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Adaptive Optics in the VLT and ELT era

Adaptive Optics in the VLT and ELT era. Optics for AO. François Wildi Observatoire de Genève Credit for most slides : Claire Max (UC Santa Cruz). Goals of these 3 lectures. To understand the main concepts behind adaptive optics systems

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Adaptive Optics in the VLT and ELT era

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  1. Adaptive Optics in the VLT and ELT era Optics for AO François Wildi Observatoire de Genève Credit for most slides : Claire Max (UC Santa Cruz)

  2. Goals of these 3 lectures • To understand the main concepts behind adaptive optics systems • To understand how important AO is for a VLT and how indispensible for an ELT • To get an idea what is brewing in the AO field and what is store for the future

  3. Content Lecture 1 • Reminder of optical concepts (imaging, pupils. Diffraction) • Intro to AO systems Lecture 2 • Optical effect of turbulence • AO systems building blocks • Error budgets Lecture 3 • Sky coverage, Laser guide stars • Wide field AO, Multi-Conjugate Adaptive Optics • Multi-Object Adaptive Optics

  4. Simplest schematic of an AO system BEAMSPLITTER PUPIL WAVEFRONT SENSOR COLLIMATING LENS OR MIRROR FOCUSING LENS OR MIRROR Optical elements are portrayed as transmitting, for simplicity: they may be lenses or mirrors

  5. Spherical waves and plane waves

  6. What is imaging? X X • An imaging system is a system that takes all rays coming from a point source and redirects them so that they cross each other in a single point called image point. An optical system that does this is said “stigmatic”

  7. Optical path and OPD Index of refraction variations Plane Wave Distorted Wavefront • The optical path length is • The optical path difference OPD is the difference between the OPL and a reference OPL • Wavefronts are iso-OPL surfaces

  8. Spherical aberration Rays from a spherically aberrated wavefront focus at different planes Through-focus spot diagram for spherical aberration

  9. Optical invariant ( = Lagrange invariant)

  10. Lagrange invariant has important consequences for AO on large telescopes From Don Gavel

  11. Fraunhofer diffraction equation (plane wave) Diffraction region Observation region From F. Wildi “OptiqueAppliquée à l’usage des ingénieurs en microtechnique”

  12. Fraunhofer diffraction, continued • In the “far field” (Fraunhofer limit) the diffracted field U2 can be computed from the incident field U1 by a phase factor times the Fourier transform of U1 • U1 (x1, y1) is a complex function that contains everything: Pupil shape and wavefront shape (and even wavefront amplitude) • A simple lens can make this far field a lot closer!

  13. Lookingat the far field (step 1)

  14. Lookingat the far field (step 2)

  15. Whatis the ‘ideal’ PSF? • The image of a point source through a round aperture and no aberrations is an Airy pattern

  16. Details of diffraction from circular aperture and flat wavefront 1) Amplitude 2) Intensity First zero at r = 1.22  / D FWHM  / D

  17. Imaging through a perfect telescope (circular pupil) With no turbulence, FWHM is diffraction limit of telescope,  ~l / D Example: l / D = 0.02 arc sec for l = 1 mm, D = 10 m With turbulence, image size gets much larger (typically 0.5 - 2 arc sec) FWHM ~l/D 1.22 l/D in units of l/D Point Spread Function (PSF): intensity profile from point source

  18. Diffraction pattern from LBT FLAO

  19. The Airy pattern as an impulse response • The Airy pattern is the impulse response of the optical system • A Fourier transform of the response will give the transfer function of the optical system • In optics this transfer function is called the Optical Transfer Function (OTF) • It is used to evaluate the response of the system in terms of spatial frequencies

  20. Define optical transfer function (OTF) • Imaging through any optical system: in intensity units Image = Object  Point Spread Function I ( r ) = O PSF  dx O( x - r ) PSF( x ) • Take Fourier Transform: F( I ) = F (O )F( PSF ) • Optical Transfer Function is the Fourier Transform of PSF: OTF = F( PSF ) convolved with

  21. Examples of PSF’s and their Optical Transfer Functions Seeing limited OTF Seeing limited PSF Intensity -1  l / D l / r0 r0 / l D / l Diffraction limited PSF Diffraction limited OTF Intensity -1  l / r0 l / D D / l r0 / l

  22. Zernike Polynomials • Convenient basis set for expressing wavefront aberrations over a circular pupil • Zernike polynomials are orthogonal to each other • A few different ways to normalize – always check definitions!

  23. Piston Tip-tilt

  24. Astigmatism (3rd order) Defocus

  25. Trefoil Coma

  26. “Ashtray” Spherical Astigmatism (5th order)

  27. Tip-tilt is single biggest contributor Focus, astigmatism, coma also big High-order terms go on and on…. Units: Radians of phase / (D / r0)5/6 Reference: Noll76

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