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.     

A parametrisation of the direct correlation function for the square-shoulder fluid

We introduce a parametrisation of the direct correlation function for the square-shoulder fluid and demonstrate that this parametrisation is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. Moreover, the radial distribution function obtained from the parametrisation reproduces quantitatively Monte Carlo simulation data. Our results show that the parametrisation is accurate over a large regime of densities for different interaction ranges and potential strengths.     

基于Zernike多项式表示色域边界的色域映射

在彩色图像的跨媒体复制中,由于不同媒体有不同的色域,所以在大多数情况下色域映射是不可避免的。不论采用何种映射算法,色域映射的第一步是确定有关媒体的色域边界。目前大多数的色域边界都是用一组测量的或用其它方法得到的离散数据来表示的。然而,由于这种表示方式是利用一组离散数据来实施色域映射的两个基本处理(即确定任一指定的等色调面平面中色域的边缘线以及确定色域边界与一条映射线的交点),比较复杂和费时,因此希望找到一种色域边界的解析表达式来解决这一问题。简述了不久前提出的一种解析函数色域边界表示方法,并用实例说明了如何利用这种解析表示(Zernike多项式)来实现上述的边缘线确定和交点确定。最后给出了几种映射算法的色域映射完整过程及其结果。     

The Paley--Wiener Theorem for the Generalized Radon Transform on the Plane

We consider the problem of reconstructing a function on the disk from its integrals over curves close to straight lines, i.e., the inversion problem for the generalized Radon transform. Necessary and sufficient conditions on the range of the generalized Radon transform are obtained for functions supported in a smaller disk under the additional condition that the curves that do not meet coincide with the corresponding straight lines.     

Thermodynamics and Hydrodynamics (Statistical Foundations): 2. Thermodynamic Equilibrium

We show that the BBGKY hierarchy in thermodynamic equilibrium degenerates into an equilibrium hierarchy. In turn, the latter can be used to obtain both the fundamental system of equations describing the state of matter inside a correlation sphere of the radius R10^-7cm and the canonical Gibbs distribution, which, according to the current concepts, describes the state of the entire macroscopic system. We show that the Gibbs distribution is indeed also local, i.e., describes the state of matter only inside the correlation sphere; in the thermostat surrounding this sphere, the Gibbs distribution degenerates into a constant. We state that these two approaches are equivalent to each other.     

Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: Modeling and simulation

A fast holographic wavefront sensor is proposed using a computer-generated hologram (CGH). This CGH is a multiplexed hologram of different Zernike mode–amplitude combinations, and is designed in such a manner as to get the corresponding spots on the detector according to the presence and strength of a particular aberration. Interference between the aberrated wavefront (with a single mode–amplitude combination) and the Fourier transform of an image with single bright pixel (defined as dot image) is numerically calculated for one hologram. Different mode–amplitude combination and corresponding different positions of bright pixels (dots) are taken to compute various holograms and then all the holograms are multiplexed to get the final hologram. When the aberrated wavefront with a particular mode–amplitude combination is incident onto the multiplexed hologram, the corresponding dot is generated in the Fourier plane. A lens performs the Fourier transform in optical domain and provides the instant detection of amplitude of the respective Zernike mode. The main advantage of the scheme is to avoid the need of any computations, which makes it really fast. The simulation results are presented with the cross-talk analysis for few Zernike terms.     

基于解耦差分泽尼克待定系数法的二维横向剪切波面重建算法

横向剪切干涉术是一种自参考干涉计量技术,其原理是被检测波前与其自身被剪开的波前之间在重叠范围内相干涉,由干涉图得到两相互剪切波前的波前差,通过波面重建算法得到待测波面.在波面重建算法中,泽尼克待定系数法是其中的一种.分析了横向剪切干涉技术的测量原理;提出了一种新的基于解耦差分泽尼克待定系数法的二维横向剪切波面重建算法....     

20单元双压电片变形反射镜的影响函数有限元分析和实验测量

影响函数是分析双压电片变形反射镜像差校正能力的重要参量,通过建立有限元模型预测实际器件的影响函数,以有限元模型的不断优化替代实际器件的尝试性改进,可以减小构造的盲目性,从而节约研发成本,缩短双压电片变形镜的实用化进程.采用Veeco干涉仪测量了20单元双压电片变形反射镜的影响函数,同时建立有限元模型进行了相应计算,并将计算结果与实际器件的测量数据进行了对比分析.结果表明,相对于实测数据而言,有限元模型计算得出的影响函数在量值上略有偏小,但其形状和峰值位置与测量数据一致性好,两者对前35项泽尼克像差的拟合曲线也基本吻合,各项拟合误差系数之差皆小于0.1.这说明通过不断改进有限元模型实现对实际器件的优化设计是切实可行的.     

自适应光学系统测试中大气湍流的时域模拟

建立了大气湍流模拟的时域模型,用于在自适应光学系统的测试中模拟大气湍流的时域变化。讨论了时域模型下随机相位屏平滑帧数和刷新频率与平均风速的关系。结果表明：对表征随机波前的随机相位屏进行时域平滑可使随机波前的变化更符合大气湍流对入射波前连续平滑渐变的影响;随机相位屏的平滑帧数仅与系统口径和大气相干长度相关,而与风速无关;随机相位屏的刷新频率与平均风速成正比,平滑后的刷新频率还与平滑帧数成正比。最后,构造了一套大气湍流模拟装置,应用功率谱分析法对时域模型的有效性进行了验证。     

波荡器位相误差对自由电子激光

对波荡器位相误差对自由电子激光小信号增益的影响进行了分析讨论。对低增益情况解析地给出了波荡器位相误差引起的增益降低因子。结果表明:与自发辐射类似增益的降低与位相误差的方差成简单的指数关系，位相误差的线性变化部分引起最大增益的位移，还表明波荡器位相误差存在时Madey定理仍然成立。对高增益情况也给出了波荡器位相误差引起的增益降低因子。