离轴抛物面反射镜模拟空间环境镜面变形分析

在卫星红外多光谱扫描仪模拟空间环境辐射定标试验中,环境模拟器舱内的稳、瞬态温度场会给光学系统成像质量带来影响.以试验中的实测温度变化作为温度载荷,借助有限元软件,分析了定标系统中通光孔径为φ400mm的离轴抛物面主镜的温度场分布和热弹性变形.选用在单位圆内正交的Zernike多项式为拟合基函数,通过坐标变换,将抛物镜表...     

Spatial impulse responses from a flexible baffled circular piston

The theory of orthogonal polynomial (Zernike) expansions of functions on a disk, as used in the diffraction theory of optical aberrations, is applied to obtain (semi-) analytical expressions for the spatial impulse responses arising from a non-uniformly moving, baffled, circular piston. These expressions are in terms of the expansion coefficients of the non-uniformity and the responses of the orthogonal expansion functions. The latter impulse responses have a closed form as finite series involving the Legendre functions and the sinc function. The method is compared with a similar method, proposed by P. R. Stepanishen [J. Acoust. Soc. Am. 70, 1176-1181 (1981)] where zeroth order orthogonal Bessel functions, rather than Zernike polynomials, are used as expansion functions.     

Modal Description of Wavefront Aberration in Non-circle Apertures

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｗｅｏｆｔｅｎｄｅｓｃｒｉｂｅｔｈｅｓｔａｔｉｃｏｒｄｙｎａｍｉｃｗａｖｅｆｒｏｎｔａｂｅｒｒａｔｉｏｎｓａｓｃｏｍｂｉｎａｔｉｏｎｏｆｄｉｆｆｅｒｅｎｔｍｏｄｅｓ,ｓｕｃｈａｓｐｉｓｔｏｎ ,ｔｉｌｔ,ｄｅｆｏｃｕｓ,ｃｏｍａ,ｓｐｈｅｒａｌａｎｄｓｏｏｎ .ＴｈｅｓｅｍｏｄｅｓａｒｅｓｉｍｉｌａｒａｓｓｏｍｅｌｏｗｅｒｏｒｄｅｒｓｏｆＺｅｒｎｉｋｅｐｏｌｙｎｏｍｉａｌｓ.ＴｈｅＺｅｒｎｉｋｅ ｐｏｌｙｎｏｍｉａｌｓａｒｅｎｏｒｍａｌｉｚｅｄｏｒｔｈｏｇｏｎａｌｉｎｃｉｒ…     

波面重构中非圆域Zernike正交基底构造方法

针对非圆域波面拟合中Zernike多项式失去正交特性、拟合系数交叉耦合的问题,提出非圆域Zernike正交基底函数构造方法。以圆Zernike为基底,采用Gram-Schimdt正交组构造方法,线性表出单位正交基底。通过构造不同遮光比环形光阑下的正交基底与环Zernike多项式进行比较,验证了此方法的正确性。然后采用圆Zernike多项式和构造的新基底对矩形光阑下的波面进行了拟合,从拟合残余误差、各项基底系数的稳定性、传递矩阵的条件数等分析,结果表明针对特定的非圆域构造的新基底可靠性和抗扰动能力优于圆Zernike多项式。此方法不需要具体求出基底的解析表达式,不同非圆域仅是正交化系数矩阵发生改变,为非圆域正交基底构造提供了一种新途径。     

Zernike-basis expansion of the fractional and radial Hilbert phase masks

The linear Hilbert phase mask or transform has found applications in image processing and spectroscopy. An optical version of the fractional Hilbert mask is considered here, comprising an imaging system with a circular, unobscured pupil in which a variable phase delay is introduced into one half of the pupil, split bilaterally.The radial Hilbert phase mask is also used in image processing and to produce optical vortices which have applications in optical tweezers and the detection of exoplanets.We subjected the fractional and radial Hilbert phase masks to Zernike function expansion in order to compute the image plane electromagnetic field distribution using Nijboer-Zernike theory. The Zernike functions form an orthogonal basis on the unit circle. The complex-valued Zernike expansion coefficients for these two phase masks were derived for use in the context of the Extended Nijboer-Zernike (ENZ) theory of image formation. The ENZ approach is of interest in that it allows a greater range of defocus to be dealt with, provides a simple means of taking a finite source size into account and has been adapted to high Numerical Aperture (NA) imaging applications.Our image plane results for the fractional Hilbert mask were verified against a numerical model implemented in the commercial optical design and analysis code, Zemax^®. It was found that the Nijboer-Zernike result converged to the Zemax^® result from below as the number of Zernike terms in the expansion was increased.     

基于主观式测量人眼波前像差的眼模型研究

通过主观式光线追踪波前像差测量方法得到用Zernike系数描述的人眼波前像差;在Gullstrand-Le Grand眼模型的基础上,引入用医用角膜地形图仪测量并用高次非球面函数拟合的实际人眼角膜形状数据,又引入角膜、前房及玻璃体厚度等个体化的眼结构参数;在光学建模软件Zemax中用所测Zernike系数建立评价函数,并对用Zernike矢高面描绘的晶状体表面进行优化.由此建立了个体化眼模型,并由此模型中可以计算得到与实际测量的波前像差值完全相同的各项Zernike系数值,从而可用于描述实际人眼的光学特性.     

子孔径合成光学成像系统像质评价研究

由于子孔径合成光学成像系统出瞳波前离散,成像特征有异于常规光学系统.对比了两种子孔径合成光学成像系统的像质评价方法,其一是直接利用干涉仪实测获得的整体出瞳波面参量,拟合成泽尼克多项式,通过快速傅里叶变换获得光学系统的调制传递函数;其二是对子出瞳波面在像面复振幅分布的衍射直接积分叠加计算系统调制传递函数.对于离散出瞳波前,拟合的泽尼克多项式不可避免有较大误差,由此计算获得的调制传递函数与实际测量值有较大区别.设计并制造了一个三子镜合成的成像光学系统,在此基础上用ZYGO GPI干涉仪验证并对比了使用两种方法对像质计算的特点.结果表明,子出瞳波面直接衍射积分叠加法的精度更高,但计算量大,且要获得更高的像质评价精度,应使用更适于表达离散不规则形状子出瞳波前的波函数.     

光学窗口形变对平行光管光学性能影响分析

由于环境工况的多变性,光学窗口设计交叉了光、机、热等多种学科。在压差、轴向温差及径向温差工况下,分析光学窗口形变对某大口径、长焦距平行光管光学性能的影响,建立了光学窗口的有限元模型,与理论结果进行对比,验证了该有限元模型的有效性。以有限元分析得出的光学窗口变形数据为输入数据,带入改进了的Zernike多项式光机分析接口程序,获得了与像差对应的Zernike系数。用得到的Zernike系数表示光学窗口面型,以波像差作为光学系统成像质量评价指标,分析光学窗口变形对大口径、长焦距平行光管系统光学性能的影响。结果表明:光学窗口变形对平行光管系统光学性能的影响可以忽略不计。     

Zernike模式像差共轭组合模型

根据Zernike模式在单位圆的同心孔径圆域内某些模式间具有一定耦合性的结论及对应Zernike模式像差在一定同心光瞳区域内的相互抵消特性,对具有相同角频率不同阶数的Zernike模式建立组合模型,同时根据同心光瞳区域内像差均方根值的降幅比参数给出了同心光瞳直径为4mm时的Zernike模式线性共轭组合模型。最后通过共轭组合模型对光学质量影响的研究发现,共轭模型组合之后能显著提高光学质量。同时也表明Zernike模式组合对光学质量的影响不具备叠加性,而对共轭组合模型表现为补偿关系。     

The Universe Accelerated Expansion using Extra-dimensions with Metric Components Found by a New Equivalence Principle

Curved multi-dimensional space-times (5D and higher) are constructed by embedding them in one higher-dimensional flat space. The condition that the embedding coordinates have a separable form, plus the demand of an orthogonal resulting space-time, implies that the curved multi-dimensional space-time has 4D de-Sitter subspaces (for constant extra-dimensions) in which the 3D subspace has an accelerated expansion. A complete determination of the curved multi-dimensional spacetime geometry is obtained provided we impose a new type of “equivalence principle”, meaning that there is a geodesic which from the embedding space has a rectliniar motion. According to this new equivalence principle, we can find the extra-dimensions metric components, each curved multi-dimensional spacetime surface’s equation, the energy-momentum tensors and the extra-dimensions as functions of a scalar field. The generic geodesic in each 5D spacetime are studied: they include solutions where particle’s motion along the extra-dimension is periodic and the 3D expansion factor is inflationary (accelerated expansion). Thus, the 3D subspace has an accelerated expansion.     

基于矢量波像差理论的计算机辅助装调技术研究

在三阶矢量波像差理论的基础上,建立了系统内失调量与系统波像差Zernike系数的关系式,并以共轴三反射光学系统为数学模型进行了仿真分析.结果表明,基于矢量波像差理论的装调技术可行,并可用于大型光学系统的装调.利用该理论对一共轴非球面三反系统进行装调,最终使系统波像差RMS<0.080λ.     

Contribution to the expression of particle movement in magnetic mirror systems in cyclic variables

The aim of this paper is to express the Hamiltonian function of a particle in a static, axially symmetric magnetic field in convenient variables. Assuming adiabaticity (the relative change of the magnetic field during one cyclotron revolution can be neglected), the Hamiltonian function is determined with cyclicity in two degrees of freedom.For the determination of the Hamiltonian function either the Carthesian, or the orthogonal curvilinear system was used as a starting coordinate system. The latter consists of a natural system of lines of force and equipotentials of the field. In both cases a Hamiltonian function of the formH=H(P₁ P ₂,P ₃,Q ₃) is obtained, where P_i are generalized impulses and Q₃ longitudinal coordinates.The form of the Hamiltonian function is very simple; it facilitates appreciably the integration of the equations of motion and provides simple expressions for the integrals of motion.The author wishes to express his thanks to Ing. J. Váa, the Director of the Institute, for his interest in the work and to Dr. M. Scidl for encouragement.     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

Optical quality in a myopic population of human eyes

An aberrometer was used to measure the monochromatic aberration of 219 eyes in a population of 113 myopic subjects. The Zernike expansion was used to describe the wavefront aberration of the human eyes. From the distribution of Zernike coefficients, the means of almost all Zernike coefficients are approximately zero, and the mean absolute values of Zernike coefficients convey the level of aberration for our study population. Based on the distribution of Zernike coefficients, the averaged optical quality was computed in different methods. The mean MTF and PSF of individual eyes represent the optical quality for a typical myopic eye. Through the calculation of the visual benefits expected from correcting Zernike modes, a large expected visual benefit can be achieved across all spatial frequencies after correcting 5 Zernike modes. Furthermore, the larger improvement of optical quality can be achieved with correcting more Zernike modes at a higher spatial frequency.     

Time Functions as Utilities

Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functions correspond to the utilities for the K ⁺ relation (Seifert’s relation). By exploiting this analogy, we are able to import some mathematical results, most notably Peleg’s and Levin’s theorems, to the spacetime framework. As a consequence, we prove that a K-causal (i.e. stably causal) spacetime admits a time function and that the time or temporal functions can be used to recover the K ⁺ (or Seifert) relation which indeed turns out to be the intersection of the time or temporal orderings. This result tells us in which circumstances it is possible to recover the chronological or causal relation starting from the set of time or temporal functions allowed by the spacetime. Moreover, it is proved that a chronological spacetime in which the closure of the causal relation is transitive (for instance a reflective spacetime) admits a semi-time function. Along the way a new proof avoiding smoothing techniques is given that the existence of a time function implies stable causality, and a new short proof of the equivalence between K-causality and stable causality is given which takes advantage of Levin’s theorem and smoothing techniques.     

Scaling pseudo-Zernike expansion coefficients to different pupil sizes

Orthogonal polynomials are routinely used to represent complex surfaces over a specified domain. In optics, Zernike polynomials have found wide application in optical testing, wavefront sensing, and aberration theory. This set is orthogonal over the continuous unit circle matching the typical shape of optical components and pupils. A variety of techniques has been developed to scale Zernike expansion coefficients to concentric circular subregions to mimic, for example, stopping down the aperture size of an optical system. Here, similar techniques are used to rescale the expansion coefficients to new pupil sizes for a related orthogonal set: the pseudo-Zernike polynomials.     

基于矢量波像差理论的两反光学系统装调研究

 为了实现对两反光学系统的精密装调,提出一种基于矢量波像差理论和波像差检测技术对失调量精确求解的装调方法。使用矢量波像差理论,将已设计的两反光学系统参数、失调量和失调光学系统的波像差之间建立方程;然后通过干涉测量法得到某一个视场的干涉图,利用条纹分析软件得到表征失调系统三阶彗差和三阶像散的泽尼克项系数,将泽尼克项系数代入方程从而求解出失调量。运用此方法对4 m口径RITCHEY-CHR-TIEN结构的天文望远镜进行模拟装调,最终求解的失调量与引入的失调量结果相互吻合,说明该装调方法正确。     

高空高速航空相机光学窗口的热光学分析

分析航空相机光学窗口的热光学特性,选定熔石英作为窗口玻璃的材料,将热流密度加权分配到窗口外表面各个区域,并考虑整个窗口玻璃的辐射来计算其在一个工作循环内的温度分布。高空高速飞行时,气动热使窗口外表面的温度急剧上升,由于熔石英的导热率很小,窗口产生很大的轴向温差,分别取轴向温差55℃,70℃和90℃时的工况计算窗口热变形;光学窗口内、外表面的变形规律为近似球面,计算了其近似曲率半径,计算由面形变化和折射率变化引起的光程差并转化为Zernike多项式;将Zernike多项式系数带入Code V中考核窗口玻璃的光学性能,得到波像差变化量,其像面离焦量为-0.114mm,调制传递函数的下降最大值小于0.01。结果表明,光学窗口满足光学性能的要求。     

基于环扇域正交多项式的频域分析

利用傅里叶变换得到了Zernike多项式和环扇域内正交多项式的功率谱密度（PSD）分布,以及正交多项式每项所对应的峰值径向空间频率和半峰值径向空间频率范围。通过对比发现,正交多项式与相同阶的Zernike多项式PSD分布相似,但是却含有更高的空间频率成分。通过计算机仿真,发现正交多项式中每一项都基本上只代表特定的空间频率范围,根据相位度量的环扇形镜面面形空间频率分布,选择适当的正交多项式的项进行拟合,不仅能够节省运算时间,而且还可以保证拟合精度。