Advanced Mirror Technology Development (AMTD) thermal trade studies

Thomas Brooks, Phil Stahl, Bill Arnold

NASA/MSFC

• Efforts associated with this presentation are performed as part of the Advanced Mirror Technology Development (AMTD) program

• Larger aperture space telescopes are required to answer our most compelling science questions.

• AMTD’s objective is to mature to TRL-6 critical technologies needed to produce 4-m or larger flight-qualified UVOIR mirrors by 2018 so that a viable mission can be considered by the 2020 Decadal Review.

•To accomplish our objective, we: • Use a science-driven systems engineering approach.• Mature technologies required to enable highest priority science AND result in a high-performance

low-cost low-risk system.

What is AMTD?

Description of Primary Mirror

• 4m Circular Monolith

• 0.152m depth front to back

• Light-weighted with a back sheet

• Areal Density is 146 kg/m2

• Optical face coated with εaluminum=0.03

• Fixed Mount

• Material Properties:

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MaterialConductivity[W/(m*K)]

Specific Heat[J/(kg*K)]

Density[kg/m3]

EmissivityCTE

[1/K]ULE 1.31 766 2210 0.82 30x10-9

Silicon Carbide 180 750 3100 0.9 2.2x10-6

Zerodur 1.46 800 2530 0.9 7x10-9

Heat Flow Through Mirror

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• Most heat enters the mirror from the heated plate and exits through the optical surface

• Heat is transported by radiation (56%) and conduction (44%)

Not to scale

Description of Telescope Architecture

• Cylindrical Shroud; 60˚ Scarf

• No secondary mirror or baffles

• MLI on outer surface of shroud & sides of mirror ε*MLI=0.03

• Inner surface of shroud painted black

• Heated plate behind mirror

• Placed at L2Mirror

Heated Plate

Shroud

Scarf

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279.925

279.950

279.975

280.000

280.025

280.050

280.075

0 10000 20000 30000 40000 50000

Shro

ud

Te

mp

era

ure

(K

)

Time(s)

WFE Contour Video

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WFE Visualization

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Sample WFE Contour Plot (50mK, 140s Period) Sample WFE with Focus, Tilts, and Astigmatisms Removed (50mK, 140s Period)

WFE Stability versus Controllability

• Material: ULE

• Period of ACS: 5000s

• Controllability of ACS: Varied

• Density of Mirror: ULE Density

• Emissivity: 0.82

• Thicknesses: Baseline Design

• Conductivity: ULE Conductivity

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0 10000 20000 30000 40000 50000

RM

S W

FE (

nm

)

Time (s)

Control to 1mK Control to 5mK Control to 10mK Control to 50mK

WFE Stability versus Controllability

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-500

-400

-300

-200

-100

0

100

200

300

400

0 10000 20000 30000 40000 50000

RM

S W

FE -

Mea

n R

MS

WFE

(p

m)

Time (s)

Control to 1mK Control to 5mK Control to 10mK Control to 50mK

1.0, 10.4

5.0, 56.6

10.0, 113.4

50.0, 567.4

y = 11.359x - 0.462R² = 1

0

100

200

300

400

500

600

0 10 20 30 40 50 60

RM

S W

FE R

ange

(p

m)

Shroud Controllability (mK)

WFE Stability versus Period

• Material: ULE

• Period of ACS: Varied

• Controllability of ACS: 50mK

• Density of Mirror: ULE Density

• Emissivity: 0.82

• Thicknesses: Baseline Design

• Conductivity: ULE Conductivity

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140.0, 16.3

200.0, 23.8

600.0, 72.4

1,800.0, 208.4

3,600.0, 412.3

y = 0.1147x + 0.7095R² = 0.9999

0

50

100

150

200

250

300

350

400

450

0 1000 2000 3000 4000

RM

S W

FE R

ange

(p

m)

Shroud Oscillation Period (s)

WFE Stability versus Conductivity

• Material: ULE

• Period of ACS: 140s

• Controllability of ACS: 50mK

• Density of Mirror: ULE Density

• Emissivity: 0.82

• Thicknesses: Baseline Design

• Conductivity: Varied

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0.25, 17.40

0.5, 17.3

1.0, 17.0

2.0, 16.54.0, 15.2

8.0, 12.5

y = -0.6341x + 17.649R² = 0.9983

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10

RM

S W

FE R

ange

(p

m)

Normalized Conductivity (Conductivity / ULE Conductivity)

WFE Stability versus Mass and Control

• Material: ULE

• Period of ACS: 140s

• Controllability of ACS: Varied

• Density of Mirror: Varied

• Emissivity: 0.82

• Thicknesses: Baseline Design

• Conductivity: ULE Conductivity

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20.00, 6.66

30.00, 9.90

40.00, 13.37

50.00, 16.77

60.00, 20.03

20.00, 2.3430.00, 3.37

40.00, 4.4050.00, 5.48

60.00, 6.61

0

5

10

15

20

25

0 20 40 60 80

RM

S W

FE R

ange

(p

m)

Shroud Controllability (mK) @ Period of 140s

1x Mass

2x Mass

3x Mass

WFE Stability versus Thicknesses

• Material: ULE

• Period of ACS: 140s

• Controllability of ACS: 50mK

• Density of Mirror: ULE Density

• Emissivity: 0.82

• Thicknesses: Varied

• Conductivity: ULE Conductivity

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0.5, 36.3

1.0, 17.3

2.0, 8.04.0, 3.5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5

RM

S W

FE R

ange

(pm

)

Normalized Rib Thickness (Simulated Rib Thickness/Design Rib Thickness)

y = 18.063/x - 0.31553xR2 = 0.9991

WFE Stability versus Emissivity

• Material: ULE

• Period of ACS: 140s

• Controllability of ACS: 20mK

• Mirror Density: ULE Density

• Emissivity: Varied

• Thicknesses: Baseline Design

• Conductivity: ULE Conductivity

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y = -1.9733x + 8.4309R² = 0.9772

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1

RM

S W

FE R

ange

(p

m)

Emissivity of Mirror Surfaces Except the Optical Face

WFE Stability versus Material

• Material: Varied

• Period of ACS: 140s

• Controllability of ACS: 50mK

• Mirror Density: Material Based

• Emissivity: Material Based

• Thicknesses: Baseline Design

• Conductivity: Material Based

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Silicon Carbide, 850.79

ULE, 22.78 Zerodur, 5.01

0

100

200

300

400

500

600

700

800

900

Silicon Carbide ULE Zerodur

RM

S W

FE R

ange

(p

m)

Quick Review

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• RMS WFE Range is directly proportional to the ACS’s controllability and period.

• RMS WFE Range is inversely proportional to the mirror’s heat capacity and has a weak, negative linear relationship with conductivity and emissivity.

• For the material properties used, Zerodur causes the easiest to meet requirements on an active control system, followed closely by ULE, and distantly by Silicon Carbide

1-D Rod Closed-Form Model

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Rod with a mass, specific heat, thermal energy, temperature and coefficient of thermal expansion of m, cp, Q, T, and CTE respectfully

Length of rod, L

𝑑𝑄

𝑑𝑡= ρ𝑉𝑐𝑝

𝑑𝑇

𝑑𝑡Equation 1

CTE)𝐿𝛥𝑇 = 𝛥𝐿 Equation 2

𝑑𝑇

𝑑𝑡 CTE)𝐿 =

𝑑𝐿

𝑑𝑡Equation 3

𝑑𝐿

𝑑𝑡=

CTE)𝐿

𝜌𝑉𝑐𝑝

𝑑𝑄

𝑑𝑡Equation 4

• Equation 1 describes heat transfer in and out of the rod

• Equation 2 describes linear thermal expansion

• Algebra and calculus then Equation 5

• Equation 4 shows variables that affect thermal strain rate

– Geometry dependent: L, V, dQ/dt (surface area)

– Material dependent: CTE, ρ, cp, and dQ/dt(emissivity and absorptivity)

Summary

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• Numerical and analytical models agree that heat capacity and CTE have very strong affects on thermal deformation rates.

• For an actively controlled substrate, the following figures of merit are proposed:

Massive Active Optothermal Stability,MAOS =𝜌𝑐𝑝𝐶𝑇𝐸

Active Optothermal Stability, AOS =𝑐𝑝

𝐶𝑇𝐸

𝑑𝐿

𝑑𝑡=

CTE)𝐿

𝜌𝑉𝑐𝑝

𝑑𝑄

𝑑𝑡

0.5, 36.3

1.0, 17.3

2.0, 8.04.0, 3.5

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

RM

S W

FE R

ange

(pm

)

Normalized Rib Thickness (Simulated Rib Thickness/Design Rib Thickness)

y = 18.063/x - 0.31553x

Summary Continued

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A data table of potential substrate materials is provided*

MaterialMassive Active Optothermal

Stability (TJ/m3)

Active Optothermal

Stability (GJ/kg)

Specific heat

(J/kg/K)

Density

(kg/m3)

Coefficient of thermal

expansion (1/K)

Fused silica 2.91 1.32 741 2202 5.60E-07

ULE 7971 112 51.1 766 2200 1.50E-08

Zerodur 83.1 32.8 821 2530 2.50E-08

Cer-Vit C-101 140 56.0 840 2500 1.50E-08

Beryllium I-70A 0.298 0.161 1820 1850 1.13E-05

Aluminum 6061-T6 0.113 0.042 960 2710 2.30E-05

Silicon Carbide CVD 0.936 0.292 700 3210 2.40E-06

Borosilicate crown E6 0.595 0.255 830 2330 3.25E-06

* Data in this table is compiled from Yoder, P.R., Opto-Mechanical Systems Design, 2nd ed., Marcel Dekker, New York, NY (1993).

Any Questions?Contact Information

Email: thomas.brooks@NASA.gov

Phone Number: (256) 544-5596

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mailto:thomas.brooks@NASA.gov

Methodology

Thermal Analysis done in Thermal

Desktop

Write NASTRAN input file

Run Thermal Deformation Analysis in

NASTRAN

Post Processes Data for Optical

Analysis

• Tasks boxed in red are handled entirely with a program written in Python.• Program saves weeks of work per analysis.• Program has been used to determine relationships between the telescope’s characteristics and

technical performance parameters like stability.

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Wavefront Error

279.925

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0 10000 20000 30000 40000 50000

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ud

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mp

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