Geometrical optics of lightguides with an oblique input end-face

The geometrical-optics relations between meridional rays of incidence and maximum aperture have been derived for the general case of a lightguide with an oblique input end-face. It is shown that the maximum angles of incidence are asymmetrical with respect to both the axis of the lightguide and the normal to the input end-face. A numerical comparison shows that for a light-guide with an oblique input end-face, in the meridional ray case, a greater or smaller angle of aperture may result, depending on the cutting angle, compared with that for a lightguide input end-face perpendicular to the optical axis. A greater angle of aperture is especially important since it means an improvement in the launching efficiency of incoherent light sources. Moreover, the maximum angle of aperture has been derived for the generalized light guide in which successive total internal reflections at the cladding/surroundings interface have been taken into account.     

衍射受限光学合成孔径成像系统像质评价

简述了光学合成孔径成像系统的原理,合成孔径成像系统在获得高截止频率的同时,降低了系统的中频性能,在空域表现为点扩展函数次峰增加。然后运用两点分辨率和光学传递函数对衍射受限光学合成孔径成像系统的像质评价问题进行了分析,指出了瑞利判据、斯派罗准则和“门限”判据的不足,认为当点扩展函数次峰大于主峰的0．5倍时,合成孔径系统与单孔径系统相比将失去优势。以光学传递函数为标准。分析三孔径合成系统子孔径尺寸、相互间距与等效系统孔径尺寸之间的关系。当子孔径直径不变时,随着其所在圆半径的增大,实际截止频率先增大,然后减小。     

稳像光学系统设计

重点沦述光学稳像的光学原理,并引用具体的平面反射镜作为光学补偿元件(也就是光稳元件)的稳像方式加以阐述,由此导出倒像系统和正像系统达到相对稳像和绝对隐像时补偿角与扰动角之间的关系式。论述采用会聚光路稳像时由棱镜的微量转动而达到绝对稳像时棱镜转动中心的求法。论述光稳元件兼作转像棱镜时光稳元件的有效孔径与转功中心和棱镜位置的关系。     

大口径光束波前采样器(孔栅)的研制

应用平面波角谱理论，分析了采样器对光波场采样和分光的基本原理以及对空间采样频率的选择规则，描述了实际研制的大口径采样器的结构设计，并通过数值方法和高能激光大气传输实验研究了高能激光经采样器前／后的远场光斑分布关系。结果表明：利用光束波前采样器能高保真地实现对高能激光束的分光。     

四种解析解设计的短程透镜卷边对损耗的影响

根据光波导短程透镜母线曲率半径与光传输损耗的关系,利用数值计算的方法,通过计算不同母线参数条件下,四种解析解设计的短程透镜母线曲率半径,研究比较了短程透镜卷边对其损耗的影响,得出了短程透镜损耗与其有效区半径关系的曲线图,发现透镜凹面半径一定时,有效区半径越小,即卷边越大时,光传输损耗越小;短程透镜的解析改进解和最优解设计的透镜卷边存在曲率奇点.并由此得出了四种解析解设计的短程透镜有效区半径选取原则及其满足低损耗条件的取值范围.     

X光能点、放大倍率及针孔尺寸对空间分辨的影响

X光针孔成像是惯性约束聚变(ICF)研究中重要的诊断方法,对其点扩散函数的计算可用于图像重建和系统空间分辨的判断。对菲涅耳衍射公式进行了化简,分析了X光能点、针孔尺寸及放大倍率对针孔点扩散函数的影响。实验在保证成像能获得足够高信噪比的条件下,通过模拟获得在最佳空间分辨时所要的针孔大小、放大倍率和X光能点等参数。在流体力学不稳定性的静态样品定标实验中,通过模拟获得了针孔的调制传递函数(MTF),结合实验测量的结果反推获得分幅相机本身的MTF值。同时采用测刀边函数的方法获得了分幅相机本身的刀边函数,进而得到相机在各空间频率下的MTF值。两种方法得到的分幅相机MTF值一致,验证了通过菲涅耳衍射模拟X光针孔成像的可行性。     

平顶高斯光束经含失调圆孔光阑的失调光学系统的传输特性

为分析平顶高斯光束通过光学系统传输时圆孔光阑失调和光学元件失调对平顶高斯光束传输特性的影响,利用失调圆孔光阑的近似展开式和适用于失调光学系统的广义衍射公式,得出了平顶高斯光束经含失调圆孔光阑的失调光学系统传输的近似解析式,给出了输出光束场分布与光束参量、光阑孔径尺寸、光阑和光学元件失调量等的定量关系.针对特定光学系统定量分析了各失调量对输出光束场分布的影响,结果表明各元件失调都对输出光束强度分布产生较大影响.但在各失调量较小的情况下,透镜失调对输出光束传输特性的影响比光阑失调对输出光束传输特性的影响更明显.     

Conditions for identical position of optimal image plane for axial imaging with different values of f-number

By analysis of the dependence of longitudinal spherical aberration on the numerical aperture, it is possible to find such values of the numerical aperture, where spherical aberration is zero. Such values of the numerical aperture are called correction zones. The work theoretically analyses the described problem and equations are given for wave aberration coefficients using correction zones for spherical aberration of the third and the fifth order. Our work presents an analysis of optimal values of correction zones and an optimal position of the center of the reference sphere based on the variance of wave aberration for the image quality evaluation. Relations are described for calculation of correction zones of an optical system having an identical position of the optimal image plane for two values of the f-number. The analysis of optical systems using correction zones is performed on an example.     

高能拍瓦激光系统中大口径离轴抛物面聚焦特性研究

为进行快点火实验,需对高能拍瓦激光聚焦系统中的核心元件即大口径离轴抛物面,进行深入量化研究,以便对其结构选型和精密调整提供准确的理论依据。利用基于严格的矢量衍射理论的数值计算方法,并结合像差分析得到了大孔径、大离轴量的抛物面镜(OAP)的物理光学成像特性。首先用理想平行光入射,得出OAP的三维平动公差与其焦深密切相关,OAP绕旋转对称轴的转动可归结为平动问题,其公差与焦深也有简单关系;入射光轴失准时,像散占主导作用,并可由一结构因子来定性描述其对像斑的影响。其次当入射光有一定的发散角时,除引起最佳像面位置变化外,还会由于OAP不对称性而引起的彗差使得像斑的峰值光强大大降低,并论述了OAP的结构参数对此的影响。     

Characteristic investigation of Golay9 multiple mirror telescope with a spherical primary mirror

The sparse aperture provides a novel solution to the manufacturing difficulties of modern super large telescopes. Golay configurations are optimal in the sparse aperture family. Characteristics of the Golay9 multiple mirror telescope having a spherical primary mirror are investigated. The arrangement of the nine sub-mirrors is discussed after the planar Golay9 configuration is analyzed. The characteristics of the entrance pupil are derived by analyzing the sub-aperture shapes with different relative apertures and sub-mirror sizes. Formulas about the fill factor and the overlay factor are deduced. Their maximal values are presented based on the derived tangency condition. Formulas for the point spread function (PSF) and the modulation transfer function (MTF) of the Golay9 MMT are also deduced. Two Golay9 MMT have been developed by Zemax simulation. Their PSF, MTF, fill factors, and overlay factors prove that our theoretical results are consistent with the practical simulation ones.     

Paraxial propagation of a partially coherent flattened Gaussian beam through apertured ABCD optical systems

By expanding the hard aperture function into a finite sum of complex Gaussian functions, some approximate analytical formulae for the cross-spectral density of a partially coherent flattened Gaussian beam (FGB) propagating through apertured aligned and misaligned ABCD optical systems are derived based on the generalized Collins formula. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. As a numerical example, the focusing properties (including average irradiance distribution and focal shift) of a partially coherent FGB focused by an apertured thin lens are studied, and it is found that the focusing properties of a partially coherent FGB are closely related to its initial coherence and the aperture width. Our results provide an effective and fast way for studying the paraxial propagation of a partially coherent FGB through apertured ABCD optical systems.     

Effects of mask-alignment error on point spread function for multi-level Fresnel diffractive lenses

The full aperture complex amplitude transmittance function of a multi-level diffraction lens with maskalignment errors was derived based on scalar diffraction theory. The point spread function(PSF) was calculated by the Kirchhoff diffraction integral. It is found that the radius of the Airy disk increases with the increase of the error in the direction of misalignment, and the image center shifts along the direction of misalignment. A fourlevel diffractive lens with a diameter of 80 mm was fabricated, and its PSF and diffraction efficiency of +1 st order were calculated and measured. The distribution of PSF is consistent with the calculated results, and the tested diffraction efficiency is slightly smaller than the calculated value; the relative error is 5.71%.     

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.     

厄米-高斯光束在内含硬边光阑光学系统中的传输

把硬边光阑从复杂光学系统中“移”出来,即把任意一个含有硬边光阑的复杂光学系统体现到含有入射光瞳和出射光瞳的光学系统中，使硬边光阑的作用转化为出射光瞳的作用，以便求出观察面上的解析解。对入射面上的二维厄米 高斯光束，利用柯林斯公式和入射光瞳与出射光瞳的物像关系，可得到所要求观察面的场分布和解析结果，通过数值模拟验证了其正确性。通过分析计算得到如下结论：对于任意一个含有硬边光阑的复杂光学系统，都可以把光阑的作用从系统中“移”出来，把其看作是出射光瞳的作用，从而可以较为简便地求出观察面上的场分布。     

Detecting the topological charge of vortex beams using an annular triangle aperture

The Fraunhofer diffraction pattern of a vortex beam by an annular triangle aperture is analyzed theoretically and experimentally. It is found that the pattern of the far-field diffraction intensity distribution exhibits a triangular lattice array, which becomes much clearer with the increase of the ratio of the inner to the outer side of the annular triangle aperture. The number of spot points of any external side of the triangular lattice array minus one is just equal to the topological charge value of the measured optical vortex. For the vortex beam with negative topological charge, the triangular diffraction pattern after the annular triangle aperture will be rotated by 180° in relation to the case of the positive topological charge. Based on the above properties, we propose a simple and feasible method to determine the magnitude and sign of the topological charge of an optical vortex beam.     

Geometrical theory of energy launching and pulse distortion in dielectric optical waveguides

In this paper the geometrical theory of pulse distortion and energy launching into multimode optical fibres is generalized when skew rays are taken into account. To this purpose, within the geometrical theory of skew rays, we firstly obtained a new expression for the numerical aperture. From this expression we derived an extensive analysis of the energy launched and the pulse response of a multimode optical fibre. A better launching efficiency and a different pulse form at the output of the fibre together with a larger broadening are obtained in comparison with the results derived from theories only for meridional rays. The theory is also applied to sources having planar geometry (such as LED) and linear geometry (such as semiconductor lasers), and the response to some rectangular-shaped pulses is investigated. Finally some considerations concerning scattering effects are described.     

大口径反射镜结构的两种参数优化方法

大口径反射镜在自重作用下发生变形,变形过大会引起镜片通光表面的峰谷值较大,难以满足光机装置打靶精度的要求。建立了典型反射镜结构的有限元仿真模型,以计算镜片表面峰谷值;优化了安装柱的位置、尺寸及镜片厚度等参数,使镜片通光表面形变峰谷值最小。分别采用了基于有限元模型的直接优化和基于代理模型的优化,均获得了结构最优参数,使形变峰谷值比初始值降低了74%。相比而言,基于代理模型的优化还可提供目标量随设计变量的变化情况以及变量灵敏度分析,更有利于设计决策。当设计变量个数多、范围宽时,可先根据先验知识或低精度代理模型缩小设计范围,然后建立紧缩范围的高精度代理模型并进行优化,可有效避免大量计算。根据“三圆柱”支撑结构的参数优化结果,建议采用“四圆柱”支撑设计,以获得更高的面形精度。     

Generation of Nearly Diffraction-Free Beams Using a New Optical System

A new optical system which can efficiently generate the nearly diffraction-free beams is proposed and its characteristics are investigated by numerical analysis. This optical system consists of a new optical element called a DCC (double-concave-cone) lens and an objective lens with a large numerical aperture, and can generate the Bessel beam and also the Bessel-Gauss beam. The maximum propagation distance of nearly diffraction-free beams generated by the system agrees with its theoretical value for the Bessel beam.     

双曲余弦高斯光束通过有光阑限制的ABCD光学系统的传输

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究,采用将矩形域函数表示为复高斯函数叠加的技巧,推导出了解析的传输公式,在特殊情况下,该公式简化为在无光阑情况下的传输公式,对双曲余弦高斯光束通过有光阑限制的薄膜镜聚焦进行了数值计算,计算结果与直接由柯林斯（Collins)公式所得结果一致,且此解析方法便于进行物理分析,可节约大量机时。