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Hard X-ray Multilayer Optimisation for
Astronomical Missions
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
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X-ray Reflection and focalization
techniques
The problem of multilayer
optimisation for hard X ray (E > 10
keV) reflection.
Multilayer mirrors optimisation for
future astronomical X-ray projects.
Conclusions
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Minimum detectable flux for past-present-future astronomical missions
GOAL!
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Resolving the XRB by focusing optics
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Total reflection
•In X ray regions refractive index are close to and little less than 1
•for grazing angles lower than a critical angle total reflection phenomenon
takes place. Present day focalising telescopes are based on it
crit 

E
At photon energies > 10 keV the
cut-off angles for total reflection are
very small also for heavy metals 
the attained geometrical areas are
in general very small
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Multilayer mirrors reflection
•For angles bigger than critical one, reflectivity is low, but not
zero..
•A multilayer consists in a sequences of bilayers (everyone composed
from a couple of light and heavy material), the waves reflected from every
interface sum in phase.
Constant bilayer thickness (d-spacing)  Bragg (constructive
interference @ 2d sin q = n l)
Variable d-spacing  Is possible to obtain high reflectivity on a
broader energy band
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Multilayer for broad band reflection not only
in tecnology, but also in nature
Artificial multilayer
(nm for X-ray reflection)
Natural multilayers (µm, for visible light)
Aspidomorpha Tecta;
1 mm
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Geometry Wolter I for grazing incidence optics
Mirror shell and optical module of SWIFT telescope
•Grazing incidence
optics employ nested
shells to improve
collecting area
•Every shell is
composed of a double
profile (parabole +
hyperbole in Wolter I
design). This scheme
gives reduced optical
aberrations and a
shorter focal length
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Ni/C multilayer onto a Si wafer substrate
Ni/C multilayer 20 bilayers
Dec 2003
E-beam depositionby OAB/Media Lario
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
How to choose the best thickness
values?
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The reflectivity vs energy curve is determined by layers thicknesses
sequence

It is possible to calculate the multilayer reflectivity for a given layers
thicknesses sequence but..
it is generally not possible to analitically design the thicknesses for a
given Reflectivity vs Energy response
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It can be useful to define a function (function of merit or FOM)
whose value indicates “how good” is the chosen solution
Employing numerical techniques the highest value of the merit
function (best design) can be find.
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
SIMPLEX ALGORITHM (amoeba)
Applicazione alla funzione dir prova:
f ( x, y )   cos (9r )e
2
(
0.15
)
r  ( x  0.5) 2  ( y  0.5) 2
Dato iniziale
R
C
E
Cmin
FINE?
no
si
USCITA
It is a quite atypical optimisation
technique:
•It does not require derivative
informations
•The method is LOCAL
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
ITERATED SIMPLEX METHOD
PRINCIPALE
Crea i dati
FUNZIONE
The SIMPLEX ALGORITHM results are strongly
dependent from starting points.
SIMPLEX
ITERATED SIMPLEX METHOD (IS) consists in
repeated execution of simplex algorithm, starting
every time from different simplexes in parameter
space.
Legge un
dato
Scrive il
risultato
no
FINE
si
USCITA
The software package “ISOXM” ( Iterated Simplex
Optimisation for X-ray Multilayers ) has been
developed following this approach. It is possible to
obtain results for different functions of merit
(FOM). The software comprises tools for results
analysis and visualization
ISOXM program functional
scheme for IS optimisation
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
PARAMETERS FOR OPTIMISATION
d-spacing sequence described by a power law:
a
di 
i  b c
with:
“a” ranging between 0 and ∞
“b” ranging between -∞ and 1
“c” ranging between 0 and ∞
• the G parameter linearly changes
along the stack
• the heavy-material top layer is of
increased size + a Carbon overcoating
is added  to allow a high response in
the soft X-ray regime
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Dispersion of parameters after an
iterated simplex optimization. Since the
starting parameters are generated in a
closed region, they are left free to
expand.
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Optimization strategy
• optimized parameters: a, b, c + the G slope
• iterated simplex optimization performed on a small number of
selected shells distributed along the sequence of the diameters by
using different FOMs
• sequential optimization of all the shells, based on the results of
the immeditely previous optimization. Every shell is optimized with
a single execution of the simplex algorithm starting from the best
result of the previous one
• it is possible to combine results obtained from different FOMs for
each group of shells, obtaining at the end the “more performing”
total effective area of the telescope.
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Integrated effective area and parameters along shells (XEUS)
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
XEUS mission
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
XMM-Newton
XMM Newton
XEUS
Focal Length
7.5 m
50 m
Number
of
modules
Max diameter
3
1
0.7 m
10.0 m
0.3 m
1.3 m
Mission
Min diameter
Geom. area
@ 1 keV
Min. angle (I)
Min. angle (II)
Max. angle (I)
Max.angle (II)
Angular
Resoltion
(HEW)
0.15 m2
(per mod.)
0.3 deg
30
m2
Credits: ESA
XEUS
0.18 deg
0.7 deg
0.67 deg
0.7 deg
1.4 deg
15 arcsec
2 arcsec
(goal
level)
Credits: ESA
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Gli specchi di XEUS
Mirror Shell, Segments & Petals
•562 shell (296 XEUS I + 266 XEUS II)
•Because of the huge dimensions, Wolter shells
must be realized assembling a big number of
segments (0.5 m x 1 m x 1 mm). Segments
(17500) are grouped in “petals” (128) that form 5
concentric rings (2 XEUS I + 3 XEUS II).
•Ø min. XEUS I = 1.3 m
•Ø max. XEUS I = 4.04 m
•Ø max. XEUS II = 9.9 m
CREDIT: ESA
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Extension of the XEUS operative range to hard X-ray (E ≥ 80 keV)
• Even if the XEUS focal length is very large, the f-number are
relatively small also for XEUS I (34 -10)  only with the use
of multilayer supermirrors it is possible the hard X-ray
extension of the XEUS operative range
• study performed in Japan (Nagooya Univ & ISAS) suggested
the use of Pt/C supermirrors based on discrete blocks of
constant bi-layers with different (constant) d-spacing
The supermirror
solution is currently
being considered by
the XEUS Telescope
Working Group
Ogasaka et al., 2003
XEUS I
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
optimization:results:
XEUS I optimization
Shells
••
2 @ 40 keV
Shells
1-250:
optimization
A
cmN=200,
eff = 2000
with power law
• The number
of bi-layers could be
a
d i on reduced
further
without a strong
(i  b) c
impact on the reflectivity
Parameters: a,b,c, Γ1, ΓN
 Reduction of the deposition time
For shells 251-296  N=30 D=80 Å
and of the roughness increase
F.O.M.
Local
minimum
70
1-118

A
eff
 E
2
dE
20
2/4
30
119-124

A
eff
 EdE
1/4
20
125-250
70

A
eff
 E
2
dE
1/1
20
251-296
D=80 Å
-
d80CW100_50
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Multilayer mirrors for XEUS II: a viable and suitable choice?
• depth-graded multilayer supermirrors for the enhancement of the hard X-ray
(E > 10 keV) response are not convenient, since with the XEUS II large angles
(0.7 – 1.4 deg) we are far from the Bragg diffraction conditions (2 d sinq = n l)
at high energy
• the use of “broad-band” multilayer supermirrors made of many bi-layers is not
viable even below 10 keV, due to the strong photoelectric absorption
HOWEVER
• the soft X-ray (0.5 – 4 keV) response of any high density material (Au, W, Ir,
Ni, Pt…) can be increased with the introduction of a low density material
overcoating, not sensitive to the photoelectric absorption effects in the total
reflection region (and anyway transparent at higher photon energies…)
• constant d-spacing multilayers (formed by a small number of bilayers) are
able to provide narrow high-reflectivity Bragg peaks in the soft X-ray region
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Effect of the XEUS II LowEnergy Enhancement
carbon overcoating
multilayer Bragg
peak
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Low-energy (0.93 keV) reflectivity
enhancement of a Ni mirror by a 50 Å
Carbon overcoating: experimental result
Test performed at the PANTER-MPE
facility (Credits: W. Burkert).
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
SIMBOL–X
P.I.: P. Ferrando
Service d’Astrophysique CEA & Fédération de Recherche APC
Progetto proposto al CNES (Bando “formation flight” 2004) da:
Francia:
Italia:
Service d’Astrophysique CEA Saclay / CESR Toulouse
LAOG Grenoble / LUTH Meudon
INAF - Observatorio Astronomico di Brera ( ma interesesse a questa
missione già mostrato anche da ricercatori di altri enti in ambito INAF,
IASF/CNR e Università)
Germania: MPE Garching / PNSensor GmbH München / IAA Tübingen
UK:
Dept of Astronomy and Astrophysics, Leicester
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
SIMBOL-X mission concept
• Formation fligth with 30 m focal length
• Can serve as XEUS pathfinder
Main features
Operative band:
0.5–70 keV
Energetical resolution:
< 130 eV
1 %
@ 6 keV,
@ 60 keV
Angular resolution: < 30 arcsec (local. < 3
arcsec)
Effective area:
Sensibility:
>
550 cm2 E < 35 keV
150 cm2 @ 50 keV
5 10-8 ph/cm2/s/keV (E < 40 keV)
(5 s, 100 ks, DE = E/2)
Si SDD (0.5 – 10 keV) detector+ CdZnTe (10 – 70
keV) detector
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
SIMBOL-X: area efficace in asse
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
80 cm diam + ML
70 cm diam
60 cm diam (baseline)
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
HEXIT-SAT mission
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
HEXIT – SAT
(High Energy X-ray Imaging Telescope - SATellite)
Mission concept to be realized for main contribute at national level
from a researchers of INAF, IASF e Universities.
• It will be presented to the international community on the
occasion of the next SPIE conference in Glasgow (Fiore et al.,
2004)
• It is based on on a multimodular telescope (4 units) with Wolter
multilayer mirrors with 8 m of focal length
• Extensable optical bench to reduce the costs
• Orbita LEO equatoriale (“SAX like”)  optimal to have a low
particles background
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
HEXIT-SAT Main features
4
Number of modules
Number of nested mirror shells
50
200 bilayers W/Si
Reflecting coating
Wolter I (lin. approx)
Geometrical profile
8000 mm
Focal Length
800 mm
Total Shell Height
26 arcsec/mm
Plate scale
800 mm
Total Shell Height
electroformed Ni
Material of the mirror walls
112 - 330 mm
Min-MaxTop Diameter
Min - Max angle of incidence
0.096 - 0.295 deg
Min-Max wall thickness
0.120 - 0.350 mm
Total Mirror Weight (1 module)
65
Field-of-View (diameter FWHM
15 arcmin
Single module effective area
75 cm2 @40 keV
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
4 modules
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Effects of using different FOMs
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The design can be chosen according to the
mission target
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
Summary and conclusions
•The software ISOXM ( Iterated Simplex Optimisation for X-ray
Multilayers ) for global Optimisation with different FOMs has been developed.
The numerical optimization of depth-graded supermirrors described by powerlaws for several missions has been executed with good results.
• future work will be done to study a possible reduction of the number of bi-layers
compared to the 200 units assumed for this study.
• At larger incidence angles multilayer reflectors can be employed to enhance the
reflectivity at low energies by mean of constant d-spacing multilayers with Carbon
overcoating. The study showed a consistent increase of the XEUS effective area
in the energy region between 0.5 and 5 keV.
• the carbon overcoating could be useful, not only to enhance the reflectivity in the
soft X-ray region, but also to prevent aging effects due to the exposure to Atomic
Oxigen fluxes.
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004
The End
Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004