Noise reduction in the Fourier spectrum of Hartmann patterns for phase demodulation

A simple method to reduce the noise in the Fourier spectrum of Hartmann patterns for filtering the fundamental sidelobes (first harmonics) is presented. The method consists on replacing the Hartmann pattern by a fringe pattern within a circular pupil. The fringes are cosine square type and the pupil is apodized with a Gaussian function. These fringes follow the centroid spots of the Hartmann pattern along the horizontal and vertical directions. The width of the fringes in each direction is constant and it is determined according to the distortion of the Hartmann pattern. In this way, it is possible to obtain the wavefront’s slopes more accurate in comparison with the traditional method. We present experimental results to show the advantages of our method.     

Analysis of the common characteristics of the Hartmann,Ronchi, and Shack–Hartmann tests

An overview of the settings of the planes for the filters and observed patterns in the Hartmann and Ronchi tests is presented. Also a new set of filters for both test were developed. In a similar way, it is easy to extend this analysis to the Shack–Hartmann test, and to propose a new Null Shack–Hartmann filter.     

Analysis on Shack–Hartmann wave-front sensor with Fourier optics

In Shack–Hartmann wavefront sensor (SHWS), the behavior of the irradiance pattern produced by the micro-lens array is important for an accurate centroid estimation. In this paper, the behavior of a micro-lens array in SHWS is analyzed using Fourier optics, and reveals that in addition to the main, expected spots, secondary spots with smaller intensities also appeared as a result of diffraction by the small dimensions of the micro-lens and interference from the different micro-lenses. This result is confirmed by comparing with a irradiance pattern taken from an actual SHWS. The additional error in centroid estimation caused by these secondary spots is discussed and relationship to the parameters of the micro-lens of SHWS is analyzed.     

基于哈特曼法球差自动测量系统的图像处理

从基于哈特曼法自动测量球差所需解决的CCD图像传感和数字图像处理技术出发，提出将哈特曼光阑图像用于存储器中的目标识别与测量时，图像映像区搜索算法和哈特曼光阑图像中测量光斑距离的中心重叠算法，解决了在一维图像存储器中准确寻找二维图像目标，随后进行相关目标计算的技术。其中利用所有光斑的质心求解哈特曼光阑图像的中心,再由光斑质心关于光阑图像中心的对称性确定光斑质心距离的中心重叠算法可减少计算次数，大大降低了算法的时间复杂度和计算复杂度。     

Figure Measurement of Concave Mirror by Fiber-Grating Hartmann Test

A new type of Hartmann test was developed using an optical fiber grating instead of the traditional Hartmann screen with multiple holes. A fiber-grating is made of short optical fibers arranged in single layers with no gaps between them. On illumination with laser light, the fiber-grating generates fan-like diverging multiple rays of almost equivalent intensities. Two gratings are overlapped at right angles to make multiple beams diverging in two directions. Rays reflected from test mirror surfaces converge to make a point focus provinding the sulface is free from aberrations. A CCD camera detects a spot pattern of beams near but out of focus, and a personal computer analyzes the spot patterns and calculates the figure error from a ideal surface. A few concave mirrors were analyzed by this method and the results compared with those obtained with a Fizeau interferometer. The data using the two systems were consistent with each other to within 1/10A.     

用哈特曼-夏克法标定平面光束

经推导给出了用哈特曼－夏克法标定平面光束的基本原理及其方法，并根据该原理作了标定平面光束的实验。如果哈特曼－夏克系统相邻子孔径在焦面的投影中心间距（焦斑点阵间距）与原标定的理想中心间距相比放大，入射光束为发散束；如焦斑点阵间距缩小，入射光束为聚焦束。该方法具有原理简单，操作方便的优点。     

散斑干涉相位条纹图的频域滤波处理

为了解决在数字散斑干涉技术测量时,散斑干涉相位条纹图像中大量噪声对相位解包裹结果和精度产生严重影响的问题,介绍了一种条纹正余弦分解和频域低通滤波结合的方法,实现了散斑干涉相位条纹图的高精度滤波。该方法的基本思路是在对相位图像进行滤波处理前,先将相位图通过正余弦函数进行映射转换成两幅图,分别经过频域滤波,然后再合成为相位图。这种分解频域滤波方法可以在滤波的同时,有效保留相位跳变信息。实验结果表明：与传统的图像降噪方法相比,该方法能够在保留图像“尖峰”信息的基础上,较好地滤除图像中的散斑噪声,方法简单有效,有效解决了传统滤波方法应用在相位条纹图中,相图灰度信息丢失10%~40%的问题。     

Creation of Multiple Subwavelength Focal Spot Segments Using Phase Modulated Radially Polarized Multi Gaussian Beam

Based on the vector diffraction theory,the effect of complex phase filters on intensity distribution of a radially polarized multi Gaussian beam in the focal region of high NA lens is theoretically investigated.It is observed that a properly designed multi belt complex phase filter can generate subwavelength novel focal patterns including splitting of focal spots and generation of multiple focal spot segments such as eight,six and four focal spots along the optical axis are obtained.We expect that such an investigation is useful for optical manipulation and material processing,multiple high refractive index particle trapping technologies.     

Experimental research on application of Hartmann micro-lens array in coherent beam combination of two-dimensional laser array

We demonstrate experimentally the application of a phase error detection method in the coherent beam combination (CBC) of a laser array. The method is based on the Hartmann micro-lens array. Both the piston and tilt errors can be detected and corrected simultaneously by combining this method with adaptive optics-correcting technology. The far-field intensity pattern of the combined beam has high energy concentration and good beam quality. The power encircled in the main lobe of the far-field pattern is 41.3%, and the contrast of the pattern reaches 81.8%. Experimental results show the great potential of the Hartmann phasing method for use in the CBC of a large number of laser beams.     

Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes

Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and its subharmonic.     

Closed-loop aberration correction by use of a modal Zernike wave-front sensor

We describe the practical implementation of a closed-loop adaptive-optics system incorporating a novel modal wave-front sensor. The sensor consists of a static binary-phase computer-generated holographic element, which generates a pattern of spots in a detector plane. Intensity differences between symmetric pairs of these spots give a direct measure of the Zernike mode amplitudes that are present in the input wave front. We use a ferroelectric liquid-crystal spatial light modulator in conjunction with a 4-f system and a spatial filter as a wave-front correction element. We present results showing a rapid increase in Strehl ratio and focal spot quality as the system corrects for deliberately introduced aberrations.     

介质阻挡放电中两种亮暗点菱形斑图的光谱研究

空气和氩气混合气体的双水电极介质阻挡放电装置中,在电压升高过程中首次发现了两种由亮点和暗点组成的亮暗点菱形斑图。通过观察斑图照片可以发现： 第一种菱形斑图(菱形斑图Ⅰ)中的暗点处于由亮点组成的菱形单元的中心;第二种菱形斑图(菱形斑图Ⅱ)中的暗点恰好处于周围其他三个亮点的中心位置。利用发射光谱法,通过采集氮分子(N₂)第二正带系(C3Π_u→B3Π_g)发射谱线和氩原子696.54 nm(2P₂→1S₅)谱线的展宽,研究了两种菱形斑图中亮点和暗点的分子振动温度和电子密度。实验发现： 两种菱形斑图中暗点的分子振动温度均高于亮点,相对菱形斑图Ⅰ来说,菱形斑图Ⅱ中的亮点和暗点的分子振动温度均升高;而菱形斑图Ⅰ中暗点的电子密度低于亮点,菱形斑图Ⅱ中亮点和暗点的电子密度却几乎相等。两种菱形斑图中电子密度表现出不同的变化趋势,且在菱形斑图Ⅱ中表现出的规律尤为特殊,因而采用高速录像机对菱形斑图Ⅱ进行短曝光拍摄观察斑图中亮点和暗点的成分,发现暗点是体放电和沿面放电共存的状态。进一步研究从菱形斑图Ⅰ到菱形斑图Ⅱ的演化过程中三种斑图中亮点的电子密度,结果发现： 演化中间过程的斑图中的亮点的电子密度最大,菱形斑图Ⅱ中亮点的电子密度最低。实验结果对于研究斑图的自组织形成过程具有参考作用。     

Entropy production in a two-dimensional reversible Gray-Scott system

The entropy production sigma is calculated in the time evolution processes toward a Turing-like pattern and a chaotic pattern in a two-dimensional reaction-diffusion system. The contributions of reaction and diffusion to the entropy production are evaluated separately. Though its contribution to total sigma is about 5%, the entropy production in diffusion foretells the moving direction of the dots (reaction spots) and the line-shaped patterns. The entropy production of the entire system sigma depicts well the cooperative dynamics and evolution of chaotic dot patterns. It is suggested that sigma can be a scalar measure for quantitative studies of hierarchic pattern dynamics. The relation is also discussed between the bifurcation parameter and the distance from thermodynamic equilibrium.     

Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model

We performed an extensive numerical study of pattern formation scenarios in the two-dimensional Gray-Scott reaction-diffusion model. We concentrated on the parameter region in which there exists a strong separation of length and/or time scales. We found that the static one-dimensional autosolitons (stripes) break up into two-dimensional radially-symmetric autosolitons (spots). The traveling one-dimensional autosolitons (wave fronts) can be stable or undergo breakup. The static two-dimensional radially-symmetric autosolitons may break up and self-replicate leading to the formation of space-filling patterns of spots, wave fronts, or spatio-temporal chaos due to the competition of self-replication and annihilation of spots upon collision. Received 6 November 2000 and Received in final form 27 February 2001     

Optimal design of FIR beamformer with frequency invariant patterns

Two approaches to the optimal design of FIR beamformers with frequency invariant patterns using second-order cone programming (SOCP) are proposed. The first approach is a two-step method, which is implemented via separately optimal array pattern synthesis and optimal FIR filters design. The array weights for each frequency bin within the working frequency band are designed to insure that the array patterns approximate the reference ones. And the FIR filter corresponding to each sensor is designed to insure that the frequency responses approximate the array weights. The second approach is a direct method, in which the beam response is expressed as a linear function of FIR filter tap weights and the filters are designed by jointly optimizing the spatial and frequency responses to achieve the desired array patterns. All the optimal design problems (array pattern synthesis, FIR filter design and joint optimization) are formulated as the SOCP, which can be solved efficiently using the well-developed interior-point methods. Results of computer simulations and lake experiment for a twelve-element semicircular array confirm satisfactory performance of the two approaches proposed in this paper.     

一种符号阵列编码结构光三维检测方法

编码结构光检测技术是一种主动视觉方法,利用投射的模式光,通过三角原理获得深度信息。根据伪随机阵列的特性,提出了一种可用于检测场景目标的一次投射模式的结构光三维检测方法。符号的拐点、交叉点比传统的基于伪随机序列及M阵列模式提供了更多的检测点。符号阵列能够提供足够多的码字使所有的子模式获得全局唯一性。基于符号链分解算法及角度变化的轮廓特征,解码方法能够识别绝大多数码字。重建实验表明可以对一定曲面变化的物体进行检测,并能重建其形廓。     

Spatial recurrence strategies reveal different routes to Turing pattern formation in chemical systems

We analyze the temporal evolution of hexagonal Turing patterns in two Belousov-Zhabotinsky reactions performed in water-in-oil reverse micro-emulsions under different experimental conditions. The two reactions show different routes to pattern formation through localized spots and through a self replication mechanism. The Generalized Recurrence Plot (GRP) and the Generalized Recurrence Quantification Analysis (GRQA) are used for the investigation of spatial patterns and clearly reveal the different routes leading to the formation of stationary Turing structures.     

介质阻挡放电系统中带晕蜂窝六边形发光斑图

为了丰富介质阻挡放电系统中斑图的多样性,利用双水电极介质阻挡放电装置,在空气和氩气按一定比例混合的气体中（氩气含量χ=25%）,发现了带晕蜂窝六边形斑图。通过观察用普通相机拍摄的斑图照片,可以发现斑图是由中心点、晕和蜂窝框架构成,且中心点位于晕的中心,中心点和晕嵌套在蜂窝框架的中心。采用带有3个通道的高速照相机对斑图进行分脉冲瞬态拍摄,结果显示带晕蜂窝六边形斑图的3套子结构在外加电压的半周期内,总是按照晕-蜂窝框架-中心点这样的顺序放电。运用光电倍增管对这3套子结构进行研究,发现晕的放电在时间和空间上具有局部选择性。利用发射光谱法,根据氮分子第二正带系（C³Π_u→B³Π_g）谱线计算了中心点、晕和蜂窝框架的分子振动温度,结果显示:中心点的分子振动温度为2 632 K,晕的分子振动温度为2 679 K,蜂窝框架的分子振动温度为2 720 K。本文利用壁电荷理论解释带晕蜂窝六边形斑图的形成机制和时空结构。     

A four-quadrant phase filter for creating two focusing spots

We present a design method of four-quadrant pure phase filter and phase modulation functions for creating two focusing spots. With the combination of a high numerical aperture objective and a four-quadrant pure phase filter, a radially polarized incident plane wave can be focused into two focusing spots with the spacing of several wavelengths along the optical axis. The filter with the phase modulation functions are verified effective by numerical simulation. The distance of the two focuses and the position of each focus can be controlled and adjusted by changing the phase modulation functions. The beam quality and longitudinally polarization purity of these two focusing spots are calculated and discussed and thus the centrally obstructed four-quadrant phase filters are proposed to improve the beam quality.     

Focal patterns of sine-azimuthal wavefront-modulated cosh-Gaussian beams by half space phase plate

The pure phase plate was introduced to alter the half-space phase value of the incident linearly polarized hyperolic-cosine-Gaussian (cosh-Gaussian) beams with sine-azimuthal variation wavefront, and focusing properties of the cosh-Gaussian beams by half space phase plate were investigated in detail. Simulation results show that focal pattern can be altered very considerably by the phase plate under condition of different beam parameters, numerical aperture, and phase parameter that indicates the phase change frequency on increasing azimuthal angle. Symmetry of the whole focal pattern can be altered remarkably, polysymmetrical focal patterns evolve into nonsymmetrical focal patterns. And some novel focal shape may appear, including cross-shape, multiple-peak focal pattern, multiple intensity lines, wheel focal pattern, swallowtail focal pattern, and dark hollow focal spots.