Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms.
Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms.
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DOI：
10.1364/josaa.20.000522
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发表时间：
2003-03
期刊：
影响因子：
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通讯作者：
S. Pei;Jian-Jiun Ding
中科院分区：
文献类型：
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作者：
S. Pei;Jian-Jiun Ding
偏移傅里叶变换（offset FT）、偏移分数阶傅里叶变换（offset FRFT）和偏移线性正则变换（offset LCT）是原始变换的空间平移和频率调制形式。它们比原始变换更具一般性和灵活性。我们推导了偏移FT、FRFT和LCT的本征函数和本征值。我们可以利用它们的本征函数来分析具有自由空间以及具有传递函数exp[j(h2x2 + h1x + h0)]（例如透镜和偏移透镜）的介质的光学系统的自成像现象。它们的本征函数对于共振现象分析、分形理论发展和相位恢复也很有用。
The offset Fourier transform (offset FT), offset fractional Fourier transform (offset FRFT), and offset linear canonical transform (offset LCT) are the space-shifted and frequency-modulated versions of the original transforms. They are more general and flexible than the original ones. We derive the eigenfunctions and the eigenvalues of the offset FT, FRFT, and LCT. We can use their eigenfunctions to analyze the self-imaging phenomena of the optical system with free spaces and the media with the transfer function exp[j(h2x2 + h1x + h0)] (such as lenses and shifted lenses). Their eigenfunctions are also useful for resonance phenomena analysis, fractal theory development, and phase retrieval.