Performance of Adaptive Optics Systems

Transcription

1 Performance of Adaptive Optics Systems Don Gavel UCSC Center for Adaptive Optics Summer School August, 2009 CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

2 Outline Performance Measures Design / error budgeting AO error contributors AO system simulation Performance analysis Examples from real systems CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

3 Performance measures Wavefront error Strehl Ratio CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

4 Lick 3m Telescope Keck 10m Telescope Strehl ratio CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

5 The Strehl is related to the wavefront variance through Marechal s approximation S = ( ) PSF 0,0 ( ) PSF 0,0 { } 2 exp σ ϕ ϕ = 0 Valid approximation for small Extended region of validity for AO-corrected wavefronts Caveat on using the Marechal approximation (next slide) Strehl Ratio 80 dof 300 dof CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

6 Marechal s condition wavefront surface focus If wavefront phase is contained within confocal spheres λ/2 apart everywhere where the intensity is significant The waves will add up at the focus Consequence of Fermat s principle Δx < λ/2 CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

7 Resolution The Rayleigh criterion: in a diffraction-limited optical system, two point sources are separately distinguishable at a separation ~λ/d In AO systems with a Strehl > 0.15, the FWHM of the corrected image is ~λ/d F. Rodier introduced the concept of Strehl-resolution = width you have to enclose to get the same energy as in the FHWM of the ideal PSF CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

8 Image contrast Contrast = ratio of halo to core surface brightness Integration time required to detect a faint object in the halo is proportional to (contrast) -2 Keck AO example at λ=2µ Contrast Ratio uncorrected Distance from the primary star, arcseconds CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

9 Energy in a spectrograph slit D.L. unc The SNR-optimal slit-width transitions to λ/d when the Strehl gets > 0.1 CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

10 Additional measures Field performance PSF stability CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

11 Field Performance of Multi-conjugate AO 7 layer model atmosphere with r 0 = 15.6 cm and θ 0 = 3.1 arcsec DM at 0 km DMs at 0,10 km DMs at 0,5,10 km CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

12 AO system error contributors Fitting error (DM) Control error (sample rate) Measurement error (Hartmann sensor) Isoplanatic error (field angle) Calibration error Laser guide-star specfic errors: cone effect, guide-star elongation To some approximation, we can add these terms in quadrature CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

13 DM fitting error d The DM corrects the wavefront up to a spatial frequency of 1/(actuator spacing) 2 σ DM = S ϕ ( k)f DM ( kd)d 2 k P Example spatial filtering function Kolmogorov turbulence CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

14 DM fitting error Influence Function Spatial Frequency Response z DM ( x ) F ( kd ) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

15 The fitting error coefficient, µ, depends on the type of deformable mirror Segmented mirror d Square segment, µ=0.174 d Hexagonal segment, µ=0.116 Continuous face sheet DM: µ=0.3 Segmented mirrors requre 3 (piston, tip, tilt) actuators per segment Rewriting the fitting error in terms of number of actuators, N a shows its more economical to use a continuous mirror: CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

16 Control bandwidth error The control loop corrects the wavefront up to a temporal frequency of Example temporal filtering function Greenwood frequency - depends on wind velocity, r0, etc., but simply defined here as the control frequency where the bandwidth term=1 radian 2 CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

17 Wavefront measurement error Reconstructor noise propagator Control loop averaging factor Spot-size factor (units: angle on the sky) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

18 Isoplanatic error If the guide star is not the science object... Light from science object Light from guide star Turbulent layer h Isoplanatic angle: CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

19 Anisoplanatic error can be controlled by MCAO DM at 0 km DMs at 0,10 km DMs at 0,5,10 km Residual error is the generalized anisoplanatism = (θ/θ m ) 5/3 (Tokovinin&LeLouarn, 2000) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

20 Laser guidestar specific errors Cone effect Laser Guidestar at finite altitude Z h e.g. h=4 km, r 0 =10cm => d 0 =4.5m CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

21 The laser guide star has a larger apparent size than a natural star The wavefront measurement error is increased accordingly Lick laser data, from Nov CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

22 Natural star Laser guide star CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

23 Optimizing the error budget In the design, select d (subaperture size =~ DM actuator spacing) to trade between DM fitting term and measurement term. This will set the NGS limiting magnitude, or sky coverage. It will also set the optimized wavelength of the AO system: λ:r 0 (λ)=d. For a laser guide star system, trade measurement error for laser power. Select the optimum d for the predicted LGS brightness. Brighter lasers (and more actuators) get to shorter wavelengths. On-line tuning: Select a frame rate that will best trade off measurement and bandwidth terms Select a natural guide star to trade off brightness (measuement error) for field angle (isoplanatic error) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

24 Optimizing the error budget Rms wavefront error, nm Simultaneous Solution 90 Subaperture size, d σ ϕ d = 0 increasing brightness Guide star magnitude, m v Contoller bandwidth, f c Subaperture size, d CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

25 Optimum contoller bandwidth, f c Guide star magnitude, m v CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

26 Simulating an AO system Heirarchy of modeling Scaling laws Analytic models (usually working in transform space) Monte-carlo wave-optic simulation Tools: Kolmogorov screen generator Wavefront propagation code DM model, WFS model Imaging model CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

27 Monte-carlo Simulation of an AO system Generate a guide star Near-field propagation Generate a phase screen, add to wavefront s phase wind Continue to propagate Generate another phase screen, add to wavefront s phase... Multiply by the aperture function Subtract the DM s phase Telescope Deformable Mirror Apply the DM actuator response model Actuators Science Camera Run through the WFS model Wavefront Sensor Controller Image residual wavefront Run through the controller model CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

28 Gathering performance data on a real AO system Telemetry: Wavefront sensor data (slopes, intensities) > controller s rejection curve, bandwidth error term, measurement error term DM actuator commands > simutaneous r 0 Image data: Open loop > r 0 Closed loop > Strehl CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

29 Error Budget Summary Key Terms in an Astronomical AO Error Budget CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

30 Lick AO System: On-line Performance Analysis The spreadsheet errorbudget.xls can help diagnose the sources of Strel loss and aid with on-line AO system parameter adjustments Other on-line metrics at the operator interface, based on AO system telemetry data analysis: Seeing r 0 Wind velocity Temporal power spectrum of turbulence Control loop rejection curves wind clearing time scale k -8/3 spectrum noise floor CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

31 Subaperture intensities Raw Hartmann images Control params Frame rate Control matrix Hartmann slopes Lick AO Telemetry Data Analysis Pipeline Average over illuminated subaps Verify proper background subtraction & photometry Measure Hartmann spot size of internal source Generate phase spectra Determine sensor noise Frame rate Determine guidestar intensity Compute the compensator function Generate controller rejection curve Electronic loop gain Fit effective loop gain Account for sensor noise in phase spectra Determine SNR Derive Hartmann spot size Compute noise averaging factor Determine wavefront measurement error Calculate integrated temporal power rejection σ SNR σ BW Actuator voltages Open-loop images Generate tilt spectra Pre-calibrate rms actuator voltage to micron ratio Calculate rms phase correction by DM Account for tilt in phase spectra Determine r0 from rms phase correction Calculate Greenwood frequency Calculate fitting error Compare to Greenwood model Actuator spacing σ DM CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

32 Modeling the effect of noise in closed loop atmosphere + To science image noise, in WFS units + H K H ol (f) Wavefront sensor + K Telemtery post-analysis Reconstructed phase residual-estimates atmosphere + equivalent noise, in phase units To science image Wavefront sensor / reconstructor + + H K H ol (f) HK = I Reconstructed phase residual-estimates CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

33 Correcting the closed loop residual phase spectrum for the effects of noise e n φ H OL φ DM Closed-loop transfer function: low-pass Correction transfer function: high-pass [ ] 2 2 S e = S e ˆ H cor H cl CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

34 ============================================= Lick 3m error budget /duck5/lickdata/sep00/lgs6data/sep08/cent_07 Saturday 09/09/00 23:03:44 PDT Fitting Error (sigmadm) nm d = cm r0hv = cm Servo Error (sigma_bw) nm fc = Hz fghv = Hz fs = 500 Hz Measurement Error (sigma2phase) nm SNR = control loop averaging factor = spotsizefactor = arcsec TOTAL: nm ============================================= CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

35 ============================================= Lick 3m error budget /duck5/lickdata/may00/lgs6/may21/cent_03 5/22/00, 5:09 UT Fitting Error (sigmadm) nm d = cm r0hv = cm Servo Error (sigma_bw) nm fc = Hz fghv = Hz fs = Hz Measurement Error (sigma2phase) nm SNR = control loop averaging factor = spotsizefactor = arcsec TOTAL: nm ============================================= CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

36 Lick seeing statistics D. Gavel, E. Gates, C. Max, S. Olivier, B. Bauman, D. Pennington, B. Macintosh, J. Patience, C. Brown, P. Danforth, R. Hurd, S. Severson, J. Lloyd, Recent Science and Engineering Results with the Laser Guidestar Adaptive Optics System at Lick Observatory, Proc SPIE, 4839, pp (2003). CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

37 Lick AO System: performance statistics CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

38 Lick AO System: performance statistics CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

39 Adaptive Optics Performance How to measure it from focal plane images? Conventional approach is using the Strehl Ratio. where both are normalised to the same volume Exactly how best to measure Strehl is currently being investigated. This depends upon generating the perfect PSF; the presence of additive noise (detector and photon); image plane sampling; the effects of incorrect bias subtraction and flat-fielding, finding the actual peaklocation etc. CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

40 Measuring Image Quality Other Approaches besides Strehl Ratio Image Sharpness (originally described by Muller and Buffington, 1974) S 1 - Size of PSF Advantage independent of knowing peak location and value. - Can be applied to extended sources. Disadvantage The numerator is contaminated by an additive noise term n 2. S 3 - Normalised peak value directly related to Strehl Ratio Disadvantage sensitive to measurement of peak location and value. Advantage No noise bias CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

41 Synthetic Data 1. Palomar pupil geometry: primary mirror diameter of 4.88m and a central obscuration of 1.8m. No secondary supports modelled. 2. H-band (1.65 microns) with different levels of AO correction. Ideal PSF CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

42 Adaptive Optics Performance - Sharpness Sharpness criteria compared with residual wavefront error from the simulations. S 1 has a steeper slope for smaller rms phases. S nm -1 S nm -1 (nm) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

43 Adaptive Optics Performance - Sharpness Relationship between S 1, S 3 and the Strehl Ratio. S 1 and S 3 values generated from noise-free simulations as part of the CfAO Strehl study. Both S 1 and S 3 are normalised to those of the ideal PSF. The effect of constant noise is shown on S 1. CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

44 Measured Point Spread Function Ideal PSF Variation in NGS PSF quality from the Lick AO system (all at 2 microns) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

45 Adaptive Optics Performance - Sharpness Sharpness (normalised S 1 ) compared with Strehl ratio for NGS Lick AO data. Data obtained with different SNR, observing conditions, nights. Dashed line obtained hueristically from the noiseless simulations.. Departure from simulations could be due to either overestimating S 1 (e.g. presence of noise) or underestimating Strehl ratio (not accurately locating the peak). Further analysis on noisy simulations needed. Accuracy of system performance measurements can be obtained from SR and S 1. CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

46 Binary Star Measurements Science Targets - Basic Astronomy; stellar classification; stellar motion orbits AO Performance - Isoplanatic Issues on-axis vs. off-axis performance - Isoplanatic angle - θ o Analysis Performance - Measurement of Photometry and Astrometry Lick Observatory Data - NGS - 0.5" Separations 12" CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

47 Binary Star Measurements Lick NGS Data σ CrB µ Cas ι Cas 7" 1" 0.5"-7" γ Del WDS Oph 9" 12" 5" CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

48 Anisoplanatism via Strehl Ratio Binary stars permit direct measurement of anisoplanatism by comparing the PSFs. An effective measure of anisoplanatism is the fall off of the Strehl ratio of the off-axis source compared to the on-axis source. where θ is the binary separation CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

49 Anisoplanatism via Strehl Ratio γ Del (sep = 9.22 arcseconds) ratio = 0.76 ± 0.04 θ o = 20.1" ± 2.1" CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

50 Anisoplanatism via Strehl Ratio 70 Oph (sep = 4.79 arcseconds) ratio = 0.84 ± 0.04 θ o = 14.3" ± 2.5" CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

51 Anisoplanatism via Strehl Ratio Summary of Binary Strehl Ratio Measurements Strehl ratio changes vary similarly for both components. Strehl ratio is quite variable for a set of observations ( seconds - minutes) up to changes of 20%. Differential Strehl ratio also varies relative position on the detector? Isoplanatic angle (as determined from differential Strehl ratio) also varies with 15" θ o 30" with some results implying minutes! CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

52 Binary Star Measurements Analysis Techniques - Iterative Blind (myopic) deconvolution (Christou-CfAO) - Parametric Blind Deconvolution (PSF Modelling) (Drummond- AFRL) Astrometry and Photometry (on following pages) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

53 Binary Star Measurements Summary of Astrometry and Photometry Astrometry between the two techniques shows good agreement ( 0.001") Differential Photometry is in general good agreement ( 0.02 mag) with a few exceptions. - σ CrB (ΔJ = 0.5) - µ Cas (ΔJ = 0.4; ΔBrγ = 0.2) - ι Cas Aa (ΔJ = 0.2; ΔK s = 0.2) - ι Cas Ac (ΔH = 0.15) Christou, J.C., Drummond, J.D., Measurements of Binary Stars, Including Two New Discoveries, with the Lick Observatory Adaptive Optics System, The Astronomical Journal, Volume 131, Issue 6, pp CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

54 High Speed PSF Measurements Data sets obtained at Lick almost monthly between July 2005 and Feb IRCAL fastsub mode ( freeze images) - t exp = 22ms and 57ms - Duty cycle ~ t exp + 30ms field size of arcseconds (64 64 pixels) Target objects: m v ~ 6-8 Typically 10 sets of data each of 1000 frames total frames CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

55 Long Term PSF Stability Ideal PSF Fiber 1 (Sep-2005) Fiber 2 (Oct-2005) 12-Oct-2005 Reference Change 18-Aug Aug Jul Jul Aug Aug Aug-2004 CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

56 17 Sep 2005 Lick AO Fiber Source 13 Oct Nov % 80% 78% Stable structure in atmospheric-free PSF Strehl Ratios typically 75% -- 82% CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

57 PSF Structure Fiber Source no better than ~ 80% Strehl ratio. What s the best we can do %? Strong high-order Residual Aberration limiting performance. Relatively stable over minutes hours days months years! No significant change with change of DM references Where is this from? DM flatness Unsensed aberrations in main path Non-common path errors Incorrect SH References Obtain Wavefront map from Phase Retrieval/Diversity measurements. Typically the image is sharpened on the sky Relative peak value metric - other metrics e.g. S 1 First 10 Zernike terms and increasing to 20. Use mirror modes? Important to understand for PSF Reconstruction algorithms. We can deal with the atmosphere but can we deal with the system? CfAO Summer Gavel, AO Performance, Aug. School on Adaptive 2009 Optics 57

58 Lick NGS Strehl Stability (10000 frames 22-57ms/frame) CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug Christou (UCSC), Gladysz (NUI)

59 Strehl Ratio Distributions Distribution of Strehl ratios (for relative stable performance) all show a similar non-gaussian behaviour. CfAO Summer Similar distributions seen Gavel, in AO data Performance, from Palomar, Aug. Keck and AEOS 59 School on Adaptive 2009 Optics

60 PDF Models CfAO Summer School on Adaptive Optics x = S x = 100 / (100 - S) x = ln(100 - S) Gavel, AO Performance, Aug

61 PDF Models Implication is that the instantaneous Strehl ratio has an underlying Gaussian distribution: of r 0! Using Hudgin and Marachel approximations produces a distribution of Strehl ratios similar to that measured, i.e. skewed to a low Strehl ratio tail. Need to obtain simultaneous r 0 and S measurements. CfAO Summer School on Adaptive Optics Speckle noise dominating. Gavel, AO Performance, Aug

62 PSF Calibration and Quantitative Analysis The complicated nature of the AO PSF makes quantitative analysis problematic. How well does deconvolution preserve astrometry and photometry? i Cas CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

63 Separation of the components of σ CrB Sub-pixel peaks located by Fourier interpolation o Six separate measurements of a binary star on different days on different positions on the IRCAL detector. o Separation depends upon location on detector o Precision for each location ~ 2 mas (= 0.03 pixels = 1.5% λ/d) o Separation dispersion ~ 50 mas CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

64 Julian C. Christou, Austin Roorda, and David R. Williams, Deconvolution of adaptive optics retinal images, J. Opt. Soc. Gavel, Am. A AO 21, Performance, Aug (2004) CfAO Summer School on Adaptive Optics 64

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74 Deconvolution of final images, using data from the wavefront sensing Image PSF Object Noise = + Fourier Transform: Then (in the Fourier domain): Then solve for object F 0 CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug

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86 Summary conclusion AO Performance Measurement AO performance-hitters (intro to error budget) AO modeling and simulation AO performance metrics Sharpness and anisoplanatism measures from the AO corrected science image Spectral analysis of telemetry from the AO system (wavefront sensor and deformable mirror signals) Astronomical AO data analysis Vision science AO data analysis CfAO Summer School on Adaptive Optics Gavel, AO Performance, Aug