# Phase Reversal Method for Damage Imaging in Composite Laminates Based on Data Fusion
## 2 Materials and Methods
### Data Fusion  
Image data fusion [22] refers to the synthesis of multiple images by using mathematical methods so as to obtain improved images. In this study, a combined addition and multiplication method of the correlation coefficient (CAMM) based on data fusion is proposed. In the theory of phase-reversal imaging, according to Equation (4), the imaging geometry characteristic denotes a hyperbola passing through damage, whose semi-real axis value is \(\Phi^{\omega}/2\). By fusing imaging hyperbolas obtained from several groups of measurement points, the damage location is determined as an intersection point of the hyperbola curves. At the same time, due to the change in external environmental parameters, such as temperature and uneven material surface, the dependence of the wave velocity and wavelength on the frequency, and interaction between defects and material geometry structure, phase and noise artifacts and distortion will appear in damage imaging results. Therefore, according to the geometric characteristics of phase-reversal imaging, the combined addition and multiplication method of the correlation coefficient is proposed. This method can effectively eliminate artifacts and improve the accuracy of damage imaging by adding and multiplying the imaging results.  
According to the theory of phase-reversal imaging, the plate-like structure of a composite material can be divided into discrete element points. In general, the distance between adjacent discrete element points should be less than the damage size to meet the requirements for positioning accuracy. In this study, it is assumed that the damage is located at discrete element points, and all the unit points are regarded as possible locations of damage. The signal of each discrete element point is reconstructed by the phase-reversal method, and the correlation coefficient of the signal is calculated. The signal correlation coefficient of the unit point is a pixel point of the damage-imaging matrix. If the unit point represents damage, the signal similarity will be high, and the damage imaging results will be displayed as a hot spot with a high pixel value.  
According to Equation (7), the imaging matrices of each group on the \(x\)-axis and \(y\)-axis can be obtained by the following:  
\[I_{n}^{x}=DI_{n}^{x}(x,y)I_{n}^{y}=DI_{n}^{y}(x,y) \tag{9}\]  
As mentioned before, three adjacent sensors in the same direction are regarded as a group. In Equation (9), \(n\) represent the sequence number of groups in the same direction, and its maximum value is the number of sensors in the same direction, i.e., \(m-2\).  
The imaging matrices along the \(x\)-axis and \(y\)-axis are fused by the combined addition and multiplication method of the correlation coefficient (CAMM) to obtain the final imaging result, as follows:  
\[I=\prod_{n=1}^{m-2}\left(I_{n}^{x}+I_{n}^{y}\right) \tag{10}\]  
By using the combined correlation coefficient addition and multiplication data fusion-based method, the effects of phase, artifacts, and distortion can be effectively reduced so that the pixel value in the final imaging result is focused on the damage scattering source. Thus, the damage imaging accuracy of the phase-reversal method is improved.