Post on 21-Jan-2016
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Periscope Configuration
Detector
Periscope Module
X
Z
Mirror Parameters
30 cm
2, 10, or 30 cm
TBD
•Active area is 30cm long x 2, 10 or 30cm wide.
•Surface figure requirement: /400 rms (at 633nm) --Mounted
•Mirror mass must be minimized
•Geometry TBD
Reflecting surface
LOS
X
Roll
Z=LOS
YPitch
Yaw
Mirror Control: X – linear
Roll about LOS Pitch
Module Control: YawPitchRoll about LOSTo Detector
Fixed Mirrors
Mirror Module Coordinate System
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
Thermal gradient
.0011
Jitter
.0006
Stability
.0013
Assembly
(neglected)
Manufacturing
.0013
Alignment
.0013
Surface distortion due to gravity
.0004
Reflective coating
.0009
Bolt preload
.0002
Adhesive strain
.0002
Bulk temp (5°C)
.0005
1g sag
.0004
Total RMS error
.0025
Error Budget for /400 RMS
Mirror Mount
All values given in RMS wavefront error
= 6328ÅMirror blank
surface figure
.0013
Mount interface
surface finish
.0003
Test
.0013
First Order Wavefront Error Budget
Motion due to gravity
(neglected)
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) 1CBolt
preload
30% Weight-relieved rectangle (1.3Kg)
5cm tall1569.7 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
Solid single arch
5 cm tall102.9 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 # pts PV rms
Bolt preload
76.9 1610 .005 .004 87 .170 .054
1g (x) 88.7 1610 .469 .091 87 .047 .013
1g (y) 92.7 1610 .673 .097 87 3.065 1.073
1g (z) 97.5 1610 .315 .086 87 .449 .161
1 deg C 81.2 1610 .463 .094 87 .175 .047
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 < /10
• Raytrace Analysis:– Limit relative Strehl ratio > 80%
Mirror Separation within a periscope
h2 h1
m1hhh 12
)sin()tan( gmgmh
DOF Equation Analytic Raytrace
X ±1.7nm ± 2nm
Y ± 3mm Not modeled
Z ± 49nm ± 70nm
X-rotation
± 0.4° Not modeled
Y-rotation
± 1.8 marcsec ± 2marcsec
Z-rotation
± 59 marcsec ±60marcsec
Analytical vs. RaytraceMirror Position Tolerances
)cos()sin( gg20
)(sin
)cos(
g20
g22
5
g )sin(
22
L10
gm
gm10
sin
sin
where = 20Å, g =2°, m = 83cm, and L = 400km
22
L10
gm
gm10g
1
sin
sinsin
10
gm )sin(
MAXIM Pathfinder Parameters
• Baseline = 2 m
• Focal Length = 200 km
• Mirror length = 30 cm
• Graze angle = 2°
• = 10Å
MAXIM Pathfinder Position Tolerances=1nm, F=200km, D=2m, m=30cm, g=2deg, dh=1m
DOF Mirror Equation Periscope Equation
MirrorTolerance
PeriscopeTolerance
X ±0.8nm ±20m
Y ±0.6mm ± 1mm
Z ±23.6nm ±8m
X-rot(yaw)
±0.2° ± 0.13°
Y-rot(pitch)
±1.3marcsec
± 10.3arcsec
Z-rot(roll)
±37.2arcsec
± 0.26°2D5
F2
)cos()sin( gg320
D5
F
10
gm )sin(
310
gm )sin(
)(sin
)cos(
g320
g22
2
2
D5
F4
35
g )sin(
15
g )sin(
h20
22
L10
gm
gm103
1 sin
sin
22
L10
gm
gm10g3
1
sin
sinsin
Full MAXIM Parameters
• Baseline = 1km
• Focal Length = 20,000 km
• Mirror length = 30 cm
• Graze angle = 1°
• = 10Å
X-direction Sensitivity
)cos()sin( gg320
F
Z
X
D
Allowable Mirror Motion: ± 1.7nm
Allowable Periscope Motion: ± 4m D5
F
Y-direction Sensitivity
310
gm )sin(
Allowable Mirror Motion: ± 0.3mm
Allowable Periscope Motion: ± 0.5mm
10
gm )sin(
XZ=LOS
Y
Z-direction Sensitivity
)(sin
)cos(
g320
g22
F
Z
X
D
Allowable Mirror Motion: ± 94.7nm
Allowable Periscope Motion: ± 0.32m
2
2
D5
F4
X-rotation “yaw” Sensitivity
mmsin(g) Z
Y
35
g )sin(Allowable Mirror Motion: ±
6.9arcmin
Allowable Periscope Motion: ± 7.8 arcmin
15
g )sin(
Y-rotation “pitch” SensitivityX
Z
D
F
Allowable Periscope Motion: ± 10 arcsec h20
Allowable Mirror Motion: ± 2.3 marcsec
22
L10
gm
gm103
1 sin
sin
Z-rotation “roll” Sensitivity
LOS
To Detector
X
Roll
Z=LOS
Y
Allowable Periscope Motion: ± 18.5 arcsec
2D5
F2
Allowable Mirror Motion: ± 0.13 arcsec
22
L10
gm
gm10g3
1
sin
sinsin
MAXIM Position Tolerances =1nm, F=20,000km, D=1km, m=30cm, g=1deg, dh=1m
DOF Mirror Equation Periscope Equation
MirrorTolerance
PeriscopeTolerance
X ±1.7nm ±4m
Y ±0.3mm ± 0.5mm
Z ±94.7nm ±0.32m
X-rot(yaw)
±6.9arcmin
± 7.8arcmin
Y-rot(pitch)
±2.3marcsec
± 10arcsec
Z-rot(roll)
±0.13arcsec
±18.5arcsec2D5
F2
)cos()sin( gg320
D5
F
10
gm )sin(
310
gm )sin(
)(sin
)cos(
g320
g22
2
2
D5
F4
35
g )sin(
15
g )sin(
h20
22
F10
gm
gm103
1 sin
sin
22
F10
gm
gm10g3
1
sin
sinsin
ISAL Raytrace Position Tolerances =1nm, F=200km, D=4m, m=30cm, g=1deg, dh=1m
DOF Mirror Equation Periscope Equation
MirrorTolerance
PeriscopeTolerance
X ±1.7nm ±10m
Y ±0.3mm ± 0.5mm
Z ±94.7nm ±2m
X-rot(yaw)
±6.9arcmin
± 7.8arcmin
Y-rot(pitch)
±2.3marcsec
± 10arcsec
Z-rot(roll)
±0.13arcsec
±7.6arcmin2D5
F2
)cos()sin( gg320
D5
F
10
gm )sin(
310
gm )sin(
)(sin
)cos(
g320
g22
2
2
D5
F4
35
g )sin(
15
g )sin(
h20
22
F10
gm
gm103
1 sin
sin
22
F10
gm
gm10g3
1
sin
sinsin
Move one mirror pair wrt other mirror pair
-
Pathlength is self-correcting
Move one mirror in Z-direction
-
cos2
2
xray2xray
xray2
202
10
10OPDand2OPD
212OPD
sinsin
sin
coscos
sin
2
Trade Studies
• Three grating sizes:– 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