在非均勻介質中，欲聚焦訊號於一個目標物是困難的，想達到訊號的高聚焦性，應用了光學中的「相位共軛法」推廣為聲學的「時間反轉法」。時間反轉法為聲波發射後，以完全相反順序迴響，直接且非常精確地回到原聲源點，此技術為目前聲學領域中最熱門的話題之一。
　　後來發現時間反轉訊號的聚焦程度會有所不同，故本文模擬在雙層固態介質中，設計幾種變因探討不同因素所呈現的聚焦解析度。吾以有限元素分析波動模擬軟體ANSYS模擬聲波的波傳過程，再使用數學運算軟體MATLAB作時間反轉處理，從原聲源之接受訊號進行分析。模擬中改變時間反轉陣列換能器元件的個數、換能器元件的間距，還有介質尺寸、激震聲源點與界面距離、激震聲源點頻率等。
　　根據結果可得知，以較高的聲源頻率、較長的換能器陣列展距和較短的陣列間距，來提供時間反轉陣列較佳的布置方式，使往後其他時間反轉研究的實驗聚焦訊號更清晰。結果也可發現，鍍膜物體的時間反轉聚焦效果會比較厚的層狀物體清楚，若不考慮鍍膜物體時，可得到目標物較靠近兩層間的界面，其時間反轉聚焦效果會越好。

目　錄
誌謝 i
摘要 ii
目錄 iv
圖目錄 vi
表目錄 ix

第一章　緒論 1
1.1　研究動機與目的 1
1.2　文獻回顧 4
1.3　論文架構 5
第二章　理論基礎 8
2.1　時間反轉法理論推導 8
2.2　時間反轉法聚焦位置證明 11
第三章　模擬分析 15
3.1　模擬參數設定 15
3.2　模擬時間反轉法波動過程 18
3.3　聚焦效果與各參數之關係 25
3.4　結果與討論 46
第四章　結論與建議 48

參考文獻 50
附錄 52
1. 有限元素法 52
2. MATLAB軟體的簡介 54
3. ANSYS軟體的簡介 56

[1] B. Y. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov(1985), Principles of Phase Conjugation , Springer-Verlag, Berlin.
[2] M.Fink, C.Prada, F.Wu, and D.Cassereau(1989), Self Focusing in Inhomogeneous Media with “Time Reversal” Acoustic Mirrors, Ultrasonics Symposium, 681-686, doi:0090-5607/89/0000-0681.
[3] M.Fink(1992), Time Reversal of Ultrasonic Fields-Part I: Basic Principles, IEEE Transactions on Ultrasonics, Ferroelectronics, and Frequency Control, Vol.39 No.5, 555-566.
[4] D. R. Jackson and D. R. Dowling(1991), Phase Conjugation in Underwater Acoustics, Acoustic Society of America, Vol.89, 171-181.
[5] W. A. Kuperman, W. S. Hodgkiss, H. C. Song, T. Akal, C. Ferla, and D. R. Jackson(1998), Phase Conjugation in The Ocean: Experimental Demonstration of An Acoustic Time-Reversal Mirror, Acoustic Society of America, Vol.103 No.1, 25-40.
[6] H. C. Song, W. A. Kuperman, and W. S. Hodgkiss(1997), A Time-Reversal Mirror with variable range focusing, Acoustic Society of America, Vol.103 No.6, 3234-3240.
[7] Science Blog(2004), Time-reversal acoustics research promises medical breakthroughs, http://www.scienceblog.com/cms/node/2575
[8] D. M. Leslie(2003), A Geophysical Application of Time Reversal, Department of Exploration Geophysics, Curtin University of Technology.
[9] M. Fink, C. Prada, D. Cassereau, and E. Kerbrat(2008), Time Reversal Techniques in Non Destructive Testing, 4th AIP International Conference and the 1st Congress of the IPIA, Journal of Physics: Conference Series 124(2008)012004, doi:10.1088/1742-6596/124/1/012004.
[10] G. Montaldo, D. Palacio, M. Tanter, and M. Fink(2003), The Time-Reversal Kaleidoscope: A New Concept of Smart Transducers for 3D Imaging, 2003 IEEE Ultrasonics Symposium, 42-45.
[11] G. F. Edelmann, H. C. Song, W. S. Hodgkiss, W. A. Kuperman, and T. Akal(2005), Underwater Acoustic Communications Using Time Reversal, IEEE Journal of Oceanic Engineering, Vol.30 No.4, 852-864.
[12] 林明宏(2006)，時間反轉陣列之聚焦解析度分析，臺灣大學工程科學及海洋工程學研究所。
[13] S. Kim, G. F. Edelmann, W. A. Kuperman, W. S. Hodgkiss, and H. C. Song(2000), Spatial Resolution of Time-Reversal Arrays in Shallow Water, Acoustic Society of America, Vol.110 No.2, 820-829.
[14] W.S. Hodgkiss, H. C. Song, and W. A. Kuperman(1999), A Long-Range and Variable Focus Phase-Conjugation Experiment in Shallow Water, Acoustic Society of America, Vol.105 No.3, 1597-1604.
[15] A. M. Sutin, J. A. TenCate, and P. A. Johnson(2003), Single-Channel Time Reversal in Elastic Solids, Acoustic Society of America, Vol.116 No.5, 2779-2784, doi: 10.1121/1.1802676.
[16] S. Catheline, N. Benech, J. Brum, and C. Negreira(2008), Time Reversal of Elastic Waves in Soft Solids, The American Physical Society, doi: 10.1103/Phy sRevLett. 100.064301.
[17] C. Draeger, D. Cassereau, and M. Fink(1997), Acoustic Time Reversal with Mode Conversion at a Solid-Fluid Interface, Applied Physics Letters, Vol.72 No.13, 1567-1569.
[18] 魏煒、汪承灝(1999)，有平界面存在時時間反轉法的自聚焦性能，應用聲學，第18卷第3期。
[19] C. Tsogka, and G. C. Papanicolaou(2002), Time Reversal through A Solid-Liquid Interface and Super-Resolution, Inverse Problems, Vol.18 No.6, doi: 10.1088/0266-5611/18/6/314.
[20] G. Butenas, and R. Kazys(2008), Investigation of Time-Reversed Ultrasonic Waves Focusing in Multilayered Media, ISSN 1392-2114 ULTRAGARSAS (ULTRASOUND), Vol.63 No.2, 43-48.
[21] P. Blomgren, G. Papanicolaou, and H. Zhao(2000), Super-Resolution in Time-Reversal Acoustics, Acoustical Society of America, Vol.111 No.1, 240-248.
[22] J.-P. Fouque, J. Garnier, and K. Solna(2006), Time Reversal Super Resolution in Randomly Layered Media, Department of Mathematics, University of California.
[23] T. Chan, S. Jaruwatanadilok, Y. Kuga, and A. Ishimaru(2008), Numerical Study of the Time-Reversal Effects on Super-Resolution in Random Scattering Media and Comparison with An Analytical Model, Wavers in Random and Complex Media, Vol.18 No.4, 627-639.
[24] L. Borcea, G. Papanicolaou, C. Tsogka, and J. Berryman(2002), Imaging and Time Reversal in Random Media, Inverse Problems, Vol.18 No.5, doi: 10.1088/0266-5611/18/5/303.
[25] S. Yon, M. Tanter, M. Fink(2002), Sound Focusing in Rooms: The Time-Reversal Approach, Acoustical Society of America, Vol.113 No.3, 1533-1543.
[26] M. Fink(2008), Time-Reversal Waves and Super resolution, 4th AIP International Conference and the 1st Congress of the IPIA, Journal of Physics: Conference Series 124(2008)012004, doi:10.1088/1742-6596/124/1/012004.