Adaptive Optics and OIR Interferometry

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1 Outline and OIR Interferometry Astro 6525 Fall 2015 November Wavefront Sensing Control Systems Error Terms and Limitations Laser Guide Stars GLAO/MCAO/MOAO 2 Optical vs Radio Telescopes Fraunhofer Diffraction S is a diffraction aperture The illumination is spatially coherent (c.f. spatially incoherent vc-z theorem) The math is (more or less) the same. Result is the complex amplitude of the far field diffraction is the 2D fourier transform of the aperture U (x, y) / ZZ A(, )e ik(x +y ) y P1 h 1K k h 30, 000K k d d O S R1 x R O0 d R2 P2 4 Before I die, I hope someone would explain quantum mechanics to me. After I die, I hope God will explain turbulence to me. Greater whorls have lesser whorls, which feed on their velocity. And lesser whorls have smaller whorls, and so on to viscosity. L.F. Richardson W. Heisenberg 5 6 Animation Credit: Stanford Center for Research

2 The Kolmogorov turbulence model, derived from dimensional analysis Kolmogorov turbulence, cartoon solar Outer scale L0 Inner scale l 0 hν v = velocity, ε = energy dissipation rate per unit mass, ν = viscosity, l0 = inner scale, l = local spatial scale Energy/mass = v2/2 v2 Wind shear convection Energy dissipation rate per unit mass ε ~ v2/τ = v2 / ( l / v) = v3 / l v ~ ( ε l )1/3 Energy v2 ~ ε 2/3 l 2/3 hν ground Page 26 Page Kolmogorov Power Spectrum 1-D power spectrum of velocity fluctuations: k = 2π / l 5NDISTURBED 7IND &LOW Φ(k) Δk v2 ε 2/3 k 2/3 or, dividing by k, Φ(k) k 5/3 (one dimension) 3-D power spectrum: use fact that Φ3D(k) = - (dφ/dk)/2πk Observatory on First Mountain Ridge Φ3D(k) k 11/3 (3 dimensions) For rigorous calculation: see V. I. Tatarski, 1961, Wave Propagation in a Turbulent Medium, McGraw-Hill, NY Page 30 Ocean Optical turbulence profiling using Stereo SCIDAR Figure 5.1: Schematic of turbulence generation in the wake of obstacles. Most worldclass observatories are located on the first mountain ridge near the coast (or on mountains on islands), with prevailing winds from the ocean. 9 9 Michelson Summer School Proceedings 10 in a Stratified Atmosphere SCIDAR Figure 8. Example turbulence profile from the JKT, La Palma, 15th September The upper plot shows the profile of the optical turbulence as a function of time. The lower plot is the same but with the layer wind velocities overlaid. The length of the arrows denote the relative wind speed and the direction corresponds to the turbulent layer direction as defined by the cardinal directions shown in the top right of the lower plot. The conjugate altitude of the analysis plane was set to 0 m. Shepherd et al 2013 (arxiv: ) 12 (a) (b) (c) (d) (e) Figure 9. Spatio temporal cross covariance functions for the data taken at a conjugate altitude of -2 km (intensity scale inverted for clarity). The plots show cross covariance functions generated with temporal delays equal to 1 frame ( 10 ms) from -2 frames (a) to +2 frames (e). The case of no temporal delay is shown in (c). By examining the position of these peaks in subsequent frames the wind velocity (magnitude and direction) can be calculated.

3 Physics of Physics of 7ARM #OLD IR DIABATIC TMOSPHERE -ECHANICAL -ECHANICAL /PTICAL.O /PTICAL Physics of Meterologist s Altitude References: Quirrenbach, Michelson Summer School Principles of Long Baseline Interferometry coursenotes.html AFGL Tech Report: Dewan et. al. A Model for Cn2 (Optical ) Profiles Using Radiosonde Data ; Tatarski The effects of the turbulent atmosphere on wave propagation ; Sasiela Electromagnetic Wave Propagation in : Evaluation and Application of Mellin Transforms Meterologist s Latitude 17 B. Geerts & E. Linacre

4 Marechal Approximation (Ruze) Think Fourier Components S e 2 Fringe Herding σ2 << 1 σ2 >> 1 Marechal Approximation Mauna Kea, H band (1.6 µm) Marechal Approximation Mauna Kea, V band (0.5 µm)

5 Lick adaptive optics system at 3m Shane Telescope DM Wavefront sensor Real Data Off-axis parabola mirror Strehl Gain Lick AO System IRCAL infrared camera

6 Deformable Mirrors (Wavefront Corrector) Elements of an adaptive optics system Most common is PZT stack + facesheet Also: MEMS Segmented Membrane Bimorph Ferrofluid Iris AO, Inc. Liquid Crystal Rigid High-Quality Mirror Segment Bondsites Actuator Platform Electrodes Temperature Insensitive Bimorph Flexure Figure 2. Schematic diagram of a deformable mirror (DM) segment. Segments are tiled into an array to form the DM. The rigid mirror segment is bonded to the actuator platform. This hybrid structure enables many different coatings and maintains excellent optical quality over large temperature ranges. A factory calibrated piston/tip/tilt controller places voltages on the electrodes based on the desired piston/tip/tilt positions or Zernike representation DM Specification Details Stroke: 5 m, 8 m Piston/tip/tilt positioning with calibrated controller enables linear position control Driver: Factory calibrated Smart Driver II drive electronics Update Rate: 3kHz (6-8 khz April 2010) Segment Size and Gap: 700 m vertex to vertex (350 µm on a side) Segment Pitch: µm center-to-center segment pitch Response Time [20%-80%]: < 150 µs Fill Factor: > 98% (6 m gaps between segments) Closed-Loop Resolution: > 12 bit Coupling Coefficient: 0% because of segmentation Segment Surface Quality: < 30 nm rms max, < 20 nm rms typical How to reconstruct wavefront from measurements of local tilt Wavefront Sensing Designs outside the scope of these specifications are possible (e.g. more Except for heterodyne, don t measure phase directly Many solutions, most come from optical metrology heritage Slope sensors Standard Optical Coatings: Gold, protected aluminum Optional Optical Coatings: Dielectric, protected silver Wavelength of Operation: Visible - IR White-light Operation: Yes Hysteresis: < 0.1% Actuator Drive Voltage: < 200V Actuator Drive Current: < 1 A Operating Temperature Range: 5 C f 70 C o -40 C f 85 C by request Mirror-Segment-Warp Temperature Dependence: <1 nm PV/ C Laser Power Handling: ~100 W/cm2 with 532 nm segments, faster response times, different coatings) but will require Iris AO, Inc. custom fabrication runs. Please contact Iris AO to discuss Bancroft Way, Berkeley, CA 94704, Phone: (510) , Fax: (510) , Rev A.8 Page 2 of 4 January 2010 Shack-Hartmann Pyramid Curvature... Interferometers Shearing interferometer Point diffraction interferometer Shack-Hartmann wavefront sensor concept measure subaperture tilts Curvature wavefront sensing f F. Roddier, Applied Optics, 27, , 1998 More intense CCD 35 Less intense CCD Normal derivative at boundary Laplacian (curvature) 36

7 Control System Control Matrix in general operates as a closed loop control 37 Control Matrix example: Waffle Wavefront sensor measurements: W M Deformable Mirror Commands Control Matrix M = CW Interaction Matrix W = AM Control Matrix vs Interaction Matrix A 1 W = (A 1 A)M = M C=A 1 Note: matrix inversion is usually approximate, and has singular values Simulations of Waffle Fried sensor/actuator geometry Control system stability 41 42