# 臺灣博碩士論文加值系統

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 中央飄移室(CDC)之二維軌跡軟體設計更新是KEK高能加速器機構-國際合作計畫Belle-II實驗中的其一項目，我的任務是完成模擬二維軌跡重建之軟體設計的演算法，這個演算法符合了在FPGA晶片中資源使用的限制，在我的論文中，將會介紹此演算法以及所模擬出來的結果。 二維軌跡重建演算法包含了幾個步驟，第一，我使用霍夫圓轉換將CDC上x-y平面的點轉換到霍夫平面上，基於FPGA晶片的限制，霍夫平面被分割成眾多格子，我們使用了CDC偶數層共有五層的Superlayer，每一層Superlayer會形成一個霍夫平面，而在五層霍夫平面上相同位置的格子，它們被AND邏輯做連結，這個過程稱作Hough Voting。在Hough Voting之後，在五層霍夫平面上都有觸發的格子被重新制定在一個霍夫平面上，稱作霍夫地圖。第二，在這地圖上被聚集在一起的格子會被合併成一個Cluster，而Cluster的中心代表一個軌跡圓的圓心。第三，我做了一個二維軌跡修正的程序，在我獨立電腦模擬產生出來Pt及Phi的直方圖和預期結果是符合的。
 The updated 2D Tracker Software Design for Central Drift Chamber is the international project related to Belle-II experient at KEK. My task is to simulate the 2D track reconstruction algorithm for CDC readout electronics. This algorithm fits the limitation of resource in the FPGA chip. In my thesis, I introduce the 2D track reconstruction algorithm and the results of my simulation.The 2D track reconstruction algorithm includes some steps. Step1, I use the Circle Hough Transformation to translate the points in the CDC \$x-y\$ plane to \$r- hi\$ plane. Based on the limitation in the FPGA chip, the Hough Planes are divided into several blocks. For those blocks in the same position of the Hough Plane, they are connected by the AND logic. This connection is called Hough voting. After Hough voting, the overall hits in the Hough plane are reorganized as a map, called Hough map. Step2, in the Hough maps, the gathered blocks are merged into one which is named a cluster. The center of a cluster represents the center of a track circle. Step3, I make a 2D fitting program. The simulated histogram of Pt and Phi are generated in my standalone program. Their resolutions are as expected.
 1 Introduction 1.1 The Belle and Belle-II Experiment 1 1.2 The Central Drift Chamber in Belle and Belle-II 3 1.3 The Readout Electronics of the CDC 92 The CDC Trigger System 2.1 Introduction 13 2.2 The main task of CDC 14 2.3 The Front-edn and the Merger 15 2.4 The Track Segment Finder(TSF) 173 The Hough Voting for 2D Tracker 3.1 Hough Transform 19 3.2 Circle Hough Transform 19 3.3 Arcs to mesh 24 3.4 Hough Voting 264 The Peaking Finding for 2D Tracker 4.1 Hough Cell Clusters 28 4.2 Scan the Hough plane 29 4.3 Center of Cluster 31 4.4 Mesh Size(2D Full Tracker) 32 4.5 FPGA Algorithm 34 4.6 The relation among Pattern I 34 4.7 The relation among Pattern II 36 4.8 Center of Cluster 39 4.9 Efficiency in 2D logic 415 The Fitter for 2D Tracker 5.1 Fitting environment 43 5.2 2D fitting formula 44 5.3 Calculation results 46 5.4 Classes for C++ to VHDL 46 5.5 Histogram of Pt and Phi 476 Summary 50
 http://legacy.kek.jp/intra-e/index.htmlKobayashi M. and Maskawa T., CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49, 652–657, (1973).http://www.nobelprize.org/Belle II collaboration, Belle II Technical Design Report, KEK-REPORT-2010-1, July 2010.http://legacy.kek.jp/intra-e/feature/2010/BelleIICDCDesign.htmlhttp://en.wikipedia.org/wiki/Hough\_transform
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 1 中央漂移室偵測器之二維軌跡重建韌體設計更新 2 Belle II 中央飄移室偵測器二維軌跡重建:模擬軟體設計

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