Image Definition and Defect Sizing in Lock-in Thermography: An Experimental Investigation

Abstract

In any imaging modality the apparent size and shape of the object in the image plane is influenced by the camera parameters and experimental conditions. To extract an accurate measurement of object size from the image, the understanding of the influence of these parameters on the apparent size and shape is important. Lock-in Thermography is one of the advanced imaging Non Destructive Evaluation techniques which is widely used for quantitative defect evaluation and material characterization. The important experimental parameter in Lock-in Thermography is the excitation frequency, which greatly affects both the apparent shape (image definition) and size in resultant phase and amplitude images. Hence, in this study, an attempt is made towards understanding the effect of frequency on the image definition (apparent shape) and defect sizing in Lock-in Thermography through experimental study. Stainless Steel plate with flat bottom holes of various sizes and depths is considered for the experiment. Both phase and amplitude images are considered for analysis. The Canny edge detection technique is implemented for studying the effect of frequency on image definition by extracting the edges of the flat bottom hole. The binary image obtained after edge detection is used for sizing calculation. The apparent shape and size were greatly affected by excitation frequency and depth in both amplitude and phase images. A relation between excitation frequency and depth was established which can be used to predict the excitation frequency where the sizing measurement is accurate.

Appendices

Appendix

Appendix A. Four Pont Correlation Method (FPC)

In a LT experiment, the modulated temperature response of the sample is captured using an IR camera which results in a 3 dimensional image matrix with dimension N_HxN_Vx(Pxf_rxn), where N_HxN_V is the size of image matrix and Pxf_rxn is the total number of images captured, where P = 1/f is the period, f_r is the frame rate and n is the number of periods. From this 3 D image matrix, one should obtain a 2 D phase and amplitude image matrices. This can be done using Four Point Correlation (FPC) method. In FPC method, initially the response of 1 pixel from 3 D image matrix is considered, which is a 1 D temperature signal. As shown in Fig. 10, all the images in 1 period (N = Pxf_r images) of the temperature signal is reduced into 4 equidistant resultant images using the equation (8),

$$T1 = {\text{\;}}\sum\nolimits_{n = 1}^\frac{N}{4} {\frac{{T_n}}{\frac{N}{4}}} ,\,\;T2 = \sum\nolimits_{n = \frac{N}{4} + 1}^\frac{N}{2} {\frac{{T_n}}{\frac{N}{4}}} ,\;T3 = \sum\nolimits_{n = \frac{N}{2} + 1}^\frac{3N}{2} {\frac{{T_n}}{\frac{N}{4}}} ,\;T4 = \sum\nolimits_{n = \frac{3N}{4} + 1}^N {\frac{{T_n}}{\frac{N}{4}}}$$

(8)

Then the amplitude and phase values for that pixel can be obtained using equations (9) and (10).

$$A= \sqrt{{\left(T3-T1\right)}^{2}+{\left(T4-T2\right)}^{2}}$$

(9)

$$\Phi =arctan\frac{T3-T1}{T4-T2}$$

(10)

This operation is repeated for all the pixels of the image matrix to generate 2 D amplitude and phase images.

Fig. 10

Schematic diagram of computing 4 resultant images from 3D LT image matrix using FPC method

Appendix B. Canny Edge Detection Method

First proposed by John Canny in 1986 [21], this method is a multi-stage approach for accurately detecting the edges in an image. The steps involved in Canny edge detection algorithm is given below.

• Step 1—Smoothing: Any edge is affected by noise present in the image. Hence the first step is to suppress these noise using suitable smoothing filters. Gaussian filters with suitable kernel is most widely used for the convolution of the grayscale image.

• Step 2 – Computing gradient magnitude and direction: The gradient magnitude (G) of the smoothed image, along x and y directions, is calculated using edge detection operators like Sobel, Prewitt etc. This magnitude tells about the strength of an edge. If G_x and G_y are the gradient vectors along x and y directions, then the gradient magnitude of the smoothed image is calculated using the following formula.

  $$G= \sqrt{{G}_{x}^{2}+{G}_{y}^{2}}$$

  (11)

Then the gradient direction (θ) is calculated which is always perpendicular to the edges using equation (12). The gradient direction value is rounded to 0° (vertical), 45° (diagonal), 90° (horizontal) and 135° (diagonal).

$$\theta = {tan}^{-1}\left(\frac{{G}_{y}}{{G}_{x}}\right)$$

(12)

• Step 3 – Non-maximum suppression: The gradient operation, executed in step 2 results in thick edged image. Non-maximum suppression is an edge-thinning technique, where along the edge, only the edge points with highest intensity values are retained, other points are suppressed.

• Step 4 – Hysteresis Thresholding: The image resulted from non-maximum suppression will have edges along with spurious lines due to noise. In this step, these noises are eliminated by double thresholding approach. In double thresholding, two threshold values, maximum and minimum, are considered. The edges pixel above maximum threshold value is marked as strong edge pixel and is retained. The edge pixel below minimum threshold value, it is suppressed. Pixel with value between maximum and minimum threshold value is marked as weak edge. This weak edge may be a true edges or may be a noise. If the weak edge is connected to the strong edge, then it is considered as edge. Any weak edges that are not connected to the strong edge are discarded.