Anonymous asked in 科學天文與太空 · 1 decade ago

請問何謂光學中的ray transfer matrix?

請問何謂光學中的ray transfer matrix?可應用在天文望遠鏡上計算長焦距的公式.請列出網頁或相關公式,贈20點



3 Answers

  • 1 decade ago
    Favorite Answer

    Ray transfer matrix:中文應該叫"光線變換矩陣"

    [edit] Definition of the ray transfer matrix

    The ray tracing technique is based on two reference planes, called the input and output planes, each perpendicular to the optical axis of the system. Without loss of generality, we will define the optical axis so that it coincides with the z-axis of a fixed coordinate system. A light ray enters the system when the ray crosses the input plane at a distance x1 from the optical axis while traveling in a direction that makes an angle θ1 with the optical axis. Some distance further along, the ray crosses the output plane, this time at a distance x2 from the optical axis and making an angle θ2. n1 and n2 are the indices of refraction of the medium in the input and output plane, respectively.

    These quantities are related by the expression



    This relates the ray vectors at the input and output planes by the ray transfer matrix (RTM) M, which represents the optical system between the two reference planes. A thermodynamics argument based on the blackbody radiation can be used to show that the determinant of a RTM is the ratio of the indices of refraction:

    As a result, if the input and output planes are located within the same medium, or within two different media which happen to have identical indices of refraction, then the determinant of M is simply equal to 1.

    A similar technique can be used to analyze electrical circuits. See Two-port networks.

    [edit] Some examples

    For example, if there is free space between the two planes, the ray transfer matrix is given by:


    where d is the separation distance (measured along the optical axis) between the two reference planes. The ray transfer equation thus becomes:


    2008-01-24 13:12:19 補充:


    2008-01-24 15:30:22 補充:


  • 1 decade ago


  • Ray transfer matrix:中文應該叫"光線變換矩陣"

    [ 編輯] 光芒調動矩陣的定義

    光芒辨別目標技術根據二架參考飛機, 叫輸入和輸出飛機, 每個垂直對系統的光學軸。沒有普通性損失, 我們將定義光學軸以便它與一個固定的坐標系的z-axis 相符。光線進入系統當光芒橫渡輸入飛機在一個距離x1 從光學軸當旅行在做一個角度?1 以光學軸的方向。某一距離進一步, 光芒橫渡產品飛機, 這時候在一個距離x2 從光學軸並且做角度?2. n1 和n2 是折射率媒介的在輸入和輸出飛機, 各自地。

    這些數量由和這關係光芒傳染媒介在輸入和輸出飛機由光芒調動矩陣的表示關係(RTM) M, 代表光學系統在二架參考飛機之間。熱力學論據根據黑體輻射可能使用表示, RTM 的定列式是折射率的比率: 結果, 如果輸入和輸出飛機位於在同樣媒介之內, 或在偶然有相同折射率的二個不同媒介之內, 那麼M 定列式是簡單地相等的到1 。

    一個相似的技術可能使用分析電子電路。參見Two-port 網路[ 編輯] 一些例子例如, 如果有自由空間在二架飛機之間, 光芒矩陣被給的調動: 那裡d 是分離距離(被測量沿光學軸) 在二架參考飛機之間。光芒調動等式因而成為

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