1. Optical Imaging in Astronomy 1st CASSDA School for Observers Observatorio del Teide, 20 – 25 April 2015 Franz Kneer Institut für Astrophysik Göttingen

4. h z

5. Gregory telescope (1661): parabolic primary mirror, eliptical secondary mirror → increase of effective focal length → possiblity for field stop ● example of coudé telescope (= bent): beam to focus fixed in space → heavy post-focus instruments, sepctrographs, …

6. Aberrations Gaussian reference sphere spherical wavefront converging from lense (or mirror) to center at image point, radius RK = f → aberration free, `stigmatic´ image point P: in reality, true wavefront W has aberration V, resulting in an aberration Δy´ in image plane

7. Primary (Seidel) aberrations 1st order: defocus F Y Δy´ = Y·Δz´/f f object (star) with principal ray in z – y plane, at angle ω with optical axis; due to rotational symmetry, upon X → -X, Y → -Y, ω → - ω: Δx´ → -Δx´, Δy´ → -Δy´ aberrations Δx´, Δy´ depend only to odd orders on X, Y, and ω, lowest order is 3rd order Seidel aberrations wavefront aberrations V depend to 4th order or higher Δz´Δz´

8. wavefront aberrations for spherical aberration (from Born-Wolf) spherical aberration near focus coma (from Born-Wolf) diffraction theory ΔxΔx

9. astigmatism and field curvature (from Born-Wolf) distortions: barrel and pincushion (from Born-Wolf) Shmidt telescopes i) spherical mirror + stop at z = R → no preferred direction, no axis → no aberrations depending on ω remaining: spherical aberration and field curvature ii) correction plate (glas) V = -(1/8)(y 4 /R 3 ) ; 4th order, difference between sphere and parabola iii) field curvature: bend detector or use correcting lens large field of view: 5° … 8°, fast: f ratio 1:3 … 1:5 for surveys

10. Diffractionprinciples of diffraction Huygens-Kirchhoff diffraction theory wave equation for disturbance U, e.g. electric vector E, at point P, caused by excitation in P 0 solving with boundary conditions, neglecting orders higher than 1 in angles between direct rays (to geometrical image) and diffracted rays → Fraunhofer diffraction

12. Point Spread Function, PSF, of unobstructed telescope with circular aperture and without aberrations: Airy function

13. intensity distribution in focus volume: (also from diffraction theory), → focus tolerance: allowed displacement Δz of detector from position with maximum intensity: where I has dropped to 0.8·I 0, Strehl ratio 0.8: Δz = ±2·λ·N 2 examples: λ = 500 nm a) N = 3 (Schmidt telescope) → Δz = 9 μm (II) b) N = 50 (solar telescopes) → Δz = 2.5 mm (II)

14. Optical Transfer Function – OTF and Modulation Transfer Function – MTF OTF = Fourier transform of PSF, MTF = modulus of OTF, OTF also called Frequency Response Function: how amplitudes at various wavenumbers are modified for aberration free telescope with circular, unobstructed pupil of diameter D:

16. angular (spatial) resolution high spatial resolution very much required: double stars, galxies, Sun: granular dynamics, small-scale waves, magnetic finestructures, …

17. significance of MTF: low-pass filter upper left: numerical simulation of granular convection on the Sun (Beeck & Schüssler, MPS), upper right: same scene seen through a 70cm telescope, lower left: reconstructed, lower right: 1% random noise added and then reconstructed

18. Focussing Scheiner-Hartmann screen, in simplest form intra- extra-focal two unsharp images, measue separation Δy vs. z ΔyΔy z extra- intra-focal x x x x x x x x x F z pupil -Δy-Δy

19. Foucault´s knife edge (from Wikipedia, ArtMechanic) principle example: astigmatism insert knife edge (piece of paper) at various positions along z and under various angles and look at image of pupil

20. x x x x x x x x x x● ● insert knife edge under 45° meridional focal line sagittal focal line x