本論文旨在於FPGA ( Field Programmable Gate Array ) 平台設計實現可自動對焦3D數位全像重建系統之硬體。
本論文之基礎建立於全像術的使用，記錄觀測樣本之相位與振幅資料，並利用本系統進行3D重建。在全像圖顯微鏡等…的應用中，可能於觀測過程中更換樣本，且需手動調整正確焦距並重建清晰影像，較耗費人力成本及時間，因而突顯出本系統自動對焦之重要性。
本系統之全像重建流程主要使用菲涅耳轉換( Fresnel Transform )進行不連續相位重建，並使用DCT-based最小均方演算法( DCT-based minimum mean square algorithm )進行相位展開、還原物體之真實連續相位，再根據重建之影像進行數值評估( Normalized Variance )，以最高清晰度作為重建之焦距依據並進行正確焦距之重建。此外，本論文也使用諸多I/O技術，降低調整焦距時重複使用原始影像傳送的時間，提升本系統還原更大尺寸全像圖之能力，進而增加系統效能。
本論文之實驗數據與效能分析顯示本系統還原大尺寸全像圖之能力與正確性。採用以餘弦轉換為基礎的相位展開法則提供更具競爭力的還原時間。
透過本系統於FPGA上與運行於個人電腦之MATLAB軟體還原程式做兩者間之比較，可得知本系統於FPGA上之還原時間遠低於MATLAB軟體還原時間；另一方面，本系統之功率消耗運行於FPGA也遠低於軟體運作於CPU上。

關鍵字：FPGA、自動對焦、全像重建、餘弦轉換

This research aims to implement the design of “Autofocusing System for 3D Digital Holography Reconstruction” on FPGA ( Field Programmable Gate Array ).
With the use of Holography to record the phase and amplitude of the samples, the system can execute the 3D reconstruction by the hologram. The change of the observed samples during the observation process caused by the application of holography microscope and the need to adjust the focal length manually for clear 3D reconstruction images were time and labour consuming. Therefore, the system highlights the importance of autofocusing.
Autofocusing System for 3D Digital Holography Reconstruction includes diffraction computation (Fresnel transform), phase unwrapping (DCT-based minimum mean square algorithm) and numerical evaluation (Normalized Variance). Diffraction computation reconstructs the wrapped phase and phase unwrapping reconstructs the unwrapped phase. Processing numerical evaluation with unwrapped phase demonstrates whether the 3D reconstructed images are in of focus or not. This system uses multiple I/O technology to decrease the time when the system changes focal length and loads the original hologram.
The experimental results and performance analysis indicates that the system has the ability to reconstruct large size hologram. And the DCT-based phase unwrapping algorithm provides competitive reconstructing time. Comparing this system implementation on FPGA, MATLAB, CPU and GPU, the system implementation on FPGA has less reconstructing time and lower power consumption.

Keyword: FPGA, Autofocusing, Hologram reconstruction, Discrete cosine transform

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