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

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5

10

15

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Instrument/Time

Ap

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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)