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

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

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OFD 3 Example: O-ring Seal

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OFD 4 Example: Indium Seal

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

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

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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

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OFD 8 Maximum Stress Outside Pressure = Atm = 760 Torr = 14.7 PSI Inside Pressure = 10E-6 Torr ~ 0 PSI Stress of the Window: S m =k t2t2 w R 2 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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OFD 9 k 1 = coefficient k 1 for circular plates w = uniform pressure across window (outside P – inside P) R = radius of Clear Aperture of window E = Youngs 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: y m =k1k1 E t 3 w R 4 Solve for t

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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: Youngs modulus = 1.06E+07 PSI Modulus of Rupture = 7600 PSI BK7: Youngs modulus = 1.19E+07 PSI Modulus of Rupture = 2400 PSI k 1 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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OFD 11 Real World Example

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OFD 12 LBTI UBC Vacuum windows Gate valve windows

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OFD 13 Window Specs Lower Gate Valve Window Material: BK7 or Fused Silica Diameter: 101.8mm / mm Thickness: 6.35mm +/- 0.25mm Wavefront: 1/4 wave across CA Clear Aperture: > 80% diameter Parallelism: < 1 arcmin Surface Quality: Upper Gate Valve Windows Material: BK7 or Fused Silica Diameter: 137.5mm / mm 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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OFD 14 Window Detail for Lower

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OFD 15 Window Detail for Upper

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OFD 16 Max Stress Maximum Stress: (Lower Gate Valve Window) S m = k t2t2 w R 2 = (14.7PSI)*(46.05mm) 2 (6.35mm) 2 (1)~773 PSI Maximum Stress: (Upper Gate Valve Window) S m = k t2t2 w R 2 = (14.7PSI)*(65mm) 2 (8mm) 2 (1)~970 PSI

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

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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 mmy m = k 1 E t 3 w R 4 (14.7PSI)*(65mm) 4 (1.19E7PSI)*(8mm) 3 (0.43)~0.019 mm Maximum Deflection: ( Upper Gate Valve Window ) =y m = k 1 E t 3 w R 4

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

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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 mmy m = k 1 E t 3 w R 4 (14.7PSI)*(65mm) 4 (1.06E7PSI)*(8mm) 3 (0.43)~0.021 mm Maximum Deflection: ( Upper Gate Valve Window ) =y m = k 1 E t 3 w R 4

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OFD 21 Conclusions Youngs Modulus Max Deflection Modulus of Rupture Max Stress Safety Factor LowerLower BK71.19E Fused Silica 1.06E UpperUpper BK71.19E Fused Silica 1.06E

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OFD 22 Window using O-ring Seal Figure 2: LN 2 CryostatFigure 1: O-ring style vacuum window

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

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OFD 24 Other Examples

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