自适应光学波前传感技术分析学习资料

1、自适应光学波前传感技术分析工作成绩哈特曼夏克波前传感哈特曼夏克波前传感 Evolution of the Hartmann test standard devices for measuring wavefront slope errors哈特曼夏克 One method for testing a lens or mirror employs an opaque mask with holes placed behind the optical element under test.Each of the holes acts as an aperture, and since the li

2、ght passing through the lens is converging, the image produced is an array of spots.With proper calibration, the position of the spots is a direct indication of the local wavefront tilt at each hole, and thus is a description of the lens quality.This test is called the Hartmann test.Hartmann test哈特曼

3、夏克 Shack placed lenses in the holes, which increased the light-gathering efficiency of the mask and, with the spots focused, reduced the disturbing diffraction effects of the holes. A lens array for this purpose was first manufactured in 1971.Members of the astronomy community began to use this sens

4、or in the late 1970s for testing of large telescope optics.Some astronomers use the term HartmannShack (or ShackHartmann) wavefront sensor, but many shorten it to simply Hartmann sensor.History哈特曼夏克 The Hartmann wavefront sensor is shown in below figure .The wavefront is divided by a mask, as in the

5、 classical test, an array of gratings, or an array of transmissive lenses.Each of the beams in the subapertures is focused onto a detector.To detect the position of the spot, various forms of modulation, detector geometry, and electro-optical processing are used. For atmospheric turbulence compensat

6、ion, the local wavefront tilt must be measured accurately in each subaperture of size .To do this, the subaperture must be large enough to resolve the isoplanatic patch.During high turbulence, is small and anisoplanatism degrades the process.Hardy discusses details of this large-versus-small subaper

7、ture trade for various optical and atmospheric parameters.Hartmann wavefront sensor0r0r哈特曼夏克Hartmann wavefront sensorHartmann wavefront sensing technique. A Hartmann sensor is composed of an array of lenses for wavefront division and typically a CCD array with multiple pixels used for spot position

8、(wavefront tilt) determination.哈特曼夏克 If that source is an extended object, the shape of the object is convolved with the subaperture diffraction pattern on the quadcell.Intensity variation can seriously degrade the measurement accuracy of the centroid.To remove the effects of extended objects resolv

9、ed by the subaperture, an optical correlation can be used. Von der Luhe suggested the use of an addressable optical mask, whose transmission is derived from the image of the reference scene.The Hartmann detector array records a cross-correlation of the mask and the scene in each subaperture.Even if

10、the object remains unresolved, the problems associated with subaperture higher-order aberrations will distort the pattern on the quadcell and decrease tilt-measurement accuracy.Extended object哈特曼夏克 Correlation TrackerFF When the wavefront source is an extended object, a centroid measurement, like th

11、at in a ShackHartmann sensor, is meaningless.Each subaperture contains a small image of the entire object with the image shifted according to subaperture tilt.To overcome this problem, one image is chosen as a reference. The cross-covariance between each image I is calculated by where x is the 2-D s

12、patial coordinate, is the 2-D image displacement, and is the forward and inverse Fourier transforms, and * indicates the complex conjugate.This method has been applied in solar telescopes where photons are plentiful, but the object is large.)(xIR哈特曼夏克 For daytime astronomy with large background radi

13、ation, a field-of-view shifted ShackHartmann wavefront sensor can be used.In solar imaging applications, each subaperture sees an image of the extended source, the sun.Cross-correlation algorithms are used to determine wavefront tilts, rather than centroids. Increases in the speed of two- dimensiona

14、l detector arrays and microprocessors have led to developments that utilize these advantages. The first such system to successfully compensate image motion of a ground-based solar telescope was the breadboard correlation tracker built by the Solar Physics Group at Lockheed Palo Alto Research Laborat

15、ory for image motion compensation on a space borne solar telescope.Daytime astronomy哈特曼夏克 根据波前径向斜率测量原理,提出一种利用五棱镜扫描方法实现了新型自基准哈特曼波前传感器，其突出优点和特点是毋需任何外部信标或标准大平面反射镜提供工作基准。这对主动光学新技术的空间应用有重要意义。对大型天文望远镜光学系统裝校检测和大口径高精度抛物面反射镜以及平行光管等的检测也具有重要的应有价值。 本方法的技术可行性强，容易实现；测量灵敏度与一般干涉法相当，但对光源的单色性和工作环境并无苛刻要求，因此便于推广应用。 本方法

16、由于采用了机械扫描采样方式，一次测量需时几分钟，所以不适用于以校正大气湍流为目的的自适应光学系统。自基准哈特曼波前传感器哈特曼夏克自基准哈特曼波前传感器),( 图中五棱镜 可单独沿被测物镜光瞳的半径方向平移,也可与五棱镜 一起绕被测物镜的光轴转动。 和 的主截面彼此平行，并与光轴方向一致。当 沿径向平移时可实现对被测物镜出射光束的离散采样。采样光束通过 和 后在相对被测物镜固定不动的CCD相机光敏面上生成一个艾利斑。测出 处于光瞳面内不同位置 时所对应的艾利斑质心坐标和相对偏移量的径向分量，由下式即可求得被测物镜出射波前斜率的径向分量1P2P1P2P1P1P2P1P哈特曼夏克 理论分析和计算机

17、仿真结果表明，在采样密度足够的情况下，根据已知波前径向斜率分量的离散采样值也完全可以以足够高的精度重构出原始波面的形状;如果径向斜率离散采样值包含有一定的随机误差，也仍能重构出精度与波前径向斜率采样精度相当的波前形状。用泽尼克径向斜率多项式作最小二乘拟合具体过程如下。对波面上每一点的径向斜率测量数据可分别写出自基准哈特曼波前传感器式中 即为单位圆上 点处第n项Zernike多项式的径向斜率值，也就是以Zernike多项式形式表示的基元波面的斜率值。 为第1至第n项Zernike多项式的系数; 为被测波面上各采样点处的径向斜率测量值;k和m分别为半径方向和圆周方向的采样点数。哈特曼夏克Hartm

18、ann wavefront sensorPrinciples: vThe telescope image pupil is reimaged on a lenset arrayvEach lenset produces a star image forming the equivalent of a Hartmann pattern, which can be recorded on a CCDvThe position of the centroid of each lenset image compared to a reference supplies the slope of the

19、wavefront (or wavefront tilt) at the location in object space corresponding to the lensetv Calibration is done with a reference plane wave 哈特曼夏克Hartmann wavefront sensorAdvantages:vCompact and ruggedvUsed for active (sampling interval of minutes) and adaptive (sampling interval of millisecond) optic

20、s applicationsvWork with broadband light (white light capability) large number of photons important for adaptive optics Since wavefront distortion introduced by atmosphere is approximately achromatic, it can be measured on wide band width Possible to use optical light to correct light in IRvIncohere

21、nt light sensing technique extended sources can be usedvHigh optical efficiencyvNo 2 ambiguityvTthe ability to use continuous or pulsed sourcesvDetection of phase singularities哈特曼夏克Hartmann wavefront sensorDrawbacks:vWavefront tilt sensitivity fixed by design cannot be changed to accommodate differe

22、nt seeing conditionsvSince they measure tilts and not phase, they cannot be used to measure wavefront errors in segmented mirrorsvOne must achieve high alignment accuracy of the array along with the required high optical quality工作成绩金字塔波前传感金字塔波前传感 Enhanced sensitivity金字塔History The Pyramid Wave-Front

23、 Sensor (PWS) J. Mod. Opt., 43 (1996) 289 was first presented as a novel slope sensor which is similar to the well-known Shack-Hartmann Sensor (SHS), with the advantage of a better sensitivity in closed loop operation Astron. Astrophys. 350 (1999) L23. Some of its properties have already been studie

24、d by the means of a descriptive approach and then in regime of partial AO correction by numerical simulations.Both works show an enhanced sensitivity in closed loop with respect to a SHS. This was also more recently confirmed by detailed numerical simulations in the framework of the first-light AO s

25、ystem of the Large Binocular Telescope.金字塔Pyramid Wavefront Sensor The image of the reference source to be sensed is focused on the top of a pyramid-shaped prism. A tip-tilt mirror located in a pupil plane permits the application of a dynamic displacement (circular in general) of the image with resp

26、ect to the pyramid. The role of this beam modulation is to increase the linearity and dynamic range of the sensor. A pupil re-imager is used to form images of the pupil relayed by the four facets of the pyramid, on the detector. 金字塔Pyramid Wavefront SensorPyramid wavefront sensor Another pupil-plane

27、 wavefront sensor uses a pyramidal prism in the image plane to create four subbeams that are then optically relayed to a detector.The intensity at position in each of the sub-beams in the detector plane ( ) is used to find the x and ywavefront slopes at .),(yxr1 , 10, 11 , 00, 0IIII),(yxr金字塔Pyramid

28、Wavefront SensorttxIrIrIrIrIrS)()()()()(1 , 11 , 00, 10, 0ttyIrIrIrIrIrS)()()()()(1 , 11 , 00, 10, 0 is the average intensity over the detector plane.One advantage of the pyramid technique over the ShackHartmann sensor is that the spatial resolution of the sensor is the size of the detector pixel in

29、 contrast to the larger lenslet subaperture size of the Shack Hartmann.tI金字塔 The path traced on the top of the pyramid by a ray coming from a given sub-aperture, effected by a local tilt, is shown in Fig. 1. For this ray, the intensity transmitted by a given facet is proportional to the time spent b

30、y the ray on it. The relation between the signal and the wave-front slope can be derived from simple geometrical considerations.Pyramid Wavefront Sensor where is the modulation angle and the wave-front phase. The equation taken in the weak perturbation regime (small signals), describes the PWS as a

31、slope sensor with an adjustable sensitivity which is inversely proportional to the modulation angle, . However,the PWS only acts as a slope sensor for very low-order aberrations.金字塔Pyramid Wavefront Sensor Principles:The“phase/slope sensor” duality of the Pyramid Wave-front SensorOn a low frequency

32、domain, for |u|/), the Fourier SNR curve for a PWS is flat (identical at all frequencies) and independent of the modulation angle .In this spatial frequency range, the signal-to-noise ratio of the measurements is of the same order as given by a Mach-Zehnder direct phase sensor where is the incoming

33、phase standard deviation and N the number of photons per sub-aperture. This property and the flatness of the Fourier SNR curve shows that the behavior of the PWS in terms of sensitivity and Fourier spectrum (for (|u|/) is very similar to a direct phase sensor. 金字塔Pyramid Wavefront Sensor On the one

34、hand, the increased sensitivity of the PWS with respect to the SHS with quad-cells on all the modes the AO system can correct (up to ) , leads to a gain in limiting magnitude, as long as (for which the modulation path length is equal to the spot size in a SHS sub-aperture). On the other hand, a PWS

35、is less sensitive than the SHS to the high-order atmospheric phase errors ( ) so that less aliasing error is expected for the PWS.cFcFcFu 金字塔Pyramid Wavefront SensorAdvantages: 金字塔传感器具有可变的增益、更大的探测波前位相动态范围、在波前低阶模式校正中具有更高的灵敏度。Drawbacks: 金字塔形分光器件加工精度需求高，对材料的光学均匀性能要求也苛刻。工作成绩曲率波前传感曲率波前传感 Other substitute

36、 of Hartmann test曲率 Roddier et al have shown how the methods of focus sensing and the Hartmann subaperture division process can be combined. The method, called curvature sensing, measures local wavefront curvature (second derivative) in each subaperture.By comparing two near-simultaneousirradiance d

37、istributions at equally spaced points on either side of the subaperture focal plane, the local curvature is found.Curvature Sensing曲率Curvature SensingWavefront curvature sensor geometry Referring to below figure,two irradiance distributions and are detected a distance s from focus on either side of

38、the focal plane.The relationship between the irradiance and the phase is given by)(1rI)(2rIwhere is the local curvature at expressed as and is the local radius of curvature.The Dirac delta represents the outward pointing normal derivatives on the edge of the signal.wcrrcw/1wrc曲率Curvature Sensing To reconstruct the wavefront from the known local curvatures and the edge derivatives, an iterative procedure can be followed to solve Poissons equation, or Zernike derivatives can be calculated. Hickson describes conditions,namely when , in which the wavefront can be reconstructed with a