Flaw detection enhancement in lockin temporal speckle interferometry
using thermal waves
Andrés E. Dolinko and Guillermo H. Kaufmann
Instituto de Física Rosario (CONICET – UNR)
Blvd. 27 de Febrero 210 bis, S2000EZP Rosario, Argentina
[email protected]
ABSTRACT
In this work, a lockin approach that takes into account the contribution of several modes from the Fourier spectrum generated
by a heat load following a triangular waveform is used in temporal speckle pattern interferometry (TSPI) to improve the nondestructive detection of flaws. Additionally, a coefficient to quantify the level of flaw detectability is presented. The use of this
coefficient allows to demonstrate that the application of the proposed lockin technique improves the detection of hidden flaws
in metal specimens.
Introduction
The detection of internal defects by means of digital speckle pattern interferometry (DSPI) combined with thermal loading has
generated great interest in the field of non destructive testing. Recently, Kaufmann et al. have shown that temporal speckle
pattern interferometry can be used to visualise time dependent deformations generated by long thermal waves [1,2]. By testing
flawed aluminium plates, it was demonstrated that the use of thermal waves rather than unmodulated heating in TPSI
improves the defect detectability. Since the detection of internal defects by means of this technique is based in the
measurement of the thermo-elastic deformations induced over the tested specimen surface, a sharp visualization of the flaws
is not possible in practice. Here, we will show that a lockin method based on a modification of a technique proposed by
Gerhard and Busse [3] introduces an additional improvement in flaw detection.
Experimental Procedure
The specimens used in the experiments were circular aluminium plates of 2 mm thick clamped along their edges. In each
specimen, different defects were milled in the form of flat bottomed slots with different depths. The back surface of each
specimen was painted black to increase thermal absorption and was heated with an IR lamp. The radiation emitted by the
lamp passed through a rotating chopper driven by a variable speed motor to modulate the heat received by the specimen.
Each flawed specimen was heated by the periodically modulated source at a frequency of approximately 0.2 Hz.
Simultaneously, a set of several hundreds of speckle interferograms was continuously recorded by means of a digital camera
at a rate of 50 Hz with temporal phase shifting carried out by a Pockels cell synchronized with it. Finally, using temporal phase
unwrapping through a whole sequence of frames enabled the determination of out of plane absolute displacement maps
varying along time.
Lockin Technique
The lockin method implemented in this work consisted basically in the modulation of the heat source along time following a
triangular waveform. The measured displacements generated along time will also show a similar modulation. The method
consisted in the Fourier transformation of the temporal history of each pixel. Afterwards, the complex value of each resonant
mode in the resulting spectrum was selected and these values were added up. Finally, the modulus of the resultant complex
value was associated to the intensity of the corresponding pixel.
As a consequence of the application of this approach, flaw detectability in metal plates resulted enhanced. The hypothesis
behind this method is that the specimen behaves like a low pass filter for the thermal wave travelling along the plate thickness.
A defect will be a region where the transfer function of the filter varies. Considering the whole set of measured modes, from the
fundamental to the highest frequency one, it was possible to obtain a better characterization of the behaviour of the plate in
response to the thermal wave.
Quantification of Detectability
In order to make a comparison between the ability for defect detection of the proposed lockin technique and previously
developed methods, we used a coefficient called sharpness S, which is defined as
def − mean
S = 10 min− max
(1)
where def is the average value of the pixels belonging to the defect, which it is possible to estimate for a known sample by
means of simple measurements, mean stands for the average value of all pixels belonging to the specimen excluding those of
the defect, and max and min are the maximum and minimum values of the pixel map, respectively. This coefficient gives
values between 1 and 10, which corresponds to the minimum and maximum detection level, respectively. Therefore, the
sharpness coefficient S allows to compare the defect detectability produced by the different speckle interferometry approaches
used in non destructive testing.
The image of a flawed specimen with four defects milled in the form of slots with different depths obtained by means of the
proposed lockin method is shown in Figure 1(a), where the defects are indicated as 1, 2, 3 and 4 and ordered in increasing
depth. Figure 1(b) shows the corresponding contour plot for the image shown in Figure 1(a).
(a)
(b)
Figure 1. (a) Phase image obtained with the proposed lockin method. (b) Contour plot corresponding to the same image.
On the other hand, the image revealing the defects obtained by the direct measurement of the out of plane displacements
generated by the periodic excitation is shown in Figure 2(a), with its corresponding contour plot displayed in Figure 2(b).
The improvement introduced by the method results evident by the observation of the images shown in Figures 1 and 2. It can
be observed that the flaws imaged by means of the proposed lockin method appears to be more selectively detected in
comparison to the images extracted from the displacement field generated by the thermal waves and measured directly. In
addition, the resulting images have a relatively constant background and the magnitude of the intensity of the displayed
defects agrees quite well with their depths, contrary to what it is observed in the images shown in Figure 2. A calculation of the
sharpness coefficient S for the defect 4 of the image obtained by the proposed lockin method gave a value of 4.09 while the
value evaluated with the image generated without the lockin technique was 2.14, showing a clear improvement in the
detectability when the approach proposed in this work was used.
Correction of Thermal Convection
After analysing several phase maps obtained by the direct measurement of the displacements generated by the periodic
excitation, it was observed that they presented an inclination whose gradient was always along the vertical direction. This
effect was observed for all the analysed samples independently of their flaw configuration.
From a dynamical point of view, it was observed that this inclination is null at the beginning of the interferogram acquisition and
becomes more important as long as the time was increased, reaching quite a large magnitude for long acquisitions of the order
of 1000 images. It was also noted that this inclination corresponds approximately to a plane according to what it was observed
at the borders of the phase maps where the influence of the defects is low.
(a)
(b)
Figure 2. (a) Phase image obtained by the direct measurement of the out of plane displacements. (b) Contour plot of the
corresponding image.
Since the samples were positioned in a vertical position, it was considered that the observed phenomenon was due to
convection effects since the upper region of the sample receives the heat due to the lamp plus the ascending heat of its lower
part, introducing a thermal gradient along the vertical direction. Additional experiments performed with the sample positioned in
a horizontal position did not show this effect and therefore supported this hypothesis.
Due to the existence of this inclination in the phase map, the defect images had low contrast. Furthermore, this phenomenon
can mask the real perturbation introduced by a defect. Consequently, it was proposed to eliminate this inclination by means of
a least squares method similar to the one utilized in Ref. [4] in order to achieve a better visualization of the defects to be
detected. In Ref. [4], the least squares method was applied to eliminate the rigid body displacement introduced in the phase
maps produced by the hole drilling method for measuring residual stresses. The method is based on the evaluation of points
along two parallel lines near the borders of the phase map where the influence of the displacements generated by hole drilling
is negligible. In the present case, the points considered for the application of the least square method were those points
contained in a one pixel width ring located in the borders of the region of valid data, where the influence of the defects is
negligible. Figure 3(a) shows a phase image obtained from a disk presenting two circular slots located quite close which
affected by convection and Figure 3(b) shows the same image when it is corrected by the least squares method.
In this case, the inclination in the phase map is not interpreted as a rigid body displacement, but as a thermal gradient resulting
from the convection effect. Finally, it can be mentioned that this method results quite useful for its use in practical applications
performed outside the laboratory, where the region to tested is in a vertical orientation.
Quantification of Defect Discrimination
We also analysed the ability of the proposed lockin method to discriminate two near defects in comparison to the image
generated by direct measurement of the displacements generated by the thermal wave. In order to perform this analysis, it
was utilized a circular aluminium plate with the same dimensions as the previous ones. Two circular defects were drilled in its
back surface having a diameter of 4 mm and a depth of 1 mm. The defects were separated by a distance equal to one
diameter along the tangential direction. The back surface of the flawed plate is shown in Figure 4(a). The two defects were
labelled as 1 and 2. Figure 4(b) shows the lockin image obtained from the front face of the specimen.
In order to determine the level of defect discrimination, the images revealing the flaws obtained by means the proposed lockin
method and by direct measurement of the displacements were compared. Both images were previously processed with the
algorithm for elimination of the convection effect described in the previous section.
As a first step for the evaluation of the level of defect discrimination, the sharpness coefficient in three different regions
corresponding to the two defects and the inter defect zone was evaluated for each image. The values of the sharpness
coefficient evaluated at these regions are listed in Table 1.
(a)
(b)
Figure 3. (a) Phase image obtained for a two defect sample affected by convection. (b) The same image when it was corrected
by the least squares method.
(a)
(b)
Figure 4. (a) Back surface of the analysed flawed plate showing the position of the two defects. (b) Lockin image of the
corresponding specimen.
As a first step for the evaluation of the level of defect discrimination, the sharpness coefficient in three different regions
corresponding to the two defects and the inter defect zone was evaluated for each image. The values of the sharpness
coefficient evaluated at these regions are listed in Table 1.
Sharpness
Displacement image
Defect 1
Defect 2
Inter defect region
2.679
2.608
2.579
Lockin image
4.888
5.031
4.809
Table 1. Sharpness coefficient calculated in the relevant zones for the study of defect discrimination.
Then, the level of defect discrimination was determined utilizing the sharpness values presented in Table 1. This level was
established as the difference existing between the sharpness value at the defects and the sharpness value at the inter defect
region. A larger difference between these values will denote a clearer separation between the defects, indicating a better
degree of discrimination in the image. Consequently, the discrimination level D was calculated as
 def − mid 
 × 100
D = 
 def

(2)
where def is the mean value between the sharpness of defects 1 and 2 and mid is the sharpness value evaluated at the interdefect region. This is a percentage value that indicates the level of defect discrimination in the analysed specimen. The
discrimination level in the image obtained with the proposed lockin method was of 3.14% while the image resulting from direct
measurement of the displacements was 2.52%. These results indicate that the flaws are discriminated better when the
proposed lockin method is applied and the image obtained by this procedure will show clearer the separation between the
defects.
Figure 5(a) shows the contour level map of the image obtained by the proposed lockin method while Figure 5(b) displays the
map produced by direct measurement of displacements. Comparing both figures, it is shown that the two defects are better
resolved in Figure 5(a).
(a)
(b)
Figure 5. Contour level of the image obtained by: (a) the proposed lockin method; (b) direct measurement of displacements.
Conclusions
This paper presents a lockin method based on a specific heat modulation following a triangular waveform. It is shown that the
application of the proposed method improves flaw visualization in metal plates. The defects appear more sharply detected
showing agreement between their intensity in the image and their depth. In addition, the image generated by the proposed
method presents a nearly constant background. Although the image obtained by direct measurement of displacements can be
filtered to improve its quality, this procedure will reduce at the same time its sharpness value. On the contrary, the image
obtained by the proposed lockin method will have a lower noise level and also a higher sharpness value.
Acknowledgments
The authors would like to thank the financial support provided by the Agencia Nacional de Promoción Científica y Tecnológica
of Argentina.
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