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**Senior Optical Engineer**

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

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**Typical Geometry Ambient Space Mounting Bolt Window Flange O-ring Seal**

Cryostat Case Cryostat Case Vacuum Space

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Example: O-ring Seal

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Example: Indium Seal

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**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

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**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”

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**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

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**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

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**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

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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

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Real World Example

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LBTI UBC Vacuum windows Gate valve windows

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**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

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**Window Detail for Lower**

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**Window Detail for Upper**

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**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

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**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

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**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

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**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

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**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

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**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

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**Window using O-ring Seal**

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

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**Window using Indium Seal**

Figure 3: Indium style vacuum window Figure 4: Balloon Cryostat

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Other Examples

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