Design and application of three-zone annular filters

We design three-zone annular filters to be applied to optical storage system. The designed filters extend the depth of focus and realize transverse superresolution simultaneously, which will improve the performance of optical storage system greatly. And we propose two feasible schemes to improve imaging resolution of three-dimensional imaging system. One scheme depends on a complex filter formed by cascading of a three-zone phase filter and a three-zone amplitude filter. The complex filter converge the optimized transverse superresolution and the optimized axial superresolution of two different filters onto a single filter. It can improve the three-dimensional imaging performances greatly. Another scheme depends on a single three-zone complex filter. We propose a three-zone complex filter with phase shift 0.8π, which presents bigger design margin, better imaging quality and stronger three-dimensional superresolution capability.     

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,但可以采用共焦扫描成像系统来加以抑制。     

Simple expressions for performance parameters of complex filters, with applications to super-Gaussian phase filters

To study the three-dimensional (3-D) behavior produced by complex filters, we have extended the expressions for the axial and the transverse gain to the case in which the best image plane is not near the paraxial focus. Super-Gaussian phase filters are proposed to control the 3-D image response of an optical system. Super-Gaussian phase filters depend on several parameters that modify the shape of the phase filter, producing tunable control of the 3-D response of the optical system. The filters are capable of producing a wide range of optical effects: transverse superresolution with high depth of focus, 3-D superresolution, and transverse apodization with different axial responses.     

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     

非对称三区光瞳滤波器实现一维横向超分辨

基于严格的光学成像矢量衍射理论,以4倍缩小倍率的成像系统和x线偏振光照明为例,得到经光瞳滤波器调制的大数值孔径光学系统焦区横向场表达式.通过详细研究非对称三区复振幅型光瞳滤波器的内外环归一化半径、各环相位分布和第一层透过率t对y方向分辨率增益比Gty,斯特尔比Sy和第一旁瓣与主瓣相对强度Iry的影响.设计了一种非对称三区相位型光瞳滤波器,实现Gty=0.8345,Sy=0.4087,Iry=0.4923,使得y方向分辨率比没有加光瞳滤波器时提高了将近20%.     

电控径向滤波器的横向超分辨与轴向焦移

提出一种光瞳滤波器来同时实现横向超分辨和轴向焦移效应的电控制.该光瞳滤波器由两偏光镜及包含有径向双折射元件的任意偏振态的电控旋光器组成.利用径向双折射元件对光偏振态的空间调制作用，结合旋光器对任意偏振态光的旋光作用，与两个偏光镜结合，实现了空间偏振态的重新分布.利用庞加莱球及琼斯理论进行了分析，结果表明，借助这种电致位相延迟来实现的偏振态调制效应，可同时实现横向超分辨与轴向焦移效应.对能够同时获得横向超分辨与轴向焦移的情况进行了分析，得到了系统各组成参量及电光调制范围.     

可调谐位相型光瞳滤波器的横向光学超分辨和轴向扩展焦深

为克服传统光瞳滤波器的缺点，实现系统光学超分辨性能的可调谐性，设计了一种新型可调谐的位相型光瞳滤波器.该光瞳滤波器包括两个λ/4波片和置于其间的λ/2波片，其中λ/2波片分为两个可作相对旋转的区域.研究结果表明，通过旋转λ/2波片的任意一区域不仅可以实现系统横向光学超分辨能力的可调性，而且可以在横向分辨能力提高的同时实现光学系统轴向焦深的扩展以及轴向焦移.     

可调谐位相型光瞳滤波器的横向光学超分辨和轴向扩展焦深

为克服传统光瞳滤波器的缺点,实现系统光学超分辨性能的可调谐性,设计了一种新型可调谐的位相型光瞳滤波器.该光瞳滤波器包括两个λ/4波片和置于其间的λ/2波片,其中λ/2波片分为两个可作相对旋转的区域.研究结果表明,通过旋转λ/2波片的任意一区域不仅可以实现系统横向光学超分辨能力的可调性,而且可以在横向分辨能力提高的同时实现光学系统轴向焦深的扩展以及轴向焦移. 关键词： 光学超分辨 位相型光瞳滤波器 可调谐     

三维超分辨光瞳滤波器的优化设计

利用matlab优化工具箱,采用非线性规划,对三区振幅型(透过率为1-0-1)和三区位相型(相位角为π-0-π)光瞳滤波器进行三维超分辨优化设计,建立了优化模型,经计算机多次迭代运算,改变斯特尔比s值,给出了优化结果.结果显示:所设计的滤波器较好地实现了横向和轴向三维超分辨,且轴向超分辨能力优于横向;相同斯特尔比下,位相型三维超分辨能力优于振幅型,并且这两种滤波器结构简单,容易实现.     

Transverse superresolution with the radial continuous transmittance filter

The radial continuous transmittance filter is presented to realize transverse superresolution. It consists of two parallel polarizers and a radial birefringent element sandwiched between of them. By adjusting the angle between optical axis of the radial birefringent element and the polarization direction of the polarizers, transverse superresolution can be realized. But transverse superresolution is obtained at the cost of the axial resolution and the increase of the side-lobes in strength. So we then mend such filter, with it not only enhance the transverse resolution but also suppress the influence of the side-lobes and the reduction of the axial resolution. At the same time, the Strehl ratio increases. The advantage of such a filter used in superresolution technique is that it is easy to fabricate because its fabrication does not deal with the variation of the phase.     

Superresolution by three-zone pure phase plate with 0, π, 0 phase variation

Superresolution is very important in imaging and optical storage systems, and has attracted much attention. In this article, concentric three-zone phase plate with 0, π, 0 phase variation has been investigated numerically to show that this kind of phase plate can be used to obtain three-dimensional superresolution. In addition, the number of intensity maximum, focal depth, focal shift, full-width half-maximum, and relative intensity of side lobe are listed for different radii of the phase zones, which paves the way for design of the phase plate. Therefore, one can choose values of radii for desired intensity distribution in focal region, such as for the purpose of radial superresolution with high focal depth in optical storage.     

电控径向双折射滤波器的横向超分辨与轴向扩展焦深

提出利用电控径向双折射光瞳滤波器实现横向超分辨性能参量的调制与轴向扩展焦深。该光瞳滤波器由两个平行偏光镜,一个电光晶体与一个径向对称双折射晶体组成。分析了电光晶体与径向双折射元件对光偏振态的空间调制作用,通过控制电光晶体的相位延迟实现径向中心处初始偏振态的控制,与径向双折射元件横向偏振态调制结合,实现了庞加莱球上偏振态演变路径与阶段的控制,从而对焦点附近偏振态进行空间调制以实现光强的重新分布。研究结果表明,外加电场调制可以实现横向上超分辨性能的调控以及轴向上焦深的扩展,并可得到相应的电光相位延迟范围。     

Phase filter design for sharper focus of radially polarized beam

Based on vector diffraction theory, a phase-only filter with cosine function is proposed and a sharper focal spot of radially polarized beam is obtained on the focal plane. The function parameters of the filter are optimized and a series of optimized filters for different Strehl ratio S are given. The optimization results show that there is a significant improvement on obtaining sharper focal spot with this new type of filter. Compared with other results, this type of filters has superior supperresolution effect and higher energy utilization ratio. The numerical calculation results about the phase filter may facilitate new approaches to get superresolution.     

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.     

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.     

Improved expressions for performance parameters for complex filters

Improved expressions are given for the performance parameters for transverse and axial gains for complex pupil filters. These expressions can be used to predict the behavior of filters that give a small axial shift in the focal intensity maximum and also predict the changes in gain for different observation planes.     

径向双折射滤波器的超分辨性能研究

超分辨技术因其可以超越经典的衍射极限而为人们所熟知．并且．在光存储和共焦扫描成像系统中有着广泛的应用。把由两个偏振器和一个圆对称的双折射元件组成的径向双折射滤波器引入超分辨技术,借助琼斯算法推导出其光瞳函数的表达式。由分析得出通过改变径向双折射滤波器中偏振器的偏振方向和双折射元件的主轴之间的夹角,即可实现光学系统的横向超分辨或轴向超分辨。同时对评价该器件超分辨性能的参量第一零点比、斯特尔比和旁瓣强度抑制比做了详细的讨论。该滤波器用于超分辨技术的优点在于其制作不涉及相位的变化而比较简单,且费用比较低。缺点是旁瓣能量过高,但可以通过采用共焦系统来抑制。     

Effect of fabrication errors on axial super-resolution property of a three-zone pupil filter

Two models have been established using the basic definitions of super-resolution characteristic parameters for normalized spot size G_A and Strehl ratio S_A, of a three-zone axial super-resolution pupil filter with fabrication errors, to quantitatively analyze the effect of these fabrication errors on the axial super-resolution property. These new models established to describe the analytic relationship of G_Ae and S_Ae of a pupil filter with its fabrication errors and its transmission function A(ρ), phase function φ(ρ) and structural parameters, directly relate the super-resolution parameters of a three-zone axial super-resolution pupil filter to its fabrication errors to make the quantitative analyses of the effect of fabrication errors easier, thereby providing a theoretical basis for the analysis, design and fabrication of a three-zone axial super-resolution pupil filter. The models established for G_Ae and S_Ae have been used to analyze the effect of the fabrication errors of a pupil filter on its super-resolution property, with a three-zone phase-only pupil filters as example.     

改善轴向分辨率的光瞳滤波器

给出了一种新型滤波器,它即能提高系统的轴向分辨率又不影响其横向分辨率。利用这种滤波器不可以控制远场旁瓣强度的最大值与主瓣强度最大值之比（Ｍ）,从而获得较好的超分辨效果,还根据扩展结果分析了光瞳滤波器的中间区对轴向分辨率的影响。