環場背投影光學系統設計與分析

Abstract

本論文的主要工作在於設計環場投影系統，全景光學成像系統已經有許多文獻提出，不論是使用多次成像或者一次性成像，全景影像已經有許多方法可以攝得。但在全景成像之外，如果想要達成與全景成像概念相似的環場投影系統，則討論並不多見。本論文設計的全景投影系統，參考前人的全景成像鏡頭型式，設計出適合環場投影使用的兩面反射式環場投影鏡頭。投影前需將要顯示的環場平面影像，先經過影像處理，轉換成投影鏡頭使用的環場投影影像源，經過一次性的投影，就可以得到環場360度的影像，除了一次性的投影，基於這樣特殊型式的投影，原本的光學畸變計算會超過10000%，不能做為參考，我們以設定其子午面線性放大的特性，提出適合用於此全景投影鏡頭的畸變定義，可以得到子午面的畸變小於4%，可以為觀察者所接受。

The main concern of this thesis study is circular projection: how to analyze and design? In literature panoramic imaging systems have been addressed for decades and the corresponding technique of panorama image taking has been well developed. However, once we want to project a cylindrical image, many new difficult issues, e.g. screen parallel to optical axis, remain unsolved. By reference to classical panoramic imaging lenses, we developed three kinds of lens design for circular projection, in which, mainly, two reflective surfaces are embedded to extend the projection ranges. To properly project a common rectangular source into a circular image, we convert the panoramic image to circular-projection source. After this proper projection, we will get a cylindrical image with good quality. On the other hand, circular projection has unique method to determine the distortion. The distortion is calculated from the error of the ray-intersects to the ideal position in meridian plane. Our projection-lenses have 4% distortion.