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近軸近似

近軸近似的誤差,圖中的cosθ是用1 - θ2/2近似

近軸近似幾何光學中的高斯光學光線追蹤英语Ray tracing (physics)用的小角度近似,可以用在光學系統(例如透镜)的分析[1] [2]

近軸光線是指光線光轴角度很小,而光線接近光學系統的軸。[1]

在近軸近似及近軸光線下,在計算光的路徑時,可以使用以下的近似(θ弧度[1]

近軸近似可用在高斯光学及一階光線追蹤英语Ray tracing (physics)[1]。像光線轉換矩陣分析就使用了這種近似方式。

有時二階近似也稱為近軸近似,對於函數,其泰勒級數的二階項為0,因此二階近似和一階近似相同,而函數的二階近似如下:

二階近似在角度小於10°時,其準確度在0.5%以內,若角度變大,誤差就會顯著提昇[3]

若光線和光軸的夾角較大時,需區分和光軸共平面的子午光线英语meridional ray及不共平面的弧矢光线英语sagittal ray

相關條目

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参考文献

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  1. ^ 1.0 1.1 1.2 1.3 Greivenkamp, John E. Field Guide to Geometrical Optics. SPIE Field Guides 1. SPIE. 2004: 19–20. ISBN 0-8194-5294-7. 
  2. ^ Weisstein, Eric W. Paraxial Approximation. ScienceWorld. Wolfram Research. 2007 [15 January 2014]. (原始内容存档于2021-09-10). 
  3. ^ Paraxial approximation error plot. Wolfram Alpha. Wolfram Research. [26 August 2014]. 

外部連結

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近軸近似
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