Aberrations of self-imaged patterns with two-dimensional periodicity

We develop a geometrical theory of aberration in the self-imaged patterns with two-dimensional periodicity. The patterns are considered to be a crossed-line grating or a periodic array of finite apertures. We first derive the raytracing equations for determining the optical path of a self-imaging ray. We then find the third- and fifth-order contributions to the wavefront aberration which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We also derive the expression of the ray aberration from the wavefront aberration. The ray aberration is classified into five distinct types by analogy with the cases in a refracting lens system. We show that the overall ray aberration is entirely undercorrected and the aberrated image patch is decentered from an ideal image point in the direction parallel to the direction tangent vector of a chief ray. The image evaluation technique discussed here will be useful in various applications related to self-image formation of two-dimensionally periodic patterns.     

Geometrical aberrations of self-imaged line gratings

We analyze the properties of a self-imaging system from the point of view of aberration theory. We examine analytically and numerically the geometrical aberrations that are observed in the self-image of a parallel-line grating. We first derive the raytracing equations for determining the optical path of a self-imaging ray with the order of diffraction l. We then obtain the third- and fifth-order contributions to ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We show that the overall ray aberrations are entirely undercorrected. The ray aberrations approach zero as the ratio of the grating constant to the wavelength of light becomes large enough. In a case of unit magnification, no curvatures are observed in the self-imaged lines. If the magnification is bigger than unity, the light rays passing through the point in a positive or negative domain of the aperture variable contribute to the formation of the curved images. The image evaluation technique discussed here can be useful in the various applications related to the self-image formation of a parallel-line grating and it can also provide insight into the self-imaging of other periodic objects.     

一种新型的光栅成象型位移传感器

光栅的成象效应是光栅被点光源或扩展光源照明后自成象的一种特殊效应。该文应用傅里叶光学原理对扩展光源照明下光栅的成象特性作了分析,并由此设计出一种新型的光栅成象型位移传感器。     

利用保角变换实现环形光栅的Talbot效应

Talbot效应是一种近场自成像效应,通常只有周期光栅可以产生Talbot效应,而环形光栅无法产生.本文通过引入保角变换,发现可以在环形光栅外部设计适当的折射率渐变层介质,使得其中也能够产生严格的Talbot效应,并计算了对应的自成像半径表达式.本文利用FDTD软件分别将一个环形光栅放置在真空中以及人工设计的折射率渐变层中进行了模拟,并对二者的结果进行了比较分析,发现这种折射率渐变层介质确实对点光源入射的环形光栅的自成像情况有着很好的改善.希望这一工作能够推广Talbot效应的应用范围.     

Diffractive self-imaging based on selective etching of a ferroelectric domain inversion grating

A hexagonal array grating based on selective etching of a 2D ferroelectric domain inversion in a periodically poled Mg O-doped Li Nb O3 crystal is fabricated. The effects to the diffractive self-imaging as a function of diffraction distance for a fixed phase difference and array duty cycle of the grating is theoretically analyzed.The Talbot diffractive self-imaging properties after selective etching of a 2D ferroelectric domain inversion grating under a fixed phase difference are experimentally demonstrated. A good agreement between theoretical and experimental results is observed.     

Effects of third-order aberrations on the irradiance of self-image

We examine the effects of third-order aberrations exerted on the irradiance of image that is observable in a coherent self-imaging system. Both spherical aberration and astigmatism degrade the visibility of the image of a sinusoidal-type grating as well as blur the outline of the image of a rectangular-type grating. Coma laterally shifts the image of a sinusoidal-type grating on the image plane as well as changes a rectangular-type pattern into an asymmetrically blurred pattern. According to our analysis, the self-image of a high-density grating with a period of two times the optical wavelength is not at all affected by spherical aberration. In general a self-imaging system can always be corrected for astigmatism by shifting the image plane in its normal direction. We show that the self-image with defect can be well explained by taking the third-order aberrations and the focus-shift aberration into consideration.     

High-order Talbot fringes for atomic matter waves

We observe the interference of de Broglie waves in the diffraction near field of a microfabricated grating. The reduction of the grating period by self-imaging of second to seventh order is spatially resolved. We investigate the dependence of this effect on the de Broglie wavelength by a time-to-flight technique.     

Talbot imaging with increased spatial frequency: a technique for replicating truncated self-imaging objects

The Talbot effect in the presence of a convergent beam of coherent light yields a demagnified image of a self-imaging object. In fact, the object does not even have to fulfill the self-imaging condition; the object with truncated self-imaging feature is sufficient to yield an image that is sufficiently accurate for many practical purposes. We have taken this approach to fabricating circular gratings with a reduced period compared to the period of the mask. Using a simple experimental setup and a concentric circular grating mask, we have created images whose periods are either one-half or one-third of the mask's period. Demagnified Talbot imaging of fully or truncated self-imaging objects provides an attractive approach to photolithographic fabrication of structures whose periods are somewhat greater than the wavelength of the light source.     

矩阵光学与单双光栅成象研究

本文首次用矩阵光学理论结合光栅衍射相干条件,推出双光栅成象的几何光学表示式,用象位移叠加的观点解释了双光栅成象系统Talbot自成象以及双光栅成象现象,首次将双光栅成象现象分为1)基于光栅和透镜组成系统对第一块光栅进行成象的双光栅成象和2)基于编码光源成象原理的双光栅成象,指出这是两种截然不同的双光栅成象,扩展了双光栅成象的物理意义。最后给出了实验结果。     

用阴影莫尔条纹偏折术测量反射表面角位移

介绍一种阴影莫尔条纹偏折术。利用光栅自成象面的倾斜引起莫尔条纹方向变化来测量反射表面的角位移。     

Generation of achromatic and propagation-invariant spot arrays by use of continuously self-imaging gratings

A particular class of Montgomery's self-imaging objects that we call continuously self-imaging gratings (CSIG's) is introduced. When they are illuminated by a plane wave, these objects produce a field whose intensity profile is a propagation- and wavelength-invariant biperiodic array of bright spots. The mathematical construction of these objects and their intrinsic properties are described. On a practical level, CSIG's are compact and achromatic nondiffracting array generators. We show that a good CSIG approximation can be realized by a two-level phase grating that is experimentally tested.     

基于塔尔博特效应的分波器和分束器

给出一个单一器件同时具有分波器和大规模分束器功能的实验结果，其设计原理基于塔尔博特自成像效应。以两波长为例，通过改变分数塔尔博特距离和光栅周期等参量，实验上实现了两波长光信号在空间上的交叉分离。     

Phase interpretation for polarization-dependent near-field images of high-density gratings

It has been described that the near-field images of a high-density grating at the half self-imaging distance could be different for TE and TM polarization states. We propose that the phases of the diffraction orders play an important role in such polarization dependence. The view is verified through the coincidence of the numerical result of finite-difference time-domain method and the reconstructed results from the rigorous coupled-wave analysis. Field distributions of TE and TM polarizations are given numerically for a grating with period d = 2.3λ, which are verified through experiments with the scanning near-field optical microscopy technique. The concept of phase interpretation not only explains the polarization dependence at the half self-imaging distance of gratings with a physical view, but also, it could be widely used to describe the near-field diffraction of a variety of periodic diffractive optical elements whose feature size comparable to the wavelength.     

在超短脉冲照射下光栅的瞬时Talbot效应的研究

本文给出了光栅在超短脉冲照射下其瞬时Fresnel衍射光场的解析解.对该解析解的数值计算表明:当脉冲光波的半极大值全宽Δτ在几十个fs内,光栅的瞬时Talbot自成象现象消失,且Δτ越小或距离越远,瞬时光强波形与初始波形差异较大.而当Δτ达到ps的数值级时,瞬时Talbot自成象现象是存在的.     

基于X射线塔尔博特效应的纳米光栅制作模拟研究

沿纳米多层膜生长方向切割可制成周期只有几纳米而厚度几十微米的切片多层膜光栅. 基于该切片多层膜光栅塔尔博特自成像效应的X射线光刻是一种新型的纳米图样制作方法. 已有学者用该方法完成了百纳米结构光栅的制作. 采用严格耦合波方法, 本文模拟计算了切片多层膜光栅在满足塔尔博特自成像条件下的后表面光场分布, 详细讨论三个影响光栅后表面成像质量的重要参数:光栅厚度、材料厚度所占比例和多层膜周期. 模拟结果表明, 光栅厚度不仅影响X射线透射率, 还会改变像面条纹衬比度. 材料厚度比的大小直接决定像面是否存在清晰条纹, 选取合适的材料厚度比, 得到了前人实验中近场反常成像现象. 计算还表明, 在一定条件下, 采用周期更小的多层膜光栅有望获得更高分辨率的纳米图形, 这说明使用塔尔博特效应制作更加精细的纳米结构图形具有可行性.     

柱面镜对光栅自成像的旋转

本文运用傅里叶频谱分析方法，研究了柱面镜对光栅自成象的调制作用，发现光栅的自成象不仅周期和位置发生变化，而且产生了方向的旋转。文章分析了其旋转规律。     

The influence of the polarization effect in Talbot self-imaging of high-density gratings

The Talbot self-imaging of high-density gratings with different period at half Talbot distance for different polarization is analyzed with the finite-difference time-domain (FDTD) method. The numerical results indicate that the Talbot self-imaging of high-density gratings is obviously different for different polarization when the period d of the grating between 2λ and 3λ, which is verified through experimental results with the scanning near-field optical microscopy (SNOM) technique. Furthermore, the Fourier spectrum (far field) generated by the gratings is also given with the rigorous coupled-wave method, which is in agreement with the near field.     

Optical alignment using Fourier imaging phenomenon and Moire technique

Optical alignment operations and Fourier imaging phenomena have the common property that both occur in space along a straight line. The self-imaging property of a circular grating is applied to centring-error detection and to alignment in space. Moiré fringes due to the interaction of Fourier (or Fresnel) images with a detecting grating provide an indicator of the alignment state. The merit of this approach is that it is easy and comfortable to make visual observations. Various applications of the method depending on the choice of the reference points used are discussed and some experimental data are presented.     

Producing and testing binary amplitude gratings using a self-imaging and double-exposure technique

The influence of illuminating beam aberrations and master grating deviations on the performance of the technique of producing arbitrary opening ratio binary gratings using the self-imaging and double-exposure technique is studied analytically and experimentally. It is shown that due to the shear effect encountered in the direction perpendicular to the grating lines and due to the lateral displacement implemented between the two exposures the technique is sensitive to the first derivative of grating in-plane displacements and to the second derivative of the beam and grating out-of-plane errors.     

Talbot experiment re-examined: demonstration of an achromatic and continuous self-imaging regime

In the original Talbot experiment, a grating made of thin slits was illuminated in polychromatic light. Reconstituting this simple experiment, we have observed that at a certain distance from the grating, achromatic lines are formed whose transverse-resolution remains unaffected over a wide propagation-distance range. To our knowledge, this phenomenon has never been reported before. A theoretical explanation of this achromatic and continuous self-imaging regime is given and experimental results are reported.