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