# Presentation: 670831

## Periscope Configuration

- Detector

- Periscope Module

## Mirror Parameters

- 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

## Mirror Module Coordinate System

- LOS

- Mirror Control:
- 	X – linear
-               Roll about LOS
-               Pitch

- Module Control:  Yaw
- 		Pitch
- 		Roll about LOS

- To Detector

- Fixed Mirrors

## 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

- 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
-  = 6328Å

- Mirror blank
- surface figure
**.0013**

- Mount interface
- surface finish
**.0003**

- Test
**.0013**

- 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

## 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 |
| Solid single arch
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 | # 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

## 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° | Not modeled |
| Y-rotation |  | ± 1.8 marcsec | ± 2marcsec |
| Z-rotation |  | ± 59 marcsec | ±60marcsec |

- Analytical vs. RaytraceMirror Position Tolerances

- where  = 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°
-   = 10Å

## MAXIM Pathfinder Position Tolerances=1nm, F=200km, D=2m, m=30cm, g=2deg, dh=1m

| DOF | Mirror Equation | Periscope 
Equation | Mirror
Tolerance | Periscope
Tolerance |
| --- | --- | --- | --- | --- |
| X |  |  | ±0.8nm | ±20m |
| 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
arcsec  | ± 0.26° |

## Full MAXIM Parameters

- Baseline = 1km
- Focal Length = 20,000 km
- Mirror length = 30 cm
- Graze angle = 1°
-   = 10Å

## X-direction Sensitivity

- F

- 

- Z

- X

- D

- Allowable Mirror Motion:  ± 1.7nm

- Allowable Periscope Motion:  ± 4m

## Y-direction Sensitivity

- Allowable Mirror Motion:  ± 0.3mm

- Allowable Periscope Motion:  ± 0.5mm

- X

- Z=LOS

- Y

## Z-direction Sensitivity

- F

- 

- D

- Allowable Mirror Motion:  ± 94.7nm

- Allowable Periscope Motion:  ± 0.32m

## X-rotation “yaw” Sensitivity

- m

- msin(g)

- Allowable Periscope Motion:  ± 7.8 arcmin

## Y-rotation “pitch” Sensitivity

- D

- F

- 

- Allowable Mirror Motion:  ± 2.3 marcsec

## Z-rotation “roll” Sensitivity

- LOS

- To Detector

- X

- Roll

- Z=LOS

- Y

- Allowable Mirror Motion:  ± 0.13 arcsec

## MAXIM Position Tolerances =1nm, F=20,000km, D=1km, m=30cm, g=1deg, dh=1m

| DOF | Mirror Equation | Periscope 
Equation | Mirror
Tolerance | Periscope
Tolerance |
| --- | --- | --- | --- | --- |
| X |  |  | ±1.7nm | ±4m |
| Y |  |  | ±0.3mm | ± 0.5mm |
| Z |  |  | ±94.7nm | ±0.32m |
| X-rot
(yaw)  |  |  | ±6.9
arcmin | ± 7.8
arcmin |
| Y-rot
(pitch) |  |  | ±2.3
marcsec | ± 10
arcsec |
| Z-rot
(roll) |  |  | ±0.13
arcsec | ±18.5
arcsec |

## ISAL Raytrace Position Tolerances =1nm, F=200km, D=4m, m=30cm, g=1deg, dh=1m

| DOF | Mirror Equation | Periscope 
Equation | Mirror
Tolerance | Periscope
Tolerance |
| --- | --- | --- | --- | --- |
| X |  |  | ±1.7nm | ±10m |
| Y |  |  | ±0.3mm | ± 0.5mm |
| Z |  |  | ±94.7nm | ±2m |
| X-rot
(yaw)  |  |  | ±6.9
arcmin | ± 7.8
arcmin |
| Y-rot
(pitch) |  |  | ±2.3
marcsec | ± 10
arcsec |
| Z-rot
(roll) |  |  | ±0.13
arcsec | ±7.6
arcmin |

## Move one mirror pair wrt other mirror pair

- -

- 

- Pathlength is self-correcting

## Move one mirror in Z-direction

- -

- 

- cos2

- 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