隨著全球資訊產業邁入擴增實境（Augmented Reality， AR）的新紀元，穿戴式智慧顯示設備已成為接替智慧型手機、實現人機互動無縫銜接的核心技術載體。然而，AR 眼鏡在商用化的過程中，始終面臨著光學系統「體積緊湊性」與「高解析影像質量」之間的權衡挑戰。傳統的折射式光學系統若要達成大視場角（FOV），往往受限於光學總長（TTL）過長，導致鏡腳笨重且配戴舒適性不佳。為了解決此一產業痛點，本研究提出並設計了一套應用於 AR 眼鏡之折反式準直光學系統（Catadioptric Collimator System）。透過折射與反射元件的高度整合，利用光路摺疊（Folding Path）之物理特性，成功在極度有限的空間內，實現了高解析度、輕量化且具備高度量產潛力的光學系統設計。 在系統架構與材料選用策略方面，本研究採用了玻璃和塑膠混合設計，重點在結合光學塑膠的成型優勢與光學玻璃的高色散補償能力。為了達成輕量化的目標，系統前端的核心光學元件「三角稜鏡」，選用具有優異光透率且密度較低的光學塑膠 PMMA。緊接稜鏡後方的補償透鏡組則由四片非球面透鏡構成，其設計分為兩部分：前端兩片非球面透鏡選用 PMMA 與 Zeonex E48R，發揮其極低吸水率、抗變形性與高量產良率之特質，確保光學系統在長時間配戴下的環境穩定性；後端的兩片透鏡則針對高階像差之修正，匹配了高折射率、高色散的光學玻璃材料Schott的SF4 與 P-LASF47。透過此種塑膠和玻璃鏡片的組合，系統能有效抑制軸向色差與場曲，為後續影像品質的提升奠定了堅實基礎。 全針對折反式系統中關鍵的能量效率問題，本研究建立了全反射（Total Internal Reflection， TIR）臨界條件的理論模型。由於 AR 系統需在有限的光路長度內傳導影像資訊，光線在介面間的反射效率直接影響了最終影像的對比度與亮度。本研究分析了全波段（C， d， F-line）以及全視場（±15°）之入射光線行為，並透過司乃耳定律（Snell′s Law）與臨界角公式進行反覆運算。計算結果顯示，系統關鍵的角度α須滿足大於26.096°之判定準則。此定量分析之重要性在於，它確保了即使在最嚴苛的工作條件，即在長波段 C-line 於最大邊緣視場入射時，光線仍能穩定處於全反射區間內。這不僅從理論源頭徹底防止了邊緣漏光現象，更大幅提升了光學系統的能量利用率。 在影像品質優化階段，本研究透過 Code V 光學軟體進行了多目標全局優化。首先，針對人眼視覺生理特點，鑒於人眼視覺系統對於影像辨識之調製轉換函數（MTF）閾值至少需達到 0.2 方能產生清晰之辨識感，本設計透過對各表面非球面係數的精密調教，成功將全視場之 MTF 表現提升至 0.3 以上。此項優化成果確保了即便在微顯示器（Micro-OLED）高像素密度輸出下，影像邊緣仍能保持銳利。緊接在清晰度優化之後，本研究重點攻克了折反式系統中常見的影像形變問題。由於反射光路對對稱性的破壞易導致顯著畸變，本設計利用Code V優化功能與幾何約束條件，成功將全視場之幾何畸變控制於 10% 以內。此數據不僅符合人眼對虛擬影像與真實環境疊加時的感官一致性要求，更有效降低了使用者在長時間配戴時可能產生的視覺疲勞與暈眩感。 最後，為評估此設計方案與實際產業生產線的製作能力，本研究執行了公差分析（Tolerance Analysis）。在現實的製造與組裝過程中，偏心（Decenter）、傾斜（Tilt）與厚度偏差皆不可避免，而公差容忍度過小的設計將直接導致製造成本暴增。本研究透過合理分配元件公差，在不犧牲系統核心性能的前提下，有效放寬了加工容忍範圍。根據 Code V 之累計機率分佈運算結果顯示，本設計在 2σ（代表約 97.7% 之製造良率預期）的嚴格統計標準下，仍能展現出高度穩定的光學效能。 總結而言，本研究所開發之折反式準直光學系統，從基礎理論推導、精密設計優化到量產可行性驗證，均展現出優異的技術指標，為未來 AR 智慧眼鏡光學模組之開發提供了一套兼具高性能、低成本與輕量化之實用設計範例。;As the global information industry enters a new era of Augmented Reality (AR)， wearable smart display devices have become the core technology carrier to replace smartphones and achieve seamless human-machine interaction. However， the commercialization of AR glasses constantly faces the trade-off between the "compactness" and "high-resolution image quality" of the optical system. If a traditional refractive optical system aims to achieve a large field of view (FOV)， it is often limited by an excessively long total track length (TTL)， resulting in bulky temples and poor wearing comfort. To address this industry pain point， this study proposes and designs a Catadioptric Collimator System applied to AR glasses. Through the high integration of refractive and reflective elements and the physical characteristics of the folding path， this study successfully realizes a high-resolution， lightweight optical system design with high mass-production potential within an extremely limited space. Regarding the system architecture and material selection strategy， this study adopts a hybrid glass and plastic design， focusing on combining the molding advantages of optical plastics with the high dispersion compensation capability of optical glass. To achieve the goal of lightweight， the core optical element at the front end of the system， the "triangular prism，" uses PMMA， an optical plastic with excellent light transmittance and low density. The compensating lens group immediately following the prism consists of four aspherical lenses， and its design is divided into two parts: the front two aspherical lenses use PMMA and Zeonex E48R， leveraging their characteristics of extremely low water absorption， deformation resistance， and high mass-production yield to ensure the environmental stability of the optical system under long-term wear; the rear two lenses are matched with Schott′s SF4 and P-LASF47， high-refractive-index and high-dispersion optical glass materials， for the correction of high-order aberrations. Through this combination of plastic and glass lenses， the system can effectively suppress axial chromatic aberration and field curvature， laying a solid foundation for subsequent image quality improvement. Aiming at the critical energy efficiency issue in catadioptric systems， this study establishes a theoretical model of the Total Internal Reflection (TIR) critical condition. Since AR systems need to transmit image information within a limited optical path length， the reflection efficiency of light between interfaces directly affects the contrast and brightness of the final image. This study analyzes the incident light behavior across all wavelengths (C， d， F-line) and the full field of view (±15°)， and performs iterative calculations using Snell′s Law and the critical angle formula. The calculation results show that the critical angle $\alpha$ of the system must satisfy the criterion of being greater than 26.096℃. The importance of this quantitative analysis lies in ensuring that even under the most severe working conditions—namely， incident at the maximum marginal field in the long-wavelength C-line—the light can stably remain within the total internal reflection range. This not only thoroughly prevents marginal light leakage from the theoretical source but also significantly improves the energy utilization efficiency of the optical system. In the image quality optimization stage， this study utilizes Code V optical software for multi-objective global optimization. First， considering the physiological characteristics of human vision， and given that the Modulation Transfer Function (MTF) threshold of the human visual system for image recognition must reach at least 0.2 to produce a clear sense of recognition， this design successfully elevates the MTF performance across the full field of view to over 0.3 through the precise adjustment of the aspheric coefficients of each surface. This optimization result ensures that even under the high pixel density output of a Micro-OLED， the image edges remain sharp. Immediately following the sharpness optimization， this study focuses on overcoming the common image distortion problem in catadioptric systems. Since the disruption of symmetry by the reflective optical path easily leads to significant distortion， this design utilizes the optimization functions and geometric constraints in Code V to successfully control the geometric distortion across the full field of view to within 10%. This data not only meets the human eye′s requirement for sensory consistency when virtual images are superimposed on the real environment but also effectively reduces the visual fatigue and dizziness that users may experience during long-term wear. Finally， to evaluate the manufacturability of this design scheme on actual industrial production lines， this study conducts a Tolerance Analysis. In the actual manufacturing and assembly process， decenter， tilt， and thickness deviations are inevitable， and a design with overly tight tolerance limits will directly lead to a surge in manufacturing costs. By rationally allocating component tolerances， this study effectively broadens the processing tolerance range without sacrificing the core performance of the system. According to the cumulative probability distribution calculation results of Code V， this design can still demonstrate highly stable optical performance under the strict statistical standard of 2σ (representing an expected manufacturing yield of approximately 97.7%). In conclusion， the catadioptric collimator optical system developed in this study demonstrates excellent technical indicators from basic theoretical derivation and precise design optimization to mass production feasibility verification， providing a practical design paradigm that combines high performance， low cost， and lightweight for the development of future AR smart glasses optical modules.
