傅里叶自函数定义的扩展及其特性

Generalized Self Fourier Function and Its Properties

将Ｃａｏｌａ对傅里叶自函数的定义Ｆ（ｕ）＝ｆ（ｕ）扩展到Ｆ（ｕ）＝ａ１ｆ（ａ２ｕ），并在扩展的定义下讨论了傅里叶自函数的合成性、相加性、尺度变换及移位等重要特性，最后，论述了傅里叶自函数在光学２Ｆ系统中的应用。

The definition of self fourier function(SFF),which is definited as F(u)=f(u) by Caola in 1991,is generalized into F(u)=a 1f(a 2u) . Its important properties are discussed,such as synthesis,scaling,addition and shift. Finally,the application of SFF in the optical 2F Fourier processor is shown.