X-Ray Three-Dimensional Reconstruction Algorithm of Plate-Like Objects Based on Filter Path Transformation
Objective Computed tomography(CT)is a widely used technique for the reconstruction of the internal structure of three-dimensional(3D)objects.The technique can obtain information about the interior of an object under non-contact and non-destructive conditions.Therefore,it is widely used in the fields of industry,medicine,geology,and material science.In the electronics industry,computed laminography(CL)is often used to collect projection data,so as to perform quality inspection and failure analysis of integrated circuits,multilayer printed boards,and other plate-like electronic devices.However,CL scanning causes interlayer aliasing in the reconstructed image.The current preferred method is to convert the CL projection to an equivalent CT projection with large cone angles using a projection transformation method called CL reprojection(CLRP)and then reconstruct them using the Feldkamp-Davis-Kress(FDK)algorithm.However,the FDK algorithm suffers from gray-scale degradation and edge artifacts during the reconstruction of large cone angles,which affects the reconstruction quality.In this study,we propose a filter path transformation algorithm based on data rearrangement.This algorithm can reduce the gray-scale degradation and edge artifacts of the reconstructed image during large cone angle reconstruction.In addition,we apply the algorithm to the 3D reconstruction of plate-like objects by combining it with the projection transformation method.It is expected to improve the reconstruction effect when the CL projection is converted to an equivalent CT projection with large cone angles.Methods In this study,a filter path transformation-based reconstruction algorithm was proposed and applied to the reconstruction of the plate-like object.This was achieved by converting the projection of the plate-like object acquired by CL scanning to an equivalent CT projection with large cone angles by the CLRP method,and then the proposed algorithm was applied to realize the 3D reconstruction of the plate-like object.This algorithm utilized two parameters to rearrange the CT projection and adjusted the projection surface to change the longitudinal coordinates of the projected data for filter path transformation.In addition,we derived the method for calculating the parameters of this algorithm during reconstruction based on the projection transformation method.With the help of these parameters,it is possible to realize the 3D reconstruction of the plate-like object.In order to investigate the effect of filter paths on the reconstruction results,we used the 3D Shepp-Logan model for simulation and reconstruction.The reconstruction errors for different parameter combinations were counted,and the error surface was plotted for demonstration.Then,we compared the proposed algorithm with other algorithms for reconstruction to verify the effectiveness of the proposed algorithm.In addition,we designed a printed circuit board(PCB)model to verify the effectiveness of the proposed algorithm combined with the projection transformation method in plate-like object reconstruction.Finally,in order to investigate the feasibility of the proposed method in practical applications,we also used CL scanning equipment to reconstruct real PCB samples and objectively analyzed the efficiency and flaws of this algorithm.Results and Discussions In this paper,we investigate the effect of filter paths on the reconstruction results of the proposed algorithm.The experimental results indicate that when reconstruction is performed under conditions of unequal parameters,black or white artifacts then appear at both ends of the reconstructed image(Fig.8).The error is minimized when the reconstruction is performed under the condition that the two parameters are equal,and the most desirable reconstruction results can be obtained(Fig.10).This shows that the proposed algorithm can optimize the reconstruction by corresponding filter path reconstruction under the condition that the two parameters are equal.We reconstruct the proposed algorithm in comparison with FDK,P-FDK,and T-FDK algorithms under this filter path.The result is that the proposed algorithm has fewer edge artifacts than other algorithms when the cone angle increases,and the reconstruction results are more satisfactory(Figs.11 and 13).The simulated reconstruction and comparison of the converted CT projection with large cone angles are carried out by using the PCB model to examine the viability of the proposed algorithm in the CL scanning reconstruction of plate-like objects.This is done based on the verification of the reconstruction effect of the proposed algorithm.The results show that compared with the FDK algorithm,the reconstruction effect of this algorithm has fewer artifacts(Fig.16),and the quantitative evaluation index of the reconstructed image is more satisfactory(Table 3).In addition,the reconstruction results of PCB samples show that the reconstructed images of the proposed algorithm have fewer artifacts and sharper images(Fig.18).These results demonstrate the feasibility of this algorithm in plate-like object reconstruction.Finally,as shown by the comparison of reconstruction time(Table 5),the proposed algorithm takes more time for reconstruction.Despite the decrease in efficiency,it has the advantage of being suitable for parallel accelerated computation and can reduce the reconstruction time to an acceptable range.Moreover,the effect of interpolation on the spatial resolution of the reconstruction of this algorithm can be solved by increasing the number of projections.Therefore,the proposed algorithm still has practical application value.Conclusions In this paper,we propose a filter path transformation-based reconstruction algorithm to improve the gray-scale degradation and edge artifacts during FDK reconstruction of large cone angles and enhance the quality of reconstructed images.The experimental results show that this algorithm can effectively reduce the edge artifacts under the condition of equal parameters.Compared to other algorithms,the proposed algorithm performs better in large cone angle reconstruction.In addition,the combination of this algorithm with the projection transformation method is applied to the 3D reconstruction of plate-like objects,and the reconstructed images are clearer and have smaller errors than images reconstructed by the FDK algorithm.Although the reconstruction speed of this algorithm is degraded,the efficiency can be improved by parallel acceleration in real engineering applications.Moreover,the degradation of the spatial resolution of the reconstructed images can be reduced by increasing the number of projections.Overall,the algorithm proposed in this paper can reduce the artifacts in FDK reconstruction with large cone angles,and it is simple and easy to implement,so it has practical applications in plate-like object reconstruction.
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