高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

量子模型分析激光驻波原子透镜的像差

采用量子模型对近共振激光驻波原子透镜会聚Cr原子束、形成纳米量级光栅结构的物理过程进行数值模拟。为提高原子透镜的成像质量,对各种像差,如衍射像差、球差、色差、及原子束发散角、原子磁支能级、原子同位素等因素引起的像差进行了理论分析。模拟结果表明,相比粒子光学模型,量子模型能更加精确地描述原子会聚结果,且能解释原子在驻波光场中的衍射现象。在各种像差中,原子束发散角是最主要的因素,其影响大于衍射像差、球差、色差。原子的磁支能级、同位素等因素对像差影响很小,可以忽略不计。激光冷却准直原子束的方法可以减小束发散角引起的像差,压缩原子速度Vz分布范围的方法可以减小色差。     

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.     

界面折射率不一致对显微成像穿透深度的限制

在运用共焦显微术及低相干显微成像术等进行光学断层成像时,要将光束聚焦到样品内部以便实现光学断层成像,然而由于生物组织等的折射率与盖玻璃以及浸液不同,因而会引入很大的球差,从而使入射电磁波发生畸变.分析了由于多层折射率不一致而引入的球差的大小,并运用所得的公式计算了折射率不一致对光在样品中穿透深度及焦面附近光场分布的影响.     

左手性介质透镜系统的赛德尔像差特性研究

根据初级像差理论，系统研究了由左手性介质构造的透镜系统的赛德尔像差特性.分析了左手性介质单折射曲面的赛德尔像差特性，发现其消初级球差的曲面类型比普通介质更为灵活且可用于实成像系统.依据薄透镜赛德尔和数公式，分析和设计了三种只有左手性介质才具备的可消部分赛德尔像差的薄透镜结构参数，提出了几种能同时消除全部五种赛德尔像差的由左手性介质构造的透镜组合系统.研究表明左手性介质相对于普通介质在消像差方面存在较大优势，在光学设计时可以采用更少的折射表面个数或更简单的表面形状即可到达同等的成像性能.     

Near-field multiple super-resolution imaging from Mikaelian lens to generalized Maxwell's fish-eye lens

Super-resolution imaging is vital for optical applications, such as high capacity information transmission, real-time bio-molecular imaging, and nanolithography. In recent years, technologies and methods of super-resolution imaging have attracted much attention. Different kinds of novel lenses, from the superlens to the super-oscillatory lens, have been designed and fabricated to break through the diffraction limit. However, the effect of the super-resolution imaging in these lenses is not satisfactory due to intrinsic loss, aberration, large sidebands, and so on. Moreover, these lenses also cannot realize multiple super-resolution imaging. In this research, we introduce the solid immersion mechanism to Mikaelian lens (ML) for multiple super-resolution imaging. The effect is robust and valid for broadband frequencies. Based on conformal transformation optics as a bridge linking the solid immersion ML and generalized Maxwell's fish-eye lens (GMFEL), we also discovered the effect of multiple super-resolution imaging in the solid immersion GMFEL.     

Changes in the intensity distribution and polarization of non-uniformly polarized beams focused by a spherically aberrated lens with annular aperture

Based on the generalized Huygens-Fresnel diffraction integral and beam coherence polarization (BCP) matrix formulation, the focusing properties of a type of non-uniformly polarized (NUP) beam through a spherical aberrated lens with annular aperture are studied. The dependence of focal shift, intensity distribution, power in the bucket (PIB) and degree of polarization on the spherical aberration coefficient, obscure ratio and polarization parameters is illustrated numerically. The focusing of NUP beams by a spherically aberrated lens with circular aperture is treated as a special case, where the inner radius of the aperture is equal to zero.     

Focusing surface plasmon polariton wave packets in space and time

The spatiotemporal focusing of surface plasmon polariton (SPP) wave packets (WPs) by planar plasmonic‐lens coupling structures is described using combined femtosecond interferometric time‐resolved photoemission electron microscopy (ITR‐PEEM) imaging and model simulations. The focusing properties of lens structures inscribed lithographically into Ag films depend on the angle of incidence of the excitation field. Severe aberrations are introduced by the phase delay in the interaction of obliquely incident plane waves with the commonly employed circular arc‐shaped lens structures. It is shown that the aberration can be corrected by accounting for propagation delays caused by the incidence angle‐dependent retardation of the optical field‐lens structure interaction. The focusing of SPP‐WPs in both space and time is demonstrated with aberration corrected lens structures.     

Study on combined immersion electrostatic-magnetic focusing lenses without crossovers

Wide electron beam focusing properties of combined immersion electrostatic-magnetic focusing system are studied; their curvilinear axis aberration coefficients are derived. Based upon ray tracing method and curvilinear axis theory of wide electron beam systems, a program was written and as an example, a practical structure of the lens is numerically simulated. The computed results show that demagnified images with high resolution of tens of nanometers can be obtained for an object field size in millimeter range.     

Aberration correction of a single aspheric lens with particle swarm algorithm

In order to design a single aspheric lens to meet the requirements of spherical aberration, the particle swarm algorithm is applied to the aberration correction for a single aspheric lens. A mathematical model is constructed, and a program code is developed. Merit functions in an optical system are employed as fitness functions, which combined coefficients of a higher order polynomial equation, a reciprocal of radius of curvature, the conic constant, thicknesses among lens surfaces and refractive indices regarding an optical system. By using this function, the automatic correction of spherical aberration is carried out. The example for a single aspheric lens design using particle swarm algorithm shows that PSO as a tool of the spherical aberration correction for a single aspheric lens is simple and effective, and easy to find a series of good design results. The asphere's more complex surface profile can reduce or eliminate easily spherical aberration at different incidence heights at one time. The automatic design and analysis of a single aspheric lens using this method from the view of a particular optical design problem are presented.     

Field confinement with aberration correction for solid immersion lens based fluorescence correlation spectroscopy

The solid immersion lens (SIL) as a tool for increasing the field confinement as well as providing optimal performance by aberration compensation in a confocal fluorescence correlation spectroscopy (FCS) system is illustrated here. Using Zernike polynomials we show that aberration compensation and the resultant pre-shaping of the incident wavefront enables near diffraction-limited performance. This is explained based on vectorial computations for high apertures in the Debye approximation. The obtained axial resolution parameters are compared with the obtained diffusion times in a SIL-FCS experiment for measurements in solutions done at the single molecule level.     

Focus depth characteristics of lenses with long focal depth designed by a focal depth function

The validity of a focal length function is investigated in designing optical element with long focal depth and high lateral resolution. The designed lenses with different starting focal length are studied. Two focusing performance measures, focal depth and lateral resolution, are presented. Comparing with the conventional lens and optical element designed by other focal length function, numerical results of the designed optics element indicate that the long focal depth and high lateral resolution are achieved. The validity of the focal length function is confirmed. Meanwhile, the designed optical element is similar with the lens with spherical aberration. It means that one can easily implement long focal depth by applying appropriate phase modulation to a lens with spherical aberration.     

基于Zemax的He-Ne激光光束聚焦物镜的设计

 为了得到一个合理的He-Ne激光光束聚焦物镜,采用以正前凸型为基础的高折射率双片结构,应用Zemax软件进行优化设计,获得了弥散斑直径为0.002mm的He-Ne激光聚焦物镜,该镜头只需校正轴上点球差。实验结果表明：设计的镜头比低折射率单片透镜得到的弥散圆直径更小,达到0.0019mm,球差被控制在-0.05mm～+0.05mm范围内,MTF曲线所围面积变大,中心点亮度增高,符合实际需要。     

部分相干光经柱面球差透镜聚焦所产生的焦移

利用Collins公式得出光强均匀部分相干光经柱面球差透镜聚焦后的轴上光强分布,并通过数值模拟的方法研究了入射光的菲涅耳数、相干度和透镜的球差对轴上点光强分布的影响.结果显示,当菲涅耳数较小、空间相干度较小的部分相干光经无球差透镜聚焦时,轴上点光强分布会产生焦移现象,而当部分相干光被球差透镜聚焦时,也会有焦移现象产生.     

球差透镜聚焦部分相干光束获得局域空心光束

基于Collins公式,研究了空间相干度为零阶贝塞耳函数的部分相干光通过球差透镜后在几何焦平面附近的光强分布情况.研究表明,通过改变部分相干光的光谱相干度,球差系数可以得到平顶光束和局域空心光束.球差系数决定了最佳聚焦点的位置.当球差系数为正时,最佳聚焦点随着球差系数的增大向远离透镜的方向运动,甚至超过几何焦点;当球差系数为负时,最佳聚焦点随着球差系数绝对值的增大向靠近透镜方向移动.另外,在正负球差绝对值相等时,光强分布以几何焦点相对称.     

Improving signal levels in intravital multiphoton microscopy using an objective correction collar

Multiphoton microscopy has enabled biologists to collect high-resolution images hundreds of microns into biological tissues, including tissues of living animals. While the depth of imaging exceeds that possible from any other form of light microscopy, multiphoton microscopy is nonetheless generally limited to depths of less than a millimeter. Many of the advantages of multiphoton microscopy for deep tissue imaging accrue from the unique nature of multiphoton fluorescence excitation. However, the quadratic relationship between illumination level and fluorescence excitation makes multiphoton microscopy especially susceptible to factors that degrade the illumination focus. Here we examine the effect of spherical aberration on multiphoton microscopy in fixed kidney tissues and in the kidneys of living animals. We find that spherical aberration, as evaluated from axial asymmetry in the point-spread function, can be corrected by adjustment of the correction collar of a water immersion objective lens. Introducing a compensatory positive spherical aberration into the imaging system decreases the depth-dependence of signal levels in images collected from living animals, increasing signal by up to 50%.     

Dielectric interface effects in subsurface microscopy of integrated circuits

We investigate the defocus and image quality affected by a dielectric interface on high numerical aperture focusing of linearly polarized illumination in aplanatic mode. Theoretical and experimental demonstration is performed on subsurface backside microscopy of silicon integrated circuits, showing that the high longitudinal magnification provided by solid immersion lens microscopy allows the observation of significant astigmatism. It is shown that a 50 micron longitudinal displacement of the objective lens with respect to the sample is necessary to achieve maximum resolutions in two directions.     

热透镜的球差效应对大基模体积激光谐振腔模式的影响

固体激光器在强抽运的条件下,激光晶体热透镜的球差效应是不容忽视的,尤其是在大基模体积的动态稳定腔中,会影响谐振腔的振荡模式,进而影响腔内损耗和输出功率.通过Fox-Li的衍射迭代算法,分析了谐振腔的自再现模,表明在热透镜球差效应作用下,基模的光强分布出现了旁瓣,并由此带来了光束质量的下降,最后通过实验结果验证了理论分析,指出光束填充因子是激光器设计的一个重要因素,其最佳值需要根据球差效应的强弱,通过实验的方法来确定. 关键词： 热透镜 球差效应 谐振腔模式     

Frequency multi-mode lens for atoms and molecules: Application to nanofabrication

We present a frequency multi-mode lens with corrected spherical aberration suitable for focusing of both atoms and molecules. The lens is formed by superposing of several harmonics of standing light waves in such a way that to create harmonic potential for all particles crossing the light field. The application to nanolithography is discussed emphasizing the possibility to improve the contrast of deposited structures.     

异常空心光束通过球差光阑透镜的聚焦和在焦区的位相奇异特性

研究了用德拜公式对异常空心这类新型光束经过光阑透镜后的聚焦特性.结果表明,异常空心光束的形状一般不能保持传输不变性,但选择合适的截断参数和球差异常空心光束在一定位置可保持其初始光强分布近似不变.在焦区位相奇点会出现移动、产生和湮灭,并与截断参数、球差和光阑透镜半角有关.当无球差时,出现鞍点,奇点对的湮灭过程与鞍点对湮灭相伴发生,导致亚波长结构.用计算例对结果做了说明,并与文献中已有工作做了比较. 关键词： 异常空心光束 球差光阑透镜 位相奇点