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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) Page 1 Goals of these 3 lectures 1) To understand the main concepts behind adaptive optics systems 2) To understand how important AO is for a VLT and how indispensible for an ELT 3) To get an idea what is brewing in the AO field and what is store for the future 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 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 Spherical waves and plane waves What is imaging? X X • An imaging system is a system that takes all rays coming so x s i i from a point source so that they cross Mthem M x and redirects a si xo scalled o each other in a single point image point. An optical system that does this is said “stigmatic” Optical path and OPD Plane Wave Index of refraction variations • The optical path length is Distorted Wavefront n( z)dz Z • The optical path difference OPD is the difference between the OPL and a reference OPL • Wavefronts are iso-OPL surfaces Spherical aberration Rays from a spherically aberrated wavefront focus at different planes Through-focus spot diagram for spherical aberration Optical invariant ( = Lagrange invariant) y11 y2 2 Lagrange invariant has important consequences for AO on large telescopes From Don Gavel Fraunhofer diffraction equation (plane wave) Diffraction region Observation region From F. Wildi “Optique Appliquée à l’usage des ingénieurs en microtechnique” Fraunhofer diffraction, continued 1 j (t kR ) U 2 ( x , y ) e U1 ( x, y) exp j kx x ky y ds R aperture can be complex • 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! Looking at the far field (step 1) Looking at the far field (step 2) What is the ‘ideal’ PSF? • The image of a point source through a round aperture and no aberrations is an Airy pattern Details of diffraction from circular aperture and flat wavefront 1) Amplitude First zero at r = 1.22 / D 2) Intensity FWHM /D Imaging through a perfect telescope (circular pupil) With no turbulence, FWHM is diffraction limit of telescope, ~ / D FWHM ~/D Example: 1.22 /D in units of /D Point Spread Function (PSF): intensity profile from point source / D = 0.02 arc sec for = 1 mm, D = 10 m With turbulence, image size gets much larger (typically 0.5 - 2 arc sec) Diffraction pattern from LBT FLAO 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 Define optical transfer function (OTF) • Imaging through any optical system: in intensity units Image = Object Point Spread Function convolved with 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 ) Examples of PSF’s and their Optical Transfer Functions Seeing limited OTF Intensity Seeing limited PSF /D / r0 D/ Diffraction limited OTF Intensity Diffraction limited PSF r0 / -1 /D / r0 r0 / D/ -1 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! Piston Tip-tilt Astigmatism (3rd order) Defocus Trefoil Coma “Ashtray” Spherical Astigmatism (5th order) Units: Radians of phase / (D / r0)5/6 Tip-tilt is single biggest contributor Focus, astigmatism, coma also big Reference: Noll76 High-order terms go on and on….