高斯光学

The propagation of cosh Gaussian beams through a first order paraxial optical system with rectanglar hard aperture is studied. By using the expansion of the rectangle function into a finite sum of complex Gaussian functions a closed form propagation equation of cosh Gaussian beams is derived.

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究，采用将矩形域函数表示为复高斯函数叠加的技巧，推导出了解析的传输公式，在特殊情况下，该公式简化为在无光阑情况下的传输公式。

The generalized Huygens–Fresnel diffraction integral for misaligned asymmetric first-order optical systems is derived by using the canonical operator method, which enables us to study propagation properties of anisotropic Gaussian Schell-model beams through misaligned asymmetric first-order optical systems.

广义惠更斯-菲涅尔衍射积分为歪斜的非对称一阶光学系统中，推导出用典型算子方法，使我们可以研究繁殖性能的各向异性高斯夏伟模型光束通过失调非对称一阶光学系统。

The principle of defocus detection by critical angle method is introduced and the expression of defocus is deduced with Gauss optical formula based on Fresnel formula and a reasonable hypothesis.

介绍了临界角法离焦检测的基本原理，通过合理假设，利用菲涅尔公式和高斯光学公式得到了离焦误差信号的计算公式。

Chapter 2、When treat propagate problem of high power laser beams, ordinary assume beam to be ideal plane wave or Gaussian. Actually, beams is not ideal Gaussian or plane wave. The reason is that is phase aberraed and intensity nonuniform. In this chapter, we have developed a method on frequency conversion of aberrated beam. Based on statistical optics method and within the limits of thin crystal, we have studies on second harmonic generation of the phase aberrted beam. And the phase aberration is assumed to be a Gaussian random variable.

第二部分：在处理高功率光束传输问题中，通常假设光束为理想平面波或高斯型，而实际光束都不可能是理想的高斯光束或平面波，均会有一定的位相畸变及光强不均匀，本部分从统计光学的观点出发，在薄晶体近似下，建立了具有高斯型随机相位畸变光束倍频转换的一种统计描述方法，并对倍频转换光束的横向空间特性进行了分析。

In order to study the propagation of partially coherent modified Bessel-Gaussian beams passing through a paraxial ABCD optical system with hard-edge aperture,the approximate analytical propagation equation was derived with the hard-edged aperture function expanded into a finite sum of complex Gaussian functions.

为了对部分相干修正贝塞尔－高斯光束通过有硬边光阑近轴4BCD光学系统的传输进行研究，采用将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，得到了近似的解析传输公式。

The propagation equations for oblique and off-axial Gaussian beams passing through cat-eye optical lens are deduced by using the theory of matrix optics and expanding the aperture function into a finite sum of complex Gaussian functions.

运用矩阵光学理论以及将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，进一步推导了倾斜离轴高斯光束通过猫眼光学镜头的解析传输公式，通过数值计算分析得到了倾斜系数和离轴量对猫眼效应反射光光强分布的影响规律。

Using the relations between Hermite and Laguerre-Gaussian modes and expanding the window function of two-dimensional rectangular hard-edged apertures into a finite sum of complex Gaussian functions, the propagation of complex- argument Laguerre-Gaussian beams through a paraxial optical ABCD system with a rectangular hard-edged aperture is studied. An analytical propagation equation is derived and used to study the diffraction at the rectangular hard-edged aperture and the focusing properties of complex-argument LG beams.

利用拉盖尔－高斯模和厄米－高斯模的变换公式，并使用将二维矩孔光阑窗口函数展开为有限个复高斯函数之和的方法，得到了复宗量拉盖尔－高斯光束通过含矩形硬边光阑近轴ABCD光学系统的变换的解析传输公式，并对复宗量LG光束通过矩形硬边光阑的衍射和聚焦特性进行了研究。

In this paper,we firstly utilize homogeneous linear coordinate transformation to express the object image conjugate theory of Gauss optic system;then compare it with the acting matrix in Theory of Motion Optics,expatiate on the relations between the coordinate transformation method and Theory of Motion Optics.

利用齐次线性坐标变换，将光学系统的高斯物像共轭理论用齐次坐标变换的方法来描述，并与动态光学理论中的作用矩阵相比较，阐述坐标变换方法与动态光学理论的关系。

Applying matrix optics to paraxial rays, which travel through different optical elements illuminated with high-power Gaussian beams, the positions of ghost image s affected by Kerr-effect-induced nonlinear refractive index of the illuminated optics are studied.

在近轴条件下，利用矩阵光学的方法研究了高功率高斯光束通过不同光学元件时，克尔效应导致的介质折射率的变化对鬼像位置的影响。

It is very difficult to realize expanding the working band of Hartmann-Shack wavefront sensor through Frequency Transfer of Nonlinear Optics. Usually three wave-mixing researches are based on plane wave or Gauss wave, so study of aberrated second harmonic generation is new and important. It could be very helpful to understand and make good use of the Frequency Transfer of Nonlinear Optics.

这说明利用非线性光学频率变换方法拓宽波前传感器件的响应波段是很难实现的，但是，通常三波相互作用过程的研究均是建立在平面波和理想高斯光束之上，因此我们对于位相畸变倍频过程的研究是非线性光学领域一个重要而有意义的新课题，它有助于人们更加深入理解非线性光学效应，为进一步合理利用之奠定了理论和实验的基础。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。