1维线阵离轴高斯光束的分数傅里叶变换

 为研究非相干的1维线阵离轴高斯光束通过分数傅里叶变换(FRFT)系统的传输特性,利用Collins积分公式,导出了其在FRFT面上的光强分布解析式,并利用此解析式作数值计算和分析。研究表明：非相干的1维线阵离轴高斯光束在FRFT面上的光强分布由FRFT的阶数和子光束数目共同决定,其归一化的光强分布随FRFT的阶数周期性变化,周期为2;子光束数目的大小及其奇偶性对归一化光强分布的影响取决于FRFT的阶数;轴上归一化光强分布也随FRFT的阶数周期性变化,变化周期也为2。     

光束分数傅里叶变换的Wigner分布函数分析方法

利用Wigner分布函数(WDF)方法，对光束的分数傅里叶变换特性进行了研究.以厄米 高斯(H G)光束为例，导出了H G光束在分数傅里叶变换面上光强分布的解析公式和H G光束在分数傅里叶变换面上束宽的解析计算公式.通过数值计算研究了H G光束光强随分数傅里叶变换阶数变化的规律.研究表明：选取适当的分数傅里叶变换阶数p，在x，y方向可以得到相等束宽的对称光强分布. 关键词： Wigner分布函数 厄米 高斯(H G)光束 分数傅里叶变换     

分数傅里叶变换面上余弦-高斯光束的变换特性

 利用Wigner分布函数的方法，研究了余弦-高斯光束的分数傅里叶变换特性。导出了余弦-高斯光束在分数傅里叶变换面上光强分布和束宽的解析计算公式，并对此进行了数值模拟计算。研究表明：分数傅里叶变换阶数对余弦-高斯光束的光强分布有明显影响，余弦-高斯光束的轴上光强随分数傅里叶变换阶数呈周期性变化，束宽随分数傅里叶变换阶数也呈周期性变化，周期为2；对给定调制参数的余弦-高斯光束，通过适当选取分数傅里叶变化阶数可以获得平顶的光强分布。     

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。     

一种基于角谱理论的光学FRFT的数值模拟算法

以角谱传播理论和分数傅里叶变换(FRFT)的单透镜和双透镜光学实现单元为理论基础,提出了一种基于实际光学结构的光学FRFT的数值模拟算法,推导了该算法中采样间隔的选取方法,并利用Matlab语言编写了相应的处理程序,将该程序对方孔分数傅里叶变换的计算结果与实际实验结果相比较,结果表明该算法是实际光学结构在理想情况下的模拟,因此,该数值计算在一定程度上可以代替柱面镜对光场实现分数傅里叶变换,也可以为实际实验提供很好的参考和指导。     

多维傅里叶变换光谱

二维或多维傅里叶变换谱的概念最早是在核磁共振(NMR) 谱学中提出的,随着激光技术 的发展,飞秒脉冲激光的实现使多维傅里叶变换谱的概念被引入到了光学领域,以脉冲激光代 替NMR 中的射频(RF) 场,激光波长从红外延伸到可见光波段。多维傅里叶变换光谱可以同时 提供的信息包括量子态上布居数以及量子态间的耦合,所以多维谱可以提供一维谱所无法获取的 反映量子系统演化动力学的信息,如量子系统中的能量转移以及分子间的相互作用等。人们使用 多维傅里叶变换光谱的方法对碱金属原子、量子阱、分子等量子系统中的动力学过程进行了一系 列的研究。     

用Wigner分布函数方法研究平顶多高斯光束的分数傅里叶变换

本文用Wigner分布函数方法分析了平顶多高斯光束的分数傅里叶变换。导出了分数傅里叶变换面上光的强度、束宽、远场发散角、M2因子和K参数的解析表达式。通过数值模拟研究了分数傅里叶变换阶数对平顶多高斯光束传输性质的影响。     

余弦高斯光束通过含球差分数傅里叶变换系统的传输

实际应用中球差作为一种普遍存在的像差,对光束在光学系统中的传输具有较大影响。为了研究球差对光束通过分数傅里叶变换系统后所产生的影响,基于柯林斯公式,推导出余弦高斯光束在有球差和无球差的分数傅里叶变换系统中的场分布,并以LohmannⅠ型系统为例,进行数值模拟计算,研究了余弦高斯光束通过有球差和无球差的分数傅里叶变换系统后输出面的横向光强分布规律以及不同变换阶数和不同调制参数下轴上光强大小与球差系数的关系。结果表明,在分数傅里叶变换系统中,透镜球差对输出面横向光强分布有较大影响,并且正球差和负球差对横向光强的影响效果有明显区别。不同变换阶数和不同调制参数下透镜球差对轴上光强的作用效果不同。     

健康人体乳腺傅里叶变换红外光谱特征参数分析

通过应用傅里叶变换红外光谱仪(FTIR)的中红外光导纤维并联合衰减全反射探头(ATR)对招募的200名女性健康志愿者的右侧乳腺外上限部位皮肤进行扫描采集相应的傅里叶变换红外光谱,由此共获取200条正常人体乳腺的傅里叶变换红外光谱图。进一步对所得的200条正常人体乳腺傅里叶变换红外光谱图中与脱氧核糖核酸、核糖核酸、蛋白质、脂类、糖类等生物化学成分相关的12条特征谱带进行分析研究,并对这些特征谱带的峰位(P)、峰强(I)、半高宽(F)等36个特征性红外光谱参数进行统计学分析,同时计算相应特征红外光谱参数的90%正常参考值范围、均值、标准差等数值。研究结果首次对正常人体乳腺傅里叶变换红外光谱图相关特征光谱参数的数据建立了正常参考范围,同时为傅里叶变换红外光谱技术进一步实现其在乳腺良恶性疾病诊断方面无创、快速、高效的特有临床应用价值提供相应的理论依据。     

傅里叶变换红外光谱仪探测器仪器响应函数研究

由于傅里叶变换红外光谱仪探测器在各个波段的仪器响应不相同,在应用过程中无论是利用光谱的绝对强度还是相对强度,都需要应用标准黑体对仪器进行定标,找出仪器响应函数。该文对加拿大BOMAN公司MR154型傅里叶变换红外光谱议配带的两个红外探测器(锑化铟InSb、碲镉汞MCT)的仪器响应函数进行了研究,并找出了它们随黑体温度(辐射亮度)的变化规律。该规律对傅里叶变换红外光谱仪的定标和保证所测辐射谱的正确性有重要意义。     

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...     

Fractional Fourier transform of Airy beams

An analytical expression of an Airy beam passing through a fractional Fourier transform (FRFT) system is presented. The effective beam size of the Airy beam in the FRFT plane is also derived. The influences of the order of FRFT, the modulation parameter, and the transverse scale on the normalized intensity distribution and the effective beam size of an Airy beam in the FRFT plane are examined. The order of FRFT controls the effective beam size and the orientation of the beam spot. The modulation parameter affects the effective beam size and the number of lateral side lobes. The normalized intensity distribution and the effective beam size are both proportional to the transverse scale.     

杨氏双缝干涉实验中光谱奇异现象的特性分析

研究了完全相干光和部分相干光分别照射双缝时,杨氏双缝干涉实验中干涉场区的光谱变化现象.根据干涉场中光谱标准矩定义了光谱的相对光谱移动和相对光谱增宽,并利用相对光谱位移和相对光谱增宽分析了光谱奇异现象的特性.研究结果表明,入射光的某些光谱参量（如源光谱宽度Γ0,中心拦截比ε,相对空间相干度Δ0）对相对光谱增宽的影响相当大.结果还表明了光谱标准矩方法是定量研究光在传输中的光谱变化以及光谱奇异现象的有效工具.     

Spectral intensity characteristics of partially coherent flattened multi-Gaussian beams with an axial shadow passing though paraxial ABCD optical systems

Based on the beam model for the flattened multi-Gaussian beams (FMGBs) with an axial shadow and partially coherent theory, the expression for cross-spectral density of partially coherent FMGBs with an axial shadow has been given, and the analytical expression for the spectral intensity of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems has been derived. The spectral shift of partially coherent FMGBs with an axial shadow focused by a thin lens has been analyzed quantitatively. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed in detail. Our results show that the spectral intensity and the spectral shift of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems depend on the source spectral density, the generalized Fresnel number of the system, the transverse coordinate, the spatially coherence parameter, as well as the beam orders.     

Spectral shift of partially coherent flattened multi-Gaussian beams with a hole passing through ABCD optical systems

Based on flattened multi-Gaussian beam model and partially coherent theory, the expression for cross-spectral density of partially coherent flattened multi-Gaussian beam with a hole was given. The analytical expression for on-axis spectrum of partially coherent flattened multi-Gaussian beam with a hole passing through a paraxial ABCD optical system was derived. The spectral shifts of the partially coherent flattened multi-Gaussian beam with a hole propagating in free space and passing through the lens have been analyzed. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed. Our results show that the inner radius of flattened multi-Gaussian beam with a hole determines its relative spectral shift in near field and its outer radius determines that in far field. For the flattened multi-Gaussian beam with a hole passing through a lens, the on-axis relative spectral shift changes sharply near the focal plane with the increase in Fresnel number and the spatial coherence parameter.     

Fractional Fourier transform of Lorentz beams

This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.     

Fractional Fourier transforms of elliptical Hermite-cosh-Gaussian beams

A new kind of laser beams named the elliptical Hermite-sinusoidal-Gaussian beams (EHSGBs) is introduced and defined by use of tensor method, and the elliptical Hermite-cosh-Gaussian beam (EHChGB) can be regarded as special case of EHSGBs. The fractional Fourier transform (FRFT) is applied to treat the propagation of EHChGBs. An analytical expression for an EHChGB passing through an FRFT system is derived by using vector integration. Some numerical simulations are illustrated for the propagation properties of EHChGBs through FRFT systems.     

The ultraviolet spectrum of SO2 in matrix isolation and the vibrational structure of the 2348 Å system

The absorption spectra of SO₂ in solid neon and argon have been observed in the spectral regions near 2200 Å and 2900 Å. The spectral shifts of the electronic transitions in the matrix relative to the vapor are reported, including a shift with aging of the matrix. Implications for the interpretation of the vibrational structure of the 2348 Å system are discussed. A large spectral shift is attributed to a shift of the vibrational frequency 2ν₃′ of the excited electronic state.     

Spectrum measurement in the fractional Fourier domain

Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of real-time measurement of the spectrum of a signal in the FRFT domain. In this paper, we propose two approaches for real-time measurement of the FRFT of a signal based on modulation and bandpass filtering systems. The relation is established between the linear frequency modulation (LFM or chirp) spectrum and the FRFT of its envelope. In addition, two applications for spectrum measurement are presented in the FRFT domain. The LFM signal can be bandlimited in the Fourier transform (FT) domain through spectrum measurement associated with bandpass filtering method. The results can also be useful in the problems related to swept-frequency filter for measurement in the FRFT domain.