Mario A. Jimenez-Garate,
Charles J. Hailey,
William W. Craig,
and Finn E. Christensen
M. A. Jimenez-Garate (mario@alum.mit.edu) is with the Center for Space Research, Massachusetts Institute of Technology, 70 Vassar Street, NE80-6091, Cambridge, Massachusetts 02139.
C. J. Hailey (chuckh@astro.columbia.edu) is with Columbia Astrophysics Laboratory, West 120th Street, New York, New York 10025.
W. W. Craig (craig1@llnl.gov) is with Lawrence Livermore National Laboratory, 7000 East Avenue, L-043, Livermore, California 94550.
F. E. Christensen (finn@drsi.dk) is with the Danish Space Research Institute, Julien Maries Vej 30, Copenhagen DK-2100, Denmark.
Mario A. Jimenez-Garate, Charles J. Hailey, William W. Craig, and Finn E. Christensen, "Thermal forming of glass microsheets for x-ray telescope mirror segments," Appl. Opt. 42, 724-735 (2003)
We describe a technology to mass-produce ultrathin mirror substrates for x-ray telescopes of near Wolter-I geometry. Thermal glass forming is a low-cost method to produce high-throughput, spaceborne x-ray mirrors for the 0.1–200-keV energy band. These substrates can provide the collecting area envisioned for future x-ray observatories. The glass microsheets are shaped into mirror segments at high temperature by use of a guiding mandrel, without polishing. We determine the physical properties and mechanisms that elucidate the formation process and that are crucial to improve surface quality. We develop a viscodynamic model for the glass strain as the forming proceeds to find the conditions for repeatability. Thermal forming preserves the x-ray reflectance and scattering properties of the raw glass. The imaging resolution is driven by a large wavelength figure. We discuss the sources of figure errors, and we calculate the relaxation time of surface ripples.
William W. Craig, Charles J. Hailey, Mario Jimenez-Garate, David L. Windt, Fiona A. Harrison, Peter H. Mao, Finn E. Christensen, and Ahsen M. Hussain Opt. Express 7(4) 178-185 (2000)
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Aeff(E), mirror effective area for a given x-ray energy E (not including detector efficiency); M/
A, mirror mass per area; HPD, half-power diameter imaging resolution; HEFT, High-Energy Focusing Telescope (balloon payload); HXT, Hard X-ray Telescope; SXT, Spectroscopy X-ray Telescope. Constellation-X is a planned spaceborne mission.
Ref. 1.
Ref. 2.
Refs. 3-5.
Refs. 6 and 7.
Refs. 8 and 9.
Ref. 8.
Listed tolerances correspond to the shape of the mirror after assembly. The error parameters are defined in Table
3. HEFT, High-Energy Focusing Telescope; HXT, Hard X-ray Telescope; SXT, Spectroscopy X-ray Telescope.
Ref. 3.
Ref. 8.
See Refs. 4 and 11-15. Orthogonal errors contributing to the HPD of a two-reflection conical telescope (the Wolter-I tolerances are nearly identical). L is the shell length; f is the focal length; re is the radius at end of the shell; rf is the radius at the front of the shell; r̅e and r̅f are the azimuthally averaged shell radii; r̅g is the globally averaged shell radius; r̅z is the axially averaged radius; reo, rfo, and r̅go are the nominal radii; rmin and rmax are the inner and outer shell radii in the optics module; ϕ is the azimuthal angle; and Δnz and Δr are the axial surface slope and radius error. Most figure errors are upper bounds derived with analytical ray tracing.
N.A., not applicable.
Schott Corporation data. We estimate that, for AF45 glass, cp increases by ∼60% when the temperature is raised from 300 to 1000 K.
Radcliffe interpolation.24
Winkelmann-Schott interpolation.24
Data for 1737 from Corning, Inc.
Haraeus Amersil Inc. data.
Thermophysical tables.25
Table 7
Convective Heat Transfer Coefficient Θ for Typical Conditionsa
Flow Type (Over Surface)
Θ (W m-2 K-1)
Low-speed airflow
10
Moderate-speed airflow (∼50 m/s)
100
Moderate-speed cross flow over cylinder
200
Vertical plate in air with ΔT = 30 °C (free convection)
Ref. 25.
In units of 10-6 K-1. Quartz crystal may have an anisotropic coefficient of thermal expansion, with 50%–100% variations.
Note: The coefficients for graphite highly depend on the type or grade of the graphic.
Table 9
Measurements of Glass Surface before and after Forminga
λ
Measurement
Raw (Before)
TFG (After)
25 Å–25 μm
σ from reflectance (8 keV)
4 Å
4 Å
1 μm–10 mm
X-ray scattering HPD (8–68 keV)
11 arc sec
11 arc sec
1–200 mm
Axial figure HPD
<15 arc sec
45 arc sec
We summarize measurements on many samples by providing approximate median values. The sample-to-sample variance is larger than measurement errors. HPD values are for two reflections. λ, spatial wavelength; σ, rms microroughness.
Aeff(E), mirror effective area for a given x-ray energy E (not including detector efficiency); M/
A, mirror mass per area; HPD, half-power diameter imaging resolution; HEFT, High-Energy Focusing Telescope (balloon payload); HXT, Hard X-ray Telescope; SXT, Spectroscopy X-ray Telescope. Constellation-X is a planned spaceborne mission.
Ref. 1.
Ref. 2.
Refs. 3-5.
Refs. 6 and 7.
Refs. 8 and 9.
Ref. 8.
Listed tolerances correspond to the shape of the mirror after assembly. The error parameters are defined in Table
3. HEFT, High-Energy Focusing Telescope; HXT, Hard X-ray Telescope; SXT, Spectroscopy X-ray Telescope.
Ref. 3.
Ref. 8.
See Refs. 4 and 11-15. Orthogonal errors contributing to the HPD of a two-reflection conical telescope (the Wolter-I tolerances are nearly identical). L is the shell length; f is the focal length; re is the radius at end of the shell; rf is the radius at the front of the shell; r̅e and r̅f are the azimuthally averaged shell radii; r̅g is the globally averaged shell radius; r̅z is the axially averaged radius; reo, rfo, and r̅go are the nominal radii; rmin and rmax are the inner and outer shell radii in the optics module; ϕ is the azimuthal angle; and Δnz and Δr are the axial surface slope and radius error. Most figure errors are upper bounds derived with analytical ray tracing.
N.A., not applicable.
Schott Corporation data. We estimate that, for AF45 glass, cp increases by ∼60% when the temperature is raised from 300 to 1000 K.
Radcliffe interpolation.24
Winkelmann-Schott interpolation.24
Data for 1737 from Corning, Inc.
Haraeus Amersil Inc. data.
Thermophysical tables.25
Table 7
Convective Heat Transfer Coefficient Θ for Typical Conditionsa
Flow Type (Over Surface)
Θ (W m-2 K-1)
Low-speed airflow
10
Moderate-speed airflow (∼50 m/s)
100
Moderate-speed cross flow over cylinder
200
Vertical plate in air with ΔT = 30 °C (free convection)
Ref. 25.
In units of 10-6 K-1. Quartz crystal may have an anisotropic coefficient of thermal expansion, with 50%–100% variations.
Note: The coefficients for graphite highly depend on the type or grade of the graphic.
Table 9
Measurements of Glass Surface before and after Forminga
λ
Measurement
Raw (Before)
TFG (After)
25 Å–25 μm
σ from reflectance (8 keV)
4 Å
4 Å
1 μm–10 mm
X-ray scattering HPD (8–68 keV)
11 arc sec
11 arc sec
1–200 mm
Axial figure HPD
<15 arc sec
45 arc sec
We summarize measurements on many samples by providing approximate median values. The sample-to-sample variance is larger than measurement errors. HPD values are for two reflections. λ, spatial wavelength; σ, rms microroughness.