荷电粒子光柱成象系统中空间电荷象差之解析计算

本文首先讨论粒子光学柱成象系统中空间电荷象差的概念,然后提出用梯形束元作为同时计算空间电荷象差、几何象差、色差和衍射象差的统一模型;最后,在此模型基础上推导并提出了所有计算成象系统中空间电荷象差的解析表达式.     

On the relation between the wave aberration function and the phase transfer function for an incoherent imaging system with circular pupil

The consideration is carried out in its general formulation: the wave aberration function is represented in terms of classical aberrations (the Zernike polynomials), the phase transfer function (argument of the complex optical transfer function) is defined by a chain of transformations originating from the generalized pupil function. Quasi-analytical quadrature formulas are derived that link the optical transfer function and the phase transfer function with the aberration terms. It is shown that the phase transfer function contains information on the odd-order aberrations, which can be retrieved from coefficients to the Taylor expansion of the derived quadrature relation. Received 16 June 2001     

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：     

X射线同轴全息术中像差的数字模拟

给出了Ｘ射线同轴全息中像差的数值模拟，分别研究了其三级波差和光线像差，用一个较为简便的方法计算出光线像差，给出了类似于光线追迹中的点列图，并由此相应地估计出像差对分辨率的限制，所有的计算都是基于一个典型的Ｘ射线激光全息实验听参数进行的，根据分析还讨论了减小像差的条件。     

Third-order aberration analysis of tilted-pupil optical systems

The aberration field of an optical system with a tilted pupil is explored through expanding the vector expressions of the third-order wavefront aberrations. First, the vector forms of the wavefront aberrations are modified to obtain the aberration expressions with the pupil tilted; full field displays of coma and astigmatism in this situation are given. Then, the third-order aberration formulas with the pupil decentered and tilted simultaneously are derived and discussed. Finally, an example is taken to certify the validity of aberration distribution properties.     

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.     

复合的电子束扫描系统象差的动态校正

本文在文献[1]的基础上讨论了复合的电子束扫描系统象差的动态校正问题。讨论了采用不同的电磁多极场作为动态校正器的可能性。推导了圆形校正透镜、偏转校正场和四极、六极校正场引起的附加象差的公式。由此证明了由这种圆形校正透镜、偏转校正场和四极校正场等组成的动态校正系统在一定条件下可以消除复合的电子束扫描系统中大多数的三级偏转象差。 关键词：     

Influence of Misalignment on High-Order Aberration Correction for Normal Human Eyes

Although a compensation device can correct aberrations of human eyes, the effect will be degraded by its misalignment, especially for high-order aberration correction. We calculate the positioning tolerance of correction device for high-order aberrations, and within what degree the correcting effect is better than low-order aberration （defocus and astigmatism） correction. With fixed certain misalignment within the positioning tolerance, we calculate the residual wavefront rms aberration of the first-6 to first-35 terms along with the 3rd-Sth terms of aberrations corrected, and the combined first-13 terms of aberrations are also studied under the same quantity of misalignment. However, the correction effect of high-order aberrations does not meliorate along with the increase of the high-order terms under some misalignment, moreover, some simple combined terms correction can achieve similar result as complex combinations. These results suggest that it is unnecessary to correct too much the terms of high-order aberrations which are difficult to accomplish in practice, and gives confidence to correct high-order aberrations out of the laboratory.     

Determination of wavefront aberrations using a Fabry-Perot cavity

A new method for detecting wavefront aberrations using a Fabry-Perot cavity is described. A Fabry-Perot cavity transmits the cavity eigenmode which satisfies a resonance condition, while the other modes are reflected from the cavity. Utilizing this mode discrimination property, we can extract aberration components from incident aberrated light as reflected light from the cavity. Under the condition of a weak aberration, the amplitude profile of the reflected light can be approximated to the wavefront aberration. We can therefore determine the wavefront aberrations in a visualized form with the technique. We present the detection scheme and the first experimental verification of the technique. The detected aberration using this technique was in good agreement with the result on the basis of a conventional wavefront sensor.     

Theory of paraxial lateral aberrations of electrostatic imaging electrostatic electron optics based on asymptotic solutions and its verification

In imaging electron optics, study of geometrical lateral aberrations of third order and paraxial lateral aberrations of second order has traditionally been paid more attention to, but the existence of paraxial chromatic aberrations of third order and paraxial chromatic aberrations of magnification of third order was almost ignored, and the general form of paraxial lateral aberration has not been studied theoretically.In the present paper, the paraxial lateral aberrations expressed in general form have been derived emphatically on the basis of asymptotic solutions of paraxial equation. The relationship between the coefficients of asymptotic solutions has been investigated, which proves that the coefficients of asymptotic solutions are related each other. Through a bi-electrode electrostatic spherical concentric system model, two special solutions expressed by asymptotic solutions and accurate solutions in a bi-electrode electrostatic spherical concentric system have been deduced, and the paraxial lateral aberrations have been verified and tested, in which the aberration coefficients are solved by asymptotic solutions of paraxial equation. Result completely proves that the approach based on asymptotic solutions to solve the paraxial lateral aberrations are practicable and accurate enough. The paraxial chromatic aberration of magnification of third order and the paraxial chromatic aberration of third order have been firstly derived, and the Recknagel-Artimovich formula of paraxial chromatic aberration of second order which possess an greatest part in the whole paraxial lateral aberrations has been deduced and confirmed. A simple and clear form for expressing paraxial lateral aberrations of imaging electron optics is suggested for practical use. Results of the present paper will have theoretical value for aberration theory of imaging electron optics and practical significance for the design of image tubes.     

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：     

Errors in ultrasonic scatterer size estimates due to phase and amplitude aberration

Current ultrasonic scatterer size estimation methods assume that acoustic propagation is free of distortion due to large-scale variations in medium attenuation and sound speed. However, it has been demonstrated that under certain conditions in medical applications, medium inhomogeneities can cause significant field aberrations that lead to B-mode image artifacts. These same aberrations may be responsible for errors in size estimates and parametric images of scatterer size. This work derives theoretical expressions for the error in backscatter coefficient and size estimates as a function of statistical parameters that quantify phase and amplitude aberration, assuming a Gaussian spatial autocorrelation function. Results exhibit agreement with simulations for the limited region of parameter space considered. For large values of aberration decorrelation lengths relative to aberration standard deviations, phase aberration errors appear to be minimal, while amplitude aberration errors remain significant. Implications of the results for accurate backscatter and size estimation are discussed. In particular, backscatter filters are suggested as a method for error correction. Limitations of the theory are also addressed. The approach, approximations, and assumptions used in the derivation are most appropriate when the aberrating structures are relatively large, and the region containing the inhomogeneities is offset from the insonifying transducer.     

宽束和细束电磁复合聚焦球面阴极透镜的象差理论

本文研究了对宽束和细束阴极透镜普遍适用的电磁复合聚焦球面阴极透镜的象差理论。在考虑物场和象场弯曲以及阴极面上磁场和横向电场不为零的情况下,导出了任意理想象面上的一级近轴横向象差和包括色象差在内的全部三级横向象差矩阵公式。所得的结果较为完整、普遍。本文详细讨论了宽束和细束阴极透镜的关系,并用轨迹法和变分法严格证明了:当考虑阴极面逸出电子具有一定的初能量和初角度分布,并采用准规范化电位表示的近轴轨迹方程来讨论系统的理想成象时,宽束和细束两类阴极透镜从象差理论以至导出的三级横向象差、象差系数表示式都可以统一起来。本文采用矢量描写轨迹,运用矩阵表示象差,形式简洁,象差系数积分收敛,适合于计算机计算。 关键词：     

Coherence function analysis of the higher-order aberrations of the human eye

We measured the wavefront aberrations of the eyes of five subjects with a Shack-Hartmann sensor sampling at 21.2 Hz and decomposed the measurements into Zernike aberration terms up to and including the fifth radial order. Coherence function analysis was used to determine the common frequency components between the aberrations within subjects. We found the results to be highly subject dependent. The coherence values were typically <0.4. Possible reasons for this are discussed. Coherence function analysis is a useful tool that can be used in future investigations to determine correlations between the aberration dynamics of the eye and other physiological mechanisms.     

两电极静电同心球系统的成像电子光学及其空间-时间像差

基于实际轨迹方程和电子运动方程对两电极静电同心球系统求解由光阴极逸出的运动电子的空间和时间轨迹,推导成像位置和电子飞行时间的精确和近似表达式,并由空间和时间轨迹的解析解出发讨论系统的空间-时间特性.对空间像差和时间像差给出统一的定义,即横向像差可视为近轴横向像差和几何横向像差的合成,时间像差可视为近轴时间像差和几何时间像差的合成,并导出了所有相应的像差表示式.     

两电极静电同心球系统的近轴电子光学及其空间-时间像差

将从近轴解出发研究两电极静电同心球系统的空-时轨迹及其像差.由近轴轨迹方程和近轴运动方程出发,先求解两电极静电同心球系统中自光阴极逸出的运动电子的近轴空间-时间轨迹,然后讨论此系统的静动态电子光学及其空间-时间像差,揭示近轴光学系统成像的一般规律.文中定义和推导了各级近轴空间像差和近轴时间像差,得到了与关于近轴空间-时间像差同样的结论,表明完全可以直接由近轴轨迹方程和近轴运动方程出发来研究理想成像及其空间-时间像差.     

高级象差理论

本文的主要目的在以近似方法讨论高级象差特性。首先由对称性讨论了二级象差的独立象差数,近似讨论了象差的几何意义,再由坐标变换的观点导出了光栏移动时象差变化的规律。由Fermat原理和同一光线可看作是各不同点发出的观点导出了物体移动时象差变化的规律。由于运用Fermat原理,所得的结果实际上是略去初级象差影响后的近似结果,因此表示式相当简单。然后我们把象差产生的原因分为二类。其一称作是本徵的,是入射光束无象差时必然产生的象差,用象差看作球差的观点导出了它们的表示式,结果表明,高级球差和本徵轴外球差是象差产生的原因,并导出了各种象差同时产生的状况。象差的另一类称作是衍生的,它们是由入射光线原有象差引起的初级象差差异,由初级象差理论即可得出它们的表示式。这一些高级象差的规律和近似表示可作为评断象差产生原因的半定量依据。最后,用Fermat原理讨论了高级色差问题,并说明Fermat原理之所以可在高级象差理论中应用的理由及不致误差过大的应用范围。     

Third-order aberration analysis of an off-axial optical system

The aberration theory applied to co-axial optical systems is extended to off-axial systems, for which third-order aberration coefficients are considered. The derived aberrations are analyzed using three-dimensional ray bundles, spot diagrams, and image charts, and classified in relation to the system symmetry. This theory is very useful for optical designers, allowing them to clarify the relationship between the structures of off-axial optical systems and the corresponding off-axial aberrations.     

Chromatic aberrations of thin refractive variable-focus lens

We present an approach to an analysis of the third order chromatic aberrations of thin refractive fluid lenses with a variable focal length. A detailed theoretical analysis is performed for a simple fluidic variable-focus lens and formulas are derived for an optical design of such lenses. Aberration coefficients of the third order of the variable-focus lens can be completely characterized by three parameters which depend only on refractive indices of fluids forming the variable-focus lens. Formulas were derived for the change of the third-order aberration coefficients with the wavelength. Calculations are provided for Varioptic lens Arctic-416.     

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.