微聚焦X射线成像的相位效应分析

根据Fresnel-Kirchhoff衍射理论,结合临床实际,考虑振幅近似和相位缓变条件,由傅里叶变换和卷积定理,导出了微聚焦X射线相衬成像（X-ray Phase-contrast Imaging,X-PCI）在像平面上焦斑尺寸范围内的能量密度分布函数.结果显示,像密度函数是吸收效应滤波函数FA(x)和相位效应滤波函数FP(x)分别与吸收项A2(x)和相位项A2(x)φ(x)作卷积运算后的和.利用mathematica软件分析讨论了该函数的分布规律,并给出了理论解释.结果表明,吸收效应对像密度的影响在焦斑范围内保持不变|相位效应对像密度的影响在焦斑范围内逐渐加强|在焦斑一定范围内,相位效应的影响远大于吸收效应.     

相位畸变光束二次谐波的相位变化

研究了基波相位畸变对二次谐波相位分布的影响。针对具有不同像差、而光强分布为高斯型光束，以KDP晶体I类匹配为例，数值计算得到其二次谐波光束的光强分布和相位分布，分析了基波的像差、离散效率以及衍射效应的影响效果。研究表明不同的像差对于谐波的影响是不同的，主要取决于由其引起的全口径上相位失配的情况；离散效应主要带来的是倾斜像差，其高阶像差的影响随着离散效应的加剧而增大；而衍射效应的影响在一般情况下都是可忽略的。最后给出了在离散效应和衍射效应的影响可以忽略的情况下，基波相位畸变对二次谐波影响的近似估算式。     

连续相位板面形的随机特性研究

根据连续相位板面形分布的随机特性,利用自相关函数和相关长度对其面形特性进行了分析.采用一个高斯型随机分布函数推导了相关长度与连续相位板远场分布之间的解析关系.利用数值算法计算了连续相位板远场分布的方差和能量利用率,并计算了不同的相关长度对连续相位板远场分布的具体影响.结果表明,连续相位板的相关长度越小,远场分布均匀性越好,焦斑形态更加接近于目标焦斑,同时具有较高的能量利用率.     

A—B效应的分析

从电子在电磁场中的狄拉克方程出发,得出电子在电磁场中波函数,分析磁矢热A引起的电子概率波的相移,结果表明:影响电子波函数的相位变化不是B而是A(x),即有一个额外相因子附加在电子概率波上,进而通过量子干涉出现图样的位移。结论是A—B效应的存在说明磁场的物理效应不能完全用B描述,而是附加在电子概率波上的相因子。     

Kerr效应对非简并双光子J—C模型中光场相位的影响

应用Pegg-Barnett相位理论研究了高Q Kerr介质腔中的二能级原子与双模光场相互作用系统中光场相位的演化特性,通过计算光场的相位几率分布函数,频率漂移量以相位涨落,分析讨论了Kerr效应对光场相位性质的影响。     

基于径向希尔伯特变换的图像边缘增强特性研究

研究了基于螺旋相位频谱滤波器滤波的径向希尔伯特变换对不同边缘分布图像的增强特性.给出了拓扑荷n=1的有限孔径螺旋相位滤波器点扩散函数的解析表达式,并利用圆孔、汉字和人像等三幅不同边缘分布密度的图像进行了边缘增强的模拟计算.结果表明,基于螺旋相位频谱滤波的径向希尔伯特变换会使边缘增强图像具有立体浮雕效果,并且随着输入图像的边缘分布密度变大,立体浮雕效果会越显著.通过理论分析得出,这一现象是由螺旋相位滤波器点扩散函数中的次极大分布与输入图像边缘卷积引起的.这一结论为图像的信息处理提供了一些有利的手段.     

一种提取物体相位变化率信息的理论和方法

利用部分相干光成像理论,推出傅科(Foucault)刀口相位检测时非相干光入射情况下的像面光强分布.分析表明,在一定条件下,可得到输入物函数相位变化率分布的信息.同时提出一种获取物相位变化率信息的装置,并分析了该装置的成像情况.     

焦斑二阶矩半径与光束近场分布的关系

为分析光束振幅畸变和相位畸变对其焦斑二阶矩半径的影响,以光波标量衍射理论中的夫琅和费衍射公式为基础,根据光斑二阶矩半径的定义,推导了直接依赖于光束近场复振幅分布的焦斑二阶矩半径的一般表达式,并进一步推导了直接依赖于光束近场强度分布和相位分布的焦斑二阶矩半径和焦斑二阶矩角半径的表达式.结果表明:畸变光束的焦斑二阶矩角半径...     

畸变光束的焦斑质心位置

 为分析振幅和相位发生畸变情况下光束焦斑质心位置所受的影响，以光波标量衍射理论中的夫琅和费衍射公式为基础，根据光斑强度分布一阶矩质心位置的定义，推导了直接依赖于光束近场复振幅分布的焦斑质心位置的一般表达式。进一步推导了焦斑质心位置对光束近场强度分布和相位斜率分布的依赖关系式，并对该式清晰的物理意义进行了阐述。利用焦斑质心位置表达式，可分析和确定由于振幅调制和相位畸变导致的质心位置偏移。最后，对无相位畸变和存在低阶泽尼克相位畸变情况下的简单畸变光束进行了相应的分析讨论。     

任意两个相干态的叠加态的相位分布和Wigner函数

从相位分布和Wigner函数两个方面研究了任意两个相干态|β〉 and |mβeiδ〉的叠加态的量子统计性质.结果表明这种叠加态的非经典特性与β2,振幅系数m,相干态间的位相差δ以及叠加系数间的位相差都有关.当参量选择合适,这种叠加态存在着量子效应.计算了两个相干态等几率混合系综的相位分布和Wigner函数,经过与前者比较,结果表明由于相干项的存在,使得叠加态具有很好的量子力学行为.     

Focal switching of partially coherent modified Bessel–Gaussian beams passing through an astigmatic lens with circular aperture

The axial intensity distribution of partially coherent modified Bessel–Gaussian (PCMBG) beams passing through an astigmatic lens with circular aperture is derived on the basis of Collins formula. The influences of truncation parameter δ and astigmatic coefficient α on the axial intensity distribution are presented. The research shows that the axial intensity changes with the variation of α, and twice focal switches have been found. Furthermore, the physical interpretation of the twice focal switches is given and is also illustrated by numerical calculations. It has been revealed that the existence of astigmatism and the effect of the truncation parameter are the two main reasons for the twice focal switches of PCMBG beams passing through an astigmatic lens with circular aperture.     

Influence of the size of the grating on Talbot effect

The Fresnel theory of the Talbot effect of the grating is reviewed in this paper, and the general formula of the Fresnel diffraction of the grating with finite aperture size is presented. The aperture effect of the grating on the Talbot image is discussed and a number of numerical calculations are performed. The variation rule of the diffraction intensity distribution at the Talbot distance with the aperture size of the grating and the case at different Talbot distances are obtained through the calculations, and the corresponding explanations of these phenomena are given in this paper. We think that these discussions provide the theoretic basis for the practical application of the Talbot effect of the actual grating.     

三环位相型光瞳滤波器的横向超分辨与轴向焦深扩展

用矢量衍射方法分析了线偏振光入射到带有三环位相型光瞳滤波器的高数值孔径物镜时,焦点的轴向和横向光强分布.数值模拟结果表明,高数值孔径物镜聚焦时需同时考虑光强的轴向和横向分布.通过加入三环位相光瞳滤波器,在实现横向超分辨的同时实现了光学系统轴向焦深扩展和轴向光强分布平坦化,并且位相调制深度变化时,会出现轴向焦移现象.对三环位相光瞳滤波器结构进行了优化,得出了优化结果. 关键词： 光学超分辨 扩展焦深 位相型光瞳滤波器 矢量衍射方法     

Optimizing the optical field distribution of solid immersion lens system by a continuous phase filter

In solid immersion lens (SIL) microscopy systems with high numerical aperture (NA), there always exists the aberration produced by Fresnel effects at the interface between SIL and the sample. This aberration may cause the degradation of the image of sample. We design a continuous phase filter and optimize the optical field distribution of SIL system. The numerical results show that when the continuous phase filter is used, the field distribution of SIL system can be optimized, and the focal depth and intensity of transmitted light can be increased. At the same time, the intensity of side-lobe and the resolution are kept almost unchanged.     

Study of spatial resolution of circular and off-axis zone plates

The effect of limiting the zone plate aperture on its resolution was studied. Analytical formulas for calculating the field in the image plane were derived. The field distribution in the focal plane of circular and off-axis zone plates was numerically simulated.     

旋光晶体在偏光干涉实验中电光效应的研究

研究了旋光晶体在偏光干涉实验中的电光效应，给出了旋光晶体在偏光干涉实验中出射光强与晶体旋光性之间关系的表达式I—Ao^2cos^2[β-（π/λ）（n1-nr)l]，以及与旋光晶体电光效应之间关系的表达式I—Ao^2cos^2[β-（π/λ）（n1-nr)l (π/λ）（n2-n1)l]。根据这些表达式给出的关系，将典型的旋光晶体La3Ga5SiO14制作成了电光Q开关，像那些用无旋光性晶体制作的Q开关一样工作良好。在中等功率输出的激光器中，La3Ga5SiO14晶体电光Q开关有可能取代氘化磷酸二氢钾(DKDP)晶体电光Q开关。     

Use of spatial filtering in imaging through a randomly inhomogeneous medium

Abstract

The possibility of improving the image quality of a coherently reflecting object, viewed through a randomly inhomogeneous medium, is investigated theoretically. Three cases of coherent illumination of the object by a plane wave are considered: illumination by unperturbed wave, illumination and viewing through different inhomogeneities of a medium, illumination and viewing through the same inhomogeneities. The spatial spectrum of the average intensity is investigated. It is shown that, when the fluctuations of the intensity in the plane of the receiving lens aperture are strong, the use of a suitable spatial filter located in the focal plane of the lens always gives an improvement of the image, but the quality of the image is better when illuminating and receiving optimal systems coincide.     

Propagation properties of Gaussian beams through cat eye optical lens with center shelter

Based on the method of matrix decomposition and expanding the aperture function into a sum of finite complex Gaussian functions, the analytical propagation equations of Gaussian beams through cat eye optical lens with center shelter are derived. Through numerical calculation, the laws governing the variation of the intensity distribution of the cat eye reflected light with the center shelter ratio and the diameter of the detector at the focal plane are given. The results show that the diffraction series and the intensity of the cat eye reflected light depend strongly on the center shelter ratio. As a further extension, it is found that the eye optical lens can be interpreted as a spatial filter, and different filter effect can be obtained by changing the pinhole size.     

A Highly Efficient Superresolving Phase Filter for a Radially Polarized Beam

We simulate the focal intensity distribution of a radially polarized beam, in view of the vector diffraction theory. We summarize two important rules: (i) the marginal ray of the aperture determines the focal size on the focal plane; (ii) the ratio of the longitudinal component to the transversal component affects the shape of the focus. We design a continuous phase filter using these rules for a confocal system. We chose the tangent of the semi-aperture angle to build up the phase function, because it is sensitive to the marginal rays, which have large aperture angles. To achieve a flexible modulation, we use a quadratic function for unwrapping the phase. We optimize the parameters of the quadratic function and achieve a transverse superresolving focus. Aiming at different Strehl ratios, we obtain a series of superresolution phase filters. Compared with others, the filter proposed has the advantages of superior superresolution effect and higher energy utilization ratios. The phase-filter design is universal and proved to be valid. It can be employed in either high or low NA systems, superresolving or donut focus applications.