菲涅耳數

Multi tool use
Multi tool use





奥古斯丁·菲涅耳


在光學裏，菲涅耳數（Fresnel number）是一個時常出現於衍射理論的無量綱量。菲涅耳數是因法國物理學者奧古斯丁·菲涅耳而命名。


假設，從光波源發射出的光波，照射於具有一個孔徑的不透明擋板。在擋板的後面，設有展示干涉圖樣的觀察屏。對於這光學系統，菲涅耳數 Fdisplaystyle FF 定義為[1]



F =def a2Lλdisplaystyle F stackrel def= frac a^2Llambda F stackrel def= frac a^2Llambda ；

其中，adisplaystyle aa 是孔徑的尺寸（例如半徑），Ldisplaystyle LL 是孔徑與觀察屏之間的距離，λdisplaystyle lambda lambda 是入射光波的波長。


依照 Fdisplaystyle FF 數值的不同，衍射理論可以分為兩種特別案例：



  • 夫琅禾费衍射：F≪1displaystyle Fll 1Fll 1 。


  • 菲涅耳衍射：F≳1displaystyle Fgtrsim 1Fgtrsim 1 。

假設 F≫1displaystyle Fgg 1displaystyle Fgg 1 ，則可以應用幾何光學的理論。



雷射


菲涅耳數可以用來描述雷射的操作性質。在這裏Ldisplaystyle LL 是共振腔長度。由於共振腔越狹窄，高階模的光束越容易因被共振腔的腔壁吸收而衰減，所以，菲涅耳數較低的雷射比較容易產生低階模的光束。[2]



參閱


  • 菲涅耳積分


  • 菲涅耳區（Fresnel zone）


  • 夫琅禾费距離（Fraunhofer distance）


參考文獻




  1. ^ Goodman, Joseph. Introduction To Fourier Optics 3rd, illustrated. Roberts and Company Publishers. 2005: pp. 85–86. ISBN 9780974707723.  引文格式1维护：冗余文本 (link)


  2. ^ Ion, John C. Laser Processing Of Engineering Materials:Principles, Procedure And Industrial Application illustrated. Butterworth-Heinemann. 2005: pp. 61. ISBN 9780750660792.  引文格式1维护：冗余文本 (link)








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