Quadric wavefront aberrations in phase-type images of binary amplitude gratings with small opening ratios

We discuss the quadric wavefront aberration of a fractional Talbot imaging ray which distorts the phase-type image of a binary amplitude grating with a small value of the opening ratio. When the opening ratio is equal to 1/2 or 1/3, the imaging rays are shown to have no quadric wavefront aberrations. For the opening ratios of 1/4 and 1/5, two different types of quadric wavefront aberrations are responsible for the three-level phase images. If the opening ratio gets to 1/6, we find that three different types of quadric wavefront aberrations distort the fractional Talbot image. The quadric wavefront aberration formulated here may be used in evaluating the phase-type image of a binary amplitude grating with an arbitrary value of the opening ratio.     

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.     

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.     

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.     

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.     

Computation of the aberrations of concave diffraction gratings. Part 2. Aberration calculations and estimation of resolving power

The aberrations of a concave grating are derived by computation; the resolving power is estimated from the intersections of the rays with the image plane. It is shown that an aspheric grating can be used to advantage in a monochromator of Zeya-Namioka type.We are indebted to V. A. Efimov for compiling the computer program.     

Phase contrast, phase retrieval and aberration balancing in shift-invariant linear imaging systems

We treat the problems of phase-contrast image formation, deterministic phase retrieval and aberration balancing, in the imaging of weak objects using two-dimensional shift-invariant linear imaging systems. Three classes of model sample are considered: weak phase objects, weak phase-amplitude objects and single-material weak phase-amplitude objects. For each class of sample we show how the various aberration coefficients, which characterise a given imaging system, contribute to the structure of the associated phase-contrast image. The corresponding inverse problem, of obtaining a closed-form expression for the input wave-field given one or more aberrated phase-contrast images of the same, is then examined. Two sample applications are considered: analyser-crystal phase-contrast imaging of weak objects using hard X-rays, and Zernike-type phase-contrast imaging. We close with a discussion of how coherent and incoherent aberrations may be “balanced” against one another, briefly mentioning the applications of this idea to both “deblur by defocus” and proximity-corrected X-ray lithography.     

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.     

基于位相变更的非相干数字全息自适应成像

菲涅耳非相干数字全息作为一种非扫描的三维成像技术具有其独特的优势,但其成像过程中会受到各种像差的影响,导致成像分辨率、再现像的质量降低.为了解决这一问题,可以结合适当的自适应光学技术对波前像差进行探测和校正.位相变更是一种基于两幅具有已知位相差的强度图像实现波前探测和像差校正的技术.本文发展了基于位相变更的非相干数字全息自适应成像技术,不需要引入引导星,利用全息记录过程中的两幅相移全息图,实现波前像差的探测.本文给出了所发展技术的数值仿真和实验结果,结合位相变更算法求解出系统像差的位相分布,将像差的共轭位相加载到光瞳面上,在全息图记录的同时校正像差,从而提高重建像的质量.     

空间高层大气遥感远紫外成像光谱仪的光学系统

空间高层大气遥感远紫外成像光谱仪主要用于观测高层大气中的远紫外辐射和实现对其内部中尺度现象成像的功能。目前我国该类的相关仪器研究基础还比较薄弱,针对这种情况,在光学系统设计的角度上给出了一种适用于130～180nm波段探测的光学系统方案。该成像光谱仪光学系统以离轴抛物镜为物镜,串联Wadsworth结构为成像光谱系统;这种串联Wadsworth成像光谱系统采用离轴抛物镜做准直镜,分光器件为平面光栅和球面光栅串联,实现二次色散,同时球面光栅起到聚焦成像作用;在像差理论的基础上,对该结构的光程函数和各像差进行了分析,获得了改进结构的宽波段完善成像条件。针对低轨空间探测应用要求设计了相关改进型Wadsworth结构成像光谱仪光学系统,设计结果证明系统像差得到了充分校正,在奈奎斯特频率(20lp/mm)下全视场全波段调制传递函数值在0.6以上。该优化结构同时具备高空间分辨率和高光谱分辨率,性能优越。     

宽光谱平像场全息凹面光栅的优化研究

基于凹面光栅的几何理论,推导了子午、弧矢聚焦曲线的数学表达式和全息平像场凹面光栅制作参数的计算关系式.提出了一种新的在整个使用波长范围内同时消除子午和弧矢像差的最佳优化设计方法.这种方法不同于以光线追迹技术为基础的标准光学设计软件如CODEV或ZEMAX的优化设计方法,而是从数学表达式出发,采用光栅优化因子,对凹面光栅的子午聚焦曲线和弧矢聚焦曲线进行拟合,从理论上找到最佳的能够使子午和弧矢像差同时趋于零的像平面,然后再根据拟合参数设计制作光栅.用Matlab软件解决了子午聚焦曲线超越方程无法解的困难;讨论了不同光栅常数和入射角度时对两聚焦曲线拟合程度的影响.提出了在宽光谱使用条件下,可以通过减小入射角度和光栅刻线数来提高光谱像质.     

复杂分光仪器中的像差研究

为提高分光仪器的性能,采用两个椭球面镜和一个椭球面消像差光栅分光。光源发出的光线被第一个椭球面镜反射,产生特定的波前,经过光栅衍射以后,不同波长的光波被第二个椭球面镜汇聚到探测器的不同位置上。系统具有复杂的像差特性和成像特性,根据费马原理,参考第二代全息变线距光栅的制作光路和理论,建立坐标系,定义两个椭球面上的入射角和反射角,确定各元件的位置变量,确立基本几何关系,将光程函数分为两部分:由衍射引起的光程变化和几何位置引起的光程变化,将两部分都按级数展开,给出了高阶像差的解析形式。对于平面、柱面、球面光栅和反射镜也可以使用这些公式。像差的解析式和光路也可以用于各种分光仪器中。     

脉冲压缩光栅光路调节新方法研究

介绍了一种简单而实用的大口径脉冲压缩光栅光路调节方法,有效解决了普通光路调节方法中轴向调节精度不高的问题。首先由全息透镜(光栅)成像公式出发,推导出了该光路调节的基本原理。并从光栅记录系统与光栅衍射波像差的关系,结合初级像差理论推导得出叠栅条纹像差为0.4786λ,大约是光栅衍射波像差(0.25λ)的两倍,利用此关系也可对光栅衍射波像差进行实时监测。从数值模拟结果可知,利用叠栅条纹法调节光路可将光栅波像差减至0.06λ,相应的轴向误差量为0.007 mm,可有效提高了轴向调节精度。     

改进型Czerny-Turner成像光谱仪光学系统设计方法

像散是目前影响Czerny-Turner结构成像光谱仪空间分辨率最大的像差。首先引入柱面反射镜,利用光焦度衡量像散大小,推导出易于计算的像散校正公式,有效地校正了像散。给出准直镜到光栅距离的计算方法,有效校正了成像光谱仪边缘视场像差。给出了成像光谱仪像面倾角的计算方法,实现了宽波段的像差校正。最终利用上述方法设计了一套用于115～200nm的改进型Czerny-Turner成像光谱仪,焦距f′=48mm,F数为5.0,全视场、全波段调制传递函数(MTF)在0.7以上。全波段光谱分辨率为0.22nm,像面大小为8mm×7mm。设计方法适用于多种结构要求的成像光谱仪。     

一种光栅型成像光谱仪光学系统设计

 成像光谱仪是一种“图谱合一”的光学遥感仪器。从光栅型成像光谱仪的使用要求出发,利用Zemax软件设计了一种光栅型成像光谱仪光学系统。其中,前置望远物镜采用反射式结构,传统的卡塞格林结构在主次镜均采用非球面时校正像差的能力依然有限,设计时采用改进后的卡塞格林结构对像差进行校正,最终设计的望远镜头传函在50 lp/mm处达到0.5,场曲控制在0.078以内,且不存在畸变。针对光谱成像系统通常采用的基于平面光栅的Czerny-Turner结构由于像差校正能力有限、成像质量较差不能满足仪器的使用要求。采用基于凸面光栅的光谱成像系统,该系统结构紧凑、可实现宽波段内像差的同时校正。最终设计的光谱成像系统光谱分辨率<5 nm,MTF在50 lp/mm时升至0.75。将前置望远物镜与光谱成像系统根据匹配原则进行组合优化后光栅型成像光谱仪系统点列图RMS半径随波长的变化均小于0.2,波长的80%的能量集中在Φ6 μm范围内,波长各视场在特征频率50 lp/mm处的光学传递函数均大于0.5。整个光学系统具有结构简单、像差校正能力强、结构尺寸较小的优点。     

Measurement of Wavefront Aberration of Human Eye Using Talbot Image of Two-Dimensional Grating

The measurement of human ocular aberration is now frequently performed because of the increase in refractive surgery on the human cornea. The Hartmann-Shack (H-S) wavefront sensor is considered to be the most useful wavefront sensor, and a calculation method for wavefront aberration has been established. New methods of measuring wavefront aberrations of human eyes, using the Talbot image of a two-dimensional grating as a wavefront sensor and local shift of the Talbot image to calculate tilt of the wavefront are shown. The shift of the Talbot image was determined by comparing the phases of fundamental spatial frequency between the grating and the local patch of the Talbot image by Fourier transformation. The actual experiment was performed using a modified commercially available wavefront analyzer. Using these methods, Talbot images were obtained from model eyes and a human eye, and wavefront shapes were successfully reconstructed. Wavefront aberrations can be measured even when the obtained image is degraded by defocusing or scattering.     

Aberration correction and its automatic control in scanning electron microscopes

An automatic aberration correction method has been implemented in scanning electron microscopes (SEM). Necessity of the automatic aberration correction is discussed. The procedure of the automatic aberration correction is explained in detail, where deconvolution techniques are used in order to extract probe information from SEM images. Due to the precise digitization and the usage of proper combinations of correction fields, linearity has been found between the amplitude of each aberration and the corresponding field strength. Experimental results are shown which demonstrate that the aberrations are corrected automatically by a linear feedback control method. After the automatic aberration correction, the image quality has been improved drastically.     

基于双波前传感器自适应光学技术的太阳光栅光谱仪

为了研究不同太阳大气高度的热力学特性,具有良好成像质量的成像型光栅光谱仪是实现这个目标的重要仪器。然而作为地基式太阳望远镜重要的终端仪器之一,光栅光谱仪的光谱成像性能不可避免的会受到动态波前像差和系统静态像差的影响。动态波前像差常通过在太阳望远镜系统中集成自适应光学系统进行补偿。针对光学系统中的由装调和光学元件加工等引起的静态波前像差,提出了一种基于自适应光学技术校正光栅光谱仪中静态波前像差的方法,并进行了数值模拟仿真和实验验证。实验结果表明,校正后系统的残余波前像差RMS≈0.025λ,此时波前像差对光谱分辨率和能量利用率的影响可忽略,提高了光栅光谱仪的光谱成像质量,证明了所提出的方法的有效性。此外它具有降低光学系统装调精度和光学元件加工精度要求的优点。