Object surface for applying a modified hartmann test to measure corneal topography

A modified Hartmann test is proposed for measuring corneal topography. The plane screen with holes used in the typical Hartmann test is replaced with a curved object surface. This object surface yields a plane image for a spherical mirror surface. We show that the object surface is an oval of revolution that can be modeled by an ellipsoid. The plane image will be formed by a square array of circular spots, all with the same diameter. To obtain the square array in the image, we calculated the spatial distribution of the spots on the object surface.     

Interferometric hartmann wave-front sensing for active optics at the 6.5-m conversion of the multiple mirror telescope

A little-used interferometric modification to the classical Hartmann optical test is being used for active optics corrections at the 6.5-m Multiple Mirror Telescope (MMT) Observatory. The technique produces compact interference spots whose positions depend on discrete wave-front phase-difference errors. A diffraction model illustrates the formation of interference spots. The limitations on wave-front sampling that are due to atmospheric seeing are estimated. Two data reduction matrix strategies are given. A single correction of collimation and primary mirror figure produces a nearly diffraction-limited telescope image. Wave-front polynomial coefficients ranging from several nanometers to several micrometers in amplitude are reliably detected.     

Estimating the precision characteristics of a hartmann sensor in detection of poisson signals

An analytic expression for the distribution density of a random variable at the output of a quadrant photodetector that performs sum-difference processing a, Poisson signal is obtained. The precision characteristics of a Hartmann sensor in the presence of Poisson and Gaussian noise are analyzed on the basis of the expression. Expressions for the mathematical expectation and variance of the noise-induced error variance and the correlation coefficents, of the results of reconstruction of the phase front are obtained. Translated from Izmeritel'naya Tekhnika, No. 9, pp. 38–42, September, 1999.     

Joint processing of hartmann sensor and conventional image measurements to estimate large aberrations: theory and experimental results

We report experimental results for what we believe to be a new technique for estimating aberrations that extends the strength of an aberration that may be sensed with Hartmann sensor technology by means of an algorithm that processes both a Hartmann sensor image and a conventional image formed with the same aberration. We find that the theory and the experiment match well within the experimental error and that strong defocus aberrations can be accurately sensed with this technique.     

Wave-front retrieval from Hartmann test data

In the classical Hartmann test the wave front is obtained by integration of the transverse aberrations, joining the sampled points by small straight segments, in the so-called Newton integration. This integration is performed along straight lines joining the holes on the Hartmann screen. We propose a modification of this procedure, considering the cells of four holes of the Hartmann screen to fit a small second-power wave front recovering each square. This procedure has some important advantages, as described here.     

Efficiency of the Hartmann test with different subpupil forms for the measurement of turbulence-induced phase distortions

The reconstruction quality of turbulence-induced phase distortions from Hartmann data is calculated for masks with different subpupil forms by means of computer simulations. Four subpupil forms are considered: the circle, the square, the hexagon, and the polar segment. We show that, for the case of a circular aperture, the mask with polar segment subpupils provides the best reconstruction quality.     

Duct flow with a transverse magnetic field at high Hartmann numbers

Finite element methods can be used for determining the flow in a straight channel under a variety of wall conductivity conditions when a uniform magnetic field is imposed perpendicular to the flow direction. At high Hartmann numbers oscillatory solutions are found unless sufficient points are placed within the Hartmann layers. In some one‐ and two‐dimensional problems it appears that it is adequate to place one or two points within the Hartmann layer to remove the oscillations. Central core values can sometimes be predicted with good accuracy even when the Hartmann layers are not resolved adequately. A nine‐point Gauss point rule has been used to evaluate the stiffness and other matrices for the eight‐node elements. Copyright © 2001 John Wiley & Sons, Ltd.     

Optical measurements of phase steps in segmented mirrors—fundamental precision limits

Phase steps are an important type of wavefront aberration generated by large telescopes with segmented mirrors. In a closed-loop correction cycle these phase steps have to be measured with the highest possible precision using natural reference stars, that is with a small number of photons. In this paper the classical Fisher information of statistics is used for calculating the Cramér–Rao minimum variance bound, which determines the limit to the precision with which the height of the steps can be estimated in an unbiased fashion with a given number of photons and a given measuring device. Four types of such measurement devices are discussed: a Shack–Hartmann sensor with one small cylindrical lenslet covering a subaperture centred on a border, a modified Mach–Zehnder interferometer, a Foucault test, and a curvature sensor. The Cramér–Rao bound is calculated for all sensors under ideal conditions, that is narrowband measurements including photon shot noise, but without other forms of noise or disturbances. This limit is compared with the ultimate quantum statistical limit for the estimate of such a step, which is independent of any measuring device. For one device, the Shack–Hartmann sensor, the effects on the Cramér–Rao bound of broadband measurements, finite sampling, and disturbances such as atmospheric seeing and detector readout noise are also investigated. The methods presented here can be used to compare the precision limits of various devices for measuring differential segment phases, and for optimizing the devices. Under ideal conditions the Shack–Hartmann and the Foucault devices nearly attain the ultimate quantum statistical limit, whereas the Mach–Zehnder and the curvature devices each require approximately twenty times as many photons in order to reach the same precision.     

Novel methods to improve the measurement accuracy and the dynamic range of Shack–Hartmann wavefront sensor

As a wavefront sensor, the Shack–Hartmann wavefront sensor plays an important role in the wavefront measurement of human eyes. However, the low measurement accuracy and the small dynamic range of Shack–Hartmann wavefront sensor limit its application. In this paper, we present a matched-filter algorithm to improve the measurement accuracy by more than an order of magnitude. Moreover, we also introduce a new algorithm to extend the dynamic range of Shack–Hartmann wavefront sensor. With this method, the recorded spots of Shack–Hartmann wavefront sensor are not constrained to stay in the corresponding pixel area of the microlens. The result shows that the dynamic range can be extended from 57.1 to 160% for the first 24 items of Zernike wavefronts, respectively. The improvement by our methods makes the Shack–Hartmann more suitable for the measurement of highly aberrated eyes.     

Finite element method for solving mhd flow in a rectangular duct

A finite element method is given to obtain the solution in terms of velocity and induced magnetic field for the steady MHD (magnetohydrodynamic) flow through a rectangular pipe having arbitrarily conducting walls. Linear and then quadratic approximations have been taken for both velocity and magnetic field for comparison and it is found that with the quadratic approximation it is possible to increase the conductivity and Hartmann number M (M ≤ 100). A special solution procedure has been used for the resulting block tridiagonal system of equations. Computations have been carried out for several values of Hartmann number (5 ≤ M ≤ 100) and wall conductivity. It is also found that, if the wall conductivity increases, the flux decreases. The same is the effect of increasing the Hartmann number. Selected graphs are given showing the behaviour of the velocity field and induced magnetic field.     

Experiments of two pupil lateral motion tracking algorithms using a Shack–Hartmann sensor

Pupil stability is one of the factors which limit the performance and operational stability of adaptive optics (AO) systems. This paper analyses two pupil-tracking methods to measure the lateral pupil shift: the first one utilizes the fluxes in all outer edge sub-apertures of a Shack–Hartmann sensor and the second one utilizes the real-time interaction matrix used in an AO system. Experiments with 9?×?9 Shack–Hartmann sensor are conducted to verify both pupil-tracking algorithms. The results show that both algorithms are effective, after two correction steps, the residual pupil shift is reduced to less than 5% of a Shack–Hartmann sub-aperture.     

Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements

Conventional Hartmann sensor processing relies on locating the centroid of the image that is formed behind each element of a lenslet array. These centroid locations are used for computing the local gradient of the incident aberration, from which the phase of the incident wave front is calculated. The largest aberration that can reliably be sensed in a conventional Hartmann sensor must have a local gradient small enough that the spot formed by each lenslet is confined to the area behind the lenslet: If the local gradient is larger, spots form under nearby lenslets, causing a form of cross talk between the wave-front sensor channels. We describe a wave-front reconstruction algorithm that processes the whole image measured by a Hartmann sensor and a conventional image that is formed by use of the incident aberration. We show that this algorithm can accurately estimate aberrations for cases in which the aberration is strong enough to cause many of the images formed by individual lenslets to fall outside the local region of the Hartmann sensor detector plane defined by the edges of a lenslet.     

中心棒哈特曼发声器声学特性研究

采用FW-H声模拟法,研究了中心棒的位置、长度和直径等因素对中心棒哈特曼发声器声学特性的影响,得出如下结论:无论中心棒置于谐振腔入口前端还是底部,只要中心棒一端处于气流入口到谐振腔入口段,哈特曼发声器就能产生较高的声压级;中心棒置于气流入口,且长度不超过喷流间距,会产生比普通哈特曼发声器更高的声压级;中心棒的半径有一个最佳值,数值模拟结果显示,不同半径中心棒哈特曼发声器声压级的大小顺序相应为:r=0.2mm、r=0.3mm、r=0.1mm、r=0.5mm,即半径r为0.2mm的中心棒哈特曼发声器产生的声压级较大,而半径r为0.5mm的声压级最较小;频谱分析发现,加中心棒会使哈特曼发声器的最大峰值频率变小。上述结论对中心棒哈特曼发声器的应用具有重要的指导意义。     

Sensing a wave front by use of a diffraction grating

A method is presented to sense the wave front at the exit of an optical surface. This method uses a set of diffracted rays generated when a He-Ne laser impinges on a rectangular diffraction grating. The grating was placed near the curvature center of the surface to be tested. After they are reflected in the test surface, the diffracted rays have the information of the slopes of the wave front, like in the Hartmann test. The Hartmann pattern was registered near the curvature center and captured with a CCD camera. The slopes for each ray are measured from the experimental pattern, and they are compared with the ideal ones simulated in a computer. The evaluation was carried out by use of Seidel polynomials to obtain the information of the aberrations of a mirror 53 cm in diameter.     

Effect of a magnetic field on natural convection in an inclined half-annulus enclosure filled with Cu–water nanofluid using CVFEM

In this paper, the effect of a magnetic field on natural convection in a half-annulus enclosure with one wall under constant heat flux using control volume based finite element method. The fluid in the enclosure is a water-based nanofluid containing Cu nanoparticles. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. Numerical simulations were performed for different governing parameters namely the Hartmann number, Rayleigh number and inclination angle of enclosure. The results indicate that Hartmann number and the inclination angle of the enclosure can be control parameters at different Rayleigh number. In presence of magnetic field velocity field retarded and hence convection and Nusselt number decreases.     

一种新型的掩膜管理控制系统的研制

研制了一种与掩膜光刻机相配套的新型掩膜管理控制系统.系统硬件由1个4自由度机械手、2个版库、粗预对准机构、精细预对准机构、PLC控制器和伺服驱动器等构成;系统软件由基于VC的上层管理程序以及基于梯形图的底层流程控制程序构成,其中上掩膜版和卸掩膜版是流程控制的主要组成部分.介绍了四象限光电探测器的对准工作原理和掩膜版的粗、精细预对准方法,实验测试了上、卸掩膜版的节拍,粗、精细预对准时间和掩膜版经过精细预对准后的重复定位精度,讨论了激光器和四象限光电探测器相对 位姿的标定方法,并指出了该系统的特点.实验结果表明,该系统性能稳定,主要指标能够满足掩膜光刻机的实际生产要求.     

Hartmann flow over a permeable bed

Hartmann flow past a permeable bed is investigated in the presence of a transverse magnetic field with an interface at the surface of the permeable bed. The flow above the bed, called Zone 1, is governed by the Hartmann equation and that below the bed, called Zone 2, is governed by the modified Darcy law. Solutions for these two zones are separately obtained and are matched at the interface using suitable boundary conditions. The mass efflux, change in volume rate of flow, the induced magnetic field and current density are evaluated to determine whether a magnetic method might be potentially useful in the study of pore-size distribution.We find that, for mercury flowing over a long permeable channel of width 0.7 cm, the effect of magnetic field (of strength 0.25 Web/m², i.e. the Hartmann number M = 8.8) in the presence of a porous wall (of porosity k = 5 × 10^?6 Darcy) is to retard the mass flow and to increase the friction factor relative to the corresponding quantities for non-magnetic flow. The amount of retardation is 22 per cent more than that obtained by Wallace et al. [12] in the experiments on the flow of mercury in porous media in a transverse magnetic field. Since the magnitude of retardation is related to the pore size distribution, our model is potentially useful to study the pore size distribution than that of Wallace et al. [12]. In addition, transition to turbulence occurs at a higher Reynolds number owing to the presence of a magnetic field.     

Shack Hartmann wave-front measurement with a large F-number plastic microlens array

A new plastic microlens array, consisting of 900 lenslets, has been developed for the Shack Hartmann wave-front sensor.The individual lens is 300 μm × 300μm and has a focal length of 10 mm, which provides the same focal size, 60 μm in diameter, with a constant peak intensity. One can improve thewave-front measurement accuracy by reducing the spot centroiding error by averaging a few frame memories of an image processor. A deformable mirror for testing the wave-front sensor gives anappropriate defocus and astigmatism, and the laser wave front is measured with a Shack Hartmann wave-front sensor. The measurement accuracy and reproducibility of our wave-front sensor are better than λ/20 and λ/50 (λ = 632.8 nm),respectively, in rms.     

Oscillatory magnetogasdynamic slip flow in a microchannel

The problem of pressure-driven magnetogasdynamic (MGD) slip flow with small rarefaction through a long microchannel is considered. The flow is driven by a steady or oscillatory pressure gradient. The study of MGD flows in microchannels is of interest since they occur in many electromagnetic microscale devices. In obtaining the microfluidic solutions in the presence of a magnetic field, some additional physical, mathematical, and numerical issues need to be considered. These issues deal with the scaling laws for microscale MGD flows and the relevant parameters such as Mach number, Reynolds number, Hartmann number, magnetic Reynolds number, and Knudsen number. For planar constant area microchannels, it is possible to obtain the analytical solutions for both steady and oscillatory pressure-driven flows at low magnetic Reynolds numbers. The flow field is assumed to be quasi-isothermal, which is a good assumption in the absence of a strong electric field. As physically expected, at higher values of the magnetic field (that is at a higher Hartmann number) the velocity profile in the channel flattens, and the pressure varies nonlinearly along the channel.     

基于哈特曼波前探测的流场层析重建系统仿真

基于哈特曼波前探测的流场层析重建技术结合了光学波前探测技术和计算机层析技术。重建系统由哈特曼传感器探测平行光束穿过流场后的投影波前,采用计算机层析技术重建流场物理量的空间分布。在介绍哈特曼流场层析重建原理的基础上,对流场重建的整个过程进行了计算机仿真,重建的RMS误差为0.0726。结果表明,该技术可以很好地实现流场的层析重建,在材料、流场研究等工程实际测量中具有良好的应用前景。