本研究討論並設計出適合MR系統使用之變焦投影鏡頭，一投影鏡頭設計由7玻璃球面及非球面鏡片組成，為了減少整體重量與製造成本，將非球面鏡片材料改為塑膠，另設計一由2片玻璃球面鏡片與5片塑膠非球面鏡片所組成。鏡頭焦距為10.622 mm～18.485 mm，對角線全視角50°～30°，水平方向全視角40.92°～24.20°，光圈位於鏡頭第一面上，入瞳大小為4 mm，F/#=2.66～4.62，設定角度解析度為25～43 PPD，則空間頻率為65 lp/mm。由於光於波導中追跡其全部賽德像差為零，且與波導之材料與厚度無關，因此投影鏡頭可單獨設計，不需考慮波導所造成之影響。而投影鏡頭在MR系統中可被視作一放大鏡，角放大率為23.54～13.52倍。面板影像經過投影鏡頭放大後，其電視畸變與橫向色差會隨影像一同被放大，用於計算直線鑑別率來分析成像情形。全玻璃鏡片投影鏡頭MTF>0.386，玻璃球面鏡片與塑膠非球面鏡片組合之投影鏡頭MTF>0.305。兩者其他成像表現皆符合設計目標，為高品質投影鏡頭。;This study presents the design and analysis of a zoom projection lens optimized for use in mixed reality (MR) systems. The proposed optical system consists of seven elements, including spherical and aspherical glass lenses. To reduce overall weight and manufacturing costs, an alternative configuration replaces the aspherical glass lenses with plastic, resulting in a hybrid system comprising two spherical glass lenses and five plastic aspherical lenses. The focal length varies from 10.622 mm to 18.485 mm, corresponding to a diagonal field of view (FOV) of 50° to 30°, and a horizontal FOV of 40.92° to 24.20°. The aperture stop is positioned at the front surface of the lens, with an entrance pupil diameter of 4 mm and an F-number ranging from 2.66 to 4.62. An angular resolution of 25–43 pixels per degree (PPD) is targeted, corresponding to a spatial frequency of 65 line pairs per millimeter (lp/mm). Because light propagation within the waveguide maintains zero total Seidel aberration and is independent of the waveguide′s material and thickness, the projection lens can be designed independently without accounting for waveguide-induced effects. In the MR system, the projection lens acts as a magnifier with an angular magnification of 13.52× to 23.54×. As the panel image is magnified, both TV distortion and lateral chromatic aberration are proportionally enlarged, and their impact is evaluated through line-pair discrimination analysis. The all-glass lens design achieves a modulation transfer function (MTF) greater than 0.386, while the hybrid lens achieves an MTF above 0.305 at 65 lp/mm. Both designs meet the imaging performance targets, confirming their suitability as high-quality projection lenses for MR applications.
