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Optical Imaging in Astronomy
1st CASSDA School for ObserversObservatorio del Teide, 20 – 25 April 2015
Franz KneerInstitut für AstrophysikGöttingen
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h
z
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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, …
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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
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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´
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wavefront aberrations for spherical aberration(from Born-Wolf)
spherical aberration near focus
coma (from Born-Wolf)diffraction theory
Δx
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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
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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
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Point Spread Function, PSF, of unobstructed telescope with circular apertureand without aberrations: Airy function
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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)
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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:
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angular (spatial) resolution
high spatial resolution very much required: double stars, galxies, Sun: granular dynamics, small-scale waves, magnetic finestructures, …
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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
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Focussing
Scheiner-Hartmann screen, in simplest form
intra- extra-focal
two unsharp images, measue separation Δy vs. zΔy
z
extra-
intra-focal
x
xx
xx
xx
x
x
F
z
pupil
-Δy
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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 xxx
x x x x x ●●
insert knife edge under 45°
meridionalfocal line
sagittalfocal line
x
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