Optical Design of Giant Telescopes for Space Jim Burge, Erin Sabatke Optical Sciences Center Roger Angel, Neville Woolf Steward Observatory University of Arizona

The need for large telescopes Push back the frontier for astrophysics –We want to study what we can barely detect –We know that increased technology will detect new things Imaging planets around other stars –Requires blocking or nulling the star light Laser projectors for interstellar vehicles –Use light momentum to push the sail for interstellar travel Earth observations from geosynchronous

Telescopes in space Hubble’s telescope Mt. Wilson 100-in 1917 Hubble Space Telescope 1990

Natural evolution to large telescopes Make the primary larger –keep it in the shade –make the f/number faster to limit length –effective optical surface using smaller segments that can be launched and deployed –maintain weight while increasing area –Requires primary mirror with density ~15 kg/m 2 Next Generation Space Telescope m aperture

Optical design issues for NGST Three mirror anastigmat, 10 arc min FOV Fine steering mirror at a pupil –image stabilization limited by field rotation, distortion Fast primary is highly aspheric and difficult to fabricate and test Science Instruments Tertiary mirror Secondary mirror 8-m primary mirror Fine Steering Mirror

Multiple Aperture Systems Increase baseline and collecting area by combining multiple apertures

Terrestrial Planet Finder 100-m array Use nulling (destructive interference) to cancel star light Detect planets and obtain low resolution spectra, looking for familiar atmospheric constituents Special Purpose Very small field of view optimized for exoplanets Solar orbit, benign thermal and gravity environment TPF as free flying array of 3.5-m telescopes Wavelength (µm) Intensity

What about giant telescopes Size is limited by mass from mirror technology NGST mirror technology could get to 5 kg/m 2 For economical launch with existing technology, need mass << 1 kg/m2 50 cm diameter mirror under construction 1 mm thick glass 7 gram actuators 1 kg/m 2 composite support

Ultralight mirrors for space optics Lower mass mirrors require thinner substrates (<< 1 mm) The difficulty is support and control Curved optics intrinsically require shape control Flat optics can be made by simply stretching a thin membrane Error in reflective surface = half of thickness variation

Control for flat membrane mirrors Start with thin, reflective membrane of uniform thickness Hold it in tension from a plane at the perimeter Define the perimeter with multiple points, each one under active control. Reduces shape control to 1 dimension - perimeter Membrane with reflective coating Shape control with actuators at nodes Tension control Rigid frame

Membrane mirror technology Numerous developments underway at University of Arizona (Stamper et al. In Imaging Technology and Telescopes, presented Sunday).

What good are flats? Collect light using diffraction –from Rod Hyde, Livermore –limited bandwidth, contrast Or use an array of flats to approximate a paraboloidal reflector –like solar collectors –downstream optics compensate for non-curvature

Primary made from flat segments

Optical design issues for primary made from flats On axis - easy –make different segments come to focus at the same place with the same path length For field of view - tricky. For each subaperture system, must also –meet sine condition (constant mapping of entrance pupil to exit pupil) –match image scale and distortion –match field curvatures The general solution is to make the effective focal ratio of the primary as long as possible

Telescope with free flying elements Faster telescopes for “conventional” rigid systems Slower designs for telescope with free flying elements

Transition to Membranes F/1 systems F/20 systems Telescope diameter 2.6m 8.0m 14m 25m 100m surface density 150Kg/m 2 16Kg/m 2 5Kg/m 2 1.6Kg/m 2 0.1Kg/m 2 Mass 800Kg 800Kg 800Kg 800Kg 800Kg Moment of Inertia 1 unit , ,000 Rotation period for same thruster expended Rotation period for same reaction wheel use , ,000 Membrane telescopes are for long observations of ultra-faint objects only. General Purpose telescopes should be restricted to rigid mirrors. The length comes at the price of system agility

Truss for large primary mirror (Tom Connors, Steward Observatory)

Optical design and analysis Simulations using Optima (from Lockheed Martin) Test case with several flat mirrors

Analysis of flat mirror telescope On axis PSF OPD 1 arc minute

Pupil mapping and phase errors Mapping distortion of entrance pupil (h) to exit pupil (h’) couples with wavefront tilt to cause phase errors Entrance pupil Exit pupil No distortion From Object To image Phase error in wavefront Wavefront is preserved Wavefront Exit pupil with non-linear mapping Entrance pupil   ’ h h’ Phase from WF ‘tilt’ Ideal mapping Distorted mapping ‘

Definition of “sine condition” Spherical entrance pupil, coordinates of sin(U) Spherical exit pupil, coordinates of sin(U’) Sine condition requires linear mapping of sin(U) -> sin(U’)

Sine condition violation Geometric pupil distortion causes violation of sine condition, which varies with field This causes images to dephase for < 1 arcmin FOV

Optical design summary The design with flat segments works! However, the field of view is limited by the apertures dephasing with field, from the sine condition violation Preliminary results indicate that a 100-m telescope of this type could be made with 6 meter segments 2 km length 7 m secondary (spherical relay) 10 meter corrector (60 cm elements) 0.3 µm rms wavefront errors for 20 arcsec FOV (40 nm rms for 6 arc seconds)

Curving the primary The system works much better if the primary can be curved Electrostatics can be used to do this A two-mirror 100-m telescope can achieve 5 arc minute FOV at f/20 with 2 km length 10 m concave secondary 0.4 µm rms wavefront error The 6 m primary segments have 4 mm sag This has 40 nm rms wavefront error at 1.6 arc minute FOV

Stretched Membrane with Electrostatic Curvature Primary mirrors with membrane reflectors can be made from slightly curved segments (using electrostatics) The moon imaged at Steward Observatory with the first telescope to use a primary mirror of Stretched Membrane with Electrostatic Curvature (SMEC). The silicon nitride membrane was 0.7 um thick and curved to a 3 m focal length by a field of 2 MV/m

What about a strip mirror Simulated performance 100m x 2m HST Slot, 1 exposure NGST Slot 18 exposures (Keith Hege, Steward Observatory)

Truss modeled for strip mirror (Tom Connors, Steward Observatory)

Summary There is no evolutionary path from today’s systems to giant telescopes in space. Launch constraints require low mass, leading to optics made from membranes. Orbital mechanics allows the use of free flying elements and sunshields. Primary mirrors, made from arrays of flat mirrors can provide corrected images. With added weight and complexity, the membranes can be moderately curved, gaining an order of magnitude in field of view.