Optical interpretation of a complex-order Fourier transform.
Optical interpretation of a complex-order Fourier transform.
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DOI：
10.1364/ol.20.001178
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发表时间：
1995-05
期刊：
影响因子：
3.6
通讯作者：
C. Shih
中科院分区：
文献类型：
--
作者：
C. Shih
它表明，分数阶傅里叶变换的定义可以扩展到复阶政权。复数阶傅里叶变换处理积分中指数函数的虚部和真实的部。因此，虽然分数阶傅里叶变换的光学实现涉及梯度折射率介质或球面透镜，但复数阶傅里叶变换的光学解释实际上是基于卷积运算和高斯孔径。利用ABCD矩阵方法，解析地得到了高斯光束经复阶傅里叶变换后的束宽。
It is demonstrated that the definition of a fractional-order Fourier transform can be extended into the complexorder regime. A complex-order Fourier transform deals with the imaginary part as well as the real part of the exponential function in the integral. As a result, while the optical implementation of fractional-order Fourier transform involves gradient-index media or spherical lenses, the optical interpretation of complex-order Fourier transform is practically based on the convolution operation and Gaussian apertures. The beam width of a Gaussian beam subjected to the complex-order Fourier transform is obtained analytically with the ABCD matrix approach.