The effects of the major features of an aerospace thermal environment on the principal components of large-aperture photographic catadioptric systems are considered. First approximation solutions to the focal shift and on-axis wavefront aberration produced by heat fluxes in windows (or corrector plates) are presented. The effects of axial heat fluxes and uniform temperature changes on mirror structures representative of current practice in lightweight-mirror technology are examined, and first approximations to the deformations of simple slab mirrors, Kanigen-coated metal mirrors, and sandwich-plate construction are derived. Some conclusions on the comparative utility of Kanigen-coated beryllium mirrors and solid or egg-crate fused-silica mirrors are drawn.
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Some Particular Solutions for Thermal Deformations of Mirror Structures
Particular solutions
Simple slab
Coated slab
Symmetrical sandwich construction—coated (coating may be asymmetric)
Subscript 1—substrate properties
Subscript 1—core properties
Subscript 2—facing properties
Subscript 3—coating properties
Subscript 2—coating properties
Additional assumptions:
1. core and facings same base material: α1 = α2
2. λ1 = f/25 λ2
3. k1 = fk2
Uniform temperature change (T − T0)
γ = 0
σr = 0
and at z = C
and at z = C
Hear flux q per unit area steady state
σr = 0
and at z = C
and at z = C
(σr)1 ≈ 0
Table IV
Material Properties, Time-to-Deformation Equilibrium, and Change in Sagitta for Simple Slab Mirrors (61-cm Diam., 2.45 cm Thick) for a Step-Function Heat Input of 6.35(10~3) W/cm2.
Approximated for material heat treated at 190°C from data in S. Jovanovic and C. S. Smith, J. Appl. Phys. 32, 121 (1961). Other data are representative values from a variety of sources.
Table V
Changes in Front Surface for 10°C Rise in Temperature
Change in sag (wavelengths at 510 nm)
Change in stress in substrate (kg/mm2)
Change in stress in Kanigen (kg/mm2)
Kanigen on aluminum
2.8 Cx
0.022 compression
2.81 tension
Kanigen on beryllium
0.16 Cc
0.004 tension
0.49 compression
Kanigen on super Invar
1.6 Cc
0.026 tension
3.24 compression
Kanigen on titanium
1.2 Cc
0.008 tension
0.98 compression
Tables (5)
Table I
Optical Path Differences and their Deviations from a Reference Sphere for the Window Example
Some Particular Solutions for Thermal Deformations of Mirror Structures
Particular solutions
Simple slab
Coated slab
Symmetrical sandwich construction—coated (coating may be asymmetric)
Subscript 1—substrate properties
Subscript 1—core properties
Subscript 2—facing properties
Subscript 3—coating properties
Subscript 2—coating properties
Additional assumptions:
1. core and facings same base material: α1 = α2
2. λ1 = f/25 λ2
3. k1 = fk2
Uniform temperature change (T − T0)
γ = 0
σr = 0
and at z = C
and at z = C
Hear flux q per unit area steady state
σr = 0
and at z = C
and at z = C
(σr)1 ≈ 0
Table IV
Material Properties, Time-to-Deformation Equilibrium, and Change in Sagitta for Simple Slab Mirrors (61-cm Diam., 2.45 cm Thick) for a Step-Function Heat Input of 6.35(10~3) W/cm2.
Approximated for material heat treated at 190°C from data in S. Jovanovic and C. S. Smith, J. Appl. Phys. 32, 121 (1961). Other data are representative values from a variety of sources.
Table V
Changes in Front Surface for 10°C Rise in Temperature