Transverse Properties of Light Distribution in the Focal Plane for Rectangular Annular Pupil Plane Filters

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｐｕｐｉｌ ｐｌａｎｅｆｉｌｔｅｒｓｃａｎｂｅｕｓｅｄｔｏｃｈａｎｇｅｔｈｅｌｉｇｈｔｉｎｔｅｎｓｉｔｙｄｉｓｔｒｉｂｕｔｉｏｎｉｎｔｈｅｆｏｃａｌｐｌａｎｅ ,ｓｏｔｈｅｙｈａｖｅｐｏｔｅｎｔｉａｌａｐｐｌｉｃａｔｉｏｎｓｉｎｔｈｅａｒｅａｓｏｆｏｐｔｉｃａｌｄａｔａｓｔｏｒａｇｅ[1～ 3 ] ,ｌｉｔｈｏｇｒａｐｈｙ[4] ,ａｎｄｍｉｃｒｏｓｃｏｐｙ[5～ 7] .Ｍａｎｙｐｕｐｉｌｆｉｌｔｅｒｓｈａｖｅｂｅｅｎｓｔｕｄｉｅｄ ,ｓｕｃｈａｓｆｉｌｔｅｒｓｗｉｔｈｖａｒｉｅｄａｍｐ…     

等宽圆环光瞳滤波器的超分辨性能研究

设计一种等宽圆环光瞳滤波器 ,并研究了它的超分辨性能。分析了光瞳中心半径和圆环数对斯特耳比、超分辨能力和旁瓣强度的影响 ,讨论了设计等宽圆环光瞳滤波器时中心半径和圆环数的优化问题。表明圆环数为奇数和偶数时 ,光瞳具有不同的超分辨性能 ;圆环数分别取 1和 2时 ,综合考虑超分辨性能较佳     

High depth of focus by combining annular lenses

In some technological applications, optical systems that produce a high depth of focus and superresolving transversal responses are required. In this paper we present a pupil design consisting in a phase pupil with binary amplitude, that added to a conventional optical system, can accomplish these goals. The pupil function is characterized by a complex amplitude that consists basically in combining two annular lenses with different focal length. Meanwhile the central portion of the pupil has an amplitude equal to 0, the external portion is modulated with two quadratic phases each one covering an annular zone. One of the phases corresponds to a convergent lens and the other to a divergent lens. The effect on the incident wavefront is to redirect the light in front of and behind the best image plane (BIP) producing a widened focus. The evolution of the transverse gain for the extended focus is also studied. Experimental results are given, and they confirm the extended focus and the superresolving behavior of the proposed pupil function.     

Focal shift of apodized truncated hyperbolic-cosine-Gaussian beam

Focal shift of hyperbolic-cosine-Gaussian beams induced by pure phase apodizer was investigated theoretically. The pure phase apodizer consists of three concentric zones: center circle zone, inner annular zone and outer annular zone. And the phase variance of the inner annular zone is adjustable. Results show that intensity peak moves far from optical aperture and then shrinks sharply for certain radii of zones with increasing phase variance of the inner annular zone. Simultaneously, one new intensity peak occurs near optical aperture, moves far from the optical aperture, and then becomes intensity maximum peak, and repeats the evolution process of the former intensity peak. Tunable focal shift occurs with focal switch. Decreasing the phase variance can change the move direction of the intensity peaks. In addition, the maximum distance between the two intensity peaks can be altered by beam parameters of cosh parts, and the distance value increases and then decreases with increasing beam parameters of cosh parts for certain radii of zones. Tunable focal shift is also discussed to construct optical tweezers.     

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。     

Improved axial resolution in confocal fluorescence microscopy using annular pupils

The axial image of a thick fluorescent layer is studied in a confocal microscope consisting of either circular or annular pupils. The response for circular pupils is sharper than that for annular pupils if a small pinhole detector is used. But when the size of the pinhole is larger than a certain value, the response in the latter case can become sharper than that in the former. This result implies that for a given detector of finite size, axial resolution in confocal fluorescence microscopy can be improved when an annular lens is used. Our experimental results qualitatively demonstrate the theoretical prediction. The strength of optical sectioning and the axial cross-section of the three-dimensional optical transfer function are also derived from the measured data.     

Improving the resolution of a solid immersion lens optical system using a multiphase Fresnel zone plate

We propose a method to improve the resolution of near-field optical system with a solid immersion lens by using a multiphase level Fresnel zone plate. The analyses are based on scalar angular spectrum theory. The results show that the multiphase Fresnel zone plate can not only decrease the spot size but also decrease the sidelobe intensity and enhance greatly the diffractive efficiency compared with annular amplitude filter or binary 2-, 3-, 4-zone phase filter.     

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。     

双模式高精度可调超分辨光瞳滤波器

基于双折射波片的特性,提出了一种具有双调节模式的连续可调超分辨光瞳滤波器。该滤波器通过两种调节模式实现超分辨,且在一定范围内连续可调。在横向旋转模式下,该滤波器为复振幅型光瞳滤波器,纵向倾斜模式下为纯相位型超分辨滤波器。通过对超分辨参量的分析,得到最佳设计参量,可以实现大的视场角,大的超分辨范围、高的调节精度。这种滤波器为实际应用提供了更多的方便。     

消色差相位型超分辨光瞳滤波器的设计研究

提出并设计了一种消色差的相位型超分辨光瞳滤波器。详细分析了滤波器的设计参数对成像系统的光斑压缩比和斯特雷尔比影响。分别以方解石晶体和石英玻璃材料为例进行了设计,当光斑压缩比为0.83时,得到两种材料的消色差超分辨光瞳滤波器,可以分别在380～555nm和300～600nm的波长范围内实现消色差,同时可以有较高的斯特雷尔比。     

Focal depth and focal splitting of truncated hyperbolic-cosine-Gaussian beam induced by phase plate

Focal depth and focal splitting of hyperbolic-cosine-Gaussian beams induced by a phase plate were investigated. The pure phase plate consists of three concentric zones: a center circle zone, an inner annular zone and an outer annular zone. The phase variance of the inner annular zone is adjustable. Simulation results show that the focal depth can be adjusted by changing the radii of zones. With the increase of the inner radius of the outer annular zone, the focal spot broadens along the optical axis and splits into two peaks. Then the two peaks combine back into one peak. There are two critical values for the inner radius of the outer annular zone, at which focal spot changes sharply. The tunable range of the focal depth varies considerably. The phase variance of the inner annular zone affects focal depth also; when the phase variance is π, the effect attains maximum. The parameters of cosh parts of the beam affect both focal splitting and focal depth evidently; focal splitting disappears with increasing parameters of cosh parts, and focal depth increases with increasing the parameters of cosh parts in both the low and the high numerical-aperture optical systems.     

Propagation characteristics of annular laser beams passing through the reflection Bragg grating with deformation

When high-power annular laser beams produced by the unstable resonator pass through the volume Bragg grating (VBG), absorption of light in the VBG will induce a temperature increment, resulting in changes in surface distortion. Considering that the surface distortion of the grating induces index and period differences, the scalar wave equations for the annular laser beams propagating in the VBG have been solved numerically and iteratively using finite-difference and sparse matrix methods. The variation in intensity distributions, the total power reflection coefficient, and the power in the bucket (PIB) for the annular laser beams passing through the reflection VBG with deformation have been analyzed quantitatively. It can be shown that the surface distortion of the VBG and the beam orders of the annular beams affect evidently the intensity distributions, the power reflection coefficient, and the PIB of the output beam. The peak intensity decreases as the deformation of the VBG increases. The total power reflection efficiency decreases significantly with the increase in deformations of the VBG. The PIB of the output beam decreases as the obscuration ratio β and the deformation of the VBG increase. For the given obscuration ratio β, the influence of deformation of reflection VBG on the PIB of the annular beams is more sensitive with increase in distortion of the VBG and decrease in beam order.     

Energy density in an image point on a square area element

The algorithm and results of calculations of the relative energy density in an image point on a square area element are described. The energy distribution in the image point is calculated for aberration-free optical systems with circular and annular pupils in the Fraunhofer diffraction approximation. Longitudinal and transverse displacements of the center of the square area element relative to the paraxial image of the point are considered.     

Scattering forces in the focal volume of high numerical aperture microscope objectives

Radiation pressure is not the only source of scattering force in the focal region of a microscope objective. Depending on the numerical aperture and the polarization characteristics of the light at the entrance pupil, the force emerging from the spin density may represent a fundamental contribution to the total force experienced by small (Rayleigh) particles when using high resolution objectives. The predicted and experimentally observed strong asymmetry of the trapping potential for linear polarization is shown to be related to non-conservative spin curl forces. We demonstrate the characteristics of this force field when using linear polarized light with circular and annular pupils and in the radial and azimuthal polarization structures.     

Limitations of superoscillation filters in microscopy applications

The idea of superresolving pupil filters comes from the concept of superoscillations that may occur in regions of a band-limited signal with small amplitude having oscillations faster than the fastest Fourier component of the signal. In optical microscopy, superresolution can be achieved by appropriate design of pupil functions where the angular aperture determines the ultimate focal spot smaller than the Abbe diffraction limit outside the evanescent field region. The angular aperture cannot be increased indefinitely and the huge sidelobes cannot be avoided that are present in superresolving filters. The limitations of using such kind of filters in microscopy applications are discussed through computational examples.     

The origin of the super-resolution via a nonlinear thin film

In laser applications, resolutions beyond the diffraction limit can be obtained with a thin film of strong optical nonlinear effect. The optical index of the silicon thin film is modified with the incident laser beam as a function of the local field intensity n(r)∼E²(r). For ultrathin films of thickness d?λ, the transmitted light through the film forms a profile of annular rings. Therefore, the device can be related to the realization of super-resolution with annular pupils. Theoretical analysis shows that the focused light spot appears significantly reduced in comparison with the diffraction limit that is determined by the laser wavelength and the numerical aperture of the converging lens. Analysis on the additional optical transfer function due to the thin film confirms that the resolving power is improved in the high spatial frequency region.     

The effect of fuel inlet turbulence intensity on H2/CH4 flame structure of MILD combustion using the LES method

Large eddy simulations (LES) are employed to investigate the effect of the inlet turbulence intensity on the H₂/CH₄ flame structure in a hot and diluted co-flow stream which emulates the (Moderate or Intense Low-oxygen Dilution) MILD combustion regime. In this regard, three fuel inlet turbulence intensity profiles with the values of 4%, 7% and 10% are superimposed on the annular mixing layer. The effects of these changes on the flame structure under the MILD condition are studied for two oxygen concentrations of 3% and 9% (by mass) in the oxidiser stream and three hot co-flow temperatures 1300, 1500 and 1750 K. The turbulence-chemistry interaction of the numerically unresolved scales is modelled using the (Partially Stirred Reactor) PaSR method, where the full mechanism of GRI-2.11 represents the chemical reactions. The influences of the turbulence intensity on the flame structure under the MILD condition are studied by using the profile of temperature, CO and OH mass fractions in both physical and mixture fraction spaces at two downstream locations. Also, the effects of this parameter are investigated by contours of OH, HCO and CH₂O radicals in an area near the nozzle exit zone. Results show that increasing the fuel inlet turbulence intensity has a profound effect on the flame structure particularly at low oxygen mass fraction. This increment weakens the combustion zone and results in a decrease in the peak values of the flame temperature and OH and CO mass fractions. Furthermore, increasing the inlet turbulence intensity decreases the flame thickness, and increases the MILD flame instability and diffusion of un-burnt fuel through the flame front. These effects are reduced by increasing the hot co-flow temperature which reinforces the reaction zone.     

The on-axis average intensity for Gaussian beam excitation limited by an annular aperture in turbulent atmosphere

Starting with a Gaussian beam excitation limited by an annular aperture, the on-axis average intensity is presented in turbulent atmosphere. The on-axis average intensity profile is evaluated by altering the outer and inner radius of an annular aperture, the propagation distance and wavelength. The results show that the outer radius of an annular aperture within a certain size impacts the on-axis intensity distributions. When the propagation distance or the outer radius of an annular aperture is large enough, the on-axis average intensity distributions is not affected by the size of the annular aperture. By calculation and analyses, the variation of the inner radius of the annular aperture and the wavelength of the Gaussian beam that impact on the axial average intensity distributions is also discussed.     

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.     

Discrete continuous-phase superresolving filters

A new type of phase-only superresolving pupil filter with a discrete continuous-phase profile is presented that is a combination of discrete multilevel-phase modulation and continuous-phase modulation. This type of filter can achieve better superresolution performance than the continuous-phase filters reported in Opt. Lett. 28, 607 (2003). Therefore, with regard to the superresolution effect, this type of filter deserves study for practical applications. More importantly, the diffraction performance of this type of filter can explain the effect of a discrete-phase filter illuminated with a continuous wave front, whose superresolving performance cannot be analyzed with previous superresolution methods.