Optical Imaging in Astronomy

1st CASSDA School for ObserversObservatorio del Teide, 20 – 25 April 2015

Franz KneerInstitut für AstrophysikGöttingen

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z

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, …

Aberrations

Gaussian reference spherespherical 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

Primary (Seidel) aberrations

1st order: defocusFY

Δy´ = Y·Δz´/ff

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 onlyto odd orders on X, Y, and ω, lowest order is 3rd orderSeidel aberrationswavefront aberrations V depend to 4th order or higher

Δz´

wavefront aberrations for spherical aberration(from Born-Wolf)

spherical aberration near focus

coma (from Born-Wolf)diffraction theory

Δx

astigmatism and field curvature (from Born-Wolf) distortions: barrel and pincushion (from Born-Wolf)

Shmidt telescopesi) spherical mirror + stop at z = R→ no preferred direction, no axis→ no aberrations depending on ω remaining: spherical aberration and field curvatureii) correction plate (glas) V = -(1/8)(y4/R3) ; 4th order, difference between sphere and parabolaiii) field curvature: bend detector or use correcting lens

large field of view: 5° … 8°, fast: f ratio 1:3 … 1:5for surveys

Diffraction principles of diffraction

Huygens-Kirchhoff diffraction theorywave equation for disturbance U, e.g. electric vector E, at point P, caused by excitation in P0

solving with boundary conditions, neglectingorders higher than 1 in angles between direct rays(to geometrical image) and diffracted rays → Fraunhofer diffraction

Point Spread Function, PSF, of unobstructed telescope with circular apertureand without aberrations: Airy function

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·I0,

Strehl ratio 0.8: Δz = ±2·λ·N2

examples: λ = 500 nm a) N = 3 (Schmidt telescope) → Δz = 9 μm (II) b) N = 50 (solar telescopes) → Δz = 2.5 mm (II)

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:

angular (spatial) resolution

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

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

Focussing

Scheiner-Hartmann screen, in simplest form

intra- extra-focal

two unsharp images, measue separation Δy vs. zΔy

z

extra-

intra-focal

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F

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pupil

-Δy

Foucault´s knife edge

(from Wikipedia, ArtMechanic)

principle

example: astigmatism

insert knife edge (piece of paper)at various positions along z andunder various angles and look at image of pupil

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x x x x x ●●

insert knife edge under 45°

meridionalfocal line

sagittalfocal line

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