Phase retrieval for high-numerical-aperture optical systems

We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functionsreproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.     

光瞳半径对纯位相调制激光束整形系统的影响

光瞳截断作用对纯位相调制激光束整形系统的系统性能有重要影响. 本文提出了一种关于光瞳半径对近场调制位相和远场系统评价函数影响的定量分析方法. 通过拉格朗日乘数法等方法分析光瞳半径对近场调制位相的影响, 结果表明: 近场调制位相随光瞳半径近似线性增加. 通过建立数学模型, 拟合分析光瞳半径对系统评价函数的影响. 结果表明: 对方形目标光强, 系统评价函数拟合精度确定系数达到99%左右, 光瞳半径为2.5倍高斯光束束腰半径时, 相关系数达到0.997, 光强偏离残差平方均值达到0.0004左右, 光瞳截断作用趋于最小; 对圆形目标光强, 系统评价函数拟合精度确定系数达到97%, 光瞳半径为3倍高斯光束束腰半径时, 相关系数与光强偏离残差平方均值变化幅度均在10^-3量级, 系统评价函数趋于收敛, 光瞳截断作用趋于最小.     

正弦变化的振幅型光瞳滤波器

光瞳滤波器作为实现超分辨的基本元件之一,它的设计以及制作都非常重要。设计了一种正弦变化的振幅型光瞳滤波器,可以通过调节少量的参量实现各种不同的超分辨模式。选择正弦函数的周期以及光瞳中心点透过率变化两个参量来实现对最终超分辨效果的调节。数值计算结果表明：在整个人射光瞳上的透过率瞳函数分布具有0．5～2个正弦振幅周期时,较为合适。小于0．5个周期将不会有任何超分辨效果,大于2个周期超分辨效果反而变差。数值计算中还注意到,当周期数为整数时,斯特雷尔比将保持0．25不变。对正弦变化振幅型光瞳滤波器的计算结果,显示了其特殊的性质,对实际中制作正弦变化振幅型光瞳滤波器有一定的指导作用。     

A hybrid optical-digital processor for image deblurring

A hybrid optical-digital image processing system is developed for deblurring out-of-focus pictures. The optical part is a dual-channel non-coherent processor which implements the Wiener filter for deblurring through appropriate pupil functions. The methods of implementing the bipolar PSF in a non-coherent processor are described, as are the methods of determining the pupil functions from the given PSFs. The digital part of the processor subtracts or demodulates the outputs from the dual-channel optical processor to give the final deblurred picture. The pupil functions are experimentally realized and the deblurred outputs are presented.     

Automatic localization of pupil using eccentricity and iris using gradient based method

This paper presents a novel approach for the automatic localization of pupil and iris. Pupil and iris are nearly circular regions, which are surrounded by sclera, eyelids and eyelashes. The localization of both pupil and iris is extremely important in any iris recognition system. In the proposed algorithm pupil is localized using Eccentricity based Bisection method which looks for the region that has the highest probability of having pupil. While iris localization is carried out in two steps. In the first step, iris image is directionally segmented and a noise free region (region of interest) is extracted. In the second step, angular lines in the region of interest are extracted and the edge points of iris outer boundary are found through the gradient of these lines. The proposed method is tested on CASIA ver 1.0 and MMU Iris databases. Experimental results show that this method is comparatively accurate.     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

Design of axially super-resolving phase filters using the method of generalized projections

The design of pupil phase filters that super-resolve the axial intensity distribution with controlled side-lobe peak intensity under high numerical aperture conditions can be accomplished by incorporating the theory of electromagnetic diffraction in the method of generalized projections (MGP). The MGP results are however strongly dependent on the starting conditions and the applied constraints. In this report we study this dependence by investigating different starting pupil functions and introducing modifications to the applied constraints. Methods are described and implemented to generate a systematic set of starting conditions that enable a more thorough search of the solutions space. This approach generated results for which 95% have a super-resolved central-lobe, yet only a subset of those solutions offer a satisfactory compromise between super-resolution of the central-lobe and increased intensity of the axial side-lobes. These solutions are presented and discussed in the context of specific applications.     

Orthonormal polynomials in analysis of single-mode fiber coupling

Zernike polynomials have been widely used for wave-front analysis because of their orthogonality over a uniform circular pupil. However, the pupil is not uniform but weighted by the backpropagated fiber mode in analyzing fiber coupling efficiency. Zernike polynomials are not appropriate for a weighted pupil due to their lack of orthogonality over such pupil. We emphasize the advantages of using orthonormal polynomials in fiber coupling systems. The orthonormal polynomials over weighted pupil are derived by matrix approach. The effects of primary aberrations are investigated based on the orthonormal polynomials. The accuracy of the Strehl ratio approximation for primary aberrations is evaluated.     

OTF synthesis: Low pass and band pass filters realized by periodic replication of the pupil function

We present a method which allows incoherent optical low and band pass filtering with high light efficiency. Our method is based on the principle of pupil function replication. The pupil functions are pure phase filters with discrete phase values. Experimental results are shown where the filters are simulated by computer generated holograms.     

瞳孔检测仪的研究及其光学系统设计

研究了一种双眼瞳孔检测仪,进行了光学系统的设计和理论计算.采用低照度CCD摄像机摄取在近红外和可见光照明情况下的瞳孔像,利用形态学等算法处理图像,可对图像进行直径精确检测和动态分析.实验表明,该仪器在0~200 lux照度级下的测量精度可达0.01 mm,完全可以满足眼科手术的精度要求.     

The modelling of the influence of a corneal geometry on the pupil image of the human eye

In normal conditions, a pupil of the eye is observed through the optical system of the cornea. The cornea is the anterior surface of the eye and is the major refractive element of the human eye. The influence of the corneal shape should not be neglected in measurements of the pupil size. The purpose of this study was to estimate the influence of the corneal geometry, the diameter of the pupil and its position in the anterior chamber on the magnification and position of the image of the pupil. The numerical calculations presented in the paper assume infinitely thin cornea, and the corneal topography was approximated by the elongated ellipsoid. The ray tracing procedure was used in our numerical modelling. The magnification of the pupil image amounted to about 10% and increases with decrease of radius of curvature and eccentricity of the corneal profile and decreases for the largest pupil. The results show also that the pupil image is placed nearer the corneal apex than the real pupil. The image of the pupil is always blurred, which limits the sharp observation of the pupil.     

基于近红外远心镜头的双目瞳孔检测仪光学系统设计

为了降低双目瞳孔检测系统放大率对瞳孔位置的敏感性,设计了一款基于近红外远心镜头的双目瞳孔检测仪。阐述了系统中的核心部件——近红外远心镜头光学参数的计算过程,分前后组进行设计,并运用Zemax完成光学系统优化,以全视场MTF、全视场最大畸变和物方远心度为指标对系统进行公差分析,利用标准圆对仪器进行标定,拟合出像素数和瞳孔大小的对应关系。结果表明,对于55 mm~75 mm的瞳距,瞳孔的直径测量精度可达0.05 mm,满足使用要求。     

利用振动光纤减弱激光散斑的研究

在激光投影显示技术中,引入振动光纤的方法能够以较小的能量损失减弱激光散斑.本文利用广义范西特-泽尼克定理对激光投影显示中采用振动光纤抑制散斑做了理论分析.结果表明,散斑衬比度的大小取决于光纤的模式数和投影系统的光瞳大小,对于相同大小的像面,收集更多的光纤模式数和增大孔径均可减弱散斑衬比度.用两种不同的多模光纤所做的对比实验定性证实了这一结论.研究结果对光纤的选择和投影系统的设计有一定的指导意义.     

Focal-shift formula in apodized nontelecentric focusing systems

A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.     

Orthogonal Aberration Functions for Microlithographic Optics

Newly developed orthogonal aberration functions are reviewed. The new functions can be utilized to express aberrations of a high NA and wide field optical system like a microlithographic projection lens. The new functions are orthogonal to each other and expressed by a simple combination of Zernike function(s) of pupil coordinates and Zernike function(s) of field coordinates.     

Anisotropic edge enhancement in optical scanning holography with spiral phase filtering

Anisotropic edge enhancement is simulated using a spiral phase plate(SPP) in optical scanning holography(OSH). We propose to use a delta function and an SPP as the pupil functions to realize anisotropic edge enhancement. The interference of these two pupils is used to two-dimensionally scan an object to record its edge-only information. This is done in three ways: first, by shifting the SPP, second, by using two offset SPPs of same charge, and finally, by using two oppositely charged SPPs. Our computer simulations show the capability of selectively enhancing the edges of a given object.     

Tight focusing of radially polarized Gaussian and Bessel-Gauss beams

We examine the effects of tightly focusing a radially polarized beam with uniform, Gaussian, or Bessel-Gauss pupil functions. The resulting FWHM is smallest for the case of a uniform amplitude profile, while the Bessel-Gauss beam results in the largest FWHM. The uniform amplitude profile also results in an axial field component that increases fastest with increasing NA. The ratio of the axial component to the transverse component is also the greatest for the uniform pupil function. On the other hand, the Bessel-Gauss beam benefits the most from the use of an annulus.     

照明光瞳非对称性对光刻成像质量的影响

研究了照明光瞳非对称性对光刻成像质量的影响。通过PROLITH软件计算了环形与四极照明条件下,光瞳非对称性对图形位置偏移量、曝光图形内水平线条与垂直线条的宽度差、曝光图形上密集线条与孤立线条之间线宽偏差的影响。研究结果表明,光瞳非对称性主要影响曝光图形的位置偏移量,光瞳非对称性引起的图形位置偏移量与光瞳非对称性的大小成线性关系。根据套刻精度的误差分配原则,计算得到光瞳非对称性的容限为5%。     

Apodization to produce a monotonically-decreasing,coherent line-spread function

A class of apodized pupil functions is derived, which have the property of producing a monotonically decreasing, coherent line-spread function. A simple example of such a function is given together with the line-spread function so produced.