Anonymous

請問何謂光學中的ray transfer matrix?

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Ray transfer matrix:中文應該叫"光線變換矩陣"

 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

where

and

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.

 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:

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2008-01-24 13:12:19 補充：

file:///C:/Documents%20and%20Settings/jenliu/Local%20Settings/Temporary%20Internet%20Files/Content.IE5/GP6R4TQN/281,30,Refraction

2008-01-24 15:30:22 補充：

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我覺得用翻譯軟體把別人的原文翻譯出破中文來回答，是不好的行為