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

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 x x 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 a x a MTF 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{ } O S P (“Structure Function”) Aper{ } = Aper { } * Aper{ }

PSF’s from a finite periodic array 6 ring SMT structure function 10 ring SMT structure function Full PSF with 10% gaps (dark bands show subarray diffraction zeros) Full PSF with 0.1% gaps (dark bands show subarray diffraction zeros)

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 with 10% gaps 15 ring hexagonal mirrors without gaps First ring of zeros in hex “Airy” function is circular

Imperfect PSFs, Edge errors 5cm random turned up/down 0.1 wave rms figure error on edge regions Edge error PSF 4 decades, 14.9” No edge errs0.1 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 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 1 m, outer scale 22m 1.1” 400 d.f. AO

AO - Dynamic Range 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 narrow- field studies (requiring spatial and photometric dynamic range)