Estimation of X-ray scattering impact in imaging degradation for the SIMBOL-X telescope

0.3 MB·English

by  D. Spiga

Mem.S.A.It.Vol.00,0
(cid:13)c SAIt 2004 Memoriedella
Estimation of X-ray s
attering impa
t in imaging
degradation for the SIMBOL-X teles
ope
D. Spiga,G. Pareschi,R. Canestrari, andV. Cotroneo
8
IstitutoNazionalediAstrofisica–OsservatorioAstronomicodiBrera,ViaE.Bianchi46,
0
I-23807Merate(LC),Italy–e-mail:[email protected]
0
2

n
Abstract. The imaging performance of X-ray optics (expressed in termsof HEW,Half-
a
Energy-Width)canbeseverelyaffectedbyX-rayscatteringcausedbythesurfaceroughness
J
of themirrors. Theimpact of X-rayscattering hasan increasing relevance for increasing
5
photonenergy,andcanbethedominantprobleminahardX-raytelescopelikeSIMBOL-
1
X. In this work we show how, by means of a novel formalism, we can derive a surface

roughnesstolerance–intermsofitspowerspectrum–fromaspecificHEWrequirement
]
h fortheSIMBOL-Xopticalmodule.
p
- Keywords.X-rays:general–Telescopes:highangularresolution
o
r
t
s
1. Introduction fectedbythemanufacturing,handling,po-
a
[ sitioningprocessofthemirrorshells.
The SIMBOL-X X-ray telescope 2. Microroughness of reflecting surfaces. It
1 (Pareschi&Ferrando (2006)) willbe thefirst
causes the scattering of reflected X-rays
v space observatory in the soft (E < 10 keV)
(XRS)(seee.g.Church&Taka´cs (1986)).
0 andhard(E >10keV)X-raybandwithimag-
This effect falls in the physical optics do-
5
ing capabilities comparable to the presently
3 main:ithasanincreasingrelevanceforin-
operated soft X-ray telescopes Newton-XMM
2 creasingphotonenergy(decreasingphoton
(15 arcsec HEW) and Swift-XRT (20 arcsec
. wavelengthλ).
1 HEW). The SIMBOL-X angular resolution
0 goal is ∼ 15 arcsec HEW at 1 keV and < As the SIMBOL-X energy band is extended
8 20arcsecHEWat30keV. up to 80 keV and beyond, XRS can be the
0
In order to ensure good imaging capabil- dominant problem at high energies. Hence, a
:
v ities to a hard X-ray grazing-incidence optic detailed study has to be carried out to estab-
i like thoseofSIMBOL-X,somecriticalpoints lishmicroroughnesstolerancesfromtheangu-
X
havetobecarefullyevaluatedandcontrolled: larresolutionmissionrequirements.Inthefol-
r lowingsectionsweshowhowthiscanbedone.
a
1. Deformation of mirrors profiles, and mir-
rorsmisalignment.TheeffectontheHEW
2. Arelationbetweentheroughness
can be considered as independent of the
PSDandtheHEW(λ)function
photon energy E, and may be estimated
using the geometricaloptics (ray-tracing). Ameaningfulsurfacesmoothnessrequirement
The impact of this factor is strongly af- depends on the formulation of a reasonable
D.Spigaetal.:EstimationofX-rayscatteringimpact... 1
HEW requirement, as a function of the pho-
tonwavelengthλ,andshouldbegiveninterms
of the power spectrum of the microroughness
(PSD,PowerSpectralDensity,seee.g.Stover
(1995)). We assume here the final HEW(λ)
to result from the quadratic sum of two inde-
pendentcontributions:theenergy-independent
HEW due to figure errorsand the HEW X-
fig
rayscatteringtermH(λ),
HEW2(λ)≈ HEW2 +H2(λ). (1) Fig.1.ThePSDsundercomparisoninthiswork.
fig
Weshallhereaftermakeuseofanovelformal-
HEW varying from 15 arcsec at 0.1 keV (es-
ism aimed at the direct translation of a given
sentially mirrorprofile errors)up to 20arcsec
H(λ)functionintoaPSD(Spiga (2007)).For
at 40 keV. From this requirement,we can de-
adoublereflectionmirrorshellwithincidence
rive a PSD directly from Eqs. (1) and (2), as-
angleθ,thePSD Patthespatialfrequency f
i 0 suming an incidence angle e.g. θ = 0.18 deg,
canbecomputedfromtheH(λ)functionalong i
intheSIMBOL-Xmirrorsrange.
withtheequation:
The computed PSD covers the low-
P(f ) d H(λ) ln(4/3) frequency regime (f < (350µm)−1, the green
0 =− . (2)
λ dλ λ ! 4π2sin3θ circlesinFig.1).Moreover,fromtheEq.(3)at
i the maximumconsideredenergy(40keV) we
Vice versa, from the numerical integration of obtainafurtherconstraintontheintegralofthe
a given PSD P(f) we can derive the foreseen PSDathigherfrequencies(Spiga (2007)),
H(λ)term,alwaysforadoublereflectionmir-
rorshell: (0.16Å)−1 1/2
σ= P(f)df <4.2Å. (5)
Zf0λ2 P(f)df = 1λ62πl2ns(i4n/23θ)i, (3) ThisZre(q35u0iµrme)m−1ent is quite exacting. For in-
stance, we plot in Fig. 1 the measured PSD
in Eqs. (2) and (3) the spatial frequency f is
0 (dashed line) of a Gold layer deposited onto
relatedtotheH(λ)functionasfollows:
a very smooth master – an optically polished
H(λ)sinθ Zerodurglass–andreplicatedbyNickelelec-
f (λ)= i. (4)
0 2λ troforming. Yet this PSD does not fulfill the
Eq. (5), because σ ≃ 6 Å; hence, it is not
The upper integration limit in the Eq. (3) can
suitable to return the required HEW trend.
bemodifiedtoaccountforthefinitesizeofthe
Fortunately, the comparison with the require-
X-ray detector in the focal plane. To be more mentsoftheXMMmandrels(the”+”signsin
conservative, we shall heretofore suppose the
Fig.1)showsthatfurtherimprovementsshould
detector to be very large to account for pho-
be possible, as better smoothness levels were
tonsscatteredatlargeangles,whichcontribute
reachedinthatcase(Gougeonetal. (1996)).
notonlytoimagingdegradation,butalsotoef-
For instance, a simulated PSD that could
fectiveareareduction.
fulfill our requirements is represented by the
solid line in Fig. 1. To check this result, we
computed from that PSD (Eqs. (3) and (4))
3. ApossiblePSDforSIMBOL-X
theexpectedHEWtrendfrom1to70keVfor
mirrors
three mirror shells of the SIMBOL-X optical
Arealisticmicroroughnessrequirementshould module.Weassumed15arcsecfigureerrorand
be derived from a slowly-increasingHEW(E) 3degasdetectorradius,muchlargerthanthat
function.Therefore,we can initially require a of SIMBOL-X (∼ 420 arcsec). The resulting
2 D.Spigaetal.:EstimationofX-rayscatteringimpact...
Fig.2. The HEW derived from the PSD model
Fig.3. ThefinalHEWforthewholeoptical mod-
in Fig. 1 (solid line), at three incidence angles of
uleofSIMBOL-X,assumingthesolidlineinFig.1
SIMBOL-X mirror shells: 0.11 deg (the smallest
asPSDofmirrorssurface.TheHEWiswithinthe
one), 0.18 deg (the angle of an intermediate shell,
requirement.
the55th),and0.25deg(thelargestone).
directly translated into important information
HEWvaluesexhibitamoderateincreaseatlow concerning the surface microroughness toler-
energies,reachawide”plateau”anddivergeat ance,convenientlyexpressedintermsofPSD.
veryhighenergies.Theincreaseismuchmore Conversely,we canusethe PSD ofthemirror
markedatthelargestincidenceangles. roughness – measured over a very wide spa-
Inordertoevaluatetheoverallangularres- tialfrequencyrange–topreviewtheHEW(E)
olutionfortheSIMBOL-Xopticalmodule,we function of a single mirror shell, in the range
performed the calculation of the HEW as a of photon energies and incidence angles of
function of the photon energy for all mirror SIMBOL-X. The HEW can be calculated for
shells,assumingthesamePSDusedinFig.2, each mirror shell from the surface PSD, and
andweaveragedtheHEWvaluesoverthere- fromthatwecaneasilyrecovertheHEWesti-
spectiveeffectiveareasAk(E): mationfortheentireopticalmodule.
Calculations performed on the PSD of
100A (E)HEW (E)
HEW (E)= k=1 k k . (6) samples replicated from smooth masters by
tot P A (E) Nickel electroforming proved that the effort
k
has to be concentrated on the damping of the
P
The final result, plotted in Fig. 3, exhibits a
microroughnessatspatialwavelengthsshorter
slow increaseofthe HEWforincreasingpho-
than ∼ 300 µm, in order to improve the an-
ton energy from 1 to 70 keV and fulfills the
gularresolutionathighenergiesandtherefore
SIMBOL-Xrequirement(HEW<20arcsecat
tomeettheSIMBOL-Xangularresolutionre-
30keV).Infact,thedampingoftheHEWin-
quirementsinsoftandhardX-rays.
creaseisalsoduetotheeffectiveareacutoffat
lowerenergiesforlargerincidenceangles,that Acknowledgements. O. Citterio, P. Conconi,
balances the steeper divergence of the HEW S.Basso(INAF/OAB)forusefuldiscussions.
(seeFig.2).
References
4. Conclusions
Church, E. L. & Taka´cs, P. Z. 1986, in Proc.
TheevaluationoftheXRS contributiontothe SPIE640,125
HEWintheSIMBOL-XhardX-raytelescope Gougeon,S.etal.1996,inProc.SPIE,2805
is a very important issue, since at high ener- Pareschi,G.&Ferrando,P.2006,Exp.Astron.
gies it can be the dominant imaging degrada- 20,139
tion factor, if the reflecting surfaces are not Stover, J. C. 1995, Optical scattering: mea-
sufficiently smooth. By means of the formu- surement and analysis (SPIE Optical
laementionedabove,agivenHEW(E)require- EngineeringPress)
ment–intheSIMBOL-Xenergyband–canbe Spiga,D.2007,A&A,468(2),772