大曲率光学零件面形的空间载频外差干涉术检测

光学零件表面面形检测的结果直接影响光学零件的质量,介绍了一种在平面干涉仪上检测大曲率球面光学零件面形的方法,通过对干涉图进行预处理、FFT提取相位、解包裹,并采用Zernike多项式拟合,得到被检球面相对平面的面形函数,与指定的球面相减后,再一次进行Zernike多项式拟合,得到了被检面相对于指定球面的面形函数,由此计算出被检球面的面形误差PV值、RMS值,N与△N,并模拟出了用球面干涉仪检测时的干涉条纹。该方法克服了接触检测的缺点,精度高,PV值的标准差σ优于λ/100,RMS值的标准差σ优于λ/700,而且可通过软件设定检测任意大曲率光学零件,为大曲率半径光学零件的检测提供了一种适用的方法。

离轴非球面加工、检测轨迹优化研究

为实现对用于红外侦察、预警相机中的非球面元件的快速加工,研制成功了具有两种运动方式、双磨头姿态的六轴联动型非球面数控光学加工中心FSGJ Ⅱ。在系统多机构自由度的优势下,对系统加工、检测轨迹进行了优化设计。同时,基于对相邻点面形变化率的比较,借助于一实际矩形离轴非球面,构建了适用于非回转对称离轴非球面加工、检测轨迹的常规方程。

Submanifolds with Parallel Mean Curvacture

In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decrease.

Effect of prestressed ultrasonic peen forming parameters on bending curvature and spherical deformation of plate

The elastic prestressed ultrasonic peen forming(UPF)was adopted in order to solve problems of insufficient bending deformation and large spherical deformation of plate during free UPF.The theoretical analysis of prestressed UPF and the influence of elastic prebending moment on deformation were analyzed.Spherical deformation coefficient was defined to quantificationally describe the spherical deformation.Experiments were conducted to compare the differences between free UPF and prestressed UPF processes and the effects of processing parameters on bending curvature and spherical deformation coefficient were studied.The results show that peening trajectory in chordwise direction is beneficial to enlarging spanwise bending deformation and decreasing spherical deformation coefficient.Large prebending curvature is helpful to increase spanwise bending deformation and decrease chordwise deformation,thereby obviously decreasing spherical deformation coefficient.Large spanwise deformation can be obtained under large firing pin velocity,small plate thickness and small offset distance.Large firing pin velocity plays a positive role in decreasing spherical deformation,while plate thickness and offset distance have little effect on it.Above all,prebending curvature and peening trajectory are the most important factors during prestressed UPF process.This study provides guidance for parameters optimization of prestressed UPF for wing plate with large thickness.

Hypersurfaces with Constant Mean Curvature in Space Forms

In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc.

The Isometry of Riemannian Manifold to a Sphere

In this paper the quasi-constant curvature space and the Riemannian manifold contained the totally umbilical hypersurface family are studied,and two theorems are given at the same time.

C~∞ Compactness for a Class of Riemannian Manifolds with Parallel Ricci Curvature

In this paper we prove that tile set of Riemannian manifolds with parallel Ricci curvature, lower bounds for sectional curvature and injectivity radius and a upper bound for volume is coo compact in Gromov-Hausdroff topology. As an application we also prove a pinching result which states that a Ricci flat manifold is flat under certain conditions.

On Conformal Minimal Immersions of Two-Spheres into CPN

A curvature pinching theorem is given on conformal immersions of two spheres into CPN in this paper.

Rigidity Theorems for Hypersurfaces in Real Space Form

In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.

Classification of hypersurfaces with two distinct principal curvatures and closed Mbius form in S^(m+1)

Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures and closed MSbius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.

A differentiable sphere theorem with positive Ricci curvature and reverse volume pinching

Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.

Classification of hypersurfaces with constant Laguerre eigenvalues in R^n

Let x:M → Rn be an umbilical free hypersurface with non-zero principal curvatures.Then x is associated with a Laguerre metric g,a Laguerre tensor L,a Laguerre form C,and a Laguerre second fundamental form B,which are invariants of x under Laguerre transformation group.An eigenvalue of Laguerre tensor L of x is called a Laguerre eigenvalue of x.In this paper,we classify all oriented hypersurfaces with constant Laguerre eigenvalues and vanishing Laguerre form.

On Ricci tensor of focal submanifolds of isoparametric hypersurfaces

A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.

Curvature estimates for the level sets of spatial quasiconcave solutions to a class of parabolic equations

We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.

The hyper-surfaces with two linear dependent mean curvature functions in space forms

We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.

The Effects of Spherical Surface and Laser Polarization on the Photodetachment Cross Section of H^-

We report the combined effects of laser polarization and curvature of the spherical surface on the detached electron spectra from H-. The Theoretical imaging method is used as a tool of investigation. The photodetachment cross sections for various polaxization angles, radii of curvatures and inter ion surface distances axe displayed. The analysis of the spectra reveals that the laser polarization angle θL, curvature of the surface τc and inter ion surface distance d strongly affect oscillations in the spectra. Therefore, a fine control on the laser polaxization and that of curvature in the surface can be used to control oscillations in the photodetachment of negative ions.

Closed Geodesics and Volume Growth of Open Manifolds with Sectional Curvature Bounded from Below

In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nifold with nonnegative sectional curvature, which improves Marenich-Toponogov＇s theorem. As an application, a rigidity theorem is obtained for nonnegatively curved open manifold which contains a clesed geodesic. Next the authors prove a theorem about the nonexistence of closed geodesics for Riemannian manifolds with sectional curvature bounded from below by a negative constant.