Abstract

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.

© 1966 Optical Society of America

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  1. The data in this section have been extracted primarily from the articles of F. Möller, D. M. Hunten, W. M. Sinton, Appl. Opt. 3, 157, 167, 175(1964). A more detailed discussion of the moon, Mars, and Venus may also be found in S. F. Singer, Ed., Progr. Astronaut. Sci.1(1962).
    [CrossRef]
  2. J. G. Baker, “Optical Systems for Astronomical Photography,” in Amateur Telescope Making, Book Three (Scientific American, Inc., New York, 1961), p. 11.
  3. A. E. Conrady, Applied Optics and Optical Design (Dover Publications, Inc., New York, 1957), p. 455.
  4. Reference 3, p. 628.
  5. Comparison with the solution of Article 42, Case (ii), H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 1st ed. (University Press, Oxford, England, 1946), 1st Col., p. 104, indicates that the energy balance written here is approximately 15% in error at θ= θ3. This error is considered inconsequential in the conclusions which are drawn, and more complex algebra would obscure the physical view of the problem. In addition, the linear thermal gradient yields the maximum deformation to be expected.
  6. R. M. Scott, Appl. Opt. 1, 387 (1962). See Table 1 on p. 393.
    [CrossRef]

1964 (1)

The data in this section have been extracted primarily from the articles of F. Möller, D. M. Hunten, W. M. Sinton, Appl. Opt. 3, 157, 167, 175(1964). A more detailed discussion of the moon, Mars, and Venus may also be found in S. F. Singer, Ed., Progr. Astronaut. Sci.1(1962).
[CrossRef]

1962 (1)

R. M. Scott, Appl. Opt. 1, 387 (1962). See Table 1 on p. 393.
[CrossRef]

Baker, J. G.

J. G. Baker, “Optical Systems for Astronomical Photography,” in Amateur Telescope Making, Book Three (Scientific American, Inc., New York, 1961), p. 11.

Carslaw, H. S.

Comparison with the solution of Article 42, Case (ii), H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 1st ed. (University Press, Oxford, England, 1946), 1st Col., p. 104, indicates that the energy balance written here is approximately 15% in error at θ= θ3. This error is considered inconsequential in the conclusions which are drawn, and more complex algebra would obscure the physical view of the problem. In addition, the linear thermal gradient yields the maximum deformation to be expected.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover Publications, Inc., New York, 1957), p. 455.

Hunten, D. M.

The data in this section have been extracted primarily from the articles of F. Möller, D. M. Hunten, W. M. Sinton, Appl. Opt. 3, 157, 167, 175(1964). A more detailed discussion of the moon, Mars, and Venus may also be found in S. F. Singer, Ed., Progr. Astronaut. Sci.1(1962).
[CrossRef]

Jaeger, J. C.

Comparison with the solution of Article 42, Case (ii), H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 1st ed. (University Press, Oxford, England, 1946), 1st Col., p. 104, indicates that the energy balance written here is approximately 15% in error at θ= θ3. This error is considered inconsequential in the conclusions which are drawn, and more complex algebra would obscure the physical view of the problem. In addition, the linear thermal gradient yields the maximum deformation to be expected.

Möller, F.

The data in this section have been extracted primarily from the articles of F. Möller, D. M. Hunten, W. M. Sinton, Appl. Opt. 3, 157, 167, 175(1964). A more detailed discussion of the moon, Mars, and Venus may also be found in S. F. Singer, Ed., Progr. Astronaut. Sci.1(1962).
[CrossRef]

Scott, R. M.

R. M. Scott, Appl. Opt. 1, 387 (1962). See Table 1 on p. 393.
[CrossRef]

Sinton, W. M.

The data in this section have been extracted primarily from the articles of F. Möller, D. M. Hunten, W. M. Sinton, Appl. Opt. 3, 157, 167, 175(1964). A more detailed discussion of the moon, Mars, and Venus may also be found in S. F. Singer, Ed., Progr. Astronaut. Sci.1(1962).
[CrossRef]

Appl. Opt. (2)

The data in this section have been extracted primarily from the articles of F. Möller, D. M. Hunten, W. M. Sinton, Appl. Opt. 3, 157, 167, 175(1964). A more detailed discussion of the moon, Mars, and Venus may also be found in S. F. Singer, Ed., Progr. Astronaut. Sci.1(1962).
[CrossRef]

R. M. Scott, Appl. Opt. 1, 387 (1962). See Table 1 on p. 393.
[CrossRef]

Other (4)

J. G. Baker, “Optical Systems for Astronomical Photography,” in Amateur Telescope Making, Book Three (Scientific American, Inc., New York, 1961), p. 11.

A. E. Conrady, Applied Optics and Optical Design (Dover Publications, Inc., New York, 1957), p. 455.

Reference 3, p. 628.

Comparison with the solution of Article 42, Case (ii), H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids, 1st ed. (University Press, Oxford, England, 1946), 1st Col., p. 104, indicates that the energy balance written here is approximately 15% in error at θ= θ3. This error is considered inconsequential in the conclusions which are drawn, and more complex algebra would obscure the physical view of the problem. In addition, the linear thermal gradient yields the maximum deformation to be expected.

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Figures (7)

Fig. 1
Fig. 1

Orbit orientation parameters of optical system. N, north ecliptic pole; S, south ecliptic pole.

Fig. 2
Fig. 2

Solar heat flux incident upon entrance aperture versus orbit angle α. (a) β = 0°, 320 km; (b) β = 0°, 960 km; (c) β = 60°, 320 km; (d) β = 60°, 960 km.

Fig. 3
Fig. 3

Surface orbital orientation coordinate system.

Fig. 4
Fig. 4

Albedo heat flux incident upon entrance aperture as a function of orbit angle α.

Fig. 5
Fig. 5

Edge-insulated window. Material: crown glass. k = 0.011 W/cm2 × °K/cm, α = 9 × 10−6/°C, N = 1.5, dN/dT = 1.8 × 10−6/°C, ν = 0.2. Insulation: kf = 0.00034 W/cm2 × °K/cm.

Fig. 6
Fig. 6

Temperature history.

Fig. 7
Fig. 7

Photograph of knife-edge test of a Kanigen-coated aluminum mirror.

Tables (5)

Tables Icon

Table I Optical Path Differences and their Deviations from a Reference Sphere for the Window Example

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Table II Optical Path Differences for Reduced Aperture of the Window Example

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Table III Some Particular Solutions for Thermal Deformations of Mirror Structures

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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.

Tables Icon

Table V Changes in Front Surface for 10°C Rise in Temperature

Equations (15)

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T = [ C ( T s - Σ h i T i + Σ q j Σ h i ) 2 π b d k ( Σ h i k d ) 1 2 I 1 [ b ( Σ h i k d ) 1 2 ] + C I 0 [ b ( Σ h i k d ) 1 2 ] ] × I 0 [ r ( Σ h i k d ) 1 2 ] + Σ h i T i + Σ q j Σ h i .
σ r = α E ( 1 b 2 0 b T r d r - 1 r 2 0 r T r d r ) ,
σ θ = α E ( - T + 1 b 2 0 b T r d r + 1 r 2 0 r T r d r ) ,
T = T s - T B χ I 1 ( χ ) + I 0 ( χ ) I 0 ( χ r b ) + T , T = 0.364 I 0 ( 4.98 r / b ) + 266 ° K .
γ [ I 3 - ( I 2 2 / I 1 ) ] = I 5 - ( I 4 I 2 / I 1 ) ,
σ r = λ ( γ z + [ ( I 4 - γ I 2 ) / I 1 ] - } .
θ 3 = 2 c 2 ( k / ρ c p ) .
I 1 = - c c λ d z = 2 c λ , I 2 = - c c λ z d z = 0 , I 3 = - c c λ z 2 d z = 2 c 3 3 λ , I 4 = λ α q k - c c ( z + c ) d z = λ α q k ( 2 c 2 ) , I 5 = λ α q k - c c ( z 2 + c z ) d z = λ α q k ( 2 c 3 3 ) .
γ = I 5 / I 3 = α q / k ,
σ r = λ [ ( α q / k ) z + ( α q / k ) c - ( α q / k ) ( z + c ) ] = 0.
I 1 = - ( c + δ ) - c λ 2 d z + - c c λ 1 d z + c c + δ λ 2 d z ,
γ = ( 3 / c ) ( λ 2 / λ 1 ) ( α 2 - α 1 ) ( T - T 0 ) ( δ + δ ) / 2 c × { 1 - ( δ + δ / 2 c ) [ 4 ( λ 2 / λ 1 ) - 1 } ,
( σ r ) 1 = λ 2 ( α 2 - α 1 ) ( T - T 0 ) { ± [ 3 ( δ + δ ) / 2 c ] + ( δ + δ ) / 2 c ] } .
( σ r ) 2 = ( λ 2 / λ 1 ) ( σ r ) 1 - λ 2 ( α 2 - α 1 ) ( T - T 0 ) .
γ Invar sandwich γ solid Be = 1 d λ Kanigen λ Invar ( α Kanigen - α Invar ) ( T - T 0 ) δ - δ 2 c 3 c λ Kanigen λ Be ( α Kanigen - α Be ) ( T - T 0 ) δ - δ 2 c = c 3 d ( 1 ) ( 2 3 ) ( 13 - 0.1 ) ( 13 - 11 ) = 10 4 ( 12.9 ) = 32.

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