Sub-surface Thermal Wave Imaging

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1 Sub-surface Thermal Wave Imaging Professor Suneet Tuli January 20, 2011 Contents 1 What is Thermal Non-Destructive Testing (TNDT) 1 2 Basic concepts of thermal imaging system Stefan s law of radiation Wien s displacement law Atmospheric transparency for infra-red waves Infra-red camera Pseudo-coloring of infra-red images Classification of thermography techniques Passive thermography Active thermography Important parameters calculated from recorded thermogram sequence Thermal contrast Phase and magnitude image Theory of 1-Dimensional thermal wave 5 6 The experiment Sample description and experimental setup Estimation of excitation frequency Capturing thermal movies Image processing: Phase and amplitude image Experimental steps (at a glance) Conclusion 13 1 What is Thermal Non-Destructive Testing (TNDT) NDT stands for Non-Destructive Testing of materials in the context of hidden defects. In recent years, industries are heavily dependent on it to ensure 100% reliability of their products. There exists many well established techniques which are deployed to search for defects inside the materials, e.g. ultrasonic testing, X-ray imaging etc. TNDT is a relatively new NDT method where thermal wave is used for sub-surface defect detection. It is a whole field technique as opposed to the traditional point-by-point ultrasonic inspection. Further it is relatively cheaper than X-ray imaging. In this technique, the sample under test produces unequal surface heating on external heat stimulus. which, in turn, carries the signature of hidden defects inside the sample. 1

2 With time many different ideas were proposed to carry out NDT using thermal techniques. This leads to two broad ways of TNDT passive thermography and active thermography. The basic concepts of thermal imaging system are discussed in the next sections. 2 Basic concepts of thermal imaging system 2.1 Stefan s law of radiation We know from our daily experience that all hot bodies radiate heat. This was quantified and explained by an Austrian physicist, Joseph Stefan ( ) who proposed a law, known as Stefan s law of radiation, which states A body radiates heat per unit area per unit time proportional to the fourth power of its absolute temperature. H = σt 4 (1) where H: Heat radiated per unit area per unit time, σ: proportionality constant, known as Stefan s constant = 5.67 x 10 8 Wm 2 K 4 and T: absolute temperature of the body. The body which follows the aforesaid law is termed as Black body. But, for any real object the law never holds true. So, another parameter was introduced to quantitatively specify the resemblance of an object to a black body. This parameter is known as emissivity (ǫ). Emissivity is defined as the ratio of heat radiated by a real object (H object ) at a given temperature to the heat that would have been radiated by an ideal black body (H black body ) at the same temperature. ǫ = H object H black body (2) Thus, ǫ = 1 signifies that the body is a perfect black body. Materials like lamp black, are having ǫ 0.95 and are considered to be a black body for all practical purposes. One common way of converting a non-blackbody to a blackbody is to apply a thin layer of black paint on it. The thin paint layer, being in contact with the body, will have the same temperature as that of the body. So overall the object will act like a blackbody. 2.2 Wien s displacement law So far, the radiated energy was referred to as heat. But strictly speaking the energy is released in the form of electro-magnetic wave. Light is an electro-magnetic wave that our eyes respond to. The typical wavelength of visible light varies from 4000Å to 8000Å (1Å = m). The red light is having the longest wavelength and is least energetic while the violet is having the shortest wavelength and is most energetic. But there is a whole lot of electro-magnetic wave lying beyond the range of visible light. They cannot be seen with the naked eye. Waves having wavelength longer than that of the red are known infra-red (IR) and are primarily emitted by hot bodies. The intensity vs. wavelength plot for a hot body is shown in figure 1. The figure shows that the intensity of the emitted radiation peaks at some specific wavelength which is the characteristic of temperature. The peak shifts toward the shorter wavelength side with the increase in temperature. This is known as Wien s displacement law. Additionally, the total amount of radiated energy, which is a function of the area under the curve, also increases with temperature as suggested by Stefan s law. 2.3 Atmospheric transparency for infra-red waves Although hot bodies emit all possible wavelength in the IR region, air does not act as transparent medium for all wavelengths of IR. Most of them gets absorbed by the air molecules. However 2

3 Power radiated at each wavelength 2000K 1750K 1500K Peak wavelength Intensity curve for each temperature 1200K Wavelength (in µ m) Figure 1: Intensity vs. wavelength plot for a hot body at different temperatures (Wien s displacement law). photons with 2 5µm and 10 12µm wavelength can pass through air. So IR imaging systems have to rely on these two IR windows of the atmosphere. 2.4 Infra-red camera An IR camera is like a ordinary black-n-white optical camera except for the fact that the sensor responds to IR or near IR photons. Since, IR camera can record only the intensity of the photon, but not its wavelength (the color), the output from the camera is a gray-scale image, i.e. a 2- dimensional array of numbers representing the intensity of received IR radiation at respective pixels. The image is also known as thermogram. One major problem in IR imaging is the radiation from the sensor itself. To overcome this problem, sophisticated IR cameras are equipped with portable compressor to liquefy air. The liquid air is used to cool down the sensor array to a low temperature (about 100K) reducing the self emission from the sensor. However low-end uncooled IR cameras are also available. One other problem in IR imaging is the optics. Ordinary glass lenses cannot be used in the camera because glass is opaque to IR. Special germanium lenses have to be made to focus IR rays on the sensor array. All these sophistications contribute to the high cost of IR imaging system. 2.5 Pseudo-coloring of infra-red images The IR image, being gray-scale in nature, is difficult to read. To ease out the process, different colors are mapped to different temperature levels of the gray-scale image generating a color image of the 2D surface temperature profile. Generally, hot portions are represented with red and cold with blue or black. This mapping can be changed according to user s choice. A typical 3

4 Figure 2: A typical color mapped IR image color mapped infrared image is show in figure 2. 3 Classification of thermography techniques 3.1 Passive thermography As mentioned earlier, TNDT is having two broad categories passive thermography and active thermography. As the name suggests, passive thermography is one where no external heat source is used to excite the sample. The sample radiates under its own heating. IR picture of human body is an example of passive thermography. Passive thermography is useful when the heat is generated inside the system itself. Other examples of passive thermography are electrical fault identification, daytime fire detection, break inspection, etc. Passive thermography cannot detect sub-surface defects. It reveals only the surface information because radiation is a surface phenomenon. 3.2 Active thermography In active thermography, the sample is heated using external heating. Active thermography uses the fact that the transient heating effect would be different on top of a defective portion of a material than its non-defective or sound portions, revealing the internal defect structures. Heating techniques are very important in active thermography. In fact, all the techniques in active thermography are named after the heating technique used. The following are a few techniques in active thermography. Stepped thermography[1]: The sample is heated with a continuous heat source. The rise in temperature on top of the defective portion will be different than that on top of a non-defective portion. Pulsed thermography[2]: The sample is heated with a heat pulse and the time variation of surface temperature profile is recorded using a IR camera. Pulsed-phase thermography[3]: This is an enhancement to pulsed thermography. A pulse is a mathematical superposition of waves of all frequencies. So, the image sequence recorded in pulse thermography is taken through Fourier transformation and the phase images are plotted corresponding to each frequency. Defects at different depths become visible at different frequencies. 4

5 Lock-in thermography[4]: The sample is heated cyclically at some fixed frequency and the images are captured when the sample has reached the steady state. The phase analysis of the movie reveals the defects. Frequency modulated thermal wave imaging[5][6]: This is another modification over pulse and lock-in thermography. A Pulse comprises of high energy in a short time. Also it contains all frequencies. For TNDT, only a certain portion of these frequencies are useful. So, in FMTWI, the heat sources are modulated at low frequency and the frequency is gradually changed over time creating a chirp signal. The images are recorded and processed. 4 Important parameters calculated from recorded thermogram sequence 4.1 Thermal contrast A thermogram (in fact any digitized image) is nothing but a collection of pixels. The intensity at each pixel represents the temperature of the corresponding region on the sample surface. In case of active thermography, generally a sequence of such thermal images (i.e. a movie) is taken and the time evolution of the surface temperature is studied. One of the parameter that could be extracted from the movie of pulsed thermography is known as the Thermal Contrast[1]. It is defined as C(t) = T defect(t) T defect (0) T sound (t) T sound (0) where T defect (t) is the temperature over the defective region at time t while T sound (t) is that over a sound region. The subtraction from the initial frame makes the thermal contrast less sensitive to surface properties. The plot of thermal contrast vs. time over a defective region of the sample goes through a peak value at some time t max which is a characteristic of the defect depth. 4.2 Phase and magnitude image In lock-in thermography, the sample is subjected to sinusoidal stimulus. Pixel-by-pixel Fourier transformation of the recorded data at the excitation frequency gives rise to two quantities amplitude and phase. The pictorial representations of the amplitude and phase data are called amplitude and phase image respectively. 5 Theory of 1-Dimensional thermal wave When a surface is heated periodically, a highly attenuated and dispersive wave propagates through the material whose equation for a semi-infinite medium can be written as ([1], page 344) ( T(x, t) = T 0 e x/µ cos ωt 2πx ) λ = A(x)cos (φ(t, x)) (4) where µ is the thermal diffusion length, expressed by 2K 2α µ = ωρc = ω 5 (3) (5)

6 where K: thermal conductivity, ρ: density, c: specific heat, ω: modulation frequency [= 2πf (rad s 1 ), f: the frequency in Hertz], α: thermal diffusivity. Physically µ is the distance over which thermal wave amplitude dies down to 1/e fraction of its value at the surface. It is used as a measure of thermal wave penetration depth. It should be more than the defect depth but less than the thickness of the material. The thermal wavelength (λ) is related to µ by λ = 2πµ (6) 6 The experiment 6.1 Sample description and experimental setup You have been given a mild steel specimen to carry out the experiment. The specimen dimensions are shown in figure 4. Figure 3 shows the block diagram of the system for active (Lock-in and FMTWI) thermography. It consists of an IR camera, external heat sources, power amplifier, function generator and a interfaced computer. The computer generates and downloads the sinusoidal heating waveform to the function generator, prior to the actual experiment. During the experiment, the waveform is played back and each of the 1000Watt tungsten-halogen flood lamps is modulated through the power amplifier. In the current setup, the function generator and the power amplifier are merged together in the arbitrary waveform generator. The material under test is kept at a distance of approximately 1 meter from the heat sources to avoid heating non-uniformity. The IR camera digitizes the surface temperature of the test material. SAMPLE UNDER TEST Arbitrary waveform generator FUNCTION GENERATOR HEAT SOURCE #1 HEAT SOURCE #2 POWER AMPLIFIER IR CAMERA Figure 3: Experimental setup 6

7 A A B 51.8 B 37.3 C C SECTION A-A SECTION B-B SECTION C-C Figure 4: Dimensions of the Mild-Steel sample (in mm). 6.2 Estimation of excitation frequency The first part of the experiment requires the estimation of the excitation frequency that have be used to carry out the actual test. You are requested to write a simple C/C++ program to Table 1: Physical properties of mild steel Material properties Values Units Thermal conductivity 46 Wm 1 C 1 Density 7900 kg m 3 Specific heat 440 Jkg 1 C 1 7

8 Table 2: A sample program to calculate thermal diffusion length as a function of excitation frequency #include <iostream> // included for std::cout and std::endl #include <cmath> // included for sqrt /****************************************************************************** * The following function runs a for loop over specified range of frequencies * and prints the values of thermal diffusion lengths as calculated * by calculatethermaldiffusionlength function below. * * The function does not return anything. So the return type is void. ******************************************************************************/ void printthermaldiffusionlengthtable (double startfrequency, double frequencyinterval, int tablesize) { for (int i = 0; i < tablesize; i++) { const double frequency = startfrequency + i * frequencyinterval; const double thermaldiffusionlength = calculatethermaldiffusionlength (frequency); } } std::cout << frequency << "\t" << thermaldiffusionlength << std::endl; /****************************************************************************** * The following function returns the thermal diffusion length * at the supplied frequency. The values of thermal conductivity, * density and specific heat have to be put in depending on the material. ******************************************************************************/ double calculatethermaldiffusionlength (double frequency) { const double thermalconductivity = <enter the value>; const double density = <enter the value>; const double specificheat = <enter the value>; const double angularfrequency = 2.0 * * frequency; } return sqrt ((2.0 * thermalconductivity) / (angularfrequency * density * specificheat)); /****************************************************************************** * In C/C++, the program execution always starts from the function main. * * The return type of main is integer. Through this value, the program * tells the oprating system whether any error has occured or not. A value * of 0 indicates no error. ******************************************************************************/ int main (void) { const double startfrequency = <enter the value>; const double frequencyinterval = <enter the value>; const int tablesize = <enter the value>; printthermaldiffusionlengthtable (startfrequency, frequencyinterval, tablesize); } return 0; 8

9 tabulate the values of thermal diffusion length as a function of frequency. The required material properties of mild steel are shown in table 1. Table 2 is a reference program given for clarification. Please do not copy-paste it in your report. 6.3 Capturing thermal movies To capture the thermal movie, you need to use two softwares a) AWG5900 and b) IRBIS- 3 Professional. AWG5900 controls the heat sources while IRBIS-3 Professional is used to control the camera and offline data analysis. Figure 5 shows the screen shots of AWG5900. Figure 5a is the main window of the software. Following is a brief description of its various buttons. AWG5900 main window CREATE: Open the waveform creator window (figure 5b) LOAD: Loads an already created waveform into computer memory. Download channel selector (drop-down): The loaded waveform is to be downloaded to the memory of AWG5900 controller hardware prior to its playback. As AWG5900 hardware can control two flood lamps independently, this button decides in which channel the loaded waveform would be downloaded. DUMP: Downloads the loaded waveform from computer memory to AWG5900 controller hardware memory. CANCEL: Abort the download process in between. Play mode (drop down): Four play modes are there. 1. CHN1: Plays back the downloaded waveform using first heat source from CHN1 memory. 2. CHN2: Plays back the downloaded waveform using second heat source from CHN2 memory. 3. MONO: Plays back the downloaded waveform using both the heat sources from CHN1 memory. This is used in this experiment. 4. STEREO: Independently plays back the downloaded waveforms in both heat sources from respective memory. START: Starts waveform playback. STOP: Stops waveform playback. AWG5900 waveform creator window Slot: Eight different types of waveform can be combined together to form the final waveform. Each of the eight waveform settings is called a slot. Wave Type (drop-down): Specifies the type of the waveform. Possible values are Sine, Square, DC and NULL. If NULL is chosen, the slot is not considered. Duration: Duration of the waveform. Maximum 1200 seconds of waveform can be created. Phase: The phase of the wave at t = 0. This is specified in degree. 9

10 (a) AWG5900 main window (b) AWG5900 waveform creator window Figure 5: Screen shots of AWG5900 heating control software 10

11 Offset: The flood lamps cannot sink any energy. So the waveform is DC shifted to bring the entire cycle into positive side. i.e. Offset must be lesser than the amplitude. Initial Freq and Final Freq: AWG5900 can produce waveform of varying frequency (linear up-chirp). These two parameters decides the frequency range. Initial Ampl and Final Ampl: AWG5900 can also produce linear amplitude modulation. These values set the initial and the final amplitude. CREATE: Creates the waveform into a file specified by Filename. LOAD: Loads settings of a previous created waveform. EXIT: Goes back to main window. Filename: The path and name of the waveform file. If nothing is specified, filename default.ewd is used. Create sinusoidal waveforms at least at three frequencies as estimated in the previous section and store them with proper name. Download the created waveform into the AWG5900 control hardware to carry on the actual test. Since AWG5900 and IRBIS-3 are not interfaced together, it is useful to have a 10 seconds delay at the start of the waveform. This time can be used to bring the IRBIS window forward. To create such a waveform, enter the parameters given in table 3 in the waveform creator window. Table 3: Recommended settings for waveform creation Parameter name Slot 0 Slot 1 Unit Wave Type DC Sine N.A. Duration seconds Phase 0-90 degree Offset 0 10 % of lamp power Initial Freq Hz Final Freq Hz Initial Ampl 0 10 % of lamp power Final Ampl 0 10 % of lamp power Filename sine-50mhz.ewd Don t care. Change depending on experimental frequency When the waveform playback is started, a clock starts running on LCD display of the AWG control hardware. Initiate thermogram recording from IRBIS-3 when this clock hits 00:00:10. Tip: ALT+TAB can be used to quickly switch between open windows. IRBIS-3 Professional Use IRBIS-3 Professional software to capture the thermogram image sequence. Figure 6 shows the Camera menu of the software. In this menu, click on the Acquisition parameters arrow to open the acquisition settings dialog box. Select the sampling frequency and movie length depending on the excitation frequency. Do not choose any sampling frequency above 10Hz as it would fill the hard-disk within a very short time. 11

12 Figure 6: IRBIS-3 Professional screen shot 6.4 Image processing: Phase and amplitude image The image processing of lock-in thermography mainly consists of the Fourier transformation of the captured data. A module has been provided to carry out the analysis in the IRBIS software itself. Prior to processing, clear the Favourite files panel in the left side of IRBIS window and open the movie of interest afresh. Next, go to Sequence menu and click on Active thermography arrow to open the parameter setup dialog box. Feed all required parameters, e.g. sampling frequency of the movie, frequency of analysis etc. in the opened dialog box. Click Execute to initiate the automatic analysis sequence. You have to show that choosing frequency too high or too low affects the image quality. It is only when the diffusion length becomes comparable to the depth of the deepest defect, the images become good. 6.5 Experimental steps (at a glance) 1. Write a simple C/C++ program to tabulate the thermal diffusion lengths for mild steel as a function of excitation frequency using equation Use the estimated frequencies (at least 3 of them) to perform lock-in thermography test on the given sample. 3. Find amplitude and phase images at the chosen excitation frequencies to show the effect of thermal diffusion length. 12

13 7 Conclusion This experiment provides an overview of sub-surface thermal imaging in the context of nondestructive testing. The relationship between material properties and excitation frequency is established and experimentally verified through lock-in thermograhy. Amplitude and phase images are extracted. The frequency is optimized to obtain the best result. References [1] X. V. Maldague, Infrared Technology for Nondestructive Testing. John Wiley & Sons, New York, [2] J. M. Milne and W. N. Reynolds, The non-destructive evaluation of composites and other materials by thermal pulse video thermography, Proceeding SPIE, pp , [3] X. V. Maldague and S. Marinetti, Pulse phase infrared thermography, Journal of Applied Physics, vol. 79, no. 5, pp , March [4] G. Busse, D. Wu, and W. Karpen, Thermal wave imaging with phase sensitive modulated thermography, Journal of Applied Physics, vol. 71, p. 3962, [5] S. Tuli and R. Mulaveesala, Defect detection by pulse compression in frequency modulated thermal wave imaging, Quantitative Infrared Thermography (QIRT), vol. 2, no. 1, p. 41, [6] S. Tuli and R. Mulaveesala, Theory of frequency modulated thermal wave imaging for nondestructive subsurface defect detection, Applied Physics Letters, vol. 89, no. doi: / , p ,

Pulse Compression Approach for Frequency Modulated Thermal Wave Imaging Based Subsurface Defect Analysis

More Info at Open Access Database www.ndt.net/?id=15134 Pulse Compression Approach for Frequency Modulated Thermal Wave Imaging Based Subsurface Defect Analysis Aparna Akula 1, 2,a, Ravibabu Mulaveesala