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Analysis of Window Thickness and Performance in Focal Plane Detectors

This document details the impact of window thickness on the stress experienced by optical windows in focal plane detectors. The relationship between the pressure on the window, its diameter, and thickness is analyzed, leading to a recommended diameter-to-thickness ratio. The performance metrics for different focal plane configurations using fused silica and various focal plane layouts are presented, including FWHM results across multiple wavelengths. Emphasis is placed on optimizing optical performance for detectors while maintaining structural integrity under mechanical stress.

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Analysis of Window Thickness and Performance in Focal Plane Detectors

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  1. ZTF Field FlattenerRev 3 P. Jelinsky 2012/07/20

  2. Window Thickness • The stress on a window, σ is • Where ν is the Poisson’s ratio, q is the pressure on the window, d is the window diameter and t is the window thickness • To first order the allowed stress is independent of the window diameter • Therefore the diameter to thickness ratio must be less than a given value. • Our mechanical engineer did an analysis and came up with a ratio of 10 (might need to be less at diameter grows) • The QUEST and PTF camera window has a ratio of 14.4 • The window thickness strongly affects the performance of the lens

  3. Assumptions • Distance from flattener to CCD is >= 3mm • Allow distance from corrector to mirror to vary • d/t <= 14.4 (same as QUEST camera) • Flattener is Fused Silica • All spherical surfaces • Aspheric surfaces did not change performance much • Optimize over 5 wavelengths in the g’, r’ bands as below (allowing a focus change). • Report results for u’ and i’ band (allowing a focus change) • u’ band seems very narrow (Maybe I read DIQ spreadsheet incorrectly?) • Optimize over 5 field points, weighted by area

  4. Focal Plane Layout • 9 detector focal plane needs a flattener with a radius of 3.8°, a 12 detector focal plane needs a flattener to a radius of 4°, a 16 detector focal plane needs a window to 5° • If field flattener is circular

  5. Layout • No filter added yet

  6. Case I Classical Schmidt • About 0.5 arcseconds FWHM for 4 ° radius • About 0.7 arcseconds FWHM for 5 ° radius • Only changed focus between bands 0.8 0.67 0.53 Average FWHM arcseconds 0.4 0.27 0.13

  7. Case I Classical Schmidt (cont)

  8. Case II Curved FP with lens (D/t = 14.4) • About 1.3 arcseconds FWHM for 4 ° radius • About 1.5 arcseconds FWHM for 5 ° radius • Only changed focus between bands 1.7 1.3 1.0 Average FWHM arcseconds 0.7 0.3

  9. Case II Curved FP with lens (D/t = 14.4) (cont)

  10. Case IIa Curved FP with lens (D/t = 25) • About 0.9 arcseconds FWHM for 4 ° radius • About 1.2 arcseconds FWHM for 5 ° radius • Only changed focus between bands 1.3 1.1 0.8 Average FWHM arcseconds 0.5 0.3

  11. Case IIa Curved FP with lens (D/t = 25) (cont)

  12. Case III Flat FP single lens (D/T = 14.4) • About 1.3 arcsecond FWHM for 4° radius • About 1.8 arcsecond for 5 ° radius • Only focus changed between bands 2 Average FWHM arcseconds 1

  13. Case III Flat FP single lens (D/T = 14.4) (cont)

  14. Case IV split flat FP (D/T = 14.4) • About 1.2 arcsecond FWHM for 4° radius • About 1.8 arcsecond for 5 ° radius • Only focus changed between bands 2 1 Average FWHM arcseconds

  15. Case IV split flat FP (D/T = 14.4) (cont)

  16. Case V 4 segment (16 CCD) FP (D/T = 14.4) • Each quadrant is flat but tilted • Forms the peak of a 4 sided pyramid • Each Quadrant has a vacuum field flattener in front • 16 total detectors

  17. Case V (cont) R Band Imaging over ¼ of field

  18. Case V (cont)

  19. Summary • The 4 segment focal plane performs as well as a curved focal plane with a vacuum lens 1.67 1.33 1.00 Average FWHM arcseconds 0.67 0.33

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