1. SPIE
Optics for EUV, X-Ray, and Gamma-Ray Astronomy VI
Montreal 2014 June 27th – 29th
Science requirements and optimization of the silicon pore optics design for the Athena mirror
Dick Willingale
University of Leicester
G. Pareschi, F. Christensen, J-W. den Herder, D. Ferreira, A. Jakobsen,
M. Ackermann, M. Collon, M. Bavdaz

2. Specification – Area – Angular Resolution
Area of 2 m2 at 1 keV
~5 times larger than the 3 XMM telescopes
sensitivity ~10-17 ergs cm-2 s keV
detect AGN z>6, WHIM…
spectroscopy ΔE~2.5 eV
Angular resolution 5 arc sec HEW
~3 times better than XMM telescopes
avoid faint point source confusion
resolve structures like clusters of galaxies
spectral imaging of SNRs, clusters…

3. Specification – Field of View
Vignetting and field of view
FOV >40 arc minutes diameter
minimize vignetting
minimize degradation of HEW off-axis
target grasp (collecting area x FOV product)
0.5 m2 deg2 at 1 keV
deep search for faint sources, AGN…

4. Si pore optics – XEUS to Athena
Si pore module – Cosine Research
~3 m aperture - focal length F=12m

5. Manufacture of SPO modules
Rib spacing
Axial profile
Kink angle≈R/2F
ESA - Cosine Research
Axial length L=4Fd/R
Short - 20 to 102 mm

6. Area of 2 m2 at 1 keV 6 sectors – radial arms width 20 mm
Module apertures ~100x50 mm
Radial gaps 10 mm
Azimuthal gaps 14 mm
Inner radius of aperture 258 mm
Outer radius of aperture 1464 mm
Total 972 modules
Inner ring R=285 mm, L=101.9 mm
Outer ring R=1437 mm, L=20.3
F=12 m

7. Area of 2 m2 at 1 keV Lowest curve outer modules
Highest curve inner modules
Black - Ir+B4C overcoat
Red - Ir

8. Angular resolution 5 arc sec HEW
Conical approximation with F=12 m –> 5.2 arc sec HEW
Radial pore width d=0.605 mm
Si wafer thickness 0.76 mm – membrane 0.15 mm
Axial curvature required – mandrel specification
equal on both surfaces d2r/dx2 = -R/16F2 = -θg2/R
sagittal Δr=0.16 microns inner module, 0.03 microns outer module
In-plane figure errors – 1 arc sec rms
Out-of-plane figure errors – 1 arc sec rms but unimportant
Focal length errors (kink angle error) – 1 mm rms (F=12 m)
Module alignment
Rotation about optical axis 2 arc sec rms
Shift in aperture plane 0.05 mm rms
Tilt errors 1 arc minute rms

9. Vignetting – off-axis area
In-plane vignetting
Radial pore size d (fixed)
Length of pores L
Drops to zero at θ≈d/2L
Out-of-plane vignetting
Rib spacing drib
Length of pores L
Drops to zero at θ≈drib/2L
Ray tracing of a single module

10. Field of view vs. drib for Athena
Ray tracing full aperture
drib 1, 2, 3, 4, 5 mm FOV at half on-axis area 1 keV

11. FOV, Photon Energy, Grasp – drib 3mm
Grasp 0.5 m2 deg2 at 1 keV for FOV 40 arc mins

12. Angular resolution off-axis
Wolter I - principal plane (join plane) flat
Wolter-Schwarzschild (W-S) Obeys Abbé sine condition
principal plane spherical radius curvature F
To implement W-S is simple
Change θg - kink angle between 1st and 2nd surfaces in module
Mount modules on the correct spherical surface

13. Using W-S Principal Plane
Black – Wolter/conical
Green – W-S/conical
Blue – Wolter
Red – W-S
Dotted – W-S limit
no errors
Error budget – 5 arc sec HEW

14. Angular resolution off-axis
Split curvature between 1st and 2nd surfaces
Keep curvature sum constant – on-axis HEW remains constant
- θg2/R 1st and 2nd st -2 θg2/R, 2nd conical

15. Angular resolution off-axis
Split curvature between
1st and 2nd surfaces
Solid black conical-conical
Solid red Wolter
Solid green curve
close to optimum
conical 1st surface
-2 θg2/R 2nd surface
Average HEW
5.6 arc sec 40 arc min FOV
5.9 arc sec 50 arc min FOV
Use W-S principal plane

16. Conclusions Area 2 m2 at 1 keV 3 m aperture F=12m ~970 SPO modules
Ir coating
Angular resolution 5 arc seconds HEW on-axis
axial curvature -2 θg2/R sum over 1st and 2nd surface
tight but achievable error budget
Minimize vignetting
rib spacing 3 mm
grasp 0.5 m2 deg2 at 1 keV 40 arc min FOV
Minimize degradation of angular resolution off-axis
W-S principal plane – change kink angle within modules
Curvature 1st conical 2nd -2 θg2/R
Mean HEW 5.6 arc sec for 40 arc min FOV

17. The End