A different algebraic method for the fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses

In this paper, differential algebraic (DA) method is applied to fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses. The magnetic fields of magnetic electron lenses, which are computed by FEM or FDM method, are in the form of discrete arrays. Thus the developed new DA method is applicable to engineering design and programs were written for computing the fifth-order combined geometric-chromatic aberrations of practical magnetic electron lenses. An example is given. The combined geometric-chromatic aberrations up to fifth order are calculated. It is proved that the numerical results for the magnetic fields in the form of discrete arrays have good accuracy compared with the results computed by using the magnetic fields expressed in analytical form. The accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors. Finally, a practical magnetic electron lens is analyzed and discussed as an example.     

阴极透镜象差的变分理论

本文运用变分原理研究了电磁复合聚焦阴极透镜的象差理论,导出了在任意象平面中象差系数的普遍公式。它们可以用Glaser导出的象差系数的线性组合来表示。这就表明了宽束与细束电子光学系统的象差都可以用统一的变分方法处理,并建立了两者之间的联系,本文采用矢量形式描写阴极透镜的近轴轨迹,并采用矩阵形式描写象差。本文所得的象差系数较之文献上已有结果形式更为简洁且适用于计算机计算。本文考虑了阴极面上磁场和横向电场不为零的情况,因而所得结果较为普遍。 关键词：     

Adaptive aberration correction of GRIN lenses for confocal endomicroscopy

Graded-index (GRIN) lenses serve as a key component for miniature endoscopes because of their small diameters and ease of assembly. However, the nonaplanatic nature of GRIN lenses causes inherent spatial aberrations that lower image resolution and sharpness. Here we present the diagnosis of the aberrations in GRIN probes and the use of adaptive optics to compensate for the wavefront errors in the endoscope. Two different operation schemes based on preset and in situ measurements are demonstrated, both resulting in a substantial reduction of the wavefront error from 0.42 to <0.1 μm.     

关于电磁复合聚焦阴极透镜的象差理论

本文对电磁复合聚焦阴极透镜的象差理论进行评述与研究,着重分析西门纪业和Бонштедт两篇代表性的文章,详细推导了两文的象差方程和象差系数。研究表明,尽管两文的象差系数在形式上迥然不同,但实质上是完全一致的,是可以互相转化的。从而证明Бонштедт对西门纪业的批评是没有根据的。按照我们的研究,成象系统的象差应在某一轴向初电位ε_(x1)而非ε_x所对应的象面上进行考察,从而导出电磁复合聚焦阴极透镜包括一级象差与三级象差在内的全部横向象差表达式 关键词：     

Pupil-segmentation-based adaptive optical correction of a high-numerical-aperture gradient refractive index lens for two-photon fluorescence endoscopy

The intrinsic aberrations of high-NA gradient refractive index (GRIN) lenses limit their image quality as well as field of view. Here we used a pupil-segmentation-based adaptive optical approach to correct the inherent aberrations in a two-photon fluorescence endoscope utilizing a 0.8 NA GRIN lens. By correcting the field-dependent aberrations, we recovered diffraction-limited performance across a large imaging field. The consequent improvements in imaging signal and resolution allowed us to detect fine structures that were otherwise invisible inside mouse brain slices.     

Experimental evaluation of X‐ray optics applied for microanalysis

The performance of x‐ray capillary lenses has been evaluated. The tests were carried out using an x‐ray tube set‐up. A single glass capillary with tapered inner channel, a monolithic glass polycapillary, and an in‐house manufactured single metallic capillary with parabolic inner channel were characterized in terms of gain, spatial resolution, and element detection limits. The spatial resolution of a confocal set‐up utilizing a monolithic glass polycapillary and a polycapillary conical collimator has also been measured. The highest gain of about 2500 was observed for the glass polycapillary. The maximum gain achieved with the single glass capillary was equal to about 25, and the gain of the metallic capillary was only slightly greater than 1. For the glass capillary and polycapillary lenses, significant filtering of the higher‐energy photons (energy > 8 keV) was observed. The lowest relative detection limits were obtained with an ordinary cylindrical collimator and the polycapillary lens. Similar absolute detection limits were achieved with the use of the polycapillary and single capillary lenses. A relation between the ratios of the detection limits of elements achieved with different x‐ray lenses and the lens parameters (spatial resolution and gain) has been proposed and was verified experimentally. The monolithic polycapillary lens was found to be an optimum focusing device for an x‐ray tube‐based scanning spectrometer. This type of x‐ray lens can be coupled with a polycapillary conical collimator or a polycapillary half‐lens to make a confocal x‐ray microscope capable of depth profiling with a spatial resolution equal to about 30 micrometers. Copyright © 2008 John Wiley & Sons, Ltd.     

Study on differential algebraic method for electron optical properties of wide electron beams in immersion electrostatic-magnetic lenses

Differential algebraic method for calculation of electron optical properties is extended to wide electron beams in combined immersion electrostatic-magnetic lenses, based on Taylor series expansion of the differential algebraic data structure of wide electron beam focusing systems. Higher order aberrations referred to off-axis central trajectories are calculated and this makes the evaluation of wide electron beam focusing properties much simplified with high-enough precision. A program was written, and a specific combined immersion electrostatic-magnetic lens is calculated as an example. Computed results show that the second aperture aberrations referred to off-axis central trajectories of the system of the primary one, whereas the third- and over third-order ones only play a secondary role.     

Differential algebraic method for computing the high order aberrations of practical electron lenses

Differential algebraic method is of an effective technique in computer numerical analysis. It implements exactly differentiation up to arbitrary high order based on the nonstandard analysis. Some complicated nonlinear dynamics problems including high order aberrations of electron optics systems can be solved by mapping properties of differential algebraic quantities. However, the existing electron optical differential algebraic method can only be applied to those problems where the electric and/or magnetic fields are expressed in analytic forms. In this paper, the principle of differential algebraic method is applied to practical electron lenses whose electric/magnetic fields are in the forms of discrete arrays, for example, the files computed by FEM or FDM method. Thus the developed new differential algebraic method is applicable to engineering design. The programs were written for computing the high order aberrations of practical electron lenses. An example is given to show that the numerical results have good accuracy compared with the results computed by using the electric fields expressed in analytical form; the accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors, and it is enough for engineering design.     

Proton Radiography for the Diagnostics of a Dense Plasma

The possibility of using high-energy proton radiography for dense plasma diagnostics is discussed. The designed telescopic ion optical system for a proton radiography installation with a 1 GeV beam is presented. The schematic diagram of the proton microscope is given. It is shown that the estimate of spatial resolution for the installation obtained with consideration of chromatic aberrations of magnetic quadrupole lenses is limited from below.     

Different algebraic method for computing the high-order aberrations of practical combined focusing-deflection systems

Differential algebraic (DA) method is an effective technique in computer numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. Some complicated nonlinear dynamics problem including high-order aberrations of electron optical systems can be solved effectively by mapping properties of DA quantities. However, the existing study applying DA method to the practical system is limited to simple electron lenses. In this paper, the application of DA method is extended to practical combined focusing-deflection systems, and the aberrations up to fifth order are calculated. The electric and magnetic fields of the electron lenses and deflectors, which are computed by finite element method (FEM) or finite difference method (FDM), are in the form of discrete arrays. Local analytical expressions for electric and magnetic field quantities are constructed from these arrays for arbitrary place where electron is traced in DA computation. Thus the developed DA method is applicable for engineering design and computing problem. Based on the study of the expressions and the structure of the aberration coefficients for the fifth-order aberrations of the combined focusing-deflection system and the local analytic expression of the practical electromagnetic field, correlative computer software was developed, whose interface is convenient to calculate the high-order aberrations of the practical systems. The new DA method and software are tested with a uniform magnetic field deflection having an analytic solution. And the results show that the accuracy is sufficiently high, only limited by machine precision. Finally, as an example, a practical combined magnetic focusing and magnetic deflection system is analyzed and discussed.     

Correcting anterior corneal aberration and variability of lens movements in keratoconic eyes with back-surface customized soft contact lenses

Customized contact lenses are limited in their correction performance, especially on irregular corneas, owing to decentration and rotation of the lenses. To overcome this limitation, we proposed to customize the back surface of soft contact lenses to match the anterior irregular corneal surface. These lenses were designed to correct anterior corneal aberrations and to improve lens stability. Although in keratoconic eyes the anterior corneal aberrations were effectively corrected, significant residual aberrations were observed. The internal optics, especially the posterior surface of the cornea, was the main source of these residual aberrations. Compared with conventional soft contact lenses, lens stability, on average over three eyes, was improved by a factor of 2 for horizontal and vertical decentrations and a factor of 5 in rotational orientation with the back-surface customized lenses.     

Coma measurement using a PSM and transmission image sensor

As feature size decreases, especially with the use of resolution enhancement technique, requirements for the coma aberrations in the projection lenses of the lithographic tools have become extremely severe. So, fast and accurate in situ measurement of coma is necessary. In the present paper, we present a new method for characterizing the coma aberrations in the projection lens using a phase-shifting mask and a transmission image sensor. By measuring the image positions at multiple NA and partial coherence settings, we are able to extract the coma aberration. The simulation results show that the accuracy of coma measurement increases approximately 20% compared to the previous straightforward measurement technique.     

基于反转光楔和泽尼克多项式的共形光学设计

采用一对反向旋转的累斯莱棱镜可以实现对目标视场的动态扫描,并应用一对内表面为泽尼克边缘矢高表面的透镜对共形光学整流罩引入的主要像差进行校正,剩余像差则由累斯莱棱镜内表面进行补充校正.设计实例中,通过比较光学系统校正前后的成像质量以验证这种校正方法的有效性.     

高能质子照相中面密度的测量和不确定性分析

 依据洛斯·阿拉莫斯国家实验室的质子照相概念,通过研究高能质子与物质的相互作用规律,给出了质子照相确定面密度的计算公式及其不确定性分析,阐述了质子照相鉴别材料组分的原理。相对于X光照相,质子通过面密度较大的物体后的通量明显增加,界面探测和密度重建更加准确。研究了多库仑散射和磁透镜系统的色散对质子照相空间分辨率的影响及解决途径。结果表明,高能质子照相在穿透能力、面密度测量、材料的组分识别、空间分辨率等方面都优于X光照相。     

Cc,Cs, and parasitic correction in quadrupole probe-forming lenses

Approximate expressions are derived for the second and third order aberrations of a quadrupole doublet, allowing for aberrations intrinsic to fields of perfect symmetry, for parasitic aberrations of imperfect symmetry, and for compensating multipole lenses. Five third-order coefficients are found, and expressed in terms of four octopole strengths and the first-order parameters of the doublet as determined by its dimensions. For compensation of third-order aberrations of achromatic quadrupole/octopole lenses, either skew octopole lenses are required externally, or lenses with more than 8 poles are required coincident with the quadrupoles. If an octopole lens is added between the quadrupoles of the achromatic doublet, the spherical aberration of a condenser lens may be compensated. Such a Cs and Cc compensated quadrupole doublet is suitable for use as a probe-forming lens in focused ion beam systems and ion microscopes.     

Design of Double Cassegrain reflective mirrors for optical system of IR cameras

IR optical systems such as Petzval doublet refractive lenses or Cassegrain reflective mirrors are either expensive or poor in image quality. Taking advantage of the low cost of reflective mirrors, here we present an optical design of Double Cassegrain reflective mirrors consisting of two sets of Cassegrain reflectors facing each other symmetrically. This symmetry also cancels many aberrations besides the chromatic aberration-free nature of reflective mirrors. Design results show that this system is better than Cassegrain reflectors in aberration correction and image resolution, but cheaper than Petzval doublet refractive lenses systems in price. IR cameras with this optical system could be widely used for body temperature measurement and security check.     

Aberration analyses for liquid zooming lenses without moving parts

Liquid lenses with an adjustable focal length are of particular interest for their potential applications in compact imaging or zooming systems. We have analyzed the aberrations for liquid zooming lenses and compared them with those of traditional lenses. Based on the 3rd order aberration theory, possible structures for the liquid zooming lens without moving mechanism were determined. We showed that a two-group liquid lens system is the simplest one that contains no moving mechanical parts and has enough parameters to correct all chromatic aberrations for any focal length and most monochromatic aberrations for certain focal lengths.     

Differential algebraic method for arbitrary-order chromatic aberration analysis of electrostatic lenses

In this paper, differential algebra is applied to calculate arbitrary high-order chromatic aberrations of electrostatic electron lenses. Expressions of differential algebraic form of high-order combined chromatic aberration coefficients are obtained and arbitrary-order chromatic aberrations can be calculated numerically. As an example, a typical Schiske's electrostatic lens has been studied. All the first- to third-order chromatic aberration coefficients of the lens have been calculated, and the pattern of the first-order chromatic aberration has been given as well.     

从像上提取非旋转对称系统的传递函数制作解卷空间滤波器

本文提出从高分辨电子显微像中,利用光学、全息和部分相干等方法,提取传递函数,制作相位和振幅滤波器,实现解卷,提高高分辨电子显微像的分辨率.