## Theory
### IR Data Non-Uniformity Compensation Method  
Currently, most commercial IR cameras use a focal plane array (FPA)-type detector. Typically, a 2D resolution of 640 \(\times\) 480 pixels is used, and each pixel detects infrared rays at the corresponding location, converts the temperature, and displays it on the image. FPA size and resolution significantly impact the performance and image quality of the IR camera, but various non-uniformity correction (NUC) problems occur due to non-uniformity in the detector arrangement and detection performance. In the case of non-destructive testing that considers thermal maps, the global correction provided by the manufacturer may have limitations, and the development and application of a correction procedure that additionally induces spatial correlation between pixels is effective [27; 28]. In general, additional equipment can be minimized through non-uniformity correction. The average image of the acquired images is considered a method of generating a uniform image by applying offset correction derived through an algorithm based on the acquired image.  
The non-uniformity correction of the IR camera can be expressed as Equation (9), in which the gain (\(G_{x,y}\)) and offset (\(O_{x,y}\)) correction of each pixel are considered in the \(x\) and \(y\) pixel position output values (\(Y_{x,y}\)) of the detector.  
\[Y_{x,y}=G_{x,y}\times T+O_{x,y} \tag{9}\]  
The halogen lamp applied to the LIT test radiates an uneven heat load due to the location and distance of the light source, irradiation direction, shape of the reflecting  
Figure 2: The principle of the four-point phase shifting method for thermal waves demodulated on the object surface.  
surface, and uneven output inside the bulb. Differences in thermal response occur on the surface of the inspection object to which this thermal load is irradiated, causing contrast in measured values in thermography images. In addition, when a light source such as sunlight or a halogen lamp is reflected on the surface and enters the camera lens, it leaves a strong thermal effect on the IR image and can affect the evaluation of thermographic testing and indication.  
In this study, absolute temperature compensation (ATC) sheet and temperature ratio compensation (TRC) sheet compensation sheets were considered to improve the accuracy and efficiency of LIT inspection. The compensation sheet adjusts other pixel temperature values equally based on a specific pixel temperature value for the frame-unit IR image acquired throughout the LIT process.  
The ATC reconstructs the difference in temperature values of other pixels in the form of a matrix based on the temperature value of a specific pixel in each frame and is defined as Equation (10).  
\[A_{n,x,y}=y_{n}-Y_{n,x,y} \tag{10}\]  
The TRC reconstructs the temperature ratio of other pixels in a matrix form based on the temperature value of a specific pixel in each frame and is defined as Equation (11).  
\[R_{n,x,y}=\frac{y_{n}}{Y_{n,x,y}} \tag{11}\]  
where \(Y_{n,x,y}\) is the temperature value matrix data of the nth IR image, \(y_{n}\) is the temperature value of the reference pixel in each IR image, and \(A_{n,x,y}\) and \(R_{n,x,y}\) are the ATC and the RTC of the same matrix size as the IR image. The calculated compensation sheet is applied to all IR images acquired from thermographic testing and is expressed in Equations (12) and (13).  
\[Y^{\prime\prime}_{n,x,y}=Y^{{}^{\circ}}_{n,x,y}+A_{n,x,y} \tag{12}\]  
\[Y^{*}_{n,x,y}=Y^{{}^{\circ}}_{n,x,y}+R_{n,x,y} \tag{13}\]