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

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

Example: O-ring Seal

Example: Indium Seal

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

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”

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

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

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

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

Real World Example

LBTI UBC Vacuum windows Gate valve windows

Window Specs Lower Gate Valve Window Upper Gate Valve Windows 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

Window Detail for Lower

Window Detail for Upper

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

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

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

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

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

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

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

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

Other Examples