Hard X-ray Multilayer Optimisation for Astronomical Missions

Vincenzo Cotroneo – OAB Merate/INAF 8/11/2004

Hard X-ray Multilayer Optimisation for Hard X-ray Multilayer Optimisation for Astronomical MissionsAstronomical Missions


X-ray Reflection and focalization X-ray Reflection and focalization techniquestechniques

The problem of multilayer The problem of multilayer optimisation for hard X ray (E > 10 optimisation for hard X ray (E > 10 keV) reflection.keV) reflection.

Multilayer mirrors optimisation for Multilayer mirrors optimisation for future astronomical X-ray projects. future astronomical X-ray projects.

ConclusionsConclusions


Minimum detectable flux for past-present-future astronomical missions

GOAL!


Resolving the XRB by focusing optics


Total reflectionTotal reflection

At photon energies > 10 keV the cut-off angles for total reflection are very small also for heavy metals the attained geometrical areas are the attained geometrical areas are in general in general very smallvery small

Ecrit

•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


Multilayer mirrors reflectionMultilayer 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 )Variable d-spacing Is possible to obtain high reflectivity on a broader energy band


1 m

Aspidomorpha Tecta;

Multilayer for broad band reflection not only in tecnology, but also in nature

Natural multilayers (µm, for visible light)Artificial multilayerArtificial multilayer(nm for X-ray reflection)(nm for X-ray reflection)


Geometry Wolter I for grazing incidence opticsGeometry Wolter I for grazing incidence optics

•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

Mirror shell and optical module of SWIFT telescope


Ni/C multilayer 20 bilayersDec 2003E-beam depositionby OAB/Media Lario

Ni/C multilayer onto a Si wafer substrate



How to choose the best thickness How to choose the best thickness values?values?

It is possible to calculate the multilayer reflectivity for a given layers It is possible to calculate the multilayer reflectivity for a given layers thicknesses sequence but..thicknesses sequence but..

it is generally not possible to analitically design the thicknesses for a it is generally not possible to analitically design the thicknesses for a given Reflectivity vs Energy responsegiven Reflectivity vs Energy response

The reflectivity vs energy curve is determined by layers thicknesses The reflectivity vs energy curve is determined by layers thicknesses sequencesequence

It can be useful to define a function (It can be useful to define a function (function of meritfunction of merit or or FOMFOM) ) whose value indicates “how good” is the chosen solutionwhose value indicates “how good” is the chosen solution

Employing numerical techniques the highest value of the merit Employing numerical techniques the highest value of the merit function function (best design)(best design) can be find. can be find.


SIMPLEX ALGORITHM (amoeba)SIMPLEX ALGORITHM (amoeba)

It is a quite atypical optimisation technique:•It does not require derivative informations•The method is LOCAL

Applicazione alla funzione di prova:

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ITERATED SIMPLEX METHOD ITERATED SIMPLEX METHOD

The SIMPLEX ALGORITHM results are strongly dependent from starting points.

ITERATED SIMPLEX METHOD (IS) consists in repeated execution of simplex algorithm, starting every time from different simplexes in parameter space.

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

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ISOXM program functional ISOXM program functional scheme for IS optimisationscheme for IS optimisation


d-spacing sequence described by a power law:

PARAMETERS FOR OPTIMISATION

cibi

ad

• the 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

with: “a” ranging between 0 and ∞∞ “b” ranging between -∞ and 1“c” ranging between 0 and ∞∞


Dispersion of parameters after an iterated simplex optimization. Since the starting parameters are generated in a closed region, they are left free to expand.


Optimization strategyOptimization strategy

• optimized parameters: a, b, c + the 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 Every shell is optimized with a single execution of the simplex algorithm starting from the best a single execution of the simplex algorithm starting from the best result of the previous oneresult 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.


Integrated effective area and parameters along shells (XEUS)


XEUS missionXEUS mission


Mission XMM -XMM -NewtonNewton

XEUSXEUS

Number of modules

3

1

10.0 mMax diameter

0.7 m

Min diameter

0.3 m

1.3 m

Geom. area @ 1 keV

0.15 m2(per mod.)

30 m2

Min. angle (I)Min. angle (II)

0.3 deg 0.18 deg 0.7 deg

Max. angle (I)Max.angle (II)

0.67 deg

0.7 deg 1.4 deg

Angular Resoltion (HEW)

15 arcsec

2 arcsec (goal level)

XEUS

XMM-Newton

Credits: ESA

Credits: ESA

Focal Length 7.5 m 50 m


Mirror Shell, Segments & PetalsMirror 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

Gli specchi di XEUSGli specchi di XEUS


Extension of the XEUS operative range to hard X-ray (E ≥ 80 keV)

XEUS I

Ogasaka et al., 2003

• 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


XEUS I optimization:

• Shells 1-250: N=200, optimization with power law

Parameters: a,b,c, Γ1, ΓN

For shells 251-296 N=30 D=80 Å

ci bi

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)(

d80CW100_50

1/11/1125-250125-250

--D=80 D=80 ÅÅ251-296251-296

1/41/4119-124119-124

2/42/41-1181-118

EdEA eff 30

20

70

20

2 dEEA eff

70

20

2 dEEA eff

Local minimum Local minimum F.O.M.F.O.M.ShellsShellsXEUS I optimization results:

• AAeff eff = 2000 cm= 2000 cm2 2 @ 40 keV @ 40 keV

• The number of bi-layers could be further on reduced without a strong impact on the reflectivity

Reduction of the deposition time and of the roughness increase


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 sin= n ) 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

HOWEVERHOWEVER

• 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


Effect of the XEUS II Low-Energy Enhancement

carbon overcoating

multilayer Bragg peak


Test performed at the PANTER-MPE facility (Credits: W. Burkert).

Low-energy (0.93 keV) reflectivity enhancement of a Ni mirror by a 50 Å Carbon overcoating: experimental result


P.I.: P. FerrandoService d’Astrophysique CEA & Fédération de Recherche APC

Progetto proposto al CNES (Bando “formation flight” 2004) da:

Francia: Service d’Astrophysique CEA Saclay / CESR ToulouseLAOG Grenoble / LUTH Meudon

Italia: 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

SIMBOL–XSIMBOL–X


• Formation fligth with 30 m focal length• Can serve as XEUS pathfinder

SIMBOL-X mission conceptSIMBOL-X mission concept

Main features

Operative band: 0.5–70 keV

Energetical resolution: < 130 eV @ 6 keV, 1 % @ 60 keV

Angular resolution: < 30 arcsec (local. < 3 arcsec)

Effective area: > 550 cm2 E < 35 keV 150 cm2 @ 50 keV

Sensibility: 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


SIMBOL-X: area efficace in asseSIMBOL-X: area efficace in asse


60 cm diam (baseline)

70 cm diam

80 cm diam + ML



HEXIT-SAT missionHEXIT-SAT mission


HEXIT – SATHEXIT – 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



Number of modulesNumber of modules 44

Number of nested mirror shellsNumber of nested mirror shells 5050

Reflecting coatingReflecting coating 200 bilayers W/Si200 bilayers W/Si

Geometrical profile Geometrical profile Wolter I (lin. approx)Wolter I (lin. approx)

Focal LengthFocal Length 8000 mm8000 mm

Total Shell HeightTotal Shell Height 800 mm800 mm

Plate scalePlate scale 26 arcsec/mm26 arcsec/mm

Total Shell Height Total Shell Height 800 mm800 mm

Material of the mirror wallsMaterial of the mirror walls electroformed Nielectroformed Ni

Min-MaxTop DiameterMin-MaxTop Diameter 112 - 330 mm112 - 330 mm

Min - Max angle of incidenceMin - Max angle of incidence 0.096 - 0.295 deg0.096 - 0.295 deg

Min-Max wall thicknessMin-Max wall thickness 0.120 - 0.350 mm0.120 - 0.350 mm

Total Mirror Weight (1 module)Total Mirror Weight (1 module) 6565

Field-of-View (diameter FWHMField-of-View (diameter FWHM 15 arcmin15 arcmin

Single module effective areaSingle module effective area 75 cm75 cm2 2 @40 keV@40 keV

HEXIT-SAT Main featuresHEXIT-SAT Main features


4 modules4 modules


Effects of using different FOMsEffects of using different FOMs The design can be chosen according to the The design can be chosen according to the

mission targetmission target


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 power-laws 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 The study showed a consistent increase of the XEUS effective area in the energy region between 0.5 and 5 keV.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.


The End

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Hard X-ray Multilayer Optimisation for Astronomical Missions