OFD 1

Oli Durney

Senior Optical Engineer

Steward Observatory

University of Arizona

Practical Knowledge of Vacuum Windows

Rev. 1.1

OFD 2

Typical Geometry

Window

Cryostat Case Cryostat Case

Mounting Bolt

Window Flange

O-ring Seal

Vacuum Space

Ambient Space

OFD 3

Example: O-ring Seal

OFD 4

Example: Indium Seal

OFD 5

Window SupportCase 1: Simply Supported

Lateral translation

Case 2: Rigidly Fixed

No Lateral translation

Pressure

Pressure

k = 1.24

k = 0.75

k1 = 0.696

k1 = 1.71

OFD 6

O-ring Groove

Window

Cryostat Case

Cryostat Case

0.150”

0.105”

~20%

Compressed O-ring

Light coating of Apiezon vacuum grease L or M

O-ring

(2-240)

0.139”

For

ce

OFD 7

Strength of Material

• 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:

S.F. =Stress

Strength

Solve for Stress

OFD 8

Maximum Stress

• Outside Pressure = Atm = 760 Torr = 14.7 PSI

• Inside Pressure = 10E-6 Torr ~ 0 PSI

• Stress of the Window:

Sm = kt2

w R2

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

OFD 9

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

Maximum Defection• 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 = k1E t3

w R4

Solve for t

OFD 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 0.696 to 0.171 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

OFD 11

Real World Example

OFD 12

LBTI UBC

Vacuum windows

Gate valve windows

OFD 13

Window Specs

Lower Gate Valve Window

• Material: BK7 or Fused Silica

• Diameter: 101.8mm +0.00 / -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 +0.00 / -0.10mm

• Thickness: 8.0mm +/- 0.10mm

• Wavefront: 1/4 wave across CA

• Clear Aperture: > 85% diameter

• Parallelism: < 30 arcsec

• Surface Quality: 40-20

OFD 14

Window Detail for Lower

OFD 15

Window Detail for Upper

OFD 16

Max Stress• Maximum Stress: (Lower Gate Valve Window)

Sm = kt2

w R2

=(14.7PSI)*(46.05mm)2

(6.35mm)2(1) ~ 773 PSI

• Maximum Stress: (Upper Gate Valve Window)

Sm = kt2

w R2

=(14.7PSI)*(65mm)2

(8mm)2(1) ~ 970 PSI

OFD 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

OFD 18

Calculations for BK7• Maximum Deflection: (Lower Gate Valve Window)

=(14.7PSI)*(46.05mm)4

(1.19E7PSI)*(6.35mm)3(0.43) ~ 0.009 mmym = k1

E t3

w R4

(14.7PSI)*(65mm)4

(1.19E7PSI)*(8mm)3(0.43) ~ 0.019 mm

• Maximum Deflection: (Upper Gate Valve Window)

=ym = k1E t3

w R4

OFD 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

OFD 20

Calculations for F.S.• Maximum Deflection: (Lower Gate Valve Window)

=(14.7PSI)*(46.05mm)4

(1.06E7PSI)*(6.35mm)3(0.43) ~ 0.010 mmym = k1

E t3

w R4

(14.7PSI)*(65mm)4

(1.06E7PSI)*(8mm)3(0.43) ~ 0.021 mm

• Maximum Deflection: (Upper Gate Valve Window)

=ym = k1E t3

w R4

OFD 21

ConclusionsYoung’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 773 9.8

Upper

BK7 1.19E+07 0.019 2400 970 2.5

Fused Silica

1.06E+07 0.021 7600 970 7.8

OFD 22

Window using O-ring Seal

Figure 2: LN2 CryostatFigure 1: O-ring style vacuum window

OFD 23

Window using Indium Seal

Figure 4: Balloon Cryostat

Figure 3: Indium style vacuum window

OFD 24

Other Examples