Correcting peak deformation in Rosetta's ROSINA/DFMS mass spectrometer

(1)

HAL Id: insu-01219657

https://hal-insu.archives-ouvertes.fr/insu-01219657

Submitted on 15 May 2020

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Distributed under a Creative Commons Attribution - NonCommercial| 4.0 International

License

Correcting peak deformation in Rosetta’s

ROSINA/DFMS mass spectrometer

Johan de Keyser, Federik Dhooghe, Andrew Gibbons, Kathrin Altwegg, Hans

Balsiger, Jean-Jacques Berthelier, Christelle Briois, Ursina Calmonte, Gael

Cessateur, Eddy Equeter, et al.

To cite this version:

(2)

InternationalJournalofMassSpectrometry393(2015)41–51

ContentslistsavailableatScienceDirect

International

Journal

of

Mass

Spectrometry

j o ur na l ho me p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m s

Correcting

peak

deformation

in

Rosetta’s

ROSINA/DFMS

mass

spectrometer

J. De

Keyser

a,b,∗

_,

_F.

_Dhooghe

a

_,

_A.

_Gibbons

a,c

_,

_K.

_Altwegg

d,e

_,

_H.

_Balsiger

d

_,

_J.-J.

_Berthelier

f

_,

Ch.

Briois

g

_,

_U.

_Calmonte

d

_,

_G.

_Cessateur

a

_,

_E.

_Equeter

h

_,

_B.

_Fiethe

i

_,

_S.A.

_Fuselier

j

_,

T.I.

Gombosi

k

_,

_H.

_Gunell

a

_,

_M.

_Hässig

d

_,

_L.

_Le

_Roy

e

_,

_R.

_Maggiolo

a

_,

_E.

_Neefs

h

_,

_M.

_Rubin

d

_,

Th.

Sémon

d

a_Space_Physics_Division,_Belgian_Institute_for_Space_Aeronomy,_Ringlaan_3,_B-1180_Brussels,_Belgium

b_Center_for_Plasma_{Astrophysics,}_Katholieke_Universiteit_Leuven,_{Celestijnenlaan}_200B,_B-3001_Heverlee,_Belgium

c_Quantum_Chemistry_and_Photophysics_Laboratory,_Université_Libre_de_Bruxelles,_Av._F._D._Roosevelt_50,_B-1050_Brussels,_Belgium d_{Physikalisches}_Institut,_University_of_Bern,_Sidlerstr._5,_CH-3012_Bern,_Switzerland

e_Center_for_Space_and_{Habitability,}_University_of_Bern,_Sidlerstr._5,_CH-3012_Bern,_Switzerland f_{LATMOS/IPSL-CNRS-UPMC-UVSQ,}₄_Av._de_Neptune_F-94100,_Saint-Maur,_France

g_Laboratoire_de_Physique_et_Chimie_de_{l’Environnement}_et_de_l’Espace,_CNRS_&_Univ._{d’Orléans,}_3A_Av._de_la_Recherche_{Scientiﬁque,}₄₅₀₇₁_Orléans,_France h_Engineering_Division,_Belgian_Institute_for_Space_Aeronomy,_Ringlaan_3,_B-1180_Brussels,_Belgium

i_Institute_of_Computer_and_Network_Engineering_(IDA),_TU_{Braunschweig,}_{Hans-Sommer-Straße}_66,_D-38106_{Braunschweig,}_Germany j_Department_of_Space_Science,_Southwest_Research_Institute,₆₂₂₀_Culebra_Road,_San_Antonio,_TX_78228,_USA

k_Department_of_Atmospheric,_Oceanic_and_Space_Sciences,_University_of_Michigan,₂₄₅₅_Hayward,_Ann_Arbor,_MI_48109,_USA

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received4August2015

Receivedinrevisedform14October2015 Accepted14October2015

Availableonline23October2015 PACS: 82.80.Ms 95.55.Pe 95.55.Ym 95.75.Pq MSC: 49M15 90C53 90C90 65K10 Keywords: Massspectrometry Planetaryinstrumentation Dataanalysis Cometatmosphere Rosetta

a

b

s

t

r

a

c

t

TheDoubleFocusingMassSpectrometer(DFMS),partoftheROSINAinstrumentpackageaboardthe EuropeanSpaceAgency’sRosettaspacecraftvisitingcomet67P/Churyumov-Gerasimenko,experiences minordeformationofthemasspeaksinthehighresolutionspectraacquiredform/Z=16,17,andtoa lesserextent18.Anumericaldeconvolutiontechniquehasbeendevelopedwithatwofoldpurpose.A ﬁrstgoalistoverifywhetherthemostlikelycauseoftheissue,alackofstabilityofoneoftheelectric potentialsintheelectrostaticanalyser,canindeedbeheldresponsibleforit.Thesecondgoalistocorrect forthedeformation,inviewoftheimportantspecieslocatedaroundthesemasses,andtoallowastandard furthertreatmentofthespectraintheautomatedDFMSdataprocessingchain.

∗ Correspondingauthorat:SpacePhysicsDivision,BelgianInstituteforSpace Aeronomy,Ringlaan3,B-1180Brussels,Belgium.Tel.:+3223730368.

E-mailaddress:Johan.DeKeyser@aeronomie.be(J.DeKeyser).

1. Introduction

DFMSisthehighresolutiondoublefocusingmassspectrometer oftheROSINAinstrument[1]onboardtheRosettaspacecraftofthe EuropeanSpaceAgency.Rosettaisvisitingcomet 67P/Churyumov-Gerasimenko.TheDFMSmassspectrometer(Fig.1)hasbeenbuilt withthepurposeofmeasuringthecompositionofthecometary http://dx.doi.org/10.1016/j.ijms.2015.10.010

(3)

42 J.DeKeyseretal./InternationalJournalofMassSpectrometry393(2015)41–51

Fig.1. TheDFMSmassspectrometerinthecleanroombeforeinstallationon Rosetta.Theinstrumententranceisundertheclosedcoverontheright;thedetector headistotheleft.Theelectronicsboxisatthebottom.

Fig.2. AschematicdrawingofthearchitectureoftheDFMSmassspectrometer showingtheinstrumententrancewiththeionsource,thetransferoptics,the elec-trostaticanalyser,thesectormagnet,thezoomsystem,andthedetectors[1].

atmosphere.Itcandetectcometaryneutralsandionsinthemass rangeof13–150amu/e.Intheformercasetheneutralsﬂowinto theinstrument,wheretheymaybeionisedwithorwithout accom-panyingfragmentationuponbombardmentwith45eVelectrons. Inthelattercase,positivecometaryionsareattractedbysetting agridinfrontoftheinstrumententranceatanegativepotential, whilethenegativespacecraftpotentialalsofacilitatestheingestion ofions.Theionsareelectrostaticallyaccelerateduponleavingthe source.Theanalysersection(Fig.2)consistsofthetransferoptics, anelectrostaticanalyserandasectormagnet,followedbyazoom system,allowingtheinstrumenttoworkinalowandahighmass resolutionmode(LRandHRmode),theHRmodeofferinga fac-torof6.4improvementinresolutionascomparedtotheLRmode. Thezoomsystemconsistsofahexapoleplustwoquadrupoles.The hexapolecanbeusedtorotate thefocalplane,whilethe com-binationoftwo quadrupolesallowstoincreasetheimagescale. Theactualzoomfactorvaries between5.0and 6.6becausethe quadrupolepotentialsareadaptedasafunctionofthe accelerat-ingpotential[2].DFMSfeaturesthreedifferentdetectors,ofwhich thecombinationofamicrochannelplate(MCP)withalinearCCD (theLinearElectronDetectorArrayorLEDAchip,whichfor redun-dancyreasonsfeaturestworowsofchargecollectinganodes)is beingusedmostoften[3,4].TheanalogCCDoutputisdigitizedby ananalog-to-digitalconverter(ADC)providinganumberofcounts perpixel,whichlateristranslatedintoanumberofdetectedions.

TheDFMS-MCP/LEDAcombinationoffersdetailedviewsofsections ofthemassrangecenteredaroundacommandedmass.Themass resolutionactuallyachievedisaroundm/m=800inLRmodeand 5000inHRmode,wheremisthefullwidthathalfmaximum ofthemasspeaks.Thehighresolutionmode,inparticular,offers interestingprospectsfordistinguishingisotopesandestablishing isotoperatios[5,6].Earlyscientiﬁcresults[7–10]conﬁrmthehigh massresolutioncapabilityoftheinstrument.

WhileDFMSoperates successfully,aproblemhasbeen spot-tedwiththeinstrumentoperatinginneutralmodeforHRspectra atmass-over-chargeratiosofm/Z=16,17,andtoalesserextent 18amu/e;thisproblemisalsomarginallypresentintheLRspectra atm/Z=16and17.Theproblemconsistsofanabnormal broaden-ingand/ordeformationofthemasspeaks.Fig.3showsHRspectra forcommandedmassesm/Z=16amu/e(upperhalfoftheﬁgure) andm/Z=17amu/e(lowerhalf)fromrowA(top)andB(bottom) obtainedon2014-08-2202:10:40and02:11:08(red♦), 2014-10-2017:44:13and17:44:47(green◦),and2014-12-2511:17:34and 11:18:04(blue䊐).Allspectrawereacquiredwithahighelectron emissioncurrent(200␮A)intheDFMSionsource.Thecurvesgive therawADCcountscollectedduring20safterremovaloftheLEDA offset(pixelandread-outnoise)asafunctionofthedetectorpixel number.Theshape ofthedeformedpeaksslowlychanges with time.Withinasinglespectrumthepeakshapeisslightlydifferent foreachmasspeak,andtherealsoaresomedifferencesbetween rowAandB.Peakpositionsalsochangewiththepropertiesofthe massanalyser,forinstance,duetothevariationofmagnetstrength withtemperature.

Themostlikelyexplanationofferedthusfarisaproblemwith theinstrumentoptics.Theelectricpotentialsatwhichtheinner andouterplatesoftheelectrostaticanalyserareset(asafunction ofcommanded mass)arebuiltfroma coarseanda fine poten-tial.Betweenm/Z=15and16amu/ethereisamajorstepinthe coarsepotential,requiringthefinepotentialtobeatitshighest valueform/Z=16amu/eandprogressivelysmalleratsubsequent masses,andthusclosetoitsdesignlimits.Theworkinghypothesis isthatthefinepotentialthenfluctuatesaroundthedesiredvalue. Thespectrathereforearedeformed,andthisismostpronounced intheHRspectra.

Thegoalofthepresentpaperis(1)tomodelthepeak defor-mationsoastoverifywhetheritiscompliantwiththeworking hypothesis,and(2)toofferawaytodeconvolvethespectrasothat theycanbeprocessedafterwardsbythenormalDFMSdata process-ingchain.Thisisparticularlyrelevantinviewoftheimportanceof thespeciesdetectedatm/Z=16–17amu/eforcometarychemistry.

2. Theoriginofthepeakdeformationeffect

ThissectionﬁrstbrieﬂyreviewshowDFMSmassspectraof neu-tralspeciesareobtainedwiththeMCP/LEDAdetector.Afterthat, thenatureofthedeformationisdiscussed.

2.1. DFMSmassspectraforneutralgas

DFMSismountedonthecomet-facingsideofRosettawithits 20◦×20◦fieldofviewacceptingtheoutflowingcometarygas. Neu-tralmoleculescandirectlyflowintotheion sourcewhere they arebombardedwithelectronsthatareemittedbyafilamentand acceleratedthrougha45Vpotential.Afractionofthemoleculesis ionisedorbrokenupintochargedfragments.Theseareaccelerated byamass-dependentaccelerationvoltageVaccel.Theanalyserhas

(4)

J.DeKeyseretal./InternationalJournalofMassSpectrometry393(2015)41–51 43

spatiallyseparated,afterwhichtheenergyslitselectsthedesired energyrange.Thekineticenergyoftheionsenteringtheanalyseris (ignoringtheinitialionenergyintheionsource)theenergygained duringacceleration

1 2m

v

2₌_ZeV accel.

Theionsfollowacirculartrajectorywithradiusriftheyexperience aconstantradialacceleration

a=

v

_{r =}2 2ZeVaccel

mr

towardsthecirclecenter.Suchaconstantaccelerationisprovided inthecircularelectrostaticanalysersectionbytheelectricﬁeldset bythedifferencebetweentheinnerandouterelectrostaticanalyser platepotentialsVouterandVinner,

EESA=

Vouter−Vinner

R ,

whereRisthewidthoftheanalyserchannel.Witha=ZeEESA/m,

theradiusofcurvatureoftheiontrajectoryis r= 2VaccelR

Vouter−Vinner

.

Thenominaldesignoftheelectrostaticanalyserissuchthatr=rESA,

thatis,thecurvatureradiusoftheionsmatchesthecurvatureofthe

circularanalyser.Ifallisnominal,onlyionswithinagivenenergy rangearoundZeVaccelarriveattheendofthecircularsection

with-outhittingthewalls,regardlessoftheirmass.Notealsothatthe energyofthoseionsdoesnotchange.Anenergyslitattheexitof theanalysernarrowsdowntheenergyrangeevenmore(nominal energy±1%).Atthesametime,theexitvelocitiesoftheparticles havebecomemorepreciselyaligned.Themagneticsectorwitha ﬁeldBandaradiusrmagnetthensortstheionsaccordingtom/Z.

Ideally,ionswiththecommandedmassm/Zwillhitthecenterof thedetectorasdictatedby

m Ze = r2 magnetB2 2Vaccel .

TheDFMSopticsallowforahighmassresolutionmodebyselecting adifferentslitafterthetransferopticsandbyusinga quadrupole-basedzoomsystem.Also,toincreasethesensitivityforheavyions (m/Z≥70amu/e)forwhichVaccelislowaccordingtotheabove

for-mula,apost-accelerationisappliedbyplacingthefrontsideofthe MCPatalowerpotentialsothattheionsgainadditionalenergy beforehittingtheMCP. The MCPconsistsof two microchannel plateswithnarrowchannelsinachevronshape.Anincomingion producesa cascadeofelectrons,theintensityofwhichdepends ontheionenergyandonthepotentialdifferencebetweentheMCP frontandbacksides[3].Theresultingelectroncascadethenhitsthe 2-row512-pixelLEDAchip[4].TheLEDAanalogmeasurementsare

(5)

convertedtoadigitalsignal,andareobtainedasADCcountsasa functionofLEDApixelnumberforbothLEDArows.TheMCP/LEDA detectorthusrecordsamassspectrumforanm/Zintervalaround theCM.Allparticleswiththesamem/Zproduceamasspeakwith afinitewidthduetotheremainingspreadinenergyand/or veloc-ityoftheionsastheyexittheanalysersection,due tothesize oftheMCPmicrochannels,andalsoduetothefinitewidthofthe electroncascaderecordedbytheLEDA foreachionincidenton theMCP,whichdependsontheMCPandLEDApixelsizesandthe MCP-LEDAseparation.Itturnsoutthatmasspeakscanbe repre-sentedbyaGaussianatthenominalionm/Zandahalf-widthof about6LEDApixels,combinedwithasecondGaussiancentered atthesamem/Z,with∼1/6thoftheamplitudeandawidththatis ∼2.5timeswider.Typically,anumberofseparateshort-duration exposuresisaccumulatedatthesameCM,inordertoproducea spectrumwhileaveragingoutnoise.TheADCcountsneedtobe correctedfortheoffsetduetopixelandread-outnoiseintheLEDA, fortheoverallMCPgainfactor,andforthepixel-dependentgain differencesmainlyduetounevenMCPaging.Bytakingintoaccount theinstrumentsensitivitiesandthefragmentationpatternsinthe ionsource,onemayderiveneutralcometgasdensities[see,e.g., thediscussionin12].Forverification,atleastforthemajorspecies (H2O,CO,CO2),across-calibrationcanbeperformedwiththe

den-sitymeasuredbytheCOPSnudegaugeand/orwiththeRTOFmass spectrometer[1].

2.2. Peakdeformation

AssumethatthereisanerrorıEESAintheelectricﬁeldapplied

intheanalyserduetoanill-setvoltage.Ifthiserrorissmall,anion inaﬁrstapproximationstillfollowsacirculartrajectory,butwith aslightlymodiﬁedradius

r₌_r₊_ır₌_r

1−ıEESA EESA

.

Thischangeinradialpositionoftheionsuponleavingtheanalyser propagatesfurtherdownthemagneticsectorandthezoomsystem. Thus,theconsequenceofaslightchangeintheanalyserpotentials isaproportionallyslightdisplacementofthemassspectrainLR mode,andamorepronounceddisplacementinHRmodeasthe effectismagniﬁedbythezoomoptics.Thisdisplacementresultsin anapparentchangeofmass.

Let us examine what happens if the analyser electric field, insteadofbeingsteady,fluctuatesoveralimitedrange.Asan exam-ple,considerthefluctuationinthepositionofthemasspeakstobe oftheform

ım=m(sint−ˇcos2t) (1)

wherem is aparameter characterisingtheﬂuctuation ampli-tude,andwhereˇisadimensionlessparameter.Theapparentmass shiftsbetweenm(−1+ˇ)andm(1+ˇ)whiletheaveragevalue remainszero.Astimeprogresses,theLEDAdetectoraccumulates chargescorrespondingtothetypicaldouble-Gaussianmasspeaks, whiletheshiftchangescontinuously. Thisleadsto“blurred” or “deformed”masspeaks.

Forˇ=0theﬂuctuationissinusoidalwithamplitudem.Fig.4, leftcolumn,showsthewaveform,thedistributionofım,andthe resultingmasspeakshapefortwodifferentratiosofthe double-Gaussianpeakwidths(w1 isthewidthoftheprimaryGaussian,

whilethewidthofthesecondary oneistakenw2=2.5w1)

rel-ativetotheﬂuctuationamplitude,w1/m=1.28and0.2;these

ratios correspond to typical LR and HR mode spectra, respec-tively.For a sinusoidal ﬂuctuation,theım/mdistributioncan beapproximatedby a binarydistribution at±1. Depending on theratiow1/m, thisresultsin a broadenedpeak or a double

peak. For thecase ˇ=0.2, shown in Fig.4, middle column,the masspeaksarenowpeakswithashoulderorasymmetric dou-ble peaks, and again thedistribution is dominated by the two extremeamplitudes.AmorecomplicatedcaseisshowninFig.4, rightcolumn, for ˇ=0.6.The ım/mdistributionis now dom-inated bythree values, andthemass peaksare deformedeven more.

WhilethetimevariationsoftheimposedVinnerandVouterare

notknown,theymustchangemorerapidlythanthetimeneeded tocollectaspectrum,andwithinalimitedrange.Whateverthe precisewaveform,onecanconcludethatthedeformedpeakshapes observedintheLRandHRspectra(doublepeaks,shoulders,...)can indeedbeexplainedbythiseffect.Moreover,itisclearthatonecan approximatesuchdeformedpeaksbyacombinationofjustafew doubleGaussians.

3. Deconvolutiontechnique

Thepresenceofthepeakdeformationeffectistroublesomeas itdegradesthemassresolution. Itmakesitdifﬁculttoevaluate thepresenceofminorspecies,especiallyifdeformedpeaks over-lap.Italsopreventstheapplicationofthenormaldatatreatment chain.Thispaperthereforeintroducesatechniquethatiscapable ofremovingthepeakdeformationeffect.

3.1. Problemformulation

The DFMS signal, afteroffset removal, mass calibration and detectorgaincorrection,providesthenumberofionsthathitthe MCP/LEDAduringtheexposureintheformofaspectrumf(m)ina massinterval[mbegin,mend].Priortoprocessingsuchaspectrum,

theremainingnoiselevelfthresholdisdetermined.

AnumberofionswithmassesMk,k=1,...,K,areknowntobe

foundinthegivenmassinterval.Wedistinguishbetween“basic” and“additional”ions(K=K+K).A“basic”ionhasa masspeak thatis (atleastpartially)unaffectedbyother overlappingmass peaks,sothatthereisnocontributionfromotherionsinan inter-val[mk,start,mk,stop] aroundMk. Foran“additional”ion nosuch

intervalisavailable.Thisisthecase,forinstance,foranionwhose masspeakformsasmallcontributioninthewingsofadominant species.

Let also the non-deformed peak shape G(;w1,w2,˛), the

aforementioneddouble-GaussianresponseoftheMCP/LEDA detec-tor,begivenasafunctionof,thedifferencefromthenominal ionmass.ThenormalisationG(0;w1,w2,˛)=1isused.Thispeak

shapeisconsideredtobethesamewhateverthemass,sothatthe masspeakduetoionswithmassMkinanon-deformedspectrum

isgivenby

kG(m−Mk;w1,w2,˛),with

ktheheightofthepeak.

GivenaGaussian g(;w)=e−w22

withhalf-widthw,thedouble-Gaussianresponseiswrittenas G(;w1,w2,˛)=(1−˛)g(;w1)+˛g(;w2), (2)

where0≤˛<1andw2>w1.Thewidthsw1andw2,andthe

rela-tivecontribution˛ofthesecondGaussiantotheresponse,areto bedeterminedinthecourseoftheprocess.

(6)

Fig.4.SyntheticdeformedpeakshapesbasedontheﬂuctuationproﬁleofEq.(1).Left,middle,andrightcolumnsareforˇ=0,0.2,and0.6,respectively.Fromtoptobottom: Waveformofthemassshiftım/masafunctionoftimet,theprobabilitydistributionP(ım/m)ofthemassshift,andtheresultingmasspeakshapesforw1/m=1.28 and0.2,respectively,correspondingtoDFMSpeakshapesatlowandhighmassresolution.

changeacrossthespectrum.Thefollowingformisadoptedherefor representingthepeakshapearoundmassMk:

Pk(m;{j},{j},w1,w2,˛,)= J

j=1 jG(m−mkj(j,);w1,w2,˛) (3) withthenormalisation

jj=1.ThisexpressesPkasalinear

com-binationofJdouble-Gaussians withcoefﬁcients j,all withthe

samew1,w2,and˛parameters.Thedouble-Gaussiansarelocated

atmassesmkj=Mk+s(Mk,)j,where s(Mk,)= 1+

Mk−mmid mrange

2 1+

M1−mmid mrange

2,

with mmid=(mbegin+mend)/2 and mrange=(mend−mbegin)/2. The

factors(Mk,)isintroducedtoallowavariablespacingbetween

thecontributingdouble-Gaussians.It isassumed thatthereis a quadraticallyincreasingdispersionawayfromthecenterofthe spectrum,determinedbyparameter>0.Fortheﬁrstbasicmass M1thefactoriss(M1,)=1andthusmkj=Mk+j,i.e.,thejexpress

therelativepositionsofthecontributingdouble-Gaussianstothe mass associated withthe deformedpeak P1. For all otherions

thepeakisconstructedbyproportionallysqueezingthe double-Gaussians togetheror positioning them farther apart, resulting

innarrowerorbroaderdeformedpeaks.Note,however,thatthe widthsoftheunderlyingdouble-Gaussiansdonotchange.Thisis compatiblewiththeideathatchangesintheelectrostaticanalyser electricﬁeldsdonotmodifythebeam-formingcharacteristicsof theinstrumentbutonlyleadtoadisplacementofthebeam.

Ifthedeformedpeakshapesareknown,theobservedspectrum canbemodelledas fmodel(m)= K

k=1

kPk(m;{j},{j},w1,w2,˛,) (4)

withthe

kgivingthecontributionofeachoftheKions.

Correctingthepeak deformationthenamountstosolvingan optimisationproblem:Minimisethediscrepancybetweenf(m)and fmodel(m)bydeterminingtheoptimalparametervalues.First,there

are theintensities

1,...,

K ofthe deformedpeaks atmasses

˜

M1,..., ˜MK.Notethat,becauseofpossibleminorerrorsinthemass

calibration, thesemassesmaydifferslightly fromthegivenion massesM1,...,MKandmustbeconsideredunknown.Next,there

aretheunknownmassdeviations1,...,Jandthe

correspond-ingcontributions1,...,J,togetherwithparameter,thatdeﬁne

thedeformedpeakshapeandhowitchangesacrossthespectrum. Notethatwechoose ˜M1=M1;otherwisetherewouldbean

ambi-guityindeﬁningthej.Finally,onehastheparametersw1,w2and

(7)

46 J. De Keyser et al. / International Journal of Mass Spectrometry 393 (2015) 41–51

Fig.5.DeformedpeakshapecorrectionforHRspectraatm/Z=16on2014-10-2019:54:20.Thepanelsshowthecalibratedspectruminblue,withthemodelﬁtresultaftereachstepoftheoptimisationprocessingreen,as explainedintheAppendix.Thebottompanelgivesthecorrectedspectrum.Thepeakscorrespondto32_S2+_,16_O+_,14_NH

2+,and12CH4+,inorderofincreasingmass;theirpositionsareindicatedbytheverticaldashedlines.The

(8)

J. De Keyser et al. / International Journal of Mass Spectrometry 393 (2015) 41–51 47

Fig.6.DeformedpeakshapecorrectionforHRspectraatm/Z=17on2014-10-2019:54:50.Thepanelsshowthecalibratedspectruminblue,withthemodelﬁtresultaftereachstepoftheoptimisationprocessingreen,as explainedintheAppendix.Thebottompanelgivesthecorrectedspectrum.Thepeakscorrespondto16_OH+_and14_NH

3+inorderofincreasingmass;theirpositionsareindicatedbytheverticaldashedlines.Theverticalsolidlines

(9)

Table1

IonsandmassesinHRspectraatm/Z=16.

Ion Mass(amu/e)

32_S2+ _15.9855 16_O+ _15.9944 14_NH 2+ 16.0182 12_CH 4+ 16.0308

succeedsinsolvingthisoptimisationproblem,onecanconstruct thedeconvolvedspectrum

fdeconvolved(m)= K

k=1

kG(m−mk;w1,w2,˛). (5) Integratingthetotaldetectedsignalunderthedeformedpeakfor anisolatedionkyields

k

+∞ −∞ Pk(m)dm=

k J

j=1 j

+∞ −∞ G()d =

k

+∞ −∞ G()d,

thatis,itisexactlyidenticaltothesignalunderthedeconvolved peak,asitshouldbe.Notethatchangingthespacingofthe con-tributingdouble-Gaussiansasspeciﬁedbyhasnoinﬂuenceon thetotalareaunderthedeformedpeak.

Theoptimisationproblemsketchedaboveisdifﬁculttosolvefor threereasons.First,theretypicallyarealargenumberofdegrees offreedom.Second,theproblemisnonlinear.Finally,theremay bea numberofsuboptimallocalminima. Tomake theproblem tractable,itisnecessarytobreakitdownintoanumberofsimpler steps.TheAppendixdescribesindetailhowthisproblemcanbe tackled.

3.2. Results

Fig.5showstheHRm/Z=16spectrumobtainedbyDFMSon 2014-10-2019:54:20forLEDArowA(left)androwB(right).We considerthreebasic ions,16_O+_,12_CH

4+ and 14NH2+,inorder of

decreasingimportance,andoneadditionalion,32_S2+_._The_masses

oftheseionsaregiveninTable1.Thecalibratedspectrumafterthe usual(automated)approximatemasscalibration,afterremovalof theLEDAoffsetandapplyingthegainandthepixelgaincorrection, andafterenhancingthemassresolution4×(asexplainedinthe

Appendix),isgivenintheﬁgurepanelsasabluecurve.Thethree majorionsappearasdoublepeakswiththepeaktothelow-mass sidelowerthantheoneatthehigh-massside,oraspeakswitha strongshoulderonthelow-massside:whilethedeformedpeakfor

16_O+_near_the_center_looks_like_a_single_peak_with_a_shoulder,_the

signatureof12_CH

4+totherightisadoublepeak.Themaximum

noiselevelisgivenbythehorizontaldashedline.

Theresultofthefirstoptimisationstep(firstpanel,greencurve) isaninitialapproximationofthepeakshapeofthefirstbasicspecies

16_O+ _within_the_given _interval _demarcated_by_the_solid _vertical

lines;only2double-Gaussiansareused.Thesecondpanelgivesthe resultofthesecondoptimisationstepinwhichthisapproximation isusedtomodelthethreebasicspeciesinthethreedemarcated intervals,bydeterminingtheparameterthatdescribeshowthe peakshapechangesacrossthespectrum.Thethirdpanelshowsthe outputofanimproveddeterminationofthedeformedpeakshape, wheremoredouble-Gaussians areintroduced(onemorein this case).Inthefourthpanelthisﬁnaldeformedpeakshapeisusedto alsomodeltheadditionalspecies.Thecorrectedspectrumisgiven astheblackcurveinthebottompanel.

Table2

ResultsforHRspectraatm/Z=16on2014-10-2019:54:20.

Subpeak RowA RowB

(amu/e) (amu/e) 1 −0.0003 0.26234 0.0003 0.30929 2 0.0026 0.73614 0.0003 0.00093 3 0.0030 0.00152 0.0034 0.68978 Ion M˜ (amu/e) (ions/s) ˜ M (amu/e) (ions/s) 32_S2+ _15.9863 _9.0 _15.9866 _5.7 16_O+ _15.9944 _1282.5 _15.9944 _1280.8 14_NH 2+ 16.0178 31.9 16.0171 34.4 12_CH 4+ 16.0302 135.9 16.0291 139.4 Parameter w1 0.00161amu/e 0.00190amu/e w2 0.00403amu/e 0.00456amu/e ˛ 0.1071 0.0768 2.5490 3.6713 Table3

IonsandmassesinHRspectraatm/Z=17.

Ion Mass(amu/e)

16_OH+ _17.0022

14_NH

3+ 17.0260

Table2liststheparametersthatareretrievedforbothLEDA rows.Typically,w1islargerforrowBthanforrowA;thisisbelieved

tobeduetoslightdifferencesinthefocussingoftheion beam. Hence,rowAisoftenpreferredfordataanalysissinceityieldsa bet-termassresolution.Atthesametime,˛islowerforrowB.Forboth rowsitseemsthatthedeformedpeaksarealreadywelldescribed byonly2doubleGaussians.ForrowA,99.8%ofthesignalis cap-turedbythem,andforrowBmorethan99.9%.Overall,theresults forrowAandBarequitesimilar,leadingtoaquantitative assess-mentoftheimportanceofthefourionsrelativetothemaximum noiselevelfthreshold∼1.5ions/s,aboutthesameforbothrows;note

thattheexposurelastedabout20s.Theendresultrevealsthe con-tributionfrom32_S2+_._For_row_A_an_isolated32_S2+_peak_is_seen,_while

forrowBitformsabumponthelow-massﬂankofthe16_O+_peak.

Thisismostlyduetothelargerw1andw2forrowB;thedifference

inthe32_S2+_peak_intensity_is_30–40%._The_values_for_the_other_peaks

differonlybyafewpercent.

Analogously,Fig.6showstheHRm/Z=17spectrumobtained byDFMSon2014-10-2019:54:50(bluecurve),rightaftertheone for m/Z=16. We consideronly 2 basicions, namely16_OH+ _and

Table4

ResultsforHRspectraatm/Z=17on2014-10-2019:54:50.

Subpeak RowA RowB

(10)

J.DeKeyseretal./InternationalJournalofMassSpectrometry393(2015)41–51 49 14_NH

3+inorderofdecreasingimportance,andnoadditionalions; themassesarelistedinTable3.Theoptimisationprocedureis sim-plerthanforthem/Z=16case.Theﬁgurepanelsshowtheresultsof thesuccessiveoptimisationsteps.Themodelreconstructionofthe deformedspectrumisshowninthefourthpanel,whilethebottom panelgivesthedeconvolvedspectrum.Table4liststheparameters forbothLEDArows.Thecharacteristicparametersw1,w2,˛and

arefoundtobelargelysimilartothoseinTable2.Theintensities

obtainedfromrowsAandBforbothspeciesdifferagainbyonlya fewpercent.

4. Discussionandconclusion

TheDoubleFocusingMassSpectrometer(DFMS)ontheRosetta spacecraftisplaguedbyminordeformationofthemasspeaksin thehighresolutionspectraaroundm/Z=16and17.Theshapeof thedeformationslowlychangeswithtime.

Themostlikelycauseisanunstableelectricpotentialinthe elec-trostaticanalyser.Modellingsuggeststhatsuchelectricpotential variationswouldleadtoanapparentshiftofthepeaksonthe detec-torwithoutmodifyingtheactualbeam-formingpattern,atypical double-Gaussianshape.Oneexpectsthatthepeaksobservedafter accumulatingobservationsovera certainperiodof timecanbe approximatedbyalinearcombinationofafewdouble-Gaussians. Infact,two double-Gaussiansoftenseem tocapture99%ofthe signalormore,indicatingthatthepotentialessentiallyalternates betweentwovalues.Byexamininghowthedeformedpeakshape changesacrossthespectrum,ithasbeenpossibletoconﬁrm,at leasttoﬁrstorder,thatthebeampatternindeedisonlyshifted withoutchangingitsshape.Theanalysispresentedheretherefore appearstocorroboratetheconclusionthatadeviationofthe elec-tricpotentialintheelectrostaticanalyserisindeedthecauseofthe problem.

Atthesametimetheanalysissuggestsatechniqueforcorrecting thepeakdeformation.Analgorithmhasbeendevelopedand imple-mented,andtheresultsforhighresolutionspectraatm/Z=16and 17lookpromising.Inthisway,theprocessingofsuchspectracan beeasilyincorporatedintheDFMSdataanalysischain.Thisgives accesstoafewimportantions,inparticular16_O+_and16_OH+_,_that

playaroleinthewaterchemistry,whichisessentialfor under-standingthecomposition ofcometary atmospheres.Also, some ionssuchas32_S2+_become_detectable,_while_they_would_otherwise

havebeenmissed.Thetypicaldifferencesindouble-Gaussianpeak shapebetweenrowAandBareconsistentlyfoundintheresultsat bothmasses.Theintensitiesobtainedfrombothrowsdifferonly byafewpercent,exceptinthecaseofminorionssuperimposed ontheflanksofamajorpeak,wheretheresultsaremoresensitive. Thereareafewcaveats.First,thetechniquerequiresasufficiently goodmasscalibrationofthegivenspectrum.Also,itishinderedif thepixelgaincorrectionisnotsufficientlyaccurate,sincethatmay affectthepeakshape.Inpractice,theseproblemscanappropriately bedealtwith.

Theunstableelectricpotentialissuethathasbeenstudiedhere forDMFSmassspectrainneutralmodeatm/Z=16and17,will lead todeformationsin thespectraat those masses in theion modeaswell.Thesemaybe,however,muchhardertocorrectsince theshapeoftheenergydistributionoftheparticlesisnotapriori known(contrarytothedouble-Gaussianpeakshapeobtainedin neutralmode).

Acknowledgements

The authors thank the following institutions and agencies, which supportedthis work: Work atBIRA-IASB was supported by the Belgian Science Policy Ofﬁce via PRODEX/ROSINA PEA 90020andanAdditionalResearchersGrant(MinisterialDecreeof

2014-12-19),aswellasbytheFondsdelaRechercheScientiﬁque grantPDRT.1073.14“Comparativestudyofatmosphericerosion”. WorkatUoBwasfundedbytheStateofBern,theSwissNational ScienceFoundation,andbytheEuropeanSpaceAgencyPRODEX Program.WorkatSouthwestResearchinstitutewassupportedby subcontractno.1496541fromtheJetPropulsionLaboratory.This workhasbeencarriedoutthankstothesupportoftheA*MIDEX project(n◦ANR-11-IDEX-0001-02)fundedbythe“Investissements d’Avenir” FrenchGovernmentprogram, managedby theFrench NationalResearchAgency(ANR).ThisworkwassupportedbyCNES grantsatLATMOSandLPC2E.WorkattheUniversityofMichigan wasfundedbyNASAundercontractJPL-1266313.Theresultsfrom ROSINAwouldnotbepossiblewithouttheworkofthemany engi-neers,technicians,andscientistsinvolved inthemission,inthe Rosettaspacecraft,andintheROSINAinstrumentteamoverthe past20yearswhosecontributionsaregratefullyacknowledged.We thankherewiththeworkofthewholeESA/Rosettateam.Rosetta isanESAmissionwithcontributionsfromitsmemberstatesand NASA. All ROSINA data are available on request until theyare releasedtothePSAarchiveofESAandtothePDSarchiveofNASA.

Appendix. Optimisationprocess

Thisappendixdescribesindetailhowtheoptimisationproblem discussedinthispaperisactuallysolved.

Preprocessingstep

Themass-calibratedandgain-correctedmassspectrumf(m)is knownatasetofdiscretepoints(mi,fi).However,itisclearthat

theunderlyingfunctionfiscontinuouslydifferentiable.Toexploit thisinformationtothefullest,thespectrumisinterpolatedtoa 4×bettermassresolutionusingcubicsplineinterpolation.While thismayseemtoincreasetheamountofcomputationalwork,it leadstoasmootherbehaviourofthetargetfunctionsinthe opti-misationproblemsoutlinedbelowandthustobetterconvergence properties.Itismostappropriatetoperformtheinterpolationon logf.

Step1

Inaﬁrststep,theshapeofthedeformedpeakaroundM1

(usu-allythemostpronounced peakin thespectrum)isdetermined approximatelyasalinearcombinationofJ0double-Gaussians.This

isachievedbyminimisingfunction

F2 1 =

i ˇi

⎡

⎣

fi− J0

j=1 jG(mi−(M1+j);w1,w2,˛)

⎤

⎦

2 ,

wherethesumrunsoverallmeasurementpoints(mi,fi)thatare

withintheunperturbedintervalmi∈[m1,start,m1,stop]andthatare

abovethenoiselevelfi>fthreshold,andwheretheparameterstoﬁt

arew1,w2,˛,{j}and {j}.Thefactor ˇi istheweighting

fac-torthatisassociatedtoeachmeasurement.Choosingˇi=1would

amounttofittingthemeasurementsinabsoluteterms;giventhe highdynamicrangeofthemeasurements(upto3–4decades)one wouldfitthetipofthedeformedpeak,butnotitsflanks. Choos-ingˇi=1/fi2wouldfitthemeasurementsinrelativeterms,which

placesequalweightsonthetipsandtheﬂanksofthepeaks.Here, theintermediatechoiceˇi=1/fiismade,or,inordertoignoredata

belowthenoisethreshold, ˇi= fi

f2

i +fthreshold2

(11)

Theproblemissimpliﬁedbyﬁxingw2=2.5w1,mainlytoavoid

situationswithmultiple localminima. We ﬁrstsolvethe prob-lemwithasingledouble-Gaussian,J0=1,thusapproximatingthe

deformedpeakwithanon-deformedone;thisisaproblemin1,

1,w1and˛.Wethenprogressivelyadddouble-Gaussiansandtry

toimproveontheoverallﬁt.Ineachstep,theinitialvaluesforthe minimisationarefoundbyre-using˛|J0 =˛|J0−1,bytakingw1|J0 =

w1|J0−1(J0−1)/J0,andbyadoptingj|J0 =j|J0−1,j=1,...,J0−1

andlocatingJ0wheretheresidualoftheapproximationremains

largest.

Sincethesystem

∂

F2

1/

∂

j=0,j=1,...,J0 islinear,oneﬁnds

theoptimalvaluesofthejforanygivensetof{j},w1,and˛

fromsolvingtheoverdeterminedlinearsystem

J0

j=1 Aijj=bi with Aij =ˇiG(mi−(M1+j);w1,w2,˛), bi=ˇifi.

This system is solved in a least-squares sense by making use ofthegeneralised inverseoftherectangularcoefﬁcient matrix. Thissystemisoverdetermined onlyif onekeepsJ0 low; ifnot,

oneis“overﬁtting”theproblem.Oneshoulddeﬁnitelyneveruse moredouble-Gaussiansthanthenumberofpixelsoverwhichthe deformedpeakissmearedout,andthatnumberisquitelimited (maximum∼10).AnotherreasontolimitJ0istokeepthe

compu-tationalcostdown.ItturnsoutthatusingonlyJ0=2isalreadyavery

goodchoice.InviewoftheresultsfoundinFig.4(leftcolumn),this suggeststhattheoscillatingelectricﬁeldisactuallybetter repre-sentedbyasquarewavethanasinusoidalone.

Aftertheﬁttingprocessends,thecoefﬁcientsarenormalised, j= j

jj ,

sothattheycanbeusedintheexpressionforthepeakshapeof Eq.(3).

Step2

Inthesecondstep,wedeterminetheparameter.Thisisdone byapplying thepeak shape foundin theﬁrst step toall basic ions;ifonlyonebasicionmassisgiven,parametervalue=0is adopted.Thevalueofcanonlybeestablishedwhile simultane-ouslydetermining ˜Mkand

kforallbasicions.Thetargetfunction

tobeminimisedis F2 2=

i ˇi

fi− K

k=1

kPk(mi;{j},{j},w1,w2,˛,)

2 ,

where {j}, {j}, w1, w2, and ˛ are the values obtained

from the previous step. The sum runs over all points mi∈

k=1,...,K[mk,start,mk,stop]forwhichthemeasuredsignalisabove

thenoiselevel.Thesameweightingfactorˇiisusedasbefore.

Forgivenand ˜Mk,onecanﬁndthe

kfromthelinearsystem

∂

F2

2/

∂

k=0,k=1,...,K.Theoverdeterminedsystemisgivenby

Aij =ˇiPk(m;{j},{j},w1,w2,˛,),

bi=ˇifi.

Attheendofthisstep,aninitialrepresentationofthedeformed peakandhowitchangesacrossthespectrumisestablished.

Step3

Inthethirdstepthedeformedpeakshapeisimprovedbyadding double-Gaussianstotherepresentation.Atthesametime,the val-uesofw1,w2(whichisnownolongertiedtothatofw1),˛and

areimproved.Thesetof{j}and{j}isprogressivelyextended

andoptimised,andalso{ ˜Mk}and{

k}areﬁne-tuned.Thisisdone

whilerepeatedlyﬁtting

F2 3=F22+

⎛

⎝

j j−1

⎞

⎠

2 +c

w2/w1 2.50 −1

2

overthesamesetofpointsasinstep2.Theﬁrstadditionalterm inthetargetfunctionservestoensurethenormalisationofthej

(ifnot,thesolutionisnotuniquelydeﬁnedandtheoptimisation problemisboundnottoconverge).Thesecondadditionalterm, with0≤c1,guidesthevalueofw2relativetow1inorderto

reg-ularisetheproblem,whereadefaultvaluew2/w1=2.50isused.In

theexpressionforthedeformedpeakshapethenumberof double-GaussiansisprogressivelyincreasedtoaﬁnalvalueJ≤J0;avalue

ofonlyJ=3isusedroutinely.Notethatthisoptimisationprocess againcanbeneﬁtfromestablishingthevaluesof

kfroman

overde-terminedlinearsystemforgivenvaluesofallotherparameters. Thisthirdstepiscomputationallydemandingsincemostofthe problemparametersaretobeoptimisedsimultaneously.Thegoal ofstep1and2isexactlytoprovideagoodinitialsolutionforthebig optimisationproblemofstep3.First,givenagoodinitialsolution, theamountofworkneededtoﬁndtheoptimumremainslimited. Second,sincetheproblemissononlinear,agoodinitialsolutionin theneighbourhoodoftheglobaloptimumisaprerequisitetoﬁnd thatglobaloptimumwithoutgettingstuckinsomelocalminimum. Step4

Theresultfromthepreviousstepisanaccuraterepresentation ofthedeformedpeaksandhowtheychangeacrossthespectrum. Thiscannowbeusedtoﬁtthefulldeformedspectrum,including alsotheadditionalions.Thetargetfunctionis

F2 4=

i ˇi

fi− K

k=1

kPk(mi;{j},{j},w1,w2,˛,)

2

wherethesumnowrunsoverallKionsandoverallpoints(mi,fi)in

thespectrum.Theunknownsarethe ˜Mk(except ˜M1=M1)and

k;

allotherquantitiesaregiven.Again,foranysetofvalues{ ˜Mk}one

canobtainthe

kfromtheoverdeterminedlinearsystemalready

usedinstep2. Postprocessingstep

Asalreadyoutlined,oncealltheparametershavebeen com-puted, it is possible to determine the deconvolved spectrum fdeconvolvedaccordingtoEq.(5),interpolatedbacktotheoriginal

massscale.Thecorrectedspectrumisdeﬁnedas fcorrected=(fdeconvolved+fnoise)+(1−)f,

thatis,alinearcombinationofthedeconvolvedspectrum(adding theaveragenoiselevel)andtheobservedspectrum,wherevaries between0and 1dependingonhowmuch theobservationsare abovethenoiselevel;here,thechoice

(12)

Optimisationtechnique

Theoptimisationtechniqueusedisacombinationofa stochas-ticsearchmethodthatprobestheenvironment ofacurrentset ofparametervalues,andtheBroyden–Fletcher–Goldfarb–Shanno algorithm[13,14]thatstartsasasteepestdescenttechniqueand progressivelyevolvestotheNewtonalgorithmasitcollects infor-mationabouttheHessianofthetargetfunctionneartheoptimum. Toimprovethenumericalbehaviour,theoptimisationparameters arejudiciouslyrescaled.

Theoptimisationstrategyalsoallowstoimposeboundsonsome oftheparameters.Ifaparameterpshouldnotexceedalimitvalue p*_,_the_target_function_F(p)_is_modiﬁed_into

F_(p)₌_F(min{p,_p∗_))[1₊_(max_{p₋_p∗_,₀_})2

],

sothatF(p)≡F(p)insidethealloweddomain,andF(p)>F(p*₎

out-side.Inpractice,suchboundshavebeenintroducedsothat 0.50w0≤ w1 ≤2w0,

1.25w0≤ w2 ≤5w0,

0.075≤ ˛ ≤0.30, 0≤ .

Furthermore,precautionshavebeentakentokeepall ˜Mkcloseto

thecorrespondingMk,andtokeepallj≥0and

k≥0. AppendixA. Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound,in theonlineversion,athttp://dx.doi.org/10.1016/j.ijms.2015.10.010 References

[1]H.Balsiger,K.Altwegg,P.Bochsler,P.Eberhardt,J.Fischer,S.Graf,A.Jäckel, E.Kopp,U.Langer,M.Mildner,J.Müller,T.Riesen,M.Rubin,S.Scherer,P.Wurz, S.Wüthrich,E.Arijs,S.Delanoye,J.DeKeyser,E.Neefs,D.Nevejans,H.Rème, C.Aoustin,C.Mazelle,J.-L.Médale,J.A.Sauvaud,J.-J.Berthelier,J.-L.Bertaux,L. Duvet,J.-M.Illiano,S.A.Fuselier,A.G.Ghielmetti,T.Magoncelli,E.G.Shelley,A. Korth,K.Heerlein,H.Lauche,S.Livi,A.Loose,U.Mall,B.Wilken,F.Gliem,B. Fiethe,T.I.Gombosi,B.Block,G.R.Carignan,L.A.Fisk,J.H.Waite,D.T.Young,H. Wollnik,Rosina–RosettaOrbiterSpectrometerforIonandNeutralAnalysis, SpaceSci.Rev.128(1–4)(2007)745–801, http://dx.doi.org/10.1007/s11214-006-8335-3.

[2]S.Wüthrich,CharacterizationoftheROSINADFMSInstrumentbyNumerical Modeling(Ph.D.thesis),PhysikalischesInstitut,UniversitätBern,Switzerland, 2007.

[3]J.-J.Berthelier,J.-M.Illiano,D.Nevejans,E.Neefs,E.Arijs,N.Schoon,High reso-lutionfocalplanedetectorforaspace-bornemagneticmassspectrometer,Int. J.MassSpectrom.215(1–3)(2002)89–100, http://dx.doi.org/10.1016/S1387-3806(02)00527-4.

[4]D.Nevejans,E.Neefs,S.Kavadias,P.Merken,C.VanHoof,TheLEDA512 integratedcircuitanodearrayfortheanalogrecordingofmassspectra,Int. J.Mass Spectrom.215 (1)(2002)77–87, http://dx.doi.org/10.1016/S1387-3806(01)00549-8.

[5]M.Hässig,K.Altwegg,H.Balsiger,J.-J.Berthelier,U.Calmonte,M.Combi,J.De Keyser,B.Fiethe,S.A.Fuselier,M.Rubin,ROSINA/DFMScapabilitiestomeasure isotopicratiosinwateratcomet67P/Churyumov-Gerasimenko,Planet.Space Sci.84(2013)148–152,http://dx.doi.org/10.1016/j.pss.2013.05.014. [6]M.Hässig,K.Altwegg,J.-J.Berthelier,U.Calmonte,J.DeKeyser,B.Fiethe,

S.A.Fuselier,T.I. Gombosi,L.LeRoy,T.Owen,M.Rubin, Thecapabilities of ROSINA/DFMS to measure argon isotopes at comet 67P/Churyumov-Gerasimenko,Planet.SpaceSci. 105(2015) 175–178,http://dx.doi.org/10. 1016/j.pss.2014.11.015.

[7]K.Altwegg,H.Balsiger,U.Calmonte,M.Hässig,L.Hofer,A.Jäckel,B.Schläppi, P.Wurz,J.-J.Berthelier,J.DeKeyser,B.Fiethe,S.A.Fuselier,U.Mall,M.Rubin, H.Rème,InsitumassspectrometryduringtheLutetiaﬂyby,Planet.SpaceSci. 66(1)(2012)173–178.

[8]K.Altwegg,H.Balsiger,A.Bar-Nun,J.-J.Berthelier,A.Bieler,P.Bochsler,C.Briois, U.Calmonte,M.Combi,J.DeKeyser,P.Eberhardt,B.Fiethe,S.A.Fuselier,S.Gasc, T.I.Gombosi,K.C.Hansen,M.Hässig,A.Jäckel,E.Kopp,A.Korth,L.LeRoy,U. Mall,B.Marty,O.Mousis,E.Neefs,T.Owen,H.Rème,M.Rubin,T.Sémon,C.-Y. Tzou,H.Waite,P.Wurz,67P/Churyumov-GerasimenkoaJupiterfamilycomet withahighD/Hratio,Science347(6220)(2014)1261952,http://dx.doi.org/ 10.1126/science.1261952.

[9]M.Hässig,K.Altwegg,H.Balsiger,A.Bar-Nun,J.-J.Berthelier,A.Bieler,P. Bochsler,C.Briois,U.Calmonte,M.Combi,J.DeKeyser,P.Eberhardt,B.Fiethe, S.A.Fuselier,M.Galand,S.Gasc,T.I.Gombosi,K.C.Hansen,A.Jäckel,H.U. Keller,E.Kopp,A.Korth,E.Kührt,L.LeRoy,U.Mall,B.Marty,O.Mousis,E. Neefs,T.Owen,H.Rème,M.Rubin,T.Sémon,C.Tornov,C.-Y.Tzou,H.Waite, P.Wurz,Timevariabilityandheterogeneityinthecomaof 67P/Churyumov-Gerasimenko,Science347(6220)(2015)aaa0276,http://dx.doi.org/10.1126/ science.aaa0276.

[10]M.Rubin,K.Altwegg,H.Balsiger,A.Bar-Nun,J.-J.Berthelier,A.Bieler,P. Bochsler,C.Briois,U.Calmonte,M.Combi,J.DeKeyser,F.Dhooghe,P. Eber-hardt,B.Fiethe,S.A.Fuselier,S.Gasc,T.I.Gombosi,K.C.Hansen,M.Hässig,A. Jäckel,E.Kopp,A.Korth,L.LeRoy,U.Mall,B.Marty,O.Mousis,T.Owen,H. Rème,T.Sémon,C.-Y.Tzou,H.Waite,P.Wurz,Molecularnitrogenincomet 67P/Churyumov-Gerasimenkoindicatesalowformationtemperature,Science 348(6231)(2015)232–235,http://dx.doi.org/10.1126/science.aaa6100. [11]E.G.Johnson,A.O.Nier,Angularabberationsinsectorshaped

electromag-neticlensesforfocusingbeamsofchargedparticles,Phys.Rev.91(1953) 10–17.

[12]M.Hässig,SensitivityandFragmentationCalibrationoftheROSINADouble FocusingMassSpectrometer(Ph.D.thesis),UniversitätBern,2013.

[13]C.G.Broyden,Theconvergenceofaclassofdouble-rankminimization algo-rithms,J.Inst.Math.Appl.6(1)(1970) 76–90,http://dx.doi.org/10.1093/ imamat/6.1.76.