自傅里叶函数及其应用

列出了一大组基本ＳＦＦ和复合ＳＦＦ，表明由Ｃａｏｌａｌ给出的并不是全部的ＳＦＦ。其次指出了由Ｃａｏｌａ以及Ｌｏｈｍａｎｎ等先后提出的由任意函数构造一个ＳＦＦ的定义式的局限性，进一步提出了由奇函数构造一个ＳＦＦ的定义式以及反相ＳＦＦ的概念。最后讨论了ＳＦＦ的一些重要性质及应用。

On Improving Self-Fourier Function Theory for Application to Optical Information Processing

In my several year research on optical information processing, I have come to find thatprevious theoretical work on self-Fourier function (in 1991, Caola [2] first used the term:"self-Fourier function" ) can be of much help. But further theoretical work needs to bedone to make it more useful in optical information processing.It is known that generally the space spectrum of an object is unlike the object itself.However, in Fourier optics, there are many important functions [1], which are their ownFourier transforms, defined as self-Fourier fUnctions (SFF's). Caola [2] has discovered aset of SFF's and proposed how to construct a SFF from an arbitrary and transformable function, i. e., Caola's SFF. Lohmann et al [3] discussed Caola's SFF and showed that Caoladiscovered all SFF's Proceeding from the cyclic property of a transform, Lohmann et al furthermore proposed that, for an arbitrary and cyclic transform, there is a self-transformfunction (STF), which can be constructed from an arbitrary and transformable function.Caola's SFF is just a special case of Lohmann's STF. In this paper, I show that the set ofSFF's as discovered by Caola does not include all SFF'S, and that the Caola's SFF is not applicable to odd functions. Eq. (26) can be used to construct a SFF from an arbitrary andtransformable odd function.