Some large-telescope design
parameter considerations:
Distributed pupil telescopes
J.R.Kuhn Institute for Astronomy, UH
• How to “distribute the glass” in a generalpurpose telescope
• Diffractive performance
• Mechanical and other issues: The NGCFHT/ HDRT Concept
Larger telescopes
Telescope Progress
22
20
15
10
10
0
'1
2
N
G
C
FH
k
ec
Instrument/Time
T
'9
7
'4
e
al
H
H
oo
ke
r
ke
s
'0
'1
8
7
1.5
0
5.1
2.6
K
5
Y
er
Aperture [m]
25
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
Area, A
overlap integral scales like axa
MTF scales like overlap area
(normalized to total area)
area, a
Sparse aperture
a = a/A
x
x
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)}
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)
Aper{
} = Aper {
PSF{
} = PSF {
} * Aper{
} X PSF{



P(k )  O(k ) S (k )
O  " Airy Function"
 
S   exp(ik  a j )
}
(“Structure Function”)
j

k  2 ( x , y )

O
S
}
P
PSF’s from a finite periodic array
P ( )  S ( )O ( )
P is telescope PSF
S is array structure function
O is subarray diffraction pattern
6 ring SMT
structure function
Full PSF with 0.1% gaps
(dark bands show subarray
diffraction zeros)
10 ring SMT
structure function
Full PSF with 10% gaps
(dark bands show subarray
diffraction zeros)
Angular displacement between S maxima : m  2
3a
Keck PSFs
Extrafocal LRIS image difference
H band AO image, 2 decades, 2.2” FOV
(Circular avg. removed)
[Courtesy M. Liu]
[Courtesy S.Acton, M. Northcott]
Mirrors are imperfect: gaps and
edge errors
15 ring hexagonal mirrors with 15 ring hexagonal mirrors without
10% gaps
gaps
First ring of zeros in hex “Airy” function
is circular
Imperfect PSFs, Edge errors
Edge error PSF
4 decades, 14.9”
5cm random turned up/down
0.1 wave rms figure error on
edge regions
No edge errs
0.1 wave errs
Pupil geometries
Segmented mirror telescope
(SMT) 72x1m
Square off-axis telescope
(SOT) 4x8m
Monolithic mirror telescope
(MMT) 17.4m
Hexagonal off-axis telescope
(HOT) 6x6.5m
22m
Circular or Hexagonal
Subapertures
15 ring circular mirrors in
hexagonal pattern. 4% gaps
Two ring circular mirrors in
hexagonal pattern, a=1.04D
PSF comparisons
X-cut
Y-cut
Circular
average
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
  (0)   (r ) 2
 6.9r / r0 5 / 3
Large phase errors between subapertures: rotational shearing interferometer (Roddier 1991)
High Dynamic Range Telescope
NG-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 narrowfield studies (requiring spatial and
photometric dynamic range)