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.     

Influences of phase shift on superresolution performances of annular filters

This paper investigates the influences of phase shift on superresolution performances of annular filters. Firstly, it investigates the influence of phase shift on axial superresolution. It proves theoretically that axial superresolution can not be obtained by two-zone phase filter with phase shift π, and it gets the phase shift with which axial superresolution can be brought by two-zone phase filter. Secondly, it studies the influence of phase shift on transverse superresolution. It finds that the three-zone phase filter with arbitrary phase shift has an almost equal optimal transverse gain to that of commonly used three-zone phase filter, but can produce a much higher axial superresolution gain. Thirdly, it investigates the influence of phase shift on three-dimensional superresolution. Three-dimensional superresolution capability and design margin of three-zone complex filter with arbitrary phase shift are obtained, which presents the theoretical basis for three-dimensional superresolution design. Finally, it investigates the influence of phase shift on focal shift. To obtain desired focal shifts, it designs a series of three-zone phase filters with different phase shifts. A spatial light modulator (SLM) is used to implement the designed filters. By regulating the voltage imposed on the SLM, an accurate focal shift control is obtained.     

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。     

三区振幅型超分辨光瞳滤波器的设计

提出运用非线性规划及目标规划法,在给定斯特雷耳比S(超分辨模型和艾里模型主瓣最大亮度比)的条件下,设计出使成像系统的横向、轴向及三维分辨率分别达到最大值的环形振幅型超分辨光瞳滤波器。给出超分辨优化设计模型和实例,并作图验证其结果。对超分辨率伴随的旁瓣效应,把滤波器应用于共焦扫描系统,可有效地抑制旁瓣,提高成像信噪比和对比度。此方案用于三区以上振幅型超分辨滤波器及环形纯相位超分辨光瞳滤波器的设计,为超分辨滤波器的设计提供了参考。     

三区振幅型三维超分辨光瞳滤波器的优化设计

光瞳滤波器是光学成像系统实现超分辨的基本元件之一，多数三维超分辨滤波器因结构复杂而难于实现。用MATLAB优化工具箱，采用非线性规划，对三区振幅型（1-0—1型）光瞳滤波器进行了三维超分辨优化设计。建立了优化模型，并给出了优化实例。结果表明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。该滤波器结构简单，容易实现。     

光学相干层析成像轴向超分辨研究

为了提高光学相干层析成像(OCT)的轴向分辨率,采用OCT与光学超分辨术相结合的方法,设计了三区相位型和振幅型两种光瞳滤波器,并将制作的光瞳滤波器应用于系统的样品臂中,分别测量不同条件下对应的轴向响应曲线,结果与理论分析基本吻合,实现了轴向分辨率10％以上的提高,从而验证了利用合适光瞳滤波器实现OCT轴向超分辨的可行性.     

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.     

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     

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。     

Two-zone pupil filters

The performance of pupil filters consisting of two zones each of constant complex amplitude transmittance is investigated. For filters where the transmittance is real, different classes of potentially useful filter are identified and optimized. These include leaky filters with an inner zone of low amplitude transmittance, pure phase filters with phase change of π, and equal area filters. The first of these minimizes the relative power in the outer rings for a given axial resolution, the second maximizes the Strehl ratio for a given transverse resolution, and the third minimizes the relative power in the outer rings for a given transverse resolution. Complex filters can give an axially shifted maximum in intensity: the performance parameters calculated relative to the true focus are investigated for some different classes of filter, but filters with phase change not equal to π are found to give inferior performance to the real value filters.     

Transverse superresolution with extended depth of focus using binary phase filters for optical storage system

This paper reports the study of superresolution and extension of depth of focus (DOF) of three-zone binary phase filters (BPFs) under high numerical aperture (NA) focusing. Two three-zone BPFs (BPF1 and BPF2) are specially designed to achieve transverse superresolution and extension of DOF simultaneously for the optical disc system with an objective lens of NA = 0.65. Numerical simulations based on the vectorial diffraction theory indicate that the transverse focal spot size of this system can be as small as that of NA = 0.85 and its DOF is as large as that of NA = 0.6 with acceptable Strehl ratios (> 0.4 for BPF1 and > 0.35 for BPF2) and low side-lobe intensity ratios (< 10%) by using these BPFs. It suggests that the storage capacity of this optical storage system may be improved to the same as that of a system with an objective lens of NA = 0.85. Moreover, the strict requirement of the focusing servo system caused by decreasing wavelength or employing higher NA objective lens can be mitigated. Therefore, these BPFs presented in this paper should be highly interesting for applications of high density optical data storage.     

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。     

Quasi-achromatic superresolving phase only pupil filters

Reported in this paper is a new design of the quasi-achromatic phase-only superresolving pupil filters (QAPSFs) relatively independent of wavelength based on the zero order Bessel function of the first kind. The effect of design parameters of the new filters on the superresolving performance parameters such as the normalized spot size (G) and the Strehl ratio (S) is discussed and analyzed in detail. As an example, the performance parameters of QAPSFs made of optical quartz glass are simulated and compared with phase only pupil filters, which indicate that this kind of filters is less independent of wavelength in the range from 300 nm to 589 nm for superresolution, and a high Strehl ratio is also obtained. The equivalent performance parameters are derived to characterize the superresolution performance of the quasi-achromatic filter.     

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.     

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.     

Analysis of Strehl ratio limit with superresolution binary phase filters

Several pupil filtering techniques have been developed in the last few years to obtain transverse superresolution(a narrower point spread function core). Such a core decrease entails two relevant limitations: a decrease of the peak intensity and an increase of the sidelobe intensity. Here, we calculate the Strehl ratio as a function of the core size for the most used binary phase filters. Furthermore, we show that this relation approaches the fundamental limit of the attainable Strehl ratio at the focal plane for any filter. Finally, we show the calculation of the peak-to-sidelobe ratio in order to check the system viability in every application.     

三区位相型三维超分辨光瞳滤波器的优化设计

用Matlab优化工具箱,采用非线性规划,对三区位相型(π-0-π型)光瞳滤波器进行了优化设计。结果显示,所设计的滤波器较好地实现了横向和轴向的三维超分辨,且轴向超分辨能力优于横向。该滤波器结构简单,容易实现。     

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。     

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%.