Three-zone pupil filters

The performance of pupil filters consisting of three zones each of constant complex amplitude transmittance is investigated. For filters where the transmittance is real, different classes of potentially useful filter are identified. These include leaky filters with an inner zone of low amplitude transmittance, pure phase filters with phase change of π, and equal area filters.     

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。     

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。     

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%.     

Zonenplatten zur Öffnungsfehlerkorrektur und zur Kontrasterhöhung

A new type of zone plate is proposed whose purpose is to increase the contrast in electron micrographs. It consists of a circular aperture and a number of concentric rings, and it is arranged in the back focal plane of an electron objective lens with spherical aberration. The diameters of the outer rings are chosen such as to leave through only such parts of the wave surface which reach the image point with a phase delay of (2n+1)π relative to its paraxial part. The intensity distribution in the image plane is calculated for this zone plate and for a similar type of zone plate suggested byHoppe whose purpose is to reduce the resolution limit. Numerical calculations are made for the special case that the intensity is constant over the plane of the zone plate. The results show that an increase of resolving power may be expected if Hoppe's plate is used, and that the image contrast may be considerably increased by the new contrast plate without any serious reduction of resolving power.     

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.     

用于波分复用系统的多峰干涉滤光片

介绍了用于波分复用系统的多峰干涉滤光片的设计原理,提出了滤光片透射峰位置的确定方法,讨论了影响滤光片半宽度和截止度的因素,给出了滤光片的膜厚容差分析结果,表明透射率监控标准偏差在<0.5%范围内,可以得到波形良好的多峰滤光片,最后给出了实验结果.     

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.     

Does the ϱ'(1600) couple to ππ? a question of analyticity

Analyticity is exploited to distinguish between classes of π⁺π^- partial wave solutions. Fixed t and fixed u dispersion relations determine the over-all phase of the amplitude and clearly select solutions with a ?'(1600) resonance of 25% elasticity.     

Physical pion-pion partial-wave equations based on three channel crossing symmetry

We present a set of closed systems of partial-wave equations for pion-pion scattering valid for ?28 m_π² ? s ? 125.31 m_π². These equations give the real part of a given partial-wave amplitude in terms of scattering lengths and a convergent series of integrals over the physical values of the absorptive parts of all partial waves. Our equations are extensions of relations previously derived from fixed-t dispersion relations. The new equations are rigorous consequences of axiomatic analyticity and three channel crossing symmetry. As an application, the effect of the f⁰-meson on the I = O S-wave is evaluated.     

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.     

Analysis of the photoproduction of pions by means of fixed t dispersion relations. I

An absolute prediction for the photoproduction of pions on protons is given in the region of the first pion nucleon resonance. The imaginary part of the amplitude was approximated by the resonant magnetic dipole amplitudeM ₁₊ ^3/2 taken from the theory of CGLN. With this approximation the real part of the amplitude was calculated by means of fixedt dispersion relations and discussed in terms of multipoles.π ⁺-andπ ⁰-excitation curves atΘ=90° for unpolarized as well as plane-polarizedγ's are compared with the experiments. In the appendix we give tables of the differential cross sections in the c.m. system.     

Measurements of ϱ - ω interference in the reaction πp → ππn at 15 GeV/c

In a study of the reaction π⁻p → π⁺π⁻n at 15 GeV/c we observe pronounced ?-ω interference effects between the transverse helicity states of the vector mesons. The relative phase of the interfering amplitudes is determined to be −1.40 ± 0.45 rad, and the branching ratio ω → 2π is found to be 2.1_−0.9^+2.8%.     

A study of transverse and longitudinal momentum correlations in proton diffraction dissociation at 14 GeV/c

We present data on momentum correlations both in and out of the production plane for the reactions π⁺p→π_f⁺(π⁺n) and π^?p→π_f^?(π^?Δ⁺⁺). The dissociation products show strikingly similar transverse momentum distributions which in terms of exchange models suggest an equal amount of pion and baryon exchange. For both reactions, we find an approximate factorization in the projectile frame between the transverse momentum of π_f and the longitudinal momenta of the dissociation products. Exchange models predict this result equally in both reactions, but it appears much more clearly in the Δ reaction. Finally, we relate the observed longitudinal and transverse momentum distributions in a way suggested by an isotropic decay model.     

Parallel-quadrature phase-shifting digital holographic microscopy using polarization beam splitter

We present a digital holography microscopy technique based on a parallel-quadrature phase-shifting method. Two π/2 phase-shifted holograms are recorded simultaneously using polarization phase-shifting principle, slightly off-axis recording geometry, and two identical CCD sensors. The parallel phase-shifting is realized by combining circularly polarized object beam with a 45° degree polarized reference beam through a polarizing beam splitter. DC term is eliminated by subtracting the two holograms from each other and the object information is reconstructed after selecting the frequency spectrum of the real image. Both amplitude and phase object reconstruction results are presented. Simultaneous recording eliminates phase errors caused by mechanical vibrations and air turbulences. The slightly off-axis recording geometry with phase-shifting allows a much larger dimension of the spatial filter for reconstruction of the object information. This leads to better reconstruction capability than traditional off-axis holography.     

Measurement of π−p → π0π0n at 6, 8 and 12 GeV/c

All γ's and the neutron from the reaction π^?p → π⁰π⁰n are detected. The magnitude of the π⁰π⁰ S-wave and the cosine of its phase angle (relative to the known D-wave) are determined. The I = 0 amplitude, S₀, is near the unitarity limit in the range 600 to 900 MeV and again around 1200 MeV.     

A study of the backward γp → π+n amplitude

We present a detailed numerical study of the phase of the backward γp → π⁺n amplitude. Use is made of experimental data, analyticity and the results of the multipole analysis. A prediction of the phase up to the third resonance region is given.     

The phase of the forward π+π− → π+π− scattering amplitude

Using methods developed by Pietarinen, we evaluate the phase of the forward scattering amplitude for the process π⁺π^? → π⁺π^? in the energy range 1.0 GeV ? √ s ? 1.8 GeV. Our results are in disagreement with previous work, unless early onset of the asymptotic behaviour of the phase of this amplitude is imposed. They tend to rule out some solutions for the partial-wave amplitudes in this energy range.