Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.     

Design of off-axis reflective projection lens using spherical Fresnel surface

In this paper, an off-axis reflective projection lens with single Fresnel reflective surface and three aspheric surfaces were designed. The design method of reflective lens using spherical Fresnel surface is discussed. The MTF (Modulation Transfer Function) of the off-axis reflective lens, with optical magnification 100×, F-number 2.5 and field of view 120°, is over 40% at 0.6 lp/mm on the image side, the distortion is less than 2%. This design method can provide reference for application of Fresnel surface in wide field of view imaging, and possesses a bright future with the continuous development of fabrication technique.     

用极值频率法分析数字全息的记录条件

根据全息理论,通过分析全息图光栅结构的极值频率,利用抽样定理以及频谱分离条件,分析了离轴菲涅耳全息的记录条件,得到了不同于以往文献的最小记录距离及参考光源设置表达式,并做了计算机模拟验证.结果表明：用该方法推得的离轴菲涅耳全息最小记录距离和参考光设置表达式是正确的.只有同时满足抽样条件和频谱分离条件,才能得到高质量的再现像.     

物光的偏振性对全息记录质量的影响

通过对菲涅耳三维漫反射全息记录光路中物光与参考光偏振状态的实验检测，发现线偏振的激光被不同表面材料的物体散射和漫反射后变成“部分偏振光”，几乎所有目标物都有显著的消偏振现象，全息干板上实际记录的是线偏振的参考光与“部分偏振”的物光形成的相干度较低的干涉条纹。物光偏振度的大幅度下降影响干涉条纹的衬比度，并增加全息图的噪声。给出实验方案和检测光路，采用在参考光路中插入1/4波片的方法，可充分利用非偏振物光各个振动方向的光能，提高条纹的衬比度。     

Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces

Radiation absorption in an infinitely long hollow cylinder with Fresnel surfaces is studied using the ray tracing method. It is found that the inner boundary can be modeled as a total reflective surface for the infinitely long hollow cylinder. Radiative absorption of hollow cylinders with Fresnel surfaces is compared to diffusive surfaces predicted by the finite volume method. Effects of refractive index, optical thickness and hole size on radiative absorption are studied. Abrupt changes in radiative absorption near τ_r/τ_Ro=1/n are observed for hollow cylinders with Fresnel surfaces. It is because the Fresnel relation predicts a critical angle at . This trend is not observed in diffusive surfaces. Refractive index and optical thickness are two competing factors that govern the radiative absorption. Higher refractive index drives higher absorption close to the inner surface, while higher optical thickness yields higher absorption near the outer surface. The results of this study can also serve as benchmark solutions for modeling radiative heat transfer in hollow cylinders with Fresnel surfaces. It is also found that the directional or hemispherical emittance can be calculated without solving the radiative transfer equation in the media when the temperature variation in the media is small.     

Passive IR field gradient detection of thermal objects in active Fresnel zones

A dual element Passive-Infrared (PIR) sensor is used with a rotating slit aperture to map a narrow scanning beam on the sensing elements through each lens of a Fresnel lens array. The stimuli generated due to each thermal object fall in the active Fresnel zones in a certain direction based on their locations and temperature variations on the surfaces of the sources. These signals are used to analyze the signatures of stationary thermal objects, their slight movements and thermal field gradient changes of the source surfaces provided the object projected area is less than the area of the active zone. Pattern matching is performed using Dynamic-Time-Warping (DTW) algorithm on STFT reduced length time vectors. The object space is divided into m-active zones that correspond to the Fresnel zones in a Fresnel lens array. Within passive IR region from each of the active zones, the system identifies not only the heat intensity changes but also detects the slight movement of the thermal source. The efficiency of the system is dependent on the number of active Fresnel zones and the angular separation between them. This single node PIR sensor system is designed to cover an angular view of ∼10° × 80° while horizontal Field of View (FOV) is divided into 4 active Fresnel zones. Generally costly Thermal-IR camera is used for thermal analysis. Our system is comparatively less costly and active coverage zones are easily configurable by increasing number of Fresnel lenses.     

Numerical analysis for finite Fresnel transform

Optical Review - The Fresnel transform is a bounded, linear, additive, and unitary operator in Hilbert space and is applied to many applications. In this study, a sampling theorem for a Fresnel...     

An indirect algorithm of Fresnel diffraction

An indirect algorithm for Fresnel diffraction calculation at any distance is presented in this paper. Using this indirect algorithm, the Fresnel diffraction on a near plane can be realized in two steps, the first is to acquire the diffractive field on a far field and the second is to obtain the diffractive field on a near plane using an inverse Fresnel integral. Compared with conventional algorithms, this algorithm is valid at any range of distance. The sampling theorem, as the basis of this indirect algorithm, is discussed in detail. Theoretical calculations show good agreements with experimental results.     

Geant4 tool for simulation of arbitrarily defined Fresnel lenses

We report on creating a module for the Geant4 toolkit for a simulation of point-by-point defined Fresnel lenses and mirrors. This module provides creation of cylindrical Geant4 shapes with one or two Fresnel surfaces, defined by the arrays of points (z(ρ)).     

应用反射型球面菲涅耳波带片的成像物镜设计

设计了一种应用球面菲涅耳波带反射面与非球面反射面结合的成像物镜。对球面结构的菲涅耳波带反射面进行分析,推导了球面菲涅耳波带反射面近似替代非球面的方法,采用单片球面菲涅耳波带反射面和三片非球面反射面设计成像物镜,在放大倍数100×、视场角120°、菲涅耳数2.5情况下,调制传递函数在放大成像侧可实现0.6 lp/mm的40%以上,畸变小于2.2%。该设计方法为菲涅耳波带片应用于可见光成像提供了参考,并随着菲涅耳器件加工技术的不断发展具有良好的应用前景。     

Fraunhofer computer-generated hologram for diffused 3D scene in Fresnel region

A Fraunhofer computer-generated hologram (CGH) is proved to be valid in display for three-dimensional (3D) objects from the Fresnel to the far-field region without a Fourier lens for reconstruction. To quickly compute large and complicated 3D objects that consist of slanted diffused surfaces in the Fresnel region, a Fraunhofer-based analytical approach using a basic-triangle tiling diffuser is developed. Both theoretical and experimental results reveal that Fraunhofer CGH can perform the same effects as Fresnel CGH but require less calculation time. Impressive 3D solid effects are achieved in the Fresnel region.     

等厚型平板菲涅尔透镜设计与研究

针对当前曲面菲涅尔透镜普遍存在的加工工艺复杂、面型精度难于控制、制作成本较高等问题,在研究非等厚型平板菲涅尔透镜设计方法的基础上,提出一种中心透镜为球面、外侧环带为倾斜面的等厚型平板菲涅尔透镜的设计方法,给出了具体的设计实例,并进行了建模和光学仿真,模拟结果表明:该菲涅尔透镜设计的光学效率达到90.7%。     

YG算法设计分数傅里叶变换衍射光学光束整形器件

针对分数傅里叶变换衍射光学光束整形器件,比较了按离散点与按菲涅耳积分计算得到的变换矩阵间的差距,从中分析得出按离散点计算的变换矩阵引入的离散化误差与分数傅里叶变换系统参数的关系.模拟计算结果表明,该离散化误差不能忽略.为了在输出面上得到真实的光强分布,应采用菲涅耳积分计算其变换矩阵.鉴于该变换矩阵非幺正,本文利用YG算法进行了光束整形器件的设计.     

悬浮进样探针原子化石墨炉原子吸收法测定地质样品中的铬

本文应用探针恒温原子化技术 ,系统研究了铬的分析性能 ,应用固体悬浮进样 ,直接测定了地质样品中的痕量铬 ,方法的 RSD为 3.0 %～ 6 .5 % ,检测限为 5 .1× 10 - 1 2 g铬 ,标准物质的测定结果满意     

基于液晶空间光调制器的全息显示

在传统的纯相位全息显示系统中, 一般基于快速傅里叶变换(FFT)算法来计算相位全息图, 在FFT的计算中需要遵循Nyquist采样定理, 因此, 重建图像的尺寸往往受限于空间光调制器的固定采样率. 这个限制可以通过卷积算法或者两步菲涅耳衍射算法来解决, 但是需要使用多个FFT的计算, 导致计算量增大. 鉴于此, 提出了一种基于透镜的纯相位全息图计算方法. 在全息图的计算中, 通过透镜的成像原理建立一个采样率可变的虚拟全息面, 通过调节相应的距离参数使得在全息图的计算中可以任意调节原始图像的采样率, 摆脱了传统方法中液晶空间光调制器带宽积对重建图像尺寸的限制, 并且这种算法只需使用一次FFT就能达到变采样率的衍射计算, 大幅提高了全息图的计算速度. 数值模拟及光学实验结果证明了此方法可以在全息显示光学系统中清晰地重建不同尺寸的图像. 同时该系统可以有效地消除由空间光调制器的像素化结构带来的零级衍射.     

二次相位采样问题的等效输入场算法

 分析了采样定理与二次相位采样问题的关系;基于菲涅耳衍射公式,推导了离焦位置光场的计算方法,避免聚焦计算中遇到的二次相位采样问题。提出了等效输入场算法思想,将聚焦过程中遇到的插入元件等效为对源场的调制,从而不需要计算插入位置的光场,解决在离焦位置有任意多个相位板的传输计算中的二次相位采样问题。将由等效输入场算法得到的输出光强与由基于菲涅耳积分公式的光场解析式计算得到的光强进行对比,在0~100 mm范围内的各离焦位置,两者相对误差小于10¹³,从而证实了等效输入场算法的正确性。     

Radiative heat transfer in axisymmetric domains of complex shape with Fresnel boundaries

A detailed study of the peculiarities of the radiative heat transfer (RHT) in axisymmetric domains bounded with Fresnel surfaces is undertaken. The analytical (exact) solutions of the RHT problem in conical and cylindrical domains with refractive index more than unity were obtained for a variety of absorption coefficient and geometrical parameters of the domains. It is shown that due to Fresnel reflections the net radiative flux strongly varies over the base of cone and cylinder. The difference in RHT processes for the cases of constant reflectivity of the boundaries and that calculated by Fresnel formula is demonstrated. The influence of specular reflection at the crystal side surface on the shape of the solid/liquid interface in growing bismuth germanate crystals is shown.     

光学介质薄膜优化的宽带消色差λ/4相位延迟器

根据全反射相变理论设计了菲涅耳菱体型相位延迟器延迟量对入射角变化不敏感的结构角。根据薄膜的偏振效应,从薄膜的特征矩阵出发,通过在菱体的两个全反射面蒸镀光学介质膜的方法拓宽了菲涅耳菱体型相位延迟的消色差宽度。在ML_EB900型镀膜机上适当控制沉积条件制备了消色差相位延迟膜,实验测试结果表明:在530~700 nm的波长范围内,可以获得90°的相位延迟量,且最大偏差小于0.7°。     

数字全息成像系统的景深和焦深分析

根据全息理论,分析了数字全息成像系统的景深和焦深.针对数字全息不同的记录光路结构,分别给出了焦深的近似表达式.结果表明：数字全息系统的景深和焦深不仅与记录波长以及记录时的数值孔径有关,还与记录时参考光波的偏置情况有关;在记录距离和CCD参量一定的条件下,离轴无透镜傅里叶变换全息对称偏置下的焦深比非对称偏置下的稍小;显微成像情况下离轴无透镜傅里叶变换全息系统的焦深大于同轴菲涅耳数字全息系统的焦深,计算机模拟表明了结果的正确性.     

空变菲涅耳联合变换相关器

提出了菲涅耳联合变换相关器(Fresnel Joint Transform Correlator,FnJTC)结构,给出了数学推导过程,并通过计算机模拟验证了可行性及其与传统相关器所不同的相关特性。在相关过程第一阶段中,菲涅耳联合变换相关器对输入的联合图像作菲涅耳变换,代替了传统联合变换相关器(JTC)的傅里叶变换。与传统相关器相比,菲涅耳联合变换相关器是空变系统,相关峰值依赖于输入参考图像与目标图像的相似性、两图像之间的相对位置及参考图像(或目标图像)的线性相位调制。