自適應(yīng)光學(xué)波前傳感技術(shù)分析學(xué)習(xí)資料

1、自適應(yīng)光學(xué)波前傳感技術(shù)分析工作成績(jī)哈特曼夏克波前傳感哈特曼夏克波前傳感 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 根據(jù)波前徑向斜率測(cè)量原理,提出一種利用五棱鏡掃描方法實(shí)現(xiàn)了新型自基準(zhǔn)哈特曼波前傳感器，其突出優(yōu)點(diǎn)和特點(diǎn)是毋需任何外部信標(biāo)或標(biāo)準(zhǔn)大平面反射鏡提供工作基準(zhǔn)。這對(duì)主動(dòng)光學(xué)新技術(shù)的空間應(yīng)用有重要意義。對(duì)大型天文望遠(yuǎn)鏡光學(xué)系統(tǒng)裝校檢測(cè)和大口徑高精度拋物面反射鏡以及平行光管等的檢測(cè)也具有重要的應(yīng)有價(jià)值。 本方法的技術(shù)可行性強(qiáng)，容易實(shí)現(xiàn)；測(cè)量靈敏度與一般干涉法相當(dāng)，但對(duì)光源的單色性和工作環(huán)境并無苛刻要求，因此便于推廣應(yīng)用。 本方法

16、由于采用了機(jī)械掃描采樣方式，一次測(cè)量需時(shí)幾分鐘，所以不適用于以校正大氣湍流為目的的自適應(yīng)光學(xué)系統(tǒng)。自基準(zhǔn)哈特曼波前傳感器哈特曼夏克自基準(zhǔn)哈特曼波前傳感器),( 圖中五棱鏡 可單獨(dú)沿被測(cè)物鏡光瞳的半徑方向平移,也可與五棱鏡 一起繞被測(cè)物鏡的光軸轉(zhuǎn)動(dòng)。 和 的主截面彼此平行，并與光軸方向一致。當(dāng) 沿徑向平移時(shí)可實(shí)現(xiàn)對(duì)被測(cè)物鏡出射光束的離散采樣。采樣光束通過 和 后在相對(duì)被測(cè)物鏡固定不動(dòng)的CCD相機(jī)光敏面上生成一個(gè)艾利斑。測(cè)出 處于光瞳面內(nèi)不同位置 時(shí)所對(duì)應(yīng)的艾利斑質(zhì)心坐標(biāo)和相對(duì)偏移量的徑向分量，由下式即可求得被測(cè)物鏡出射波前斜率的徑向分量1P2P1P2P1P1P2P1P哈特曼夏克 理論分析和計(jì)算機(jī)

17、仿真結(jié)果表明，在采樣密度足夠的情況下，根據(jù)已知波前徑向斜率分量的離散采樣值也完全可以以足夠高的精度重構(gòu)出原始波面的形狀;如果徑向斜率離散采樣值包含有一定的隨機(jī)誤差，也仍能重構(gòu)出精度與波前徑向斜率采樣精度相當(dāng)?shù)牟ㄇ靶螤睢Ｓ脻赡峥藦较蛐甭识囗?xiàng)式作最小二乘擬合具體過程如下。對(duì)波面上每一點(diǎn)的徑向斜率測(cè)量數(shù)據(jù)可分別寫出自基準(zhǔn)哈特曼波前傳感器式中 即為單位圓上 點(diǎn)處第n項(xiàng)Zernike多項(xiàng)式的徑向斜率值，也就是以Zernike多項(xiàng)式形式表示的基元波面的斜率值。 為第1至第n項(xiàng)Zernike多項(xiàng)式的系數(shù); 為被測(cè)波面上各采樣點(diǎn)處的徑向斜率測(cè)量值;k和m分別為半徑方向和圓周方向的采樣點(diǎn)數(shù)。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工作成績(jī)金字塔波前傳感金字塔波前傳感 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: 金字塔傳感器具有可變的增益、更大的探測(cè)波前位相動(dòng)態(tài)范圍、在波前低階模式校正中具有更高的靈敏度。Drawbacks: 金字塔形分光器件加工精度需求高，對(duì)材料的光學(xué)均勻性能要求也苛刻。工作成績(jī)曲率波前傳感曲率波前傳感 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