The Computation of Diffraction Patterns in the Presence of Aberrations

The diffraction integral for the disturbance produced in the image plane normal to the optical axis by an extra-axial pencil has been shown to lead to a Fourier transform provided the exit pupil surface is taken to be that of the reference sphere. It has been shown also that, except for small aperture and field sizes, the effect on the wave-front aberration of a shift of the image plane is not represented with sufficient accuracy merely by a term proportional to the aperture squared. Both of these results have been respected in formulating a numerical technique for the calculation of point spread functions. The diffraction integral is evaluated in polar coordinates, and is such that no error is made in approximating the domain of the exit pupil in cases where this may be represented by an ellipse. A study of the accuracy obtained has shown that, if each quadrant of the pupil is divided into a 20 × 20 mesh of elementary areas, the error in the intensity is not expected to exceed 0·8 per cent of the intensity at the focus of a diffraction limited system. The method takes account of the first derivatives of the wave aberration at each mesh point, and the results are therefore expected to be more accurate than those obtained by merely replacing the integral by a simple sum. Results are given for a case of primary and secondary coma, and of a study of the influence of secondary spectrum and spherical aberration on the images formed by 2 mm achromatic microscope objectives of numerical aperture equal to 1·40.     

角谱理论用于衍射光学元件数字仿真

本文采用衍射角谱理论对衍射光学元件的光场分布进行数字计算。该理论包括两种表达方式:既可用含有传递函数的等式表达,也可用含有点扩散函数的等式表达。这两种计算方法在本质上是一致的。然而,在MATLAB计算过程中,它们又具有不同的适用条件,通过分析,将它们分为近场算法和远场算法,并且展示了它们的计算实例。结果表明,在标量衍射理论成立的条件下,不改变衍射元件抽样间隔和抽样点数,利用这两种算法能够快速、准确计算不同位置处的衍射图样。该方法对衍射光学元件像面光场分布的精确计算具有重要的意义。     

The Numerical Investigation of Diffraction Image Quality of Gradient-index Lenses

A method for the exact calculation of the light intensity distribution in the focal plane of a gradient-index lens is presented. A modification is proposed based on a method exploited in classical systems of small aperture. The results of an investigation performed on selected lenses are shown.     

An Analytical Solution of Vector Diffraction for Focusing Optical Systems

Abstract

Vector diffraction theory for optical systems has been of interest for a long time. Ignatovsky and Wolf have formulated these problems in terms of diffraction integrals and Wolf has presented very interesting results. Usually, the quadrature of diffraction integrals is numerically intensive, therefore these problems have remained of interest and many authors have worked on the Ignatovsky-Wolf formulation or some variation thereof. This paper presents yet another method of solving diffraction integrals. Since a certain part of the kernel of these integrals is Riemann integrable in the interval [0, π], the Weierstrass theorem says that it can be approximated by a uniformly convergent series of orthogonal functions. Thus it is possible to expand these functions into a series of Gegenbauer polynomials of the first kind. Once these expansions are substituted in the diffraction integrals, the resulting integrals are readily evaluated, over the surface of unit sphere, in terms of the spherical Bessel functions and Gegenbauer polynomials. The results are particularly simple if the image plane is the focal plane. In this paper, we evaluate the diffraction integrals for several optical systems of arbitrary numerical aperture with or without obscuration, and for a parabolic reflector. The results presented here are in agreement with previously published results. The numerical computations are easy since all the functions are evaluated by adding a finite series. The calculations which for the basis of results presented in this paper were performed on a personal computer.     

A Study of the Possibility of Image Optimization by Apodization Filters in Optical Systems with Residual Aberrations

A systematic study to optimize the image in real optical systems, by fitting the filter transmission function on the exit pupil to different polynomial types is developed. The systems we have treated, whose residual aberrations are larger than the tolerance values, could be carried to tolerance by the use of an adequate filter, making the Strehl ratio higher than 0·8. The influence of the apodization filter on the optical transfer function is also studied.     

光学传递函数双胶合标准镜头的比对

双胶合标准镜头是国际上具有代表性的光学传递函数标准镜头,本文所介绍的由中国计量科学研究院设计加工的双胶合标准镜头的计算程序比对和国内验证比对实验的情况.     

A Study of the Propagation of Optical Spectra Using a Wavelength Independent Formulation of Diffraction Theory and Coherence Theory

Abstract

Basic relations in diffraction theory and coherence theory are rederived in spatial coordinates in units of a wavelength for each monochromatic component of the field. It is found that each component behaves identically in these coordinates independent of wavelength. This theory makes it clear that there is an intrinsic spectral shift that always occurs for any deterministic field as it propagates from a region near its sources into the far field. This theory also leads to a set of special conditions under which a partially coherent field has the same spectrum over a plane near its sources and also at every point in its far field. These conditions are believed to be satisfied by the fields radiated by natural thermal sources. Equations are given describing the relationships between the spectra of the source, the field near the source, and the radiation field under a wide range of conditions.     

Methods of Checking the Optical Characteristics of Soft Contact Lenses

A new classification is proposed for contact lenses based on standard specimens (tolerance monitoring). The best wavelengths have been determined for measuring the spectral transmission coefficients of the standard specimens, and realistic bounds have been defined for the tolerance fields for the most common colors of these lenses.     

The Effect of Electron Beam Irradiation on Electron Diffraction Patterns of Bi-Sr-Ca-Cu-O High- Tc Superconductors

The effect of electron irradiation having the energy of 75, 100, and 200 keV on structural modifications of Bi-2212 superconducting samples has been studied. For the last energy, the irradiation time from zero to 150 min was used. At a constant energy of the electrons, the observed phenomena consist in the disappearance of the incommensurate unidimensional modulation, in the decreasing of spots' intensity and their elongation along the equivalent crystallographic axis a, and even spot splitting with the occurrence of double extra spots, with the increase of the irradiation time.After electron irradiation with energy of 75 and 100 keV, the structural modifications lead to some spot patterns consisting of some planar lattices (in some cases a pseudo-tetragonal one) that are twisted on each other at different angles (8°, 13.6°, 19°, etc.) around the axis of the incident electron beam. For the irradiation at increased doses of thin microcrystals having reduced lateral dimensions, the electron diffraction spots were arranged in discrete or partial continuous Debye rings or continuous concentric Debye rings characteristic for the polycrystalline state.After electron irradiation with energy of 200 keV, the effects of electron irradiation on Bi-2212 samples depend strongly on irradiation fluence rate and time and consisted in the following: disordering defects in the diffraction patterns (disappearance of some spots, spot intensity modification, streaks occurrence, spot elongation); alteration and disappearance of incommensurate structural modification; conversion of single crystal particle areas into polycrystalline material; and quasi-amorphization.A simple approach based on the evaluation of the displacement yield of in-plane oxygen atoms vs. irradiation time for the different incident energy and electron fluence rates could explain the general trend of irradiation damage in HTS materials.     

基于微扰理论的静电电子透镜的缺陷电场计算

研究了用于计算电子光学系统的缺陷电场和容差的微扰理论。基于微抗原理，推导了计算静电电子透镜由于电极偏心、倾斜和加工不圆造成的电场变化及其旁轴多极场展开函数的九点有限差分公式，编制了计算软件。建立了两个电场解析模型，通过该模型的解析解与数值计算结果的对比，证实了算法及软件的正确性，并据此讨论了微扰理论用于容差计算的适用范围。计算了几个静电电子透镜的例子，给出了不同电极缺陷的电位分布和微扰多极场分布。     

The Computation of Aberrational Diffraction Images for Catadioptric Systems

The entrance pupil for an extra-axial object point associated with a system having a central obscuration is found to be well approximated by the region contained between two ellipses, which are generally of different eccentricities and not concentric. The diffraction integral associated with an annular-type aperture for a disturbance in the image plane normal to the optical axis is treated as the difference between two integrals, one for the whole pupil and the other for the central obstruction. Each of these integrals is of the same form as the integral describing the behaviour of the diffraction pattern associated with an elliptical aperture. A computer programme has been written to calculate the diffraction integral using Hopkins' algorithm [6]. The programme has been checked thoroughly against several analytical examples. These results suggest that the error is not likely to exceed 0·0005, where the intensity at the geometrical focus for an aberration-free case is taken to be 1·0000. As a practical example, a study has been made of an F/1·4 telescope objective with an angular field of 5° designed by Canzek [2].     

热轧TA1钛的电子背散射衍射分析

简介了EBSD技术原理,并利用EBSD技术分析了工业纯钛TA1,简要说明了EBSD实验中的试样制备、实验过程、所得数据和数据处理.通过分析得出,热轧工业纯钛中晶界大多数为大角度晶界,晶粒大多已回复和再结晶,存在的织构为(10(-)11)[(-)1(-)123]和(10(-)15)[(-)2(-)131].     

Glare Characteristics of Lenses and Optical Instruments in the Visible Region

An automatic laboratory glare photometer has been constructed and used to measure the glare characteristics of some typical lenses, and a focal systems by the elementary source method. From the glare distributions produced by the instrument, the concept of a glare spread function (g.s.f.) has been developed and it has been shown that the use of g.s.f.'s permits the glare characteristics of an optical system to be expressed in a manner more basic than has hitherto been possible. The numerical values of the g.s.f. depend only on the system under test and not on the geometry of the test equipment. Glare spread functions can be useful in several contexts. They can be used as procurement standards prior to design or manufacture and the measured g.s.f.'s of existing instruments can be used to calculate glare distributions in particular situations, different from the one actually used for the measurement.     

复合优化理论在不共轴光学系统CAD中的应用

讨论在不同轴光学系统的计算机辅助设计中如何用“复合优化”理论，主要是如何模拟评价函数，又怎样进行适应法处理，“复合优化”有何特色，并列举实例说明。     

Optical Diffraction in Close Proximity to Plane Apertures. IV. Test of a Pseudo-Vectorial Theory

Rayleigh’s pseudo-vectorial theory of the diffraction of polarized light by apertures which are small compared to the wavelength of light is analyzed with respect to its mathematical rigor and physical significance. It is found that the results published by Rayleigh and Bouwkamp for s-polarized incident do not obey the conditions assumed in their derivation and must therefore be dismissed. It is also found that the theory leads to paradoxical predictions concerning the polarization of the diffracted field, so that the pseudo-vectorial approach is intrinsically incapable of describing polarization effects.