Comparison of the Optical Lock-in Thermography using the Reflection Mode and the Transmission Mode

. Optical lock-in thermography is a non-destructive testing method. The surface of the sample is excited using the thermal waves and the response is recorded by the thermal camera. This image thermal sequence is processed using the image processing method named lock-in method. Optical lock-in thermography can be used to detect cracks and damages in metal or composite material. Two position modes are used: the reflection and the transmission mode. In this paper, are compared these two modes. An experiment is carried out on a printed composite plane with the square blinded holes placed in the different depths below the surface. The phase images are created using the lock-in method for both position modes. The results are compared and the advantages and the disadvantage of these position modes find out.


Introduction
Over the last 20 years, thermography has been divided into active and passive thermography. At present, scientists are mainly focusing on the development of new methods in the field of active thermography. Active thermography differs from passive thermography in that the measured object must be excited by external source, e.g. using heat wave. Subsequently, the response is recorded using a thermal camera. Active thermography includes non-destructive testing (NDT) using thermographic systems [1][2][3][4], thermoelastic stress analysis [5][6][7][8][9], methods for assessing the fatigue of materials [10][11][12][13][14][15][16] etc. The bestknown methods in the field of active thermography include:  thermoelastic stress analysis (TSA),  pulse thermography,  pulse phase thermography,  lock-in thermography,  vibrotermography,  rapid method for determining the fatigue limit.

Lock-in thermography
In the case of modulated heating of the body surface with a frequency f, a damped and scattered heat wave propagates in the subsurface region. In the plane layers of the body, it is possible to use the relation to evaluate the temperature T at the depth z and at time t [17]: where is the depth of penetration of the heat wave at which the temperature drops to 1 0 , where 0 is the surface temperature of the body. The equation for is as follows [17]: . Lock-in thermography is based on heat waves generated inside the measured object by periodic (sine) excitation signal. The periodic excitation signal has a frequency called the lock-in frequency . The heat wave (usually sinusoidal) penetrates the measured object and at the anomaly in the structure of the body is reflected to the surface. Interference of radiated and incident infrared radiation occurs on the surface of the object. As a result, the scanned thermograms are modified by a returning heat wave from inside of the measured object. In the lock-in thermography the frequency is changed to lock-in frequency . A response is obtained for the selected from a depth below the surface of the measured object. In this way, it is theoretically possible to obtain a response over the entire material thickness range using different values of . The main idea of the lock-in thermography is the assumption that when the excitation signal has a sinusoidal character with frequency , the recorded response will also have a sinusoidal character with the same frequency. It follows that the equation of the response can be written in the form: It is assumed that the amplitude of a given function s( )can be very small and the measured signal S( ) contains many times higher noise N( ), according to the relation: If ( ) is subsequently expressed by a Fourier series, where the noise ( )is the term in square brackets: Then for , , 1 , 1 are equations as follow: ( 1 ) (7) The estimation of the parameters , is determined by the estimates , using the relations of the discrete Fourier transform as follows: number of images in the recording from the thermal camera, i-th frames from a series of frames, -time when the i-th image was taken. Subsequently, for the phase of the harmonic function s( ) is the equation as follow:

Experimental measurement
Experimental measurement was performed in cooperation with the company TMVSS s.r.o. with office in Prague. The company lent the OTvis optical excitation system, the necessary InfraTecImageIR thermal camera and the premises in its building for the given experimental measurement.

3.1.Composite samples made on a 3D printer
Before the measurement, it was necessary to design and made test specimens. Two variants of test specimens -plates with dimensions 120 x 120 x 5 mm were proposed. The samples were made using a Mark TWO 3D printer and were made of Onyx material. No reinforcing fibers were used. The first variant contained 9 defects with a square cross-section with sides 10 x 10 mm (see Fig. 1). Defects were designed as blind holes of varying depth(from 0.5 to 4.5 mm, with 0.5 mm increments).  The second variant contained 9 block-shaped defects with dimensions 10 x 10 x 0.5 mm, spaced 20 mm apart. These were distributed at different depths below the surface (from 0.5 mm to 4.5 mm with 0.5 mm increments) (see Fig. 3).

3.2.Settings of experiment measurement
Test samples were measured using optical lock-in thermography. A halogen lamp with the power 2.5 kW was used as the excitation source. An InfraTecImageIR thermal camera with a resolution of 640 x 480 pixels was used to record the response. The DisplayIMG software was used to process the measured data and evaluate the phase images. Ten records were measured for the reflection method and 10 records for the transmission method, for both test samples. Ten records were made with different lock-in frequencies in order to obtain a response at ten different locations below the surface. Lock-in frequencies were calculated using the appropriate material properties as follows: Since the thermal conductivity and the specific heat are not defined by the manufacturer of the Onyx material, their values could be expressed approximately (because the percentage of the individual components was known) using a mixing rule. Onyx is composed of 93% nylon and 7% carbon and therefore and could be calculated as follows: In the Table 1, the lock-in frequencies are calculated for the specified depths below the surface. The thermal camera and the halogen lamp were placed at a distance of 1 m from the measured sample at an angle of approximately 40°. The lamp power was set to 50% of the power and the recording length was set to 4 excitation periods.

Reflection method
The reflection method consists in that the thermal camera and the excitation source (halogen lamp) are placed next to each other and the measured object is placed opposite (see Fig. 5). The figure Fig. 6 and Fig. 7 shows the phase images for the individual responses from a depth below the measuring surface. Both variants of the test specimens were designed so that the first defect (defect in the lower left corner) was located 0.5 mm below the surface and each additional defect was placed 0.5 mm lower. Material properties involved in the calculation of lock-in frequencies (thermal conductivity and specific heat of Onyx) were only approximately calculated (equations (14) and (15) Fig. 6 and Fig. 7). In the figures of Fig. 6 and Fig. 7 it can be seen that the first defect (in the lower left corner) is displayed at a depth of = 0.5 mm and the second defect is slightly displayed at = 1 mm. The third defect is displayed at depth = 1.5 mm. The fourth defect is slightly displayed already at a depth of = 1.75 mm. The fifth defect is only minimally displayed at a depth of = 2.5 mm. From a given measurement, it could be assumed that the calculated material properties of the values of and were calculated correctly using the mixing rule (14) and (15).

Transmission method
The transmission method differs from the reflection method in that the measured object is placed between the thermal camera and the source of excitation. The thermal camera records the front / measuring surface of the object and the excitation source excites its back side (see Fig. 8).
The thermal camera was placed as in the reflection method and the halogen lamp was placed 1 m from the back surface of the polystyrene plate. The power setting of 50% and the recording length of 4 periods remained unchanged.
The figures Fig. 9 and Fig. 10 shows the phase images for both samples. It can be seen how the results for the reflection and transmission methods differ significantly. It can be seen from the measured data that it is possible to detect defects before they should be displayed according to heat wave theory. From the phase images, it can be observed that all nine defects can be detected. The quality of the phase image display gradually increases up to a depth of μ = 1.5 mm. Subsequently, the image quality decreases and at a depth of μ = 2.25 mm, the phase image is damaged due to the saturation of the thermal camera detector.

Conclusion
From the measured data it can be seen that each of the methods (reflection and transmission) has its advantages and disadvantages. The advantage of the reflection method is that it is governed by heat wave theory. For this reason, it makes it possible to obtain information about the presence of a defect in the measured object and especially at what depth it is located below the surface. In this way, it was possible to gradually determine the depth at which the individual defects are located. On the other hand, the disadvantage is that the depth from which the response can be obtained is approximately 2.5 mm for the Onyx composite material. Due to this limitation, only five of the nine defects in the test plate could be detected. Also, the disadvantage is that the phase image obtained from a greater depth below the surface has a deteriorated imaging quality of the actual shape of the defects. The transmission method isn´t follow the standard rules of heat wave theory, because defects were displayed earlier than they should have been. Therefore, it was not possible to obtain a response from a specific depth below the surface of the measured object (it was not possible to define at what depth below the surface the defects are located). However, the advantage over the reflection method is that with both variants of the test plates it was possible to detect all nine defects, which is also the main goal of the lock-in thermography. The transmission method has a higher ability to detect the presence of defects (qualitative evaluation), while the reflection method provides good information on the morphology / shape and position of the defects (quantitative evaluation). Another goal of the paper was to verify whether the values of the material parameters and were calculated correctly using the mixing rule (14) (15). From the results of measurements using the reflection method we can observe that defects are displayed at lock-in frequencies at which they should be displayed according to the theory of heat wave. Therefore, we can consider the material parameters and calculated using the mixing rule are correct.