How to “distribute the glass” in a general-purpose telescope Diffractive performance

1. 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

2. Larger telescopes

3. 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)

4. 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)}

5. Pupil geometry • Sparse aperture suffers s/n degradation by factor of a • Use a pupil geometry that maximizes core image “Strehl”

6. Making bigger mirrors (arrays) Aper{ } = Aper { } * Aper{ } PSF{ } = PSF { } X PSF{ } (“Structure Function”) O S P

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

8. 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]

9. 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

10. Imperfect PSFs, Edge errors No edge errs 0.1 wave errs Edge error PSF 4 decades, 14.9” 5cm random turned up/down 0.1 wave rms figure error on edge regions

11. Pupil geometries Square off-axis telescope (SOT) 4x8m Segmented mirror telescope (SMT) 72x1m Hexagonal off-axis telescope (HOT) 6x6.5m Monolithic mirror telescope (MMT) 17.4m 22m

12. Circular or Hexagonal Subapertures 15 ring circular mirrors in hexagonal pattern. 4% gaps Two ring circular mirrors in hexagonal pattern, a=1.04D

13. PSF comparisons X-cut Y-cut Circular average

14. 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)

15. 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

16. Atmospheric Performance • Fried parameter: 1m at 1m, outer scale 22m 400 d.f. AO 1.1”

17. AO - Dynamic Range Large phase errors between subapertures: rotational shearing interferometer (Roddier 1991)

18. 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

19. HDRT Optics

20. HDRT OSS

21. 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)