失调分数傅里叶变换及其光学作用

利用失调光学系统的衍射积分公式,分析了失调的Lohmann分数傅里叶变换光学系统和准非对称非均匀介质的衍射特性,得到了两者具有相同的失调衍射积分表达式,表明两者具有等效性,从中提出了失调分数傅里叶变换新概念. 关键词： 分数傅里叶变换 失调光学系统 衍射积分 梯度折射率介质     

失调光学系统衍射的分数傅里叶变换表述

本文对一般的失调多元件光学系统衍射积分公式进行了整理分析,在空域和频域中分别引进缩放变量,讨论得到了满足一定条件下失调多元件光学系统衍射的分数傅里叶变换表述.     

失调单球面折射系统的衍射积分和分数傅里叶变换

根据球面的几何特征，分析了单球面折射光学系统折射面倾斜和偏心时的失调特征；由失调元件矩阵和共轴元件矩阵的依次相乘，得到了完备的描述失调单球面折射光学系统的矩阵；从系统衍射积分与失调矩阵元的关系导出了该系统的失调衍射积分，并利用单球面折射光学系统的分数傅里叶变换结构参数得到了系统失调时的分数傅里叶变换结果.这些结果可用于数值计算和模拟该系统失调时对输入复振幅的衍射和分数傅里叶变换.     

一阶光学系统分数傅里叶变换的相空间分析

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.     

超洛伦兹-高斯光束SLG11模的分数傅里叶变换特性

 引入了一簇互相正交的超洛伦兹-高斯光束以描述半导体激光器所产生的大角度高阶模远场分布。将分数傅里叶变换应用于超洛伦兹-高斯光束SLG­₁₁模的传输特性的研究中。利用傅里叶变换的卷积原理,导出了SLG₁₁模经分数傅里叶变换系统后场分布的解析表达式。根据所得到的公式进行了数值计算,系统分析了分数傅里叶变换阶数和光束各参数对SLG₁₁模在分数傅里叶变换面上光强分布的影响。结果显示：SLG₁₁模在分数傅里叶变换面上的归一化强度分布随分数傅里叶变换的阶数呈周期性变化,周期为2;随着光束参数的增大,SLG₁₁模在分数傅里叶变换面上的光斑尺寸增大。     

求解分数傅里叶变换衍射积分的一种快速算法

在对Lohmann 二型分数傅里叶变换(FRT)和菲涅耳衍射积分进行比较的基础上,给出基于快速傅里叶变换(FFT)求解该分数傅里叶变换和菲涅耳衍射积分的快速算法及算法适用范围.数值模拟实验证明了理论的可靠性和算法的高效性.此快速算法为分数傅里叶变换在工程实际中的进一步广泛应用奠定了基础.     

分数域滤波的分数傅里叶变换光学成像性能分析

将分数域滤波同光学成像相结合,提出了一种基于Lohmann Ⅰ型的带有滤波孔径的两级联分数傅里叶变换光学成像系统.根据分数傅里叶变换和菲涅耳衍射之间的关系以及分数傅里叶变换的分数阶可加性,结合分数域滤波分析了分数傅里叶变换光学成像的基本理论.以点扩散函数和调制传递函数作为评价成像质量的准则,详细分析了不同分数阶光学系统...     

抗癌药物铂络合物构效关系的物理方法研究

本文用X射线衍射、傅里叶变换红外光谱、差热分析等物理方法研究了抗癌药物铂络合物特性、结构以及构效关系。研究结果表明:cis-[Pt(NH₃)₂Cl₂]属简单斜方晶系,晶格常数a=0.9221nm,b=0.8771nm,c=0.6890nm.草酸二氨合铂的结构为斜方晶系,其晶格常数为:a₁=1.0721nm,a₂=0.6402nm,a₃=1.8570nm,并用傅里叶变换红外光谱、差热分析、元素分析等方法对它们理化特性进行了研究.     

用时域ABCD矩阵对调Q锁模激光器的研究

用时域ABCD矩阵讨论了调Q锁模脉冲激光器输出脉冲的宽度和啁啾特性,主要给出了调Q元件作为幅度调制元件时的时域ABCD矩阵,并将光脉冲在激光腔中往返一周的ABCD矩阵写出,用此矩阵讨论了它对锁模脉冲的影响.给出了Nd:YAG激光器中用Cr⁴⁺:YAG作调Q元件时的调Q锁模脉冲激光器特性,并讨论了腔内色散、饱和吸收强度、增益带宽对输出脉冲特性的影响.用时域ABCD矩阵大大简化了计算过程.     

失调光学系统的衍射积分公式

从Collins衍射积分理论出发,用增广的4×4阶变换矩阵元表示衍射积分的核,得出了失调光学系统的衍射积分公式。 关键词：     

Fractional Fourier transform for partially coherent beam in spatial-frequency domain

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.     

Analytical formula for a circular flattened Gaussian beam propagating through a misaligned paraxial ABCD optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a misaligned paraxial ABCD optical system in the cylindrical coordinate system, analytical formula for a circular flattened Gaussian beam propagating through such optical system is derived. Furthermore, an approximate analytical formula is derived for a circular flattened Gaussian beam propagating through an apertured misaligned ABCD optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Numerical examples are given.     

Propagation Effect of Hollow Gaussian Beams Passing through a Misaligned Optical System

A generalized formula of hollow Gaussian beams through the first-order misaligned ABCD systems is derived by using the generalized diffraction integral formula. It is shown that the hollow Gaussian beam passing through the misaligned system becomes a decentred hollow Gaussian beam. The propagation properties of the output beam are investigated when it propagates through a simple misaligned lens system. These results provide a powerful theoretical tool for applications of optical traps.     

Propagation characteristics of Bessel-like beams through ABCD optical system

Based on the Collins diffraction integral formula, this work focus to the study of the propagation properties of a Bessel-like beam through an ABCD optical system. As it is not easy to develop an analytical expression describing the transformation of the Bessel-like beams by an ABCD optical system, numerical integration method was indispensable to conduct this research. The characteristics of the transformation of Bessel-like beams by three optical systems: free space, Fourier transform, Fractional Fourier transform system and quadratic graded-index system are numerically examined and treated as examples of optical systems in this investigation. Some numerical results are carried-out to show how the superposition of multiple Airy beams propagates and transforms by an ABCD optical system.     

Propagation of hollow Gaussian beam through a misaligned first-order optical system and its propagation properties

Propagation properties of hollow Gaussian beam through a misaligned first-order ABCD system is studied using the generalized Huygens-Fresnel diffraction integral, augmented matrix. It is shown that, as a hollow Gaussian beam passes through the misaligned first-order ABCD system, the beam shape is not preserved, the out-put beams have differences when passing different misaligned optical systems. We can adjust the size of dark region through adjusting the misaligned transverse vector E.     

Propagation of elliptical cosh-Gaussian beams in a misaligned optical system

On the basis of the generalized diffraction integral formula for misaligned optical systems in spatial domain, an analytical propagation expression for the elliptical cosh-Gaussian beam (EChGB) passing through misaligned optical systems is obtained by using vector integration. Some numerical simulations are illustrated for the propagation properties of an EChGB through a misaligned optical transforming system with a misaligned thin lens. As an application example, the propagation of off-axial EChGBs passing through misaligned optical systems is studied, and further extensions are also pointed out.