1. Senior Optical Engineer
Practical Knowledge of Vacuum Windows
Rev. 1.1
Oli Durney
Senior Optical Engineer
Steward Observatory
University of Arizona

2. Typical Geometry Ambient Space Mounting Bolt Window Flange O-ring Seal
Cryostat Case
Cryostat Case
Vacuum Space

3. Example: O-ring Seal

4. Example: Indium Seal

5. Window Support Case 1: Simply Supported Pressure Lateral translation
k = 1.24
k1 = 0.696
Case 2: Rigidly Fixed
Pressure
k = 0.75
No Lateral translation
k1 = 1.71

6. O-ring Groove Window Force
Light coating of Apiezon vacuum grease L or M
~20%
0.139”
Cryostat Case
Cryostat Case
O-ring
(2-240)
0.105”
Compressed O-ring
0.150”

7. Strength of Material Strength S.F. = Stress
Rule of Thumb: Safety Factor = 10
Use reference book to get strength of material [in PSI]
Normally the Modulus of Rupture (MOR) is used
Safety Factor is:
Strength
S.F. =
Stress
Solve for Stress

8. Maximum Stress w R2 Sm = k t2 Solve for t
Outside Pressure = Atm = 760 Torr = 14.7 PSI
Inside Pressure = 10E-6 Torr ~ 0 PSI
Stress of the Window:
w R2
Sm = k t2
k = coefficient k for circular plates
w = uniform pressure across window (outside P – inside P)
R = radius of Clear Aperture of window
t = thickness of window
Solve for t

9. Maximum Defection ym = k1 E t3 w R4 Solve for t
Window ‘bowing’ can affect optical design
Deflection causes plano window to have power, thus creating a meniscus lens
Optical design will govern amount of deflection (sag) allowable
If window is Simply Supported and O-ring does not compress fully:
ym = k1
E t3
w R4
k1 = coefficient k1 for circular plates
w = uniform pressure across window (outside P – inside P)
R = radius of Clear Aperture of window
E = Young’s modulus
t = thickness of window
Solve for t

10. Rules of Thumb
Typical k value for stress calculation used in practice is 1.00
Reasonable (and typical) material choice for NIR waveband is Fused Silica or BK7
Fused Silica: Young’s modulus = 1.06E+07 PSI
Modulus of Rupture = 7600 PSI
BK7: Young’s modulus = 1.19E+07 PSI
Modulus of Rupture = 2400 PSI
k1 for deflection calculations vary from to depending on whether window is constrained by Case 1 or 2
Typically use 0.43
O-ring types:
Buna-N has highest permeation and retains water
Viton has lowest permeation and minimal water retention

11. Real World Example

12. LBTI UBC
Vacuum windows
Gate valve windows

13. Window Specs Lower Gate Valve Window Upper Gate Valve Windows
Material: BK7 or Fused Silica
Diameter: 101.8mm / -0.25mm
Thickness: 6.35mm +/- 0.25mm
Wavefront: 1/4 wave across CA
Clear Aperture: > 80% diameter
Parallelism: < 1 arcmin
Surface Quality: 20-10
Upper Gate Valve Windows
Material: BK7 or Fused Silica
Diameter: 137.5mm / -0.10mm
Thickness: 8.0mm +/- 0.10mm
Wavefront: 1/4 wave across CA
Clear Aperture: > 85% diameter
Parallelism: < 30 arcsec
Surface Quality: 40-20

14. Window Detail for Lower

15. Window Detail for Upper

16. Max Stress Maximum Stress: (Lower Gate Valve Window) Sm = k t2 w R2 =
(14.7PSI)*(46.05mm)2
(6.35mm)2
(1) ~
773 PSI
Maximum Stress: (Upper Gate Valve Window)
Sm = k t2
w R2 =
(14.7PSI)*(65mm)2
(8mm)2
(1) ~
970 PSI

17. Calculations for BK7 Safety Factor: (Lower Gate Valve Window) S.F. =
Max Stress
Modulus of Rupture =
773
2400
= 3.1
Safety Factor: (Upper Gate Valve Window)
S.F. =
Max Stress
Modulus of Rupture =
970
2400
= 2.5

18. Calculations for BK7 Maximum Deflection: (Lower Gate Valve Window)
w R4
(14.7PSI)*(46.05mm)4
ym = k1 =
(0.43) ~
0.009 mm
E t3
(1.19E7PSI)*(6.35mm)3
Maximum Deflection: (Upper Gate Valve Window)
w R4
(14.7PSI)*(65mm)4
ym = k1 =
(0.43) ~
0.019 mm
E t3
(1.19E7PSI)*(8mm)3

19. Calculations for F.S. Safety Factor: (Lower Gate Valve Window) S.F. =
Max Stress
Modulus of Rupture =
773
7600
= 9.8
Safety Factor: (Upper Gate Valve Window)
S.F. =
Max Stress
Modulus of Rupture =
970
7600
= 7.8

20. Calculations for F.S. Maximum Deflection: (Lower Gate Valve Window)
w R4
(14.7PSI)*(46.05mm)4
ym = k1 =
(0.43) ~
0.010 mm
E t3
(1.06E7PSI)*(6.35mm)3
Maximum Deflection: (Upper Gate Valve Window)
w R4
(14.7PSI)*(65mm)4
ym = k1 =
(0.43) ~
0.021 mm
E t3
(1.06E7PSI)*(8mm)3

21. Conclusions Young’s Modulus Max Deflection Modulus of Rupture
Max Stress
Safety Factor
Lower
BK7
1.19E+07
0.009
2400
773
3.1
Fused Silica
1.06E+07
0.010
7600
9.8
Upper
0.019
970
2.5
0.021
7.8

22. Window using O-ring Seal
Figure 1: O-ring style vacuum window
Figure 2: LN2 Cryostat

23. Window using Indium Seal
Figure 3: Indium style vacuum window
Figure 4: Balloon Cryostat

24. Other Examples