基于极坐标的星模拟器星点能量中心修正的研究--毕业论文设计外文文献翻译.doc

声明： 以下内容均是本人原创翻译，绝无抄袭，可放心使用。本人系英语翻译专业研究生硕士毕业，手持英语专业八级和四级证书,全国外语翻译证书以及剑桥商务英语证书；曾供职于外企长达三年，现成为译员近四年，笔译实践量超570万字，累计服务过4800位客户以及300多家公司团体。 本人还可提供外文文献或者英语论文翻译以及文字图片或pdf转word格式的服务，有英语作业不愿做的或者论文不愿写的，+扣扣(q，q):五一三二七九五九三(五一三二七九五九三是数字)。无账号下载本文档的，可，+微信号：jpd八八零三一五（八八零三一五是数字）。Star Point Energy Center Correction of Star Simulator Based on Polar Coordinates 基于极坐标的星模拟器星点能量中心修正的研究Abstract ： In this paper, various aberrations have been analyzed. Not only the effects of aberration on geometrical center position are taken into account, but also the deviation of displayed star position energy center caused by aberration is analyzed. These two aspects have been taken into comprehensive evaluation and star position correction. The correction method based on polar coordinates is proposed, and cumbersome partition correction and calculated quantity based on two-dimensional coordinates can be simplified. The experimental results show that the correction processing based on polar coordinates is simpler and easier compared with any other correction methods. In addition,the correction results are significantly more accurate.摘要：本文分析了许多不同的像差。不仅考虑到了几何中心位置像差的影响还分析了像差对显示星点能量中心位置造成的偏差。对这两个方面进行了综合评估以及星点的修正。提出了一种基于极坐标的星点位置修正方法，该方法简化了基于二维坐标轴分区修正的过程，减少了数据计算量.实验结果表明极坐标修正过程较以往修正方法简单快捷，且修正结果更加准确.Key words Aberration, Energy center, Correction, Polar coordinates关键词： 像差， 能量中心，修正，极坐标 Introduction引言The calibration of star sensor is the main function of star simulator. However, with the development of star sensor and star simulator technology, the high requirements of specifications and accuracy have become the key of designing and manufacturing of starsimulator.星敏感器的校准作用是星模拟器的主要功能。然而，随着星敏感器和星模拟器技术的发展，对规格和准确性的高要求变成了星模拟器设计和制造的关键部分。For previous star simulator, except for the requirement of hardware with high accuracy, the improvement of correction and operating rate based on software is indispensable. But the correction of optial system aberration still relies on theodolite testing with human eyes, by recording the experimental data and correcting the data to realize the correction,or just correcting the displayed geometrical center of star point caused饰distortion. Only the influence of distortion on geometrical center can be corrected and the energy center deviation caused by other aberrations is neglected, while the star sensor recognizes the star point by recognizing the energy center. Simultaneously, the former correction regards the image plane as a two-dimensional surface, and realizes the correction establishing two-dimensional coor-dinates, and separating the regions of coordinates system according to different positions in correction.But the optical system of star simulator is coaxial system completely composed of spherical lens, and the aberration in the same field of view through the free directions of optical system is rotationally symmetric surrounding the optical system. The correction appears to be complicated under separated regions according to the two-dimensional system.对于星模拟器, 除了高精度的硬件要求, 软件修正及运算速度的提升也必不可少.但现有研究对于光学系统像差的修正只停留在通过人眼使用经纬仪进行测试的阶段, 记录实验数据后, 对数据进行处理修正, 或者只对畸变造成的星点显示几何中心位置误差进行修正, 这样只是修正了畸变对几何中心的影响, 忽略了其他像差对能量中心造成的偏移, 而星敏感器对于星点的识别往往是对能量中心的识别.同时以往的修正方法只是将像面看作是一个二维平面, 修正时建立一个二维坐标系, 根据不同的位置进行分区， 但星模光学系统完全是由球面镜组成的共轴光学系统, 通过系统光轴的任意方向上相同视场的像差绕着光轴旋转对称, 使得在二维坐标下分区的方法略为繁琐. On the basis of the summaries of the former star point error correction, taking a star simulator with 220 field of view as example, a new correction method is proposed in this paper, and the method to ensure the position of energy center by analyzing the point distribution function of optical system and correcting the error based on polar coordinates is also proposed.在总结以往的星点误差修正方法的基础上, 本文以22 视场星模为例, 提出了一种通过分析光学系统的点分布函数来确定能量中心位置, 并在极坐标系上进行修正的方法.1 Working Principle of Star Simulator and Aberration Analysis1.1 Working Principle of Star Simulator1 星模拟器工作原理及像差分析1.1 星模拟器工作原理As the calibration device of star sensor, the star simulator provides infinity star simulation for star sensor,and realizes the star point display by the displaying device. While the emergent rays of star point passing through the collimation optical system, they will be parallel and image at the entrance pupil of star sensor, which finally fulfill the simulation of infinity star point, as shown in Figure 1.星模拟器作为星敏感器的模拟测试设备, 为星敏提供无穷远星点的模拟, 其模拟过程是通过显示器件来完成. 星图经过准直光学系统成平行光出射, 在星敏感器的入瞳处成像, 由此完成对无穷远星图的模拟, 如图1.1.2 Aberration Analysis1.2 像差分析The aberration of optical system is divided into monochromatic aberration and chromatic aberration.The monochromatic aberration includes spherical aberration, coma, astigmatism, field curvature and distortion, while the chromatic aberration includes光学系统的像差分为单色像差和色差, 其中单色像差分为球差, 慧差, 像散, 场曲和畸变, 而色差包括Fig. 1 Interrelation of star simulator compositions axial chromatic aberration and lateral chromatic aberration. Due to the existence of various aberrations in collimation optical system, the actual energy center and theoretical energy center are different,which will result in the loss of simulation accuracy of star simulator.图一 为星模拟器组成的轴心色差像和横向色差像的相互关系。由于准直光学系统中各种像差的存在，实际的能力中心和理论上的能量中心是不同的，这导致了星模拟器的模拟准确性失真。 (1) Spherical aberration. While the emergent light beam from on-axis object point pass through the optical system, the rays with different angels which is relative to optical axis intersect in different posidons on axis, and the image plane presents a circular dispersion spot.1)球差。当轴上物点发出的光束经光学系统后, 与光轴呈不同角度的光线交光轴于不同位置, 使星点在像面上形成一个圆形弥散斑. (2) Coma. The off axis object point locates off the main axis, emits monochromatic cone-beam to optical system. The existed light beam is refracted by optical system and imaged unclearly on ideal image point, and the image point brings bright tail and forms a comet dispersion spot.2)慧差。 由位于主轴外的星点, 向光学系统发出的单色圆锥形光束, 经光学系统折射后, 在理想平面处不能结成清晰点, 而是结成拖着明亮尾巴的彗星形弥散斑. (3) Astigmatism and field curvature. As the 1uminescence object point is off the axis of optical system, the emitted beam has inclined angle with optical axis. The light beam is refracted by lens and the convergence of meridian beamlet and sagittal beamlet is not on the same point. That is the beam convergent in different point and the image is unclear, finally forms elliptical dispersion spotl.3)像散和场曲。 当发光星点不在光学系统的光轴上时, 它所发出的光束与光轴有一倾斜角.该光束经透镜折射后, 其子午细光束与弧矢细光束的汇聚点不在一个点上.即光束不能聚焦于一点, 成像不清晰, 形成椭圆形弥散斑 (4) Distortion. While the astigmatism and field curvature are corrected to be zero, the chief ray is not duplication with ideal image point, and this only causes the position error of star point and there will be no disperse spot4)畸变。当像散场曲校正为零时,主光线不与理想像点重合, 只引起像星点的位置误差, 并不产生弥散斑. (5) Axial chromatic aberration. Similar with spherical aberration, while various light passing through the lens, the beam cannot converge to be image point on image plane and form colorful circular dispersion spot.5)位置色差影响:类似于球差的影响, 星点发出的各色光通过透镜时, 由于位置色差的存在不能在象平面上会聚成一个象点, 形成彩色圆形弥散斑. In conclusion, the aberrations of optical system almost all have influences on star point energy center. In order to induce the deviation of energy center Caused by aberration, an optical system with 22 field of view and 56.0006 mm focal length is designed.光学系统的所有像差几乎都对星点的能量中心显示产生影响.为了尽量减小像差产生的能量中心偏移, 设计视场22 , 焦距56.0006mm的光学系统.2 Correction Processing of Energy Center2. 能量中心修正过程In the star simulator optical system, the position and orientation of the actual incident ray is uncertain. In order to simulate the actual path of light propagation,non-sequential ray tracing method is used. Monte Carol algorithm is used to generate the stochastic rays emitted from the star point, and these rays are used to simulate the light path for ray tracing. Finally,the simulation produces the image point distribution function, and the computer calculation is used to analyze the data of this function, and to determine the offset relationship between the actual energy center position and the theoretical energy center position.在星模光学系统中, 实际光线的位置和方向是不确定的, 为了模拟实际光线传播的路径, 采用非序列光线追迹方法.利用Monte Carlo算法模拟星点产生的随机光线来模拟光线路径, 进行光线追迹.通过模拟出的像点分布函数, 利用计算机进行数据分析, 确定能量中心位置与理论设计时能量中心位置的偏移关系.Monte Carlo ray tracing method selects random based on the probability function and the sampling algorithm, and the normalized probability function isMonte Carlo光线追迹方法中随机光线的选择基于概率函数及算法中的抽样, 归一化的概率函数为where x value,represents the random variable, and for any . The corresponding point式中x代表随机变量, 对任意的x, 有P(x) 0.其相应的积分为According to a given probability function P(x),the algorithm to obtain a series of random number consists of two steps: (1) To select a uniformly distributed random number p during the interval of 【0,1】 (2) Using in the cumulative distribution function curves to calculate the corresponding value Repeating these two steps and you can get according to . According to ZEMAX correlation function, the differences between actual energy center and the theoretical energy center in each field can be figured out,which is shown in Table 1.根据一个给定的概率函数P(x)来获得一系列的随机数xp, 运算法则步骤为1)选择一个在区间0, 1上均匀分布的随机数p;2)在累积分布函数曲线中利用p=D(xp)来计算相应的值xp, 重复这两步就可以得到根据P(x)分布的数xp3.根据Zemax相关函数求解出不同视场实际能量中心与理论能量中心差异, 结果见表1. Through the position deviations between the theoretical and actual energy center calculated from the point distribution function, the curve and surfaces can be fitted along the polar direction通过理论与实际能量中心之间的点分布函数计算的位置偏差，曲线和表面可沿着极坐方向来拟合。With the least square method, the correspon dente function between the actual energy center and the theoretical energy center is fitted, and theoretical energy center correction is made. So the amended actual energy center is displayed on the screen, which is consistent with the theoretical energy center.通过最小二乘法拟合出实际能量中心与理论能量中心的对应关系, 对理论能量中心进行修正, 使屏幕显示的实际能量中心, 经修正后与理论能量中心一致.According to the point distribution function analyzed from ZEMAX, the energy centers offset of anyfield of view can be obtained. These offsets can be fitted with a correction curve。, which shows the actual theoretical energy center after correction.Using the principle that make the sum of squares minimum as根据Zemax分析出的点分布函数可知任意视场点能量中心的偏移量, 根据这些偏移量可拟合出修正后的实际理论能量中心曲线 = ( ), 用偏差的平方和最小的原则即最小二乘法, 拟合出修正曲线, 即also called least squares method, the fitting curve canbe figured out as:也成为最小啊二乘法，拟合曲线可以表达为：After correction, according to the direction of corrected point azimuth angle B, the point coordinates is restored from the polar coordinates into the form of two-dimensional coordinate system like，the star point at the corresponding coordinate position is lit on the screen. The conversion formula is:修正后, 再根据被修正点的方位角 , 恢复出二维坐标系xoy下的(x, y)坐标形式在屏幕上对应的像素坐标位置点亮星点.转换公式为：Here is the azimuth angle of the star point needed to be lit before the correction.式中 为修正前需要被点亮星点的方位角.3 Error Analysis3.误差分析According to the system requirements for precision,the single star position error 22 shows that for the field of view w, its permissible error bw must satisfy that the error is less than a single star position error, . According to the fitting equation,the inferred maximum truncation error is 0.25413,which is much smaller than the requirements that the single star position error should be22根据系统要求精度, 单星位置误差 22可知, 视场 允许误差必须满足截断误差项小于单星位置误差, 即 22.根据拟合方程可推断出最大截断误差为0.41832, 远小于22, 满足单星位置精度的要求.For static star simulator, bias based on the star point energy center displayed on the star check board is the correction error, which can meet the accuracy requirements.对于静态星模拟器, 在星检板上直接刻画的星点对于读取能量中心产生的偏差即为修正误差4.本系统静态修正误差即为系统最大截断误差0.41832, 满足精度要求.However; due to the dynamic star simulator display device restrictions, the star point movement on LCOS per unit is 0.008 mm. The maximum error of the impact of display device is但对于动态星模拟器由于显示器条件限制, 星点在LCOS上的单位移动量为0.008 mm, 即器件影响产生的最大误差为Sub-pixel display technology is utilized in dynamic star simulator, and interpolation algorithm is used to refine a pixel into smaller pixel unit, such as 1/2pixel, 1/5 pixel, 1/10pixel. Sub-pixel is a method to make a pixel divided into smaller units. Taking the 8 bit system as an example, the gray level of the pixelvalue is 255, then in such systems a pixel could be divided into small units of 255 using the interpolation algorithm cooperated with surrounding points gray value, to make the star point position display precision reach decimal range.对动态星模拟器采用亚像素显示技术, 通过插值算法将一个像素细化成更小的像素单位, 如1 /2 个像素, 1 /5 个像素, 1 /10 个像素.亚像素就是将一个像素分为更小的单位, 以8bit 的系统为例, 该像素的灰度值级别为256, 那么对这类系统进行亚像素计算就要把这一个像素分为255 个小单位5, 并通过插值算法通过与周围像素灰度值进行配合, 使得星点显示像素位置移动精度达到小数范围. Mass center is the star theoretical position on the map. To make sure of the star position, method of back stepping each pixels gray value in the display area from the mass center can be used in order to increase the display accuracy up to tenths.质心是地图上的星理论上的位置。为了确定星的位置，来自质心展示区中的反向递推每个像素的灰值的方法被用以增加十分位的显示误差。 To ensure the accuracy of the simulator, the Gaussian distribution function is chosen to simulate the light spot grey value distribution:为了确保模拟器的准确性，高斯分布函数被选用来模拟光斑灰值分布：where ；are the theoretical center coordinates; are the pixel coordinates on the display device; A, B are the Gaussian distribution parameters.Both sides of the equation can be transformed by logarithmic computation:在该方程式中，X0,Y0是理论中心坐标，XP,YP是显示设备上像素的坐标，A,B是高斯分布参数。通过对数计算，方程的两边可以转化为：Whenfurther linear function relation is shown as Using the least squares fitting, the fitting coeffident can be calculated out通过最小平方拟合，拟合系数可以计算出来Here are date points.The specific value can be calculated according to the pixels value inside the star light point. Finally, the real pixels value can be obtained by back-stepping the fitting equations. Taking a 6 x 6 pixels array for example as shown in Figure 2, a star point centroid accuracy of 0.1 is shown in Figure 3, where shows the corresponding pixel value of LCOS display device.是时间点。比值可以通过星点中的像素值来计算出。最后，通过反推拟合方程式可以获得真实的像素值。如图2展示的以6 x 6像素值为例，图3中星点图心的准确值，Py是LCOS显示设备上相应的像素值。Through experimental analysis, after subpixel display, the precision can be improved to a higher level, and the energy distribution effect is improved substantially and is more closed to real star image, as shown in Figure 4.通过实验分析，亚像素显示后，之前的值可以提高到一个新的程度，能量分布效果也大大提高并且如图4显示的，越来越接近真实星图The usage of sub-pixel star point display method increase the energy center position display precision 0.1 pixel, and the influence error is利用亚像素星点显示方法将能量中心位置显示精度提高到0.1个像元后, 影响误差为After error accumulation, the error still can satisfy the system required precision.误差累积后依然满足系统精度要求.4 In conclusionThe experimental result shows that the method by analyzing the point distribution function of the optical system to ensure the offset between actual energy center position and theoretical energy center position, and correct