傳統層析X射線攝影合成（X-ray computed tomosynthesis）應用於工業檢測下所建立之剖面影像因殘影效應（shadowing effect）的發生，無法準確判斷瑕疵或真實材料的邊界所在位置。
過去對殘影效應之認知主要建立在實驗影像或模擬影像的定性觀察，本研究推導殘影效應之影響範圍公式，首先探討單一薄板之殘影效應，並建立殘影效應之等效模型，由公式面驗證過去實驗觀察而知的特性；接著利用單層薄板之結論，推廣至連續體軸對稱材料（圓球）狀之殘影效應分析，將球體內外任意點殘影效應之厚度公式化，並比較所推導之公式與實際模擬影像殘影厚度之差距，以修正其誤差。
本研究亦將利用所推導之厚度公式，發展一方法以偵測瑕疵與真實材料所在位置之上下界，以解決過去無法從X射線剖面影像檢測中直接推估元件或瑕疵所在位置之問題。

[1] Z. des Plantes, “Eine neue Method zur Differenzierung der Röntgenographie,” Acta Radiol, Vol. 19, No. 2, pp. 182-192, 1932.
[2] Avinash C. Kak, and M. Slaney, “Principles of Computerized Tomographic Imaging,” IEEE Press, 1988.
[3] 李國翔，含BGA電路板之X光3D影像重建技術，國立清華大學碩士論文，2005.
[4] 高欣，新型迭代圖像重建算法的理論研究與實現，浙江大學博士論文，2004.
[5] S. T. Kang, and H. S. Cho, “A projection method for reconstructing X-ray images of arbitrary cross-section,” NDT&E International, Vol. 32, No. 1, pp. 9-20, 1999.
[6] S. M. Rooks, B. Benhanin, and K. C. Smith, “Development of inspection process for ball-grid-array technology using scanned-beam X-ray laminography,” IEEE Transactions on Components, Packaging, and Manufacturing Technology Part A, Vol. 18, No. 4, pp. 851-861, 1995.
[7] James T. Dobbins III, and Devon J. Godfrey, “Digital X-ray Tomosynthesis: Current state of the art and clinical potential,” Physics in Medicine and Biology, Vol. 48, No. 19, pp. 65-106, 2003.
[8] Y. J. Roh, K. W. Koh, H. S. Cho, H. C. Kim, H. Joo, S. K. Kim, “Inspection of ball grid array (BGA) solder joints using X-ray cross-sectional images,” Proceedings of SPIE – The International Society for Optical Engineering, Vol. 3836, pp. 168-178, 1999.
[9] Y. J. Roh, K. W. Koh, H. S. Cho, J. Y. Kim, H. C. Kim, J. E. Byun, “The calibration of X-ray digital tomosynthesis system including the compensation of the image distortion,” Proceedings of SPIE – The International Society for Optical Engineering, Vol. 3521, pp. 248-259, 1998.
[10] Y. J. Roh et al, “Correcting image distortion in the X-ray digital tomosynthesis system for PCB solder joint inspection,” Image and Vision Computing, Vol. 21, pp. 1063-1075, 2003.
[11] Thomas D. Moore, D. Vanderstraeten, and Pia M. Forssell, “Three-dimensional X-ray Laminography as a Tool for Detection and Characterization of BGA Package Defects,” IEEE Transactions on Components And Packaging Technologies, Vol. 25, No. 2, pp. 224-229, 2002.
[12] S. Gondrom, and S. Schröpfer, “Digital Computed Laminography and Tomosynthesis – Functional Principles and Industrial applications,” Proc. Int. Symp. Comput. Tomography Ind. Applicat. Image Process. Radiology, Vol. 4, No. 7, pp. 75-81, 1999.
[13] S. Black, “Generating Three Dimensional Models of Solder Joints Using X-ray Laminography,” Electronics Manufacturing Technology Symposium, Thirteenth IEEE/CHMT International, pp. 191-194, 1992.
[14] D. Meyer-Ebrecht, and H. Weiss, “Tomosynthesis – 3D X-ray imaging by means of holography or electronics,” Modern Optics, Vol. 24, No. 4, pp. 293-303, 1977.
[15] 陳宏吉，應用X射線薄層描繪法於PCB與BGA檢測之研究，國立清華大學碩士論文，2007.
[16] H. P. Hiriyannaiah, “X-ray Computed Tomography for Medical Imaging,” IEEE Signal Processing Magazine, Vol. 14, No. 2, pp. 42-59, 1997.
[17] D. J. Godfrey, R. J. Warp, and J. T. Dobbins, “Optimization of matrix inverse tomosynthesis,” Proceedings of SPIE – The International Society for Optical Engineering, Vol. 4320, pp. 696-704, 2001.
[18] D. J. Godfrey, R. J. Warp, and J. T. Dobbins, “Practical strategies for the clinical implementation of matrix inversion tomosynthesis (MITS),” Proceedings of SPIE – The International Society for Optical Engineering, Vol. 5030, pp. 379-390, 2003.
[19] C. Neubauer, “Intelligent X-ray Inspection for Quality Control of Solder Joints,” IEEE Transactions on Components, Packaging, and Manufacturing Technology Part C, Vol. 20, No. 2, pp. 111-120, 1997.
[20] W. A. Kalender, “Review: X-ray computed tomography,” Physics in Medicine and Biology, Vol. 51, pp. 29-43, 2006.