1. Athermal bond thickness for axisymmetric optical elements Tutorial by Eric Frater

2. Introduction Motivations – Survival of optics – Survival of bond – Performance of optics Concerns – Thermal stress Radial stress Shear stresses – Glass distortion r z r

3. Example design Cell: Aluminum 6061-T6 Optic: Schott N-BK7 Adhesives: – MG chemicals RTV 566 – 3M 2216 B/A (gray) Design: – Bond provides constraint – Uniform and continuous bond-line – Zero-strain in materials at nominal bonding temp

4. Material constants MATERIALα(ppm/°C)Poisson ratio, νE (Gpa) N-BK77.1.2182 6061-T624.3369 2216 B/A (gray) [1] 102~.4369 RTV 566200~.499~.003 α c r c αbαb α o r o Quick note: 2216 B/A and RTV 566 very different adhesives. As seen in the table, RTV compliance highly dependent on aspect ratio of bond. Subscript notation: “ c ”: cell “ b ”: bond “ o ”: optic Required: α b > α c > α o or α b = α c = α o [1] Yoder, Paul R. Mounting Optics in Optical Instruments

5. Bayar equation ΔTΔT z r r Example: h= 2.75mm (2216 B/A), h= 1.22mm (RTV 566) ΔTΔT (Bayar equation [2] ) Note: This vastly over-predicts thickness, neglects ν [2] Bayar, Mete. “Lens Barrel Optomechanical Design Principles”

6. Radial strain and Hooke’s Law

7. Van Bezooijen equation ΔTΔT z r r ΔTΔT Example: h= 1.03mm (2216 B/A), h= 0.40mm (RTV 566) (van Bezooijen equation [3] ) Note: This under-predicts thickness, neglects axial bulging of bond [3] Van Bezooijen, Roel. “Soft Retained AST Optics”

8. Modified van Bezooijen equation ΔTΔT z r r ΔTΔT Example: h= 1.50mm (2216 B/A), h= 0.60mm (RTV 566) (modified van Bezooijen equation [4] ) Note: This over-predicts thickness, allows excessive axial bulging [4] Monti, Christpher L. “Athermal bonded mounts: Incorporating aspect ratio into a closed-form solution”

9. Aspect ratio z r Varies from 1-2 between limits of van Bezooijen eq.’s Unconstrained in z if h=L

10. Closed-form aspect ratio approximation ΔTΔT z r r ΔTΔT Example: h= 1.13mm (2216 B/A), h= 0.41mm (RTV 566) (Aspect ratio approximation [4] ) Note: Provides a best-guess for h in closed-form [4] Monti, Christpher L. “Athermal bonded mounts: Incorporating aspect ratio into a closed-form solution”

11. Conclusions Bayar equation – Good conceptual starting point – Tends to vastly over-estimate h – Applicable to highly segmented bonds THICKNESS EQUATION2216 B/ARTV 566 Bayar2.75 mm1.22 mm van Bezooijen1.03 mm0.40 mm Modified van Bezooijen1.50 mm0.60 mm Aspect ratio approximation1.13 mm0.41 mm [5] Michels, Gregory, and Keith Doyle. “Finite Element Modeling of Nearly Incompressible Bonds”

12. References 1.Yoder, Paul R. Mounting Optics in Optical Instruments, 2nd ed. SPIE Press Monograph Vol. PM181 (2008), p. 732. 2.Bayar, Mete. “Lens Barrel Optomechanical Design Principles”, Optical Engineering. Vol. 20 No. 2 (April 1981) 3.Van Bezooijen, Roel. “Soft Retained AST Optics” Lockheed Martin Technical Memo 4.Monti, Christpher L. “Athermal bonded mounts: Incorporating aspect ratio into a closed-form solution”, SPIE 6665, 666503 (2007) 5.Michels, Gregory, and Keith Doyle. “Finite Element Modeling of Nearly Incompressible Bonds”, SPIE 4771, 287 (2002)