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.     

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.     

Ray aberrations of two-dimensional oblique lattices on the self-image plane

We extend the geometrical theory of aberration for a self-imaging system to the case of two-dimensional oblique lattices. In our approach, the fundamental translation vectors of the lattice are not restricted in both length and orientation. Evaluating the disturbance of light through the oblique lattice under coherent illumination, we find the conditions of constraint which limit the self-imaging of the oblique lattice. Various types of oblique lattices are shown to obey the self-imaging conditions. We derive the equations to trace the optical paths of self-imaging rays and then analyze the ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of the corresponding actual ray. The ray aberrations are shown to disappear when the periods of the lattice are large compared with the wavelength of light. We find that the ray aberrations carried by self-imaged oblique lattices are totally undercorrected and the aberrated image patches are displaced along the direction tangent vector of a chief ray.     

First-order aberration of a misfocused self-imaging system

We analyze the characteristics of a self-imaging system that appear across a misfocused image plane. We approach this problem from the point of view of aberration theory. First, we derive the aberration functions (corresponding to several self-imaging rays of different orders) which are linear in a small shift of focus, and then we examine their roles in the amplitude spectra of misfocused self-images. We show that the aberration of the mth-order self-imaging ray is responsible for a lateral shift of the image amplitude component of frequency m/Mp, where M is the magnification of the system and p is the fundamental period of an object grating. We also analyze the role of wavefront aberrations in the image irradiance as an observable quantity. We then show that the theoretical estimation of irradiance of the aberrated image is in good agreement with the experiment and the focus-shift aberration can exert a severe effect on the irradiance spectrum of image in a complicated way.     

畴腐蚀掺镁铌酸锂可调阵列光分束器的研究

研究了不同畴腐蚀深度的掺镁铌酸锂二维六角可调阵列光分束器的分数Talbot效应.对不同Talbot分数β和不同畴腐蚀深度的阵列光分束器Talbot衍射像进行了数值模拟理论研究.模拟结果表明,Talbot分数β可以改变Talbot衍射像的周期及结构分布,而畴腐蚀深度可有效调制衍射像的光强分布.在理论研究的基础上,设计并制备了具有不同畴腐蚀深度的掺镁铌酸锂二维六角阵列光分束器,对其在不同Talbot分数β条件下的分数Talbot效应进行了通光实验研究,实现了畴腐蚀阵列光分束器对近场Talbot衍射光强分布的调制,实验结果与理论研究结果一致.     

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.     

泽尼克多项式校正全息阵列光镊像差的实验研究

像差会影响光镊对粒子的捕获效果. 全息阵列光镊中, 像差不仅来自光学元件, 由特定算法设计的光阱相位片也会在光路中引入像差. 本文通过液晶空间光调制器加载泽尼克多项式相位图, 对全息阵列光镊中由光栅透镜组型算法引起的像差进行校正. 结果显示: 利用三阶泽尼克多项式可有效消除光路中由光栅透镜组型算法引 起的慧差, 使得捕获2 μm聚苯乙烯小球的阵列光阱刚度提高了约40%; 对比不同项的像差校正结果发现, 全息阵列光镊中由算法引起的慧差 与光学元件引起的像差一样, 也会对阵列光阱的捕获效果产生较大影响; 同时根据一阶像差校正结果可得光栅透镜 组型算法对于一阶泽尼克像差具有鲁棒性. 实验结果表明, 对全息阵列光镊中由 算法引起的像差进行校正, 对于提高光阱的捕获效果和深化对算法特性的认识都具有重要意义.     

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。     

Aberrations in fractional-Talbot images of periodic binary gratings

We discuss the ray-optical aberrations which appear in the fractional-Talbot image of a periodic binary grating with coherent illumination. First we examine the complex amplitude of an aberration-free imaging field at a fractional-Talbot plane. We then trace the path of a diffracted ray of specific order which contributes to the fractional-Talbot imaging. Next we formulate the focus-shift and third-order aberrations which arise from a focusing error and a fourth-order approximation of the path length, respectively. We then evaluate the amplitude and phase of an aberrated imaging field that are represented in terms of aberration functions. When the grating period decreases to approach the optical wavelength, the aberrations of lower-order rays are shown to be more influential on the fractional-Talbot imaging field than those of higher-order rays. The theory of aberration discussed here could be very useful in evaluating the fractional-Talbot image of a periodic binary grating.     

Aberration theory of plane‐symmetric grating systems

Aberration theory of plane‐symmetric optical systems of mirror and grating has been developed based on the wavefront aberration method. A toroidal reference wavefront surface is used to define the wavefront aberration. Based on the ray geometry, the coordinate mapping relationships of the ray between the optical element and the incident and aberrated wavefronts are derived using a polynomial‐fit method; this enables the resultant coefficients of the wavefront and the transverse aberration to be kept to the fourth‐order accuracy of the aperture‐ray coordinates. By setting up the transfer equations of the field and aperture rays, the contribution to wavefront aberrations from each mirror and grating can be added to make the aberration calculation of multi‐element systems feasible. The theory is validated by the analytic formulae of the spot diagram.     

Aberrations of plane-symmetric multi-element optical systems

Based on a recently developed aberration theory of plane-symmetric grating systems, its aberration coefficients are firstly extended to be applicable to the plane-symmetric refractive optical surface. To justify the linear approximation of aperture ray in a multi-element system, the ray aberrations of double-element systems with the third-order accuracy of aperture ray are derived and expressed as the form of wave aberrations. The numerical comparisons are then made between the ray tracing, the aberration expressions with the linear and with third-order accuracy of the aperture ray. Moreover, the modifications of the wave and ray aberrations are discussed in the paper when the position of the principal ray changes.     

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.     

Unveiling Talbot Effect under Fresnel Diffraction at a Fork-Shaped Grating

The near-field effect of diffraction image self-reproduction or self-imaging of a periodic grating illuminated by quasi-monochromatic wave is well-known as the Talbot effect. Introducing a dislocation to a periodic structure provides a fork-shaped modulation of the phase/amplitude, which produces discrete diffraction pattern in a far-field consisting of optical vortices. In this paper, Fresnel diffraction at amplitude fork-shaped grating is theoretically and experimentally studied. The coexistence of spatial ordering and local violation of translational symmetry of the structure manifests itself in a strict diffraction pattern consisting of optical vortices in the far-field, which is shown to be accompanied by formation of a spatially ordered intensity distribution in the near-field, reminiscent the Talbot carpets for periodic structures. These results demonstrate the first evidence of Talbot effect occurred under light diffraction at fork-shaped gratings, being promising for deep understanding of near-field singular optics phenomena.     

Automated collimation testing in Lau interferometry using phase shifting technique

We demonstrate an automated procedure for detection of collimation position of an incoherent beam in Lau interferometry using phase shifting technique. The experimental arrangement consists of a Lau-based interferometer in which light from a source grating illuminates a set of two coarse gratings separated by self-imaging distance. Phase shifting procedure is incorporated by translating the detector grating, corresponding to different positions of the collimating lens. The phase map is plotted corresponding to each position. The slope of the phase map is indicative of the collimation position of the optical beam. The technique is fully automatic and provides good accuracy and high precision.     

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.     

Design of an augmented reality display based on polarization grating

A new optical system for an augmented reality(AR) display is proposed in this paper.The optical system mainly includes a ray deflector, coupling input grating, optical waveguide, and coupling output grating.Both the ray deflector and the coupling input grating are designed based on the diffraction characteristics of the polarization grating, and the coupling output grating is the Bragg reflection grating.Compared with other AR schemes, this AR optical system not only reduces the number of projections from two to one, but also improves the efficiency of light coupling into the optical waveguides.The energy loss is reduced by utilizing the single-order diffraction characteristics of the polarization grating in its coupling input structure.The light deflector uses the polarization selectivity of the polarization grating and the characteristics of the rotating light of the twisted nematic liquid crystal layer to realize beam deflection.The working principle of the optical system is experimentally and theoretically demonstrated.     

Accordion lattice based on the Talbot effect

We introduce an idea of producing an optical lattice relied on the Talbot effect. Our alternative scheme is based on the interference of light behind a diffraction grating in the near-field regime. We demonstrate 1D and 2D optical lattices with the simulations and experiments. This Talbot optical lattice can be broadly used from quantum simulations to quantum information. The Talbot effect is usually used in lensless optical systems, therefore it provides small aberrations.     

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.     

Detection of wave aberrations in the human eye using a retinoscopy-like technique

The influence of optical aberrations on the retinoscopic reflex is theoretically analyzed from a geometrical point of view. The relationship between the wave aberrations to the ray aberrations is applied to explain the appearance of the retinoscopic patterns for different types of ocular aberrations. Several schematic models of the human eye are tested numerically, showing that a careful retinoscopic examination can detect the usual eye aberrations.     

论平面光栅单色计的光学质量

本文包括下列结果:1.以矢量代数方法一般地讨论了狭缝形状和谱线形状的关系;导出了一般的角色散公式。2.讨论了由于光栅角倍率特点所残留的不对称象差及其校正方法和其他象差之值,并举出一个校正象差的例。3.探讨了完全校正象差的可能有的结构及其特性。 关键词：