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Optical Imaging in Astronomy
1st CASSDA School for Observers
Observatorio del Teide, 20 – 25 April 2015
Franz Kneer
Institut für Astrophysik
Göttingen
z
h
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 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
Primary (Seidel) aberrations
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
Y
F
Δz´
1st order: defocus
f
Δy´ = Y·Δz´/f
spherical aberration near focus
wavefront aberrations for spherical aberration
(from Born-Wolf)
coma (from Born-Wolf)
diffraction theory
Δx
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)(y4/R3) ; 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
Diffraction
principles of diffraction
Huygens-Kirchhoff diffraction theory
wave equation for disturbance U, e.g. electric vector
E, at point P, caused by excitation in P0
solving with boundary conditions, neglecting
orders 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 aperture
and 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
pupil
intra-
extra-focal
z
x
Δy
two unsharp images,
measue separation Δy vs. z
x
x
F
x
x
extra-
z
x
intra-focal
-Δy
x
x
x
principle
Foucault´s knife edge
example: astigmatism
(from Wikipedia, ArtMechanic)
insert knife edge (piece of paper)
at various positions along z and
under various angles and look at
image of pupil
meridional
focal line
x
sagittal
focal line
x
x
x
x
x
x
●
x
x
x
insert knife edge under 45°
x●