IMAGE ROTATION, WIGNER ROTATION, AND THE FRACTIONAL FOURIER-TRANSFORM
IMAGE ROTATION, WIGNER ROTATION, AND THE FRACTIONAL FOURIER-TRANSFORM
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DOI：
10.1364/josaa.10.002181
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发表时间：
1993-10-01
影响因子：
1.9
通讯作者：
LOHMANN, AW
中科院分区：
文献类型：
--
作者：
LOHMANN, AW
在这项研究中，普通傅里叶变换的阶数\(p = 1\)。分数阶傅里叶变换，例如阶数\(P = 1/2\)，如果连续应用两次则执行一次普通傅里叶变换。奥扎克塔斯和门德洛维奇[“分数阶傅里叶变换及其光学实现”，《光学通讯》（待发表）]基于一段适当长度的渐变折射率（GRIN）光纤将执行傅里叶变换这一事实，将分数阶傅里叶变换引入光学领域。将那段GRIN光纤切割成更短的片段相当于将普通傅里叶变换分解为分数阶变换。我通过另外两种方式来探讨分数阶傅里叶变换这一主题。首先，我指出了图像旋转、维格纳分布函数的旋转以及分数阶傅里叶变换之间的算法同构。其次，我提出了两种能够执行分数阶傅里叶变换的光学装置。
In this study the degree p = 1 is assigned to the ordinary Fourier transform. The fractional Fourier transform, for example with degree P = 1/2, performs an ordinary Fourier transform if applied twice in a row. Ozaktas and Mendlovic [''Fourier transforms of fractional order and their optical implementation,'' Opt. Commun. (to be published)] introduced the fractional Fourier transform into optics on the basis of the fact that a piece of graded-index (GRIN) fiber of proper length will perform a Fourier transform. Cutting that piece of GRIN fiber into shorter pieces corresponds to splitting the ordinary Fourier transform into fractional transforms. I approach the subject of fractional Fourier transforms in two other ways. First, I point out the algorithmic isomorphism among image rotation, rotation of the Wigner distribution function, and fractional Fourier transforming. Second, I propose two optical setups that are able to perform a fractional Fourier transform.