Periscope Configuration Detector X Z Periscope Module

Mirror Parameters Active area is 30cm long x 2, 10 or 30cm wide. Reflecting surface 30 cm TBD Active area is 30cm long x 2, 10 or 30cm wide. Surface figure requirement: l/400 rms (at 633nm) --Mounted Mirror mass must be minimized Geometry TBD

Mirror Module Coordinate System Mirror Control: X – linear Roll about LOS Pitch LOS X Roll Z=LOS Y Pitch Yaw Fixed Mirrors Module Control: Yaw Pitch Roll about LOS To Detector

Mirror Geometry and Figure Mirror geometry must: Meet the surface figure requirement 1g release Operating temperature range Thermal gradient Mount distortions Have minimum mass Accommodate mount and mechanisms Survive launch and environment extremes

First Order Wavefront Error Budget Error Budget for /400 RMS Mirror Mount All values given in RMS wavefront error  = 6328Å Thermal gradient .0011 Jitter .0006 Mount interface surface finish .0003 Mirror blank surface figure .0013 Stability .0013 Assembly (neglected) Surface distortion due to gravity .0004 Manufacturing .0013 Test .0013 Alignment .0013 Motion due to gravity (neglected) Reflective coating .0009 Bolt preload .0002 Adhesive strain .0002 Bulk temp (5°C) .0005 1g sag .0004 Total RMS error .0025

Initial Geometries considered: Rectangular, held from back Various lightweighting patterns/pockets cut from back Single Arch Various thicknesses Double arch over length on backside Lightweighting pockets in back of main rib Z X Y

First Order FEM results of different geometries for 1m long mirror Geometry: 1m L x 5cm W Surface Deflection (nm) 1g (z) 1g (y) 1g (x) 1C Bolt preload 30% Weight-relieved rectangle (1.3Kg) 5cm tall 1569.7 1143.5 156.2 437.4 1038.9 Solid single arch 1.8 cm tall (1.04Kg) 807.5 1188.7 252.4 770.4 1037.3 5 cm tall 102.9 2659.4 114.9 269.0 974.6 Single arch w/ double arch along length 131.0 2354.8 179.5 387.1 1043.2

Attempted Wavefront Analysis Solid single arch, 5cm tall 3 posts on back side 1 wave = 633nm, Tilt and piston removed % data points w/ fit error > .010 waves Wavefront using surface of actual data points Wavefront using Zernike polynomial surface/grid points # pts PV rms Bolt preload 76.9 1610 .005 .004 87 .170 .054 1g (x) 88.7 .469 .091 .047 .013 1g (y) 92.7 .673 .097 3.065 1.073 1g (z) 97.5 .315 .086 .449 .161 1 deg C 81.2 .463 .094 .175

Wavefront analysis Wavefront analysis not adequate: Zernike polynomials do not fit to long rectangular optical surface Consider using LeGendre polynomials? Good for cylindrical optic fits (used Chandra mirror analysis) Orthogonal polynomials? Ref. Integrated Optomechanical Analysis Doyle, Genberg, Michels, p.61

Optical Tolerances Goal: Good fringe clarity at the focal plane Maintain phase information as it passes through each channel of the interferometer simultaneously Analytical Analysis: Limit OPD < l/10 Raytrace Analysis: Limit relative Strehl ratio > 80%

Mirror Separation within a periscope

Analytical vs. Raytrace Mirror Position Tolerances DOF Equation Analytic Raytrace X ±1.7nm ± 2nm Y ± 3mm Not modeled Z ± 49nm ± 70nm X-rotation ± 0.4° Y-rotation ± 1.8 marcsec ± 2marcsec Z-rotation ± 59 marcsec ±60marcsec where l = 20Å, g =2°, m = 83cm, and L = 400km

MAXIM Pathfinder Parameters Baseline = 2 m Focal Length = 200 km Mirror length = 30 cm Graze angle = 2° l = 10Å

MAXIM Pathfinder Position Tolerances l=1nm, F=200km, D=2m, m=30cm, g=2deg, dh=1mm DOF Mirror Equation Periscope Equation Mirror Tolerance X ±0.8nm ±20mm Y ±0.6mm ± 1mm Z ±23.6nm ±8m X-rot (yaw) ±0.2° ± 0.13° Y-rot (pitch) ±1.3 marcsec ± 10.3 arcsec Z-rot (roll) ±37.2 ± 0.26°

Full MAXIM Parameters Baseline = 1km Focal Length = 20,000 km Mirror length = 30 cm Graze angle = 1° l = 10Å

X-direction Sensitivity F X D y Z Allowable Mirror Motion: ± 1.7nm Allowable Periscope Motion: ± 4mm

Y-direction Sensitivity X Z=LOS Y Allowable Mirror Motion: ± 0.3mm Allowable Periscope Motion: ± 0.5mm

Z-direction Sensitivity F D y Z X Allowable Mirror Motion: ± 94.7nm Allowable Periscope Motion: ± 0.32m

X-rotation “yaw” Sensitivity Z Y msin(g) m Allowable Mirror Motion: ± 6.9arcmin Allowable Periscope Motion: ± 7.8 arcmin

Y-rotation “pitch” Sensitivity X Z F y D Allowable Mirror Motion: ± 2.3 marcsec Allowable Periscope Motion: ± 10 arcsec

Z-rotation “roll” Sensitivity LOS X Z=LOS Roll Y Allowable Mirror Motion: ± 0.13 arcsec Allowable Periscope Motion: ± 18.5 arcsec To Detector

MAXIM Position Tolerances l=1nm, F=20,000km, D=1km, m=30cm, g=1deg, dh=1mm DOF Mirror Equation Periscope Equation Mirror Tolerance X ±1.7nm ±4mm Y ±0.3mm ± 0.5mm Z ±94.7nm ±0.32m X-rot (yaw) ±6.9 arcmin ± 7.8 Y-rot (pitch) ±2.3 marcsec ± 10 arcsec Z-rot (roll) ±0.13 ±18.5

ISAL Raytrace Position Tolerances l=1nm, F=200km, D=4m, m=30cm, g=1deg, dh=1mm DOF Mirror Equation Periscope Equation Mirror Tolerance X ±1.7nm ±10mm Y ±0.3mm ± 0.5mm Z ±94.7nm ±2m X-rot (yaw) ±6.9 arcmin ± 7.8 Y-rot (pitch) ±2.3 marcsec ± 10 arcsec Z-rot (roll) ±0.13 ±7.6

Move one mirror pair wrt other mirror pair -d +d Pathlength is self-correcting

Move one mirror in Z-direction dcos2q 2q -d dsinq

Trade Studies Three grating sizes: Optimize graze angle vs. mass 2cm, 10cm, and 30cm wide x 30 cm long Optimize graze angle vs. mass Lower graze angle can loosen some tolerances Lower graze angle will reduce throughput or increase mass