On aberrations of eikonal in planar lens antennas

A formula for the eikonal distribution over the surface of a cylindrical dielectric lens with an error on the fourth-order of the displacement of the source from the focus is found. The accuracy of this formula and the first three terms of its expansion in this parameter for describing the eikonal and its aberrations are analyzed. A method for finding the parameters of the optical aplanatic lens (with minimum aberrations) is proposed. An approximate equation of the focal curve is derived.     

Eikonal aberrations in planar double-reflector antennas

A formula describing the eikonal distribution on the main reflector of a 2D double-reflector system is derived for an arbitrary direction of the offset of the source from the focus, the second focus being at infinity. The formula takes into account four terms of the expansion of the eikonal in the powers of the offset of the source. The accuracy of the formula is analyzed by comparing the results of calculation of the eikonal in a 2D Schwarzschild system with the exact geometric-optics calculation. Formulas for the focal curve, the phase front inclination angle, and aberrations in an arbitrary double-reflector telescopic system are obtained. The formula obtained is used for the analysis and minimization of aberrations in a 2D Schwarzschild system.     

Maxwell鱼眼微球透镜对有限远物点的成像及其像差

本文在文献［１］的基础上用变折射率介质中的光线理论研究了Ｍａｘｗｅｌｌ鱼眼球透镜对有限远物点成像的可能，导出了它对有限运物点的像距和纵、横向球差的计算公式。数值计算的结果表明该种球透镜不仅可以对有限远物点成像，且其纵、横向球差甚小．若合适选取透镜的参数，其纵、横向球差可比均匀折射率球透镜小两、三个数量级，在短物距时也比自聚焦棒透镜小。从而进一步显示了它在集成光学和微型光学系统中应用的可能性。     

A method to overcome the limitations of G.O. in axis-symmetric dielectric lens shaping

The design of a cylindrically symmetric dielectric lens antenna is presented for the case of a very squeezed fan-beam. One makes use of geometrical optics (G.O.) to establish the profile of the lens in a first step. A half-integrated solution of Green's formula for bodies with cylindrical symmetry and circularly polarized surface fields is then derived to calculate the radiation pattern. Since the use of G.O. is restricted to some conditions which were observed unsatisfied in our study, a two-steps procedure to reach an acceptable lens shape is then presented. The first step is based on weighting the source beam of the antenna; and the second one is based on simple geometrical interpolation. Prototypes provided experimental results that are consistent with the predicted radiation characteristics and interesting features of such antennas are pointed out.     

电磁复合场三级几何像差方程的修正与像差系数

本文基于作者提出的“函数逼近的数值迭代概念”，修正了电磁复合场中电子成像系统的三级几何像差方程式，给出了具有更高精度的像差计算公式和用集中参数形式描述的像差系数表达式，为像差的数值计算和电子光学系统的计算机优化设计提供了实用的理论依据。     

Design of a novel LED collimating element based on freeform surface

A novel element for collimating LED light is designed based on non-imaging optics. It is composed of a refraction lens and a reflector. The upper surface of the lens is freeform and calculated by geometrical optics and iterative process. The lens makes the rays in the range of 0°-45°from the optical axis collimated. The rays in the range of 45°-90°from the optical axis are collimated by the reflector. The inner surface of the reflector is parabolic with its focus located in the LED chip. The designed element is applicable to LED source of any emitting type. For a certain application, the simulation results of the designed element in Tracepro show that it has a very compact structure and good collimating performance. Just investigating the loss in the lens surfaces, this element has high light output efficiency of nearly 99%. Most lighting area radii are no more than 20 mm when the illuminated plane is 5 m away from the LED source.     

聚光光伏系统菲涅耳聚光器性能分析与仿真

对太阳能聚光光伏发电技术中的聚光系统进行了研究,分析了菲涅耳透镜应用于太阳能聚光器的优点、聚光特性以及光学效率,推导并获得了平面向外、菲涅耳面向太阳电池的点聚焦菲涅耳透镜的设计公式。在ZEMAX软件的非序列模式中实现了基于非成像光学理论的光线追迹仿真,对某一尺寸的菲涅耳透镜的焦平面上光斑能量分布情况进行了分析与模拟。研究结果表明,利用通常的菲涅尔透镜实现聚光作用的聚焦光斑的光能量主要集中在太阳电池的中心部位,呈现为从中心往外围能量越来越弱的同心圆环。要使太阳电池接收到的光能量尽可能均匀,则需要增加二次聚光元件。     

Analysis of an EHF aplanatic zoned dielectric lens antenna

Zoned dielectric lenses, designed for wide-angle scanning characteristics, are serious contenders to reflector systems for multiple-beam communications and radar applications at EHF frequencies. An analysis is presented in which the zoned lens is approximated by an ideally thin spherical shell (phase transformer) in evaluating the phase aberrations in its aperture plane which are caused by off-axis scanning and deviations from the design frequency. Those results are used to produce a set of universal curves which predict the decrease in directive gain of the lens as a function of scan angle and frequency. Gain and radiation pattern measurements on a90 lambdazoned dielectric lens show agreement with these predictions and with ray-tracing and geometric optics calculations. This study establishes the validity of the spherical shell analysis as a means for rapid estimation of lens parameters for specific system requirements.     

High-frequency analysis of integrated dielectric lens antennas

A high-frequency method for the three-dimensional analysis of integrated dielectric lens antennas is presented. This method consists on improving the physical optics (PO) currents on the lens surface by modifying, via suitable transition functions, the spreading factor of those rays from the source point which arrive at the lens-air interface close to the critical angle of incidence. Invoking the locality principle of the high-frequency phenomena, the method uses the rigorous canonical solution of the semi-infinite dielectric space locally tangent at the lens surface. A uniform asymptotic evaluation of this canonical solution is provided with the introduction of a new transition function for the TM case. The present formulation provides significant correction from the PO currents of an elliptical lens, with a consequent improvement of the radiation pattern prediction, testified by comparisons with results from a full-wave analysis.     

Comparison of Diffraction Fields of Lens by Two Calculation Formulas

Diffraction fields in the focal space of some lens is investigated by using ray tracing and Stratton-Chu formulas. Two formulas are used. One is surface integration formula, and for another a line integration is added. Comparison of two calculation results is given. It is shown that for hyperbolic lens two calculations results are same and for extended hemi-ellipsoidal lens there are a lilt difference between them.     

On eikonal aberrations in axisymmetric double-reflector telescopic systems

A formula describing the eikonal distribution on the surface of the main reflector of a doublereflector system of a general form is derived and its expansion in powers of the offset of the source from the focus up to the fourth-order terms is obtained. The analysis and minimization of aberrations for a doublereflector aplanatic Schwarzschild system are performed.     

Optimization of planar reflector systems for a set of quality indices

Characteristics of a planar double-reflector aplanatic Schwarzschild system that allow estimation of the efficiency of its application in devices of integrated microwave optics are analyzed. The results of multicriteria optimization of the system’s quality indices are obtained. The aplanatic system is compared to systems with parabolic reflectors: a single-reflector system and a double-reflector system with flat subreflector. It is shown that the results of optimization obtained in the approximation of physical optics agree well with the results of the analysis and minimization of aberrations in the reflector system performed with the use of the proposed criterion of rms aberrations. Scanning characteristics of Pareto-optimal planar aplanats are presented.     

自由曲面LED汽车前照灯光学透镜设计方法

由于LED配光特性不同于传统光源,为了将LED 应用于汽车照明中需对LED 进行二次光学设计。文中根据LED 汽车前照灯的配光特性,提出了一种自由曲面LED 汽车前照灯光学透镜的设计方法。首先由能量守恒原理,在接收屏上的坐标和透镜自由曲面上的坐标之间建立能量的一一对应关系,基于非成像光学理论,采用照度优化设计法,运用数值计算求解出光学透镜曲面各个点坐标的坐标值,并使用三维模型软件制作出透镜光学模型。通过蒙特卡洛模拟法来追迹光线仿真,最后的配光效果完全满足《汽车用LED前照灯》（GB25991-2010）标准,系统的光学效率得到显著提高,可达到91%。     

LED照明的光学器件设计与仿真

大功率LED集成光源在实际照明工程应用很多,但是集成光源的照明效果不是很理想。为了解决大功率LED集成光源难以直接应用于照明的问题,根据非成像光学理论,设定合适的初始参数,利用能量守恒建立LED光源与目标照明面之间的映射,设计了筒灯反射器和透镜。并用Tracepro软件对这两类光学器件进行模拟仿真,均得到了良好的均匀圆形照明光斑。仿真结果表明,设计出的反射器和透镜,随着发光光源面积增大,照度均匀性都降低,当光源尺寸均设置为1 mm1 mm时,照明面上照度均匀性都达到95%以上,当光源尺寸增大10 mm10 mm时,照明面的照度均匀性下降到85%,符合对均匀性很高的室内照明设计标准。     

平顶高斯光束通过硬边光阑传输算法的改进

用傅里叶级数和复高斯函数的乘积对硬边光阑的窗口函数进一步拟合,对平顶高斯光束通过硬边光阑光学系统的模拟算法作了改进,并给出了近似解析传输公式.对直接积分Collins公式和使用Wen方法的数值计算结果作了比较.研究表明,只要傅里叶级数项数不少于30,改进后的算法比直接用复高斯函数展开具有更高的计算精度.     

用于室内照明的自由曲面均匀配光透镜设计

以非成像光学为基础,设计了一种在大发散角范围内均匀配光的大功率LED室内照明二次配光透镜方案。采用划分网格法建立光源LED和接收面的映射关系,推导透镜自由曲面面形的一般方程,采用差分法求解透镜面形方程获得面形轮廓数据,再用三维软件建立透镜模型,通过光学仿真软件对所建模型进行光线追迹。结果表明:此方案适用于40°～140°配光角度要求的均匀配光;仿真配光角度120°的照明系统,当透镜的口径与LED发光面直径之比大于等于10时,照明系统的均匀性优于0.9,能量利用率大于92%,且照明效果不受接收面高度的影响。该设计方法为实现大功率LED室内均匀照明系统的小型化和简单化提供了一种有效的途径。     

一种基于Shack-Hartmann传感器的自适应波前重建算法

波前重建是自适应光学系统中的一个重要环节,对系统性能影响明显。研究了一种无参考输入光条件下,基于Shack-Hartmann波前传感器的自适应波前重建算法,能根据实际光斑图的特点,自动确定探测窗口、计算实际质心、参考质心、选择重建区域和获取入射波前的Zernike模式系数,讨论了参考质心选择对波前重建结果的影响。搭建自适应光学系统,通过测量和校正模拟大气像差对重建算法进行了验证。实验结果表明,基于该重建算法的自适应光学系统可以把大气扰动引起的波前像差校正到0.1 λ以下,获得接近衍射极限的成像质量,说明该重建算法具有可靠性与实用性。     

激光束的像散补偿

提出了两种补偿激光束像散的方法:控制面形公差的正负号和插入倾斜球面透镜。导出了相应的计算公式,计算值和实验结果良好地符合。     

附加相位修正副面的多波束环面天线方向图

首先利用等光程条件导出了抛物环面上的点与副面上的点的关系公式；其次，巧妙地利用微波光学强度定律、几何光学法和物理光学法给出了计算“附加相位校正副面的多波束抛物环面天线”的辐射方向图公式；最后，利用所得的辐射方向图公式对一个实际天线进行了理论计算，理论计算值和实验测试值吻合异常良好。     

An exact line integral representation of the physical opticsscattered field: the case of a perfectly conducting polyhedral structureilluminated by electric Hertzian dipoles

An exact line integral representation of the electric physical optics scattered field is presented. This representation applies to scattering configurations with perfectly electrically conducting polyhedral structures illuminated by a finite number of electric Hertzian dipoles. The positions of the source and observation points can be almost arbitrary. The line integral representation yields the exact same result as the conventional surface radiation integral; however, it is potentially less time consuming and particularly useful when the physical optics field can be augmented by a fringe wave contribution as calculated from physical theory of diffraction equivalent edge currents. The final expression for the line integral representation is lengthy but involves only simple functions and is thus suited for numerical calculation. To illustrate the exactness of the line integral representation, comparisons of numerical results obtained from the surface and the line integral representations are performed