波前感測器(wavefront sensor)在適應性光學系統(adaptive optics system，AOS)中是不可或缺的，作為偵測波前相位並回饋給AOS作為回授依據。此論文主要開發高速且容易整合至AOS的Shack-Hartmann波前感測器(Shack-Hartmann wavefront sensor，SHWS)，並以前14項Zernike多項式係數輸出資料表示擬合整體的波前。依使用的微透鏡陣列和相機，規格上，使用26 × 26個微透鏡陣列，波前可量測動態範圍± 8.06 mrad，最大可量測的波前變化量±31.45 μm。在速度方面，影像傳輸的速度和波前重建的計算時間皆會影響感測器的偵測速度，為了追求速度上的極限，選擇Camera Link影像傳輸介面的相機、Camera Link介面影像擷取卡嵌入式現場可程式邏輯閘陣列(field-programmable gate array，FPGA)做即時平行運算，迴圈可精準至每秒260幀率以上(frames per second，fps)，並在同一信號處理卡上的可編程輯閘陣列元件(field programmable gate array，FPGA)模組來直接控制可調變聚焦鏡(deformable mirror，DM)，調控通道電壓以及相對應的輸出，並收集多通道的驅動電壓輸入以及相對應的多通道Zernike係數輸出作多通道輸入及多通道輸出(multichannel input multichannel output，MIMO)的系統識別。儲存的輸入輸出資料在MATLAB上做離線分析，藉由數值次狀態空間系統鑑別方法(numerical subspace state space system identification)來得到以100 Hz迴圈之開迴路控制系統速度的系統狀態模型，目前在1輸入2輸出的系統所鑑別出的吻合度約84%，32輸入8輸出鑑別出的系統吻合度約70 ~ 80%。

In this thesis, a field programmable gate array (FPGA)-based Shack-Hartmann wavefront sensor (SHWS) programmed on LabVIEW can be highly integrated into customized applications such as adaptive optics system (AOS) for performing real-time wavefront measurement. A Camera Link frame grabber embedded with FPGA is adopted to enhance the sensor speed reacting to variation considering its advantage of the highest data transmission bandwidth. Instead of waiting for a frame image to be captured by the FPGA, the Shack-Hartmann algorithm are implemented in parallel algorithm and let the image data transmission synchronize with the wavefront reconstruction. On the other hand, we design a mechanism to control the deformable mirror in the same FPGA and verify the Shack-Hartmann sensor speed by controlling the frequency of the deformable mirror dynamic surface deformation. This FPGA-bead SHWS design can achieve a 266 Hz cyclic speed limited by the camera frame rate. For the further use of AOS, the system identification with the control loop of 100 Hz can be implemented. The fitting result in 1-input/2-output is 84 % and in 32-input/8-output is around 70 ~ 80 %.

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