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The relation between the 2nd fractional Fourier transform and the imaging process of an optical system is discussed. By changing the coordinate scales of the input plane in respect to the magnification of the optical imaging system, the fractional Fourier transform can be a powerful tool in designing specific imaging system. The Gaussian imaging formula of single lens is obtained by using the tool. Finally the procedures are generalized for designing a double-lens imaging system through an example. 相似文献
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透镜组合实现光学分数傅里叶变换 总被引:4,自引:0,他引:4
从光学系统脉冲响应函数理论的角度分析了秀镜组合实现光学分数傅里叶变换的结构及标准焦距的物理意义,推导了几种较普遍的实现光学分数傅里叶变换的结构,利用该结构可以方便地改变其标准焦距,这对设计由多级数傅里叶变换级联构成的空间变化滤波系统具有重要的指导意义。 相似文献
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提出了一种基于分数阶傅里叶变换的模式测控一体化方法。利用分数阶傅里叶变换光路对光纤模式耦合态进行空间调制和相位调制,以实现模式的有效分解。与双重傅里叶变换(F2)法以及空间和频谱成像(S2)法相比,采用的分数阶傅里叶变换法,通过改变分数阶参数,控制模式的空间分布以及模式间的叠加状态,更易于分解出高阶模式。基于分数阶傅里叶变换的模式测量方法可在更广泛空间,研究模式的空间和相位叠加以及模式分解,也可退化为F2法和S2法。 相似文献
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Based on the coherent optical theory, we extend the fractional Fourier transform of first-order correlation to a fractional Fourier transform of second-order correlation. An optical system for implementing a second-order fractional Fourier transform was designed. As a numerical example, we investigate the second-order fractional Fourier transform for a single slit. 相似文献
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一阶光学系统分数傅里叶变换的相空间分析 总被引:1,自引:0,他引:1
在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件. 相似文献
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分数傅里叶变换和失调光学系统的衍射积分公式 总被引:3,自引:2,他引:1
空域中光束通过失调的ABCD光学系统的衍射积分公式在满足一定条件下,可实现分数傅里叶变换.同时,对角谱通过失调的ABCD光学系统变换的频域衍射积分公式也可实现分数傅里叶变换.最后,以单透镜失调光学系统为例说明其应用. 相似文献
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We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function (PSF) of an incoherent defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invariant to the defocus-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function. 相似文献
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The recent progresses on the propagation, generation and application of partially coherent beam (PCB) are reviewed in this
paper. A new tensor ABCD law for treating the propagation of partially coherent Gaussian-Schell model (GSM) beams through
a paraxial optical system is derived. The focusing, spectral shift and fractional Fourier transform of the GSM beam are investigated
by using the tensor method. The generation of PCB with special optical resonator is studied both theoretically and experimentally.
Furthermore, the ghost imaging and superluminal propagation of the PCB is discussed. The results show clearly that the coherence
of light have strong influences on the ghost imaging and superluminal propagation.
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Fractional Fourier transform for partially coherent beam in spatial-frequency domain 总被引:1,自引:0,他引:1 下载免费PDF全文
By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatial-frequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian-Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatial-frequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain. 相似文献
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The beam waist-to-waist transformation of Gaussian beams between input and output reference planes described by the scaled fractional Fourier transform is analyzed in this paper. We obtain the transfer matrix of ABCD optical system that corresponds to the scaled fractional Fourier transform. The results show that the beam waist-to-waist transformation of Gaussian beams can be described by the scaled fractional Fourier transform when the ABCD optical system has a suitable transfer matrix. The relationship between the input and output waist planes and some particular cases when a Gaussian beam passes through a thin lens is also discussed. 相似文献
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为满足红外成像光谱仪大光通量、高稳定性的应用需求,提出了一种基于多级阶梯微反射镜的静态化、无狭缝式、新型红外时空联合调制型傅里叶变换成像光谱仪结构.对其工作原理和光程差的产生方式进行了分析.作为该成像光谱仪的重要部件,前置成像系统决定了光程差的分布,其性能直接影响到目标物体的图像质量.根据系统光程差的产生方式,分析和设计了像方远心光路结构的前置成像系统.利用被动光学消热差方法对前置成像系统进行了消热差研究.结果表明:当温度在-20—60?C的范围内时,各个视场的调制传递函数均达到衍射极限,在多级阶梯微反射镜的总阶梯高度范围内成像质量良好;在不同的温度下,各视场处主光线在像面上的最大入射角小于0.02?. 相似文献
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基于级联分数傅里叶变换系统的数字水印技术 总被引:1,自引:0,他引:1
提出一种基于分数傅里叶变换和随机相位编码的光学加密数字水印技术,可成为一种信息隐藏及保护的有效方案.该数字水印技术对于噪音叠加和常见的图像处理操作具有较强的稳健性.该技术根据光学级联分数傅里叶变换系统,利用两个随机相位分布函数对水印信息编码并经过迭代分数傅里叶变换嵌入到变换域的载体图像中.在水印检测和提取过程中,两个相位分布函数作为密钥.随机相位编码技术的引入,进一步提高了数字水印系统的密钥空间.增强了系统的安全性.该数字水印技术基于光学分数傅里叶变换原理,可以利用光学变换系统方便地实现. 相似文献
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基于随机分数傅里叶变换的双图像加密算法 总被引:3,自引:2,他引:1
利用光学随机分数傅里叶变换设计了一种双图像加密算法,并给出了相应的光学实现.加密算法中,将两幅原始图像分别作为加密系统输入复函数的振幅和位相分布函数,利用随机分数傅里叶变换进行加密,所得复函数的振幅即为加密图像,而位相部分是变换的输出相位,随机位相作为加密算法的密码.在数值模拟中,二值文本图像和灰度图像分别被作为原始图像用于加密结果分析和加密安全测试,结果表明该加密算法具有很好的安全性. 相似文献