复振幅光瞳滤波器的三维超分辨性能研究

超分辨技术中现有的纯振幅型或纯相位型光瞳滤波器，大部分只能实现轴向或横向超分辨而不能实现三维超分辨，三维超分辨在三维成像系统中有着重要的作用。因此为提高成像系统中的三维分辨能力，设计了一种复振幅光瞳滤波器，并对其三维超分辨性能进行了研究。详细分析了该光瞳滤波器的第一区半径和透射率对施特雷尔比、轴向和横向超分辨因子以及旁瓣能量的影响。通过一系列的模拟证明，借助于复振幅光瞳滤波器可以实现三维超分辨。该滤波器的优点是容易实现三维超分辨，且有比较高的施特雷尔比，缺点是三维超分辨的实现总是伴随着旁瓣能量的增加，但可

Three-dimensional superresolution by three-zone complex pupil filters

Complex pupil filters are introduced to improve the three-dimensional resolving power of an optical imaging system. Through the design of the essential parameters of such filters, the transmittance and radius of the first zone, three-dimensional superresolution is realized. The Strehl ratio and the transverse and axial gains of such filters are analyzed in detail. A series of simulation examples of such filters are also presented that prove that three-dimensional superresolution can be realized. The advantage of such filters is that it is easy to realize three-dimensional superresolution, and the disadvantage is that the sidelobes of the axial intensity distribution are too high. But this can be overcome by the application of a confocal system. (C) 2005 Optical Society of America.

Tunable transverse superresolution with phase-only pupil filters

A new set of pure phase filters for realizing transverse superresolution is presented in this paper. The filters, whose significant features are their ability to tune and their simplicity, consist of one half-wave plate between two quarter-wave plates; the half-wave plate is made of two zones that can rotate with respect to each other. By rotating any zone of the half-wave plate, the central lobe width of the irradiance point spread function (PSF) in the transverse direction can be tunably reduced. At the same time, the axial intensity distribution is analysed in detail.

Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.

Design of adjustable superresolving filters based on birefringent crystals

A two-mode adjustable superresolving filter based on a birefringent filter is proposed. This kind of filter has superresolution in two modes of adjustment. One is rotation of the binary pupil filter on the optical axis of the system and the other is the tilt of the filter away from the pupil plane on axis parallel or perpendicular to the optical axis of the crystal. The filters act as complex amplitude filters in the former mode, and as pure phase filters in the latter. By analyzing two superresolving parameters, we obtain the optimal design parameters that ensure a large field of view, a large superresolving range, and a high setting accuracy. This kind of filter can provide more flexibility in practical applications. (c) 2006 Optical Society of America.

Designing superresolution optical pupil filter with constrained global optimization algorithm

In this paper, a new method for designing three-zone optical pupil filter is presented. The phase-only optical pupil filter and the amplitude-only optical pupil filters were designed. The first kind of pupil for optical data storage can increase the transverse resolution. The second kind of pupil filter can increase the axial and transverse resolution at the same time, which is applicable in three-dimension imaging in confocal microscopy. (C) 2007 Elsevier GmbH. All rights reserved.

Laser tunable Toraldo superresolution with a uniform nonlinear pupil filter

We demonstrate that it is possible to reduce the focal spot size by inserting a uniform nonlinear thin film at the aperture of a focusing lens. The reduction of spot size is tunable by adjusting the incoming laser power. In comparison with the original diffraction spot, the transverse spot size can be reduced 0.65 times. The nonlinear thin film acts effectively as a Toraldo filter, and the phase and amplitude modulation stems from the laser-induced variances in the transmission of the thin film. The proposed technique removes the need of fabricating annular pupil filters. (C) 2008 Optical Society of America.

正弦变化的振幅型光瞳滤波器

光瞳滤波器作为实现超分辨的基本元件之一，它的设计以及制作都非常重要。设计了一种正弦变化的振幅型光瞳滤波器，可以通过调节少量的参量实现各种不同的超分辨模式。选择正弦函数的周期以及光瞳中心点透过率变化两个参量来实现对最终超分辨效果的调节。数值计算结果表明：在整个人射光瞳上的透过率瞳函数分布具有0．5～2个正弦振幅周期时，较为合适。小于0．5个周期将不会有任何超分辨效果，大于2个周期超分辨效果反而变差。数值计算中还注意到，当周期数为整数时，斯特雷尔比将保持0．25不变。对正弦变化振幅型光瞳滤波器的计算结果，显示

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

强散射体产生的像面散斑对比度与随机表面及成像系统关系的研究

We study the statistical properties of the image speckles produced by strong-scattering objects in the 4f optical imaging system. Using the generic expression of the complex amplitude of speckles and the approximation of the double-exponential function, we first obtain the ensemble average of the speckle intensity. Then we derive the variance of the speckle intensity based on the rotational transformation of the real and imaginary parts of the complex amplitude of speckles. We finally obtain the expression for the contrast of the. speckles, which is explicitly related to the statistical parameters of random surface and to the parameters of the imaging system. Our results are an obvious improvement compared with those reported in the literature, where the relations including such implicit quantities as the average size of the scattering grains of the random surface and the number of scattering grains are usually used. The results of this paper would be helpful for the characterization of random surface by speckle contrast.

洛仑兹脉冲光束的复振幅包络解和复解析信号解的比较研究

使用复振幅包络表示式和复解析信号表示式推导了洛仑兹脉冲光束的传输公式．通过具体数值计算对脉冲光束的复振幅包络解和复解析信号解在不同带宽时的传输进行了对比研究．数值结果表明脉冲光束为窄带时，在传输方向轴中心的一定范围内两种解是一致的，而对于宽带脉冲光束，复振幅包络解在轴中心较近的距离即表现出奇异性，复解析信号解才是符合物理意义的表示式．由数值计算得出了选择脉冲光束研究方法的条件，并从所得公式对复振幅包络解出现奇异性的现象进行了解释．

窄带和宽带双曲正割脉冲光束的解析传输式

从近轴波动方程出发推导了窄带和宽带双曲正割脉冲光束的解析传输公式。通过数值计算比较了分别采用复振幅包络(CAE)表示式和复解析信号(CAS)表示式得到的脉冲光束，得出了选择脉冲光束研究方法的条件。结果表明复振幅包络表示式得到的解会存在空间奇异性，使光束出现不符合物理意义的非光束行为。对于宽带光束，复振幅包络解的奇异点的位置距离轴中心较近，使复包络解不能正确表示脉冲光束，而对于奇异点位置远离轴中心的窄带光束，对脉冲光束产生的影响可以忽略。因此，窄带脉冲光束可以采用复振幅包络和复解析信号两种表示式来研究，而对