Some large-telescope design parameter considerations: Distributed pupil telescopes J.R.Kuhn...
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Transcript of Some large-telescope design parameter considerations: Distributed pupil telescopes J.R.Kuhn...
Some large-telescope design parameter considerations:
Distributed pupil telescopes
J.R.Kuhn Institute for Astronomy, UH
• How to “distribute the glass” in a general-purpose telescope
• Diffractive performance
• Mechanical and other issues: The NG-CFHT/ HDRT Concept
Larger telescopes
Telescope Progress
1.5 2.65.1
10
22
0
5
10
15
20
25
Instrument/Time
Ap
ertu
re [
m]
How Sparse? General Concerns• Consider SNR of an image in the spatial
frequency domain. a is “sparseness” -- fraction of filled aperture area. – “interferometers”: small a– “telescopes”: a approaches 1
• Image signal scales as MTF. (general telescope imaging argues against using “special” symmetries to solve the imaging problem with a sparse telescope)
MTF
Sparse aperture a = a/A
Area, A
area, a
xx
MTF MTF a
In general, normalized MTF of sparse array is smaller by factor of a:
Image S/N at mid-frequencies is lower by factor of a than filled array
{See Fienup, SPIE, 4091, 43 (2000)}
overlap integral scales like axaMTF scales like overlap area (normalized to total area)
Pupil geometry
• Sparse aperture suffers s/n degradation by factor of a
• Use a pupil geometry that maximizes core image “Strehl”
Making bigger mirrors (arrays)
PSF{ } = PSF { } X PSF{ }
),(2
)exp(
Function"Airy "
)()()(
yx
jj
k
akiS
O
kSkOkP
O S P
(“Structure Function”)
Aper{ } = Aper { } * Aper{ }
PSF’s from a finite periodic array
patternn diffractiosubarray is O
function structurearray is S
PSF telescopeis P
)()()( OSP
6 ring SMT structure function
10 ring SMTstructure function
Full PSF with 10% gaps(dark bands show subarraydiffraction zeros)
Full PSF with 0.1% gaps(dark bands show subarraydiffraction zeros)
a32 :maxima Sbetween nt displacemeAngular m
Keck PSFs
H band AO image, 2 decades, 2.2” FOV
(Circular avg. removed)
Extrafocal LRIS image difference
[Courtesy S.Acton, M. Northcott]
[Courtesy M. Liu]
Mirrors are imperfect: gaps and edge errors
15 ring hexagonal mirrors with10% gaps
15 ring hexagonal mirrors withoutgaps
First ring of zeros in hex “Airy” functionis circular
Imperfect PSFs, Edge errors
5cm random turned up/down0.1 wave rms figure error on edge regions
Edge error PSF4 decades, 14.9”
No edge errs 0.1 wave errs
Pupil geometries
Hexagonal off-axis telescope(HOT) 6x6.5m
Square off-axis telescope(SOT) 4x8m
Monolithic mirror telescope(MMT) 17.4m
Segmented mirror telescope(SMT) 72x1m
22m
Circular or Hexagonal Subapertures
15 ring circular mirrors in hexagonal pattern. 4% gaps
Two ring circular mirrors inhexagonal pattern, a=1.04D
PSF comparisons
X-cut
Y-cut
Circularaverage
Hexagonal close-packed
• Perfect mirrors (no edge errors) hexagonal circular mirrors have a PSF which is marginally different from hexagonal mirrors
• Perfect large or small mirrors show marginal PSF differences for small (<1% gaps)
Large vs. Small Mirrors
• Edge to area ratio increases with number of mirror segments, N, at fixed total area
• Expect mirror Strehl to decrease linearly with N if mirror edge wavefront errors are important (and this is unlikely to be corrected with the AO system)
• Mechanical complexity cost: expect required MTBF of mirror actuators to increase linearly with N
Atmospheric Performance
• Fried parameter: 1m at 1m, outer scale 22m
1.1” 400 d.f. AO
AO - Dynamic Range 3/5
02 /9.6)()0( rrr
Large phase errors between subapertures: rotational shearing interferometer (Roddier 1991)
High Dynamic Range TelescopeNG-CFHT Concept
– Minimal sparse, a>0.5, maximize PSF core energy, hexagonal circular subapertures
– Maximize area/edge ratio– Minimize “complexity” costs for mirror support– With ay0.5 versatile optical mechanical bench
support structure is possible• primary defines pupil without obstruction
• wide and narrow-field modes natural
• secondary optics can be small (e.g. M2 diameter 20cm)
– Adaptive optics technology is believable
HDRT Optics
HDRT OSS
HDRT
• A flexible, general purpose, 22+ m telescope
• Diffraction limited over > 10”x10”
• Seeing limited over > 1x1 (3x3) deg
• The optical bench concept is a modular use of technology available now
• A qualitative advance in wide- and narrow-field studies (requiring spatial and photometric dynamic range)