1. Periscope Configuration
Detector X Z
Periscope Module

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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%

11. Mirror Separation within a periscope

12. 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

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

14. 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°

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

16. X-direction SensitivityF X D y Z
Allowable Mirror Motion: ± 1.7nm
Allowable Periscope Motion: ± 4mm

17. Y-direction SensitivityX
Z=LOS Y
Allowable Mirror Motion: ± 0.3mm
Allowable Periscope Motion: ± 0.5mm

18. Z-direction SensitivityF D y Z X
Allowable Mirror Motion: ± 94.7nm
Allowable Periscope Motion: ± 0.32m

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

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

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

22. 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

23. 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

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

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

26. 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