Astronomical Observing Techniques Lecture 13: Adap<ve Op<cs

Transcription

1 Astronomical Observing Techniques Lecture 13: Adap<ve Op<cs Christoph U. Keller

2 Overview 1. The Power of Adaptive Optics 2. Atmospheric Turbulence 3. Basic Principle 4. Key Components 5. Error Terms 6. Laser Guide Stars 7. Adaptive Optics Operations Modes 25 Nov Astronomical Observing Techniques: Adaptive Optics 2

3 ExPo Adap<ve Op<cs at WHT 25 Nov Astronomical Observing Techniques: Adaptive Optics 3

4 Star with and without AO cfao.ucolick.org/pgallery/stellar.php 25 Nov Astronomical Observing Techniques: Adaptive Optics 4

5 Io with and without AO cfao.ucolick.org/pgallery/io.php 25 Nov Astronomical Observing Techniques: Adaptive Optics 5

6 NGC 7469 cfao.ucolick.org/ao/why.php 25 Nov Astronomical Observing Techniques: Adaptive Optics 6

7 Seeing star solar photosphere 25 Nov Astronomical Observing Techniques: Adaptive Optics 7

8 Seeing: r 0, τ 0, θ 0 (from Lecture 2) Fried parameter r 0 : average turbulent scale over which RMS opdcal phase distordon is 1 rad r 0 increases as λ 6/5 Seeing Δθ at good sites at 0.5μm: cm atmospheric coherence (or Greenwood delay) Dme: maximum Dme delay for RMS wavefront error to be < 1 rad ( ν is mean propagadon velocity) IsoplanaDc angle θ 0 : angle over which RMS wavefront error is smaller than 1 rad 6/5 2 r0 ( λ) = λ Cn ( z) dz 0 λ Δθ = r 0 3/5 1/5 ~ λ τ 0 = r 0 v θ 0 = 0.314cosζ r 0 h 25 Nov Astronomical Observing Techniques: Adaptive Optics 8

9 Resolu<on & Sensi<vity Improvement λ 1. Angular resoludon: θ = θ = r0 2. Point source sensidvity: S / N ~ D λ D gain = D r 2 0 gain in t 1 int ~ 4 D PHARO LGS Ks image 500s integ., 40" FOV, 150 mas FWHM WIRO H image Kobulnicky et al. 2005, AJ 129, Nov Astronomical Observing Techniques: Adaptive Optics 9

10 Adap<ve Op<cs Principle Maximum scale of tolerated wavefront deformadon is r 0 à subdivide telescope into apertures with diameter r 0 r 0 Measure wavefront deformadon Correct wavefront deformadon by bending back the patches of size r 0 Number of subapertures is (D/ r 0 ) 2 at observing wavelength à requires hundreds to thousands of actuators for large telescopes D 25 Nov Astronomical Observing Techniques: Adaptive Optics 10

11 Adap<ve Op<cs Scheme (SCAO) 25 Nov Astronomical Observing Techniques: Adaptive Optics 11

12 Wavefront Descrip<on: Zernike Polynomials Expansion into a series of orthogonal terms: 25 Nov Astronomical Observing Techniques: Adaptive Optics 12

13 Zernike Amplitudes for Kolmogorov Turbulence Units: Radians of phase / (D / r 0 ) 5/6 Tip-tilt is single biggest contributor Focus, astigmatism, coma also big High-order terms go on and on. Reference: Noll 25 Nov Astronomical Observing Techniques: Adaptive Optics 13

14 Wavefront Sensors Shack Hartmann Most common principle is the Shack Hartmann wavefront sensor measuring sub-aperture tilts: f Pupil plane Image plane 25 Nov Astronomical Observing Techniques: Adaptive Optics 14

15 ExPo Wavefront Sensor at WHT 25 Nov Astronomical Observing Techniques: Adaptive Optics 15

16 Wavefront Sensing Sunspot wavefront sensor images at 955Hz 25 Nov Astronomical Observing Techniques: Adaptive Optics 16

17 Deconvolu<on from Wavefront Sensing deconvolution from wavefront sensing provides AO-like results 106 subapertures over 1m aperture at 950 nm at McMath-Pierce telescope 25 Nov Astronomical Observing Techniques: Adaptive Optics 17

18 WFSs: Curvature and Pyramid Sensors Curvature Wavefront Sensor Pyramid Wavefront Sensor 25 Nov Astronomical Observing Techniques: Adaptive Optics 18

19 Deformable Mirrors Basic principle: piece- wise linear fit of the mirror surface to the wavefront. r 0 sets the number of degrees of freedom. Two general types: segmented mirrors and condnuous face- sheet mirrors: Note that the (piezo) actuator stroke is typically only a couple of micrometers à requires separate Dp- Dlt mirror. 25 Nov Astronomical Observing Techniques: Adaptive Optics 19

20 Membrane Deformable Mirror micromachined deformable mirror (OKOtech/Flexible OpDcs) with 37 actuators 600- nm thick, 15- mm diameter silicon nitride membrane electrostadc actuators Individual Actuators Mirror Surface 25 Nov Astronomical Observing Techniques: Adaptive Optics 20

21 Adap<ve Secondary Mirrors Concept: integrate DM into the telescope à adapdve secondary mirrors Advantages: no addidonal opdcal system needed à lower emission, higher throughput large surface à higher actuator density larger stroke à no Dp- Dlt mirror needed...but also more difficult to build, control, and handle DM for MMT Upgrade 25 Nov Astronomical Observing Techniques: Adaptive Optics 21

22 { Shack- Hartmann Wavefront Analysis centroid (center of gravity) calculadon on each subaperture: Δx = i max i=i min i max j max j= j min j max I(i, j) i I(i, j), Δy = i max i=i min i max j max j= j min j max I(i, j) j I(i, j) i=i min j= j min i=i min j= j min Zero Position { Δy Δx Finding Star Positions 25 Nov Astronomical Observing Techniques: Adaptive Optics 22

23 Influence Matrix slope of mirror surface and Shack- Hartmann star posidons are propordonal to actuator posidon linear reladonship between actuator a and star posidon c: c n = N k=1 a k b nk (For a single spot x- offset or y- offset) Combine equadons for each spot posidon n into matrix equadon: C = BA C = star posidons A = actuator posidons B = influence matrix describing influence of specific actuator posidon on star posidons 25 Nov Astronomical Observing Techniques: Adaptive Optics 23

24 Measuring the Influence Matrix need to know actuator posidon change that will correct wavefront solve for A (control vector) given C (star posidons) first find B (influence matrix) through direct measurement Step each actuator k through the possible posidons and measure the star posidons at each step For the k th actuator and the n th subaperture, the slope of the best fit line is the element (n, k) of the influence matrix B Influence matrix gives the resuldng star posidons when muldplied by a control vector (list of actuator posidons) Spot Offset (pixels) Actuator 1, Trial 1, Spot 17 (horizontal) r = E+00 2.E+04 4.E+04 6.E+04 8.E+04 Squared Voltage 25 Nov Astronomical Observing Techniques: Adaptive Optics 24

25 Solving for the Control Vector Influence matrix B is known, C is given by wavefront sensor Find A (control vector) to correct for error in wavefront Invert equadon C = BA: A = B 1 C Overdetermined system: More subaperture star posidon measurements than actuators No exact soludon A exists for any given set of star posidons No exact B - 1 exists (B is rectangular) Singular Value DecomposiDon: Generates approximate B - 1 that won t solve equadon, but will represent best possible soludon 25 Nov Astronomical Observing Techniques: Adaptive Optics 25

26 Typical AO Error Terms Fitting errors from insufficient approximation of the wavefront (finite actuator spacing, influence function of actuators, etc.). 2 σ fit 0.3 D r 0 5/3 Temporal errors from the time delay between measurement and correction (computing, exposure time). σ 2 temp t τ 0 5/3 Measurement errors from the WFS (S/N!) 2 σ measure ~ S / N Calibration errors from aberrations in the noncommon path between sensing channel and imaging channel. 2 σ calibration ~??? Angular anisoplanatism from sampling different lines of sight through the atmosphere. 2 σ aniso θ θ 0 5/3 25 Nov Astronomical Observing Techniques: Adaptive Optics 26

27 Angular Anisoplana<sm Angular anisoplanadsm severely limits wide- field imaging sky coverage (finding a guide star within the isoplanadc angle) 25 Nov Astronomical Observing Techniques: Adaptive Optics 27

28 Typical Correc<on and Residuals cfao.ucolick.org/pgallery/gc.php 25 Nov Astronomical Observing Techniques: Adaptive Optics 28

29 Sky Coverage To sense the wavefront one needs a bright reference/guide star within the isoplanadc angle. 1 Galactic Equator ( l < 5 ) Intermediate Latitudes (- 35 < l < - 25 ) Galactic Pole (l < - 80 ) All sky average (- 90 < l < 90 ) Cummulative Sky Coverage (mi < mag) Sky coverage given by star counts integrated over given bands in galactic latitude from USNO- B1.0 catalog. Star counts are cummulative, i.e., guide star sky coverage is for all stars brighter than given magnitude Guide Star Magnitude (I) Cumulative sky coverage, i.e., the chance of finding stars brighter than given magnitude, for a random target as a function of I-band magnitude using the USNO-B1.0 catalogue. 25 Nov Astronomical Observing Techniques: Adaptive Optics 29

30 Laser Guide Stars SoluDon to the sky coverage problem: create your own guide star Two principle concepts: Sodium LGS excite atoms in sodium layer at aldtude of ~ 95 km. Rayleigh beacon LGS scatering from air molecules sends light back into telescope, h ~ 10 km Since the beam travels twice (up and down) through the atmosphere, Dp- Dlt cannot be corrected à LGS- AO sdll needs a natural guide star, but this one can be much fainter (~18mag) as it is only needed for Dp- Dlt sensing. 25 Nov Astronomical Observing Techniques: Adaptive Optics 30

31 Sodium Beacons Layer of neutral sodium atoms in mesosphere (height ~ 95 km, thickness ~10km) thought to be deposited as smallest meteorites burn up. Resonant scatering occurs when incident laser is tuned to D2 line of Na at 589 nm. 25 Nov Astronomical Observing Techniques: Adaptive Optics 31

32 WHT Rayleigh Guide Star 25 Nov Astronomical Observing Techniques: Adaptive Optics 32

33 Rayleigh Beacons Due to interacdons of the electromagnedc wave from the laser beam with molecules in the atmosphere. Advantages: cheaper and easier to build higher power independent of Na layer Disadvantages: larger focus anisoplanadsm laser pulses à Dming 25 Nov Astronomical Observing Techniques: Adaptive Optics 33

34 Focus Anisoplana<sm The LGS is at finite distance H above the telescope and does not sample all turbulence and not the same column of turbulent atmosphere ( cone effect ): The contribudon to the wavefront error contribudon from focus anisoplanadsm is: 2 σ FA D = d 0 5/3 d 0 ~ λ 6/5 where depends only on wavelength and turbulence profile at the telescope site. H à very large telescopes need muldple LGSs due to this cone effect. 25 Nov Astronomical Observing Techniques: Adaptive Optics 34

35 Ground Layer AO GLAO Useful if ground layer (= ground + dome + mirror seeing) is the dominant component Uses several WFS and guide stars within a large FOV (several arcmin) WFS signals are averaged à control one DM ReducDon of FWHM ~ factor of two (only!) GLAO is thus a "seeing enhancement" technique Advantage: wider fields and shorter wavelengths 25 Nov Astronomical Observing Techniques: Adaptive Optics 35

36 Laser Tomography AO LTAO Uses muldpe laser beacons each laser has its WFS combined informadon is used to opdmize the correcdon by one DM on- axis. reduces the cone effect system performance similar to natural guide star AO but at much higher sky coverage. 25 Nov Astronomical Observing Techniques: Adaptive Optics 36

37 Mul<- Conjugate AO MCAO to overcome anisoplanadsm, the basic limitadon of single guide star AO. MCAO uses muldple NGS or LGS. MCAO controls several DMs each DM is conjugated to a different atmospheric layer at a different aldtude at least one DM is conjugated to the ground layer best approach to larger corrected FOV. 25 Nov Astronomical Observing Techniques: Adaptive Optics 37

38 Side note: MCAO: Performance 25 Nov Astronomical Observing Techniques: Adaptive Optics 38

39 Mul<- Object AO MOAO MOAO provides correcdon not over the endre FOV of several arcmin but only in local areas within several arcmin à muld- object spectroscopy. needs (several) guide stars close to each science target. picks up the WFS light via small "arms inserted in the FOV. each science target has its DM systems work in open loop (!) 25 Nov Astronomical Observing Techniques: Adaptive Optics 39

40 Extreme AO XAO XAO is similar to SCAO high Strehl on- axis and small corrected FOV however, Strehl values in excess of 90% requires many thousands of DM actuators requires minimal opdcal and alignment errors main applicadon: search for exoplanets, SPHERE on VLT 25 Nov Astronomical Observing Techniques: Adaptive Optics 40

41 Student- Built ExPo Adap<ve Op<cs 25 Nov Astronomical Observing Techniques: Adaptive Optics 41

42 MSc Astronomy & Instrumenta<on lectures: Astronomical Telescopes and Instruments DetecDon of Light (renewed) High Contrast Imaging Astronomical Systems Design Project Management opdon to take courses at TU Del{ (not required) opdon for major research thesis in industry 25 Nov Astronomical Observing Techniques: Adaptive Optics 42