mm, (d) 0.8 mm and, (e) 1.0 mm depth.

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As expected, the highest PSNR were obtained in the defects located at 0.2 mm depth (see for instance Figure 8a). Furthermore, there is a considerably reduction of the PSNR as the depth of the defects increase, produced by the blurring effects which is more sensitive in deeper defects.

DAC presented a good performance at earlier times (in other words, shallower defects); however, as the times elapses the noise content in the signal is greater than amplitude of the thermal contrast. For this reason the PSNR for the defects with lateral size 5 mm and 3 mm and located at 0.8 mm and 1.0 mm depth are negligible (see Figure 8d and 8e). The best detectability for the deepest defects is obtained with first derivative images and PPT, even for the smallest defects. In general terms best results can be achieved using TSR (first derivative), being PPT affected with high frequency noise. However, different de-noising methods for PPT are being considered in order to reduce harmonic oscillations [9].

7. CONCLUSIONS The theory and application of three of the most popular signal processing methods were revised and discussed in this work. The implementation of these techniques was carried out on raw data obtained from a Pulsed Thermography inspection of a carbon fiber reinforced polymer. Results obtained from the application of TSR and DAC on raw thermographic data showed that there is a limit – which depends on defect depth and observation time – until which those techniques can be effectively employed. The range of application using TSR is greater than in DAC. In the other hand, PPT is strongly affected by high frequency oscillation of the signal after the application of the Fourier transform. Recent studies suggest that it is possible to apply de-noising in order to eliminate or reduce such oscillations. Nevertheless, even considering these drawbacks, PPT provided the best probing capabilities together with first derivative images.

REFERENCES

[1] Maldague, X., [Theory and Practice of Infrared Technology for Nondestructive Testing], John Wiley & Sons, New York, (2001).

[2] Ibarra-Castanedo, C., Bendada, A. and Maldague X., "Thermographic image processing in NDT," in IV Conferencia Panamericana de END, (2007).

[3] Shepard, S.M. "Advances in pulsed thermography," in The International Society of Optical Engineering, Thermosense XXVIII, ( 2001).

[4] Shepard, S.M., Lhota, J.R., Rubadeux, B.A., Ahmed, T. and Wang, D., "Enhancement and reconstruction of thermographic NDT data," in SPIE - The International Society for Optical Engineering, Thermosense XXIV, (2002).

[5] Pilla, M., Klein, M., Maldague, X. and Salerno, A., "New Absolute Contrast for Pulsed Thermography," in Proc. QIRT, Dubrovnik, (2002).

[6] Maldague, X. and Marinetti, S., "Advances in pulsed phase thermography," Infrared Physics and Technology, (42), 175-181 (2002).

[7] Ibarra-Castanedo, C., Genest, M., Guibert, S., Piau, J., Maldague, X. and A. Bendada, "Inspection of aerospace materials by pulsed thermography, lock-in thermography and vibrothermography: a comparativr study," in SPIE, Thermosense XXIX, (2007).

[8] Bracewell, R., [The Fourier Transform and its Application], McGraw-Hill, Toronto, (1965).

[9] Huynh-Thu, Q. and Ghambari, M. "Scope of validity of PSNR in image/video quality assesment,"Electronic Letters, 44(13), 800-801 (2008).

[10] Ibarra-Castanedo, C., Piau, J., Guilbert, S., Avdelidis, N., Genest, M., Bendada, A. and Maldague, X."Comparative study of active thermography techniques for the nondestructive evaluation of honeycomb structures," Research in Nondestructive Evaluation, (20), 1-31 (2009).

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