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Optical subsystems calibration and derived radiometricinstrument response of the PHEBUS spectrometer on

board of the BepiColombo MissionP Zuppella A J Corso V Polito Jean-Franccedilois Mariscal Nicolas Rouanet

Jean-Luc Maria P Nicolosi Eric Queacutemerais M G Pelizzo

To cite this versionP Zuppella A J Corso V Polito Jean-Franccedilois Mariscal Nicolas Rouanet et al Optical subsys-tems calibration and derived radiometric instrument response of the PHEBUS spectrometer on boardof the BepiColombo Mission Journal of Instrumentation IOP Publishing 2012 7 (10) P10023 (14p)1010881748-0221710P10023 hal-00750714

Journal of Instrumentation

OPEN ACCESS

Optical subsystems calibration and derivedradiometric instrument response of the PHEBUSspectrometer on board of the BepiColomboMissionTo cite this article P Zuppella et al 2012 JINST 7 P10023

View the article online for updates and enhancements

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This content was downloaded from IP address 77141181228 on 18072020 at 2009

2012 JINST 7 P10023

PUBLISHED BY IOP PUBLISHING FOR SISSA MEDIALAB

RECEIVED July 3 2012REVISED September 18 2012

ACCEPTED October 2 2012PUBLISHED October 25 2012

Optical subsystems calibration and derivedradiometric instrument response of the PHEBUSspectrometer on board of the BepiColombo Mission

P Zuppellaa1 AJ Corsoab V Politoab JF Mariscalc N Rouanetc JL Mariac

P Nicolosib E Quemeraisc and MG Pelizzob1

aCNR mdash IFN UOS PadovaVia Trasea 7 35131 Padova Italy

bUniversity of Padua Department of Information EngineeringVia Trasea 7 35131 Padova Italy

cLATMOS-CNRS11 Boulevard drsquoAlembert 78280 Guyancourt France

E-mail zuppelladeiunipdit pelizzodeiunipdit

ABSTRACT Probing of Hermean By Ultraviolet Spectroscopy (PHEBUS) is a double spectrometerthat will fly onboard of the BepiColombo mission It will investigate the composition and dynamicof Mercuryrsquos exosphere to better understand the coupled surface - exosphere - magnetosphere sys-tem of the planet The radiometric calibration tests are ongoing and an approach based on theMueller Matrix formalism has been adopted to determine the pure efficiency of the instrument Toour knowledge this is the first time that a such complete method is applied to the calibration ofspace instrumentation

KEYWORDS Spectral responses Spectrometers Space instrumentation Polarisation

1Corresponding authors

ccopy 2012 IOP Publishing Ltd and Sissa Medialab srl doi1010881748-0221710P10023

2012 JINST 7 P10023

Contents

1 Introduction 1

2 PHEBUS optical configuration 2

3 Matrix Mueller formalism 3

4 Experimental 5

5 Results and discussions 7

6 Conclusions 9

1 Introduction

PHEBUS is a double spectrometer (Chassefiere [1]) working in the Extreme UltraViolet (EUV)and Far UltraViolet (FUV) spectral ranges that will investigate the composition and dynamic ofMercuryrsquos exosphere onboard of the BepiColombo Mission Its distinctive feature is to work in theEUV region (55ndash155 nm) allowing for the first time observations of additional species like He Arand N (Chassefiere [1] Yoshioka [2]) The ground calibration activities include the characteriza-tion of the optical subsystems and the the measure of the efficiency and the geometrical acceptancein term of etendue at the full instrument level The purpose of such calibrations is the developmentof a full radiometric model in which all the instrument parameters are taken into account Thiswork shows the results of the subsystems calibration and the model that has been built to describethe response of the full instrument in term of efficiency An exhaustive approach that takes into ac-count the polarization state of the light entering into the instrument and its polarization dependenceresponse has been adopted and mathematically formalized in term of the Mueller Matrix theoryThe purpose of the experimental measurements has been the determination of the Mueller Matrixassociated to each optical component while the Mueller Matrix associated to the full instrumenthas been built properly combining the results obtained at the subsystems characterization levelThe proposed approach has a general validity and allows to improve the astronomical capabilitywhen applied to a flight instrument In the case of PHEBUS the Mercuryrsquos exosphere that isstill under study is supposed to be slightly polarized then the residual dependence to polarizationmust be evaluated to fully characterize the response of the instrument (Killen [3] Buenzli [4]) Aradiometric calibration is properly addressed by assuming that each optical instrument induces apolarization effect on the propagating light resulting the instrument response a very complex func-tion strongly dependent on the polarization status of the incoming light In particular it must beunderstood that each optical component not only affects the throughput but introduces a phase shiftin the incoming beam whenever the incident angle is different from 0 This happens in a cascade

ndash 1 ndash

2012 JINST 7 P10023

when there is a series of optical components In general these dependencies are not expressed inthe calibration of optical instruments being sometimes neglected in name of rdquothe normal incidenceconfigurationrdquo usually adopted The importance of this approach is even more dramatic if the in-strument as in the case of PHEBUS is provided by a scanning system which changes dynamicallythe mutual position of the optical elements In the present analysis the Mueller Matrix has beenexperimentally determined by characterizing the optical components for the nominal incidence an-gle which actually is defined by following the optical path of the chief ray of the central field ofview of the instrument The full field of view and aperture and the curvature of the optical surfacesthat geometrically affect the optical path of the beam resulting in the local variation of the angle ofincidence of the entering rays with respect to the chief ray must be taken into account during theradiometric simulation tool as a secondary effects

The model that has been built allows the determination of the Mueller Matrix for any positionof the scanning system resulting therefore in a very flexible tool for the data analysis The futureexperimental sessions dedicated to the full instrument efficiency measurement and the etenduedetermination will be interpreted as an experimental verification of the model proposed with forselected position of the scanning system

The first part of the manuscript is devoted to the instrument by defining the optical design andthe basic characteristics of the optics then it moves to the description of the method supportedby a Mueller formalism recall The theory will be fundamental to select and drive the proper mea-surements and the consequent experimental results modeling The Mueller parameters of PHEBUShave been finally determined and critically discussed in light of PHEBUS instrument configurationand theoretical predictions

2 PHEBUS optical configuration

PHEBUS (see figure 1) is a French led spectrometer implemented in a cooperative project involvingJapan Russia and Italy It consists of two distinct channels working in the EUV (55-155 nm) andFUV (145-315 nm) spectral ranges with an extension for two extra visible lines at 4047 nm and4228 nm (Chassefiere [1]) The paraxial field of view of the instrument is 2 by 01 The opticalscheme (see figure 2) includes two drawing blocks the collecting and the spectrometer parts

The collector one is composed of the straylight rejection baffle the primary mirror and theentrance slit The mirror is a Silicon Carbide (SiC) off-axis parabola 50 incidence angle and 170mm focal length The SiC has been chosen for its efficiency performances in the whole 55 - 315 nmspectral range and for its mechanical and thermal properties The coating has been manufacturedby CVD process The nominal surface roughness has been specified as 05 nm RMS in orderto minimize the straylight inside the instrument The mirror is positioned at the baffle exit andaccommodated inside a scanner rotating mechanism The main function of the scanner mechanismis to point the spectrometerrsquos toward the selected line-of-sight selected in order to provide thewhole coverage of the Merury exosphere The spectrometer is instead composed by two channelsthe EUV and the FUV one Two holographic gratings share the same mechanical mount and areaccommodated in front of the slit The light is then diffracted and collected by two Multi ChannelPlates (MCPs) detectors The aberration corrected holographic gratings of PHEBUS are made ofaluminum covered by platinum coating The holograph process has been adopted in order to obtaina Variable Line Space Gratings with a mean groove density of 1600 groovesmm for the FUV

ndash 2 ndash

2012 JINST 7 P10023

Figure 1 PHEBUS inner view The light incoming from the baffle impinges on the off-axis parabolic mirrorand is focused on the entrance slit

Figure 2 PHEBUS optical layout The spectrometer consists of two distinct channels working in the EUVand FUV respectively with a common collecting part

and 2700 groovesmm for the EUV one respectively The groove profiles are laminar ion-etchedoptimized for the respective spectral range

3 Matrix Mueller formalism

A block diagonal Mueller matrix is associated to each optical component at each wavelength

Mmg =

|rmg

TM |2+|rmgTE |2

2|rmg

TM |2minus|rmgTE |2

2 0 0|rmg

TM |2minus|rmgTE |2

2|rmg

TM |2+|rmgTE |2

2 0 00 0 real(rmg

TM rmgTE ) image(rmg

TM rmgTE )

0 0 minusimage(rmgTM rmg

TE ) real(rmgTM rmg

TE )

(31)

ndash 3 ndash

2012 JINST 7 P10023

such matrix can be easily derived by considering the gratings and the mirror as a combination ofa polarizer and a phase retarder (Fundamentals of Photonics [5] Polarized Light [6]) The termsrmg

T MT E (rmgT MT E are the complex conjugates) are respectively the Fresnel reflection (efficiency for

the grating) coefficients of the TM and TE components of the electric fields Since |rmgT MT E |

2 =

RmgT MT E the Mueller parameters will depend on the reflectanceefficiency of the optical components

and correspondent phase shift Φm = φ mTMminusφ m

TE The scanning system is described by the rotationmatrix reported below

Ms =

1 0 0 00 cos2θ sin2θ 00 minussin2θ cos2θ 00 0 0 1

(32)

where θ is the scan angle By combining the matrices (31) and (32) the Mueller Matrix Massociated to the spectrometer can be derived

M = MgtimesMstimesMm =

M00 M01 M02 M03

M10 M11 M12 M13

M20 M21 M22 M23

M30 M31 M32 M33

(33)

From a general point of view the matrix M is an operator acting on the polarization state of thelight described by the Stokes vectors

S =

S0

S1

S2

S3

=

|ETM|2 + |ETE|2

|ETM|2minus|ETE|2

2real(ETEETM)2image(ETEETM)

(34)

where ET MT E are the T MT E component of the electric field

If we assume Sinput and Soutput are the Stokes vectors associated to the incoming light and tothe beam impinging the detector (Polarized Light [6]) the relationship

Soutput = MtimesSinput

can be written The detectors used to collect the radiation are MCPs In general the quantumdetection efficiency ηd associated to them depends on the polarization state of the incoming lightand on the bias angle in the first stack (Tomc [7] Yoshioka [2] Yoshioka [8]) In this respect somepreliminar analysis have been done and a fully characterization will be carried on during the propercalibration activities

Then taking into account the efficiency of the MCP at fixed wavelenght and polarization stateof the light the detected signal is the following

Soutput0 = ηd(M00Sinput

0 +M01Sinput1 +M02Sinput

2 +M03Sinput3 ) (35)

ndash 4 ndash

2012 JINST 7 P10023

Figure 3 The normal incidence reflectometer at CNR-IFN UOS Padova It consists of a Johnson-Onakamonochromator with a 600 groovesmm toroidal grating optimized for the UV range

and the relevant terms of the M Mueller matrix of the spectrometer are the coefficients of thefirst row

M00 =Rg

TM +RgTE

2Rm

TM +RmTE

2+

RgTMminusRg

TE2

RmTMminusRm

TE2

cos2θ (36)

M01 =Rg

TM +RgTE

2Rm

TMminusRmTE

2+

RgTMminusRg

TE2

RmTM +Rm

TE2

cos2θ (37)

M02 = RmTMRm

TERg

TMminusRgTE

2cosΦ

msin2θ (38)

M03 = minusRmTMRm

TERg

TMminusRgTE

2sinΦ

msin2θ (39)

4 Experimental

The experimental characterization of the PHEBUS Flight Model (FM) optical subsystems has beenperformed by using the normal incidence reflectometer (see figure 3) at CNR-IFN UOS Padova(Garoli [9]) It consists of a Johnson-Onaka monochromator with a 600 groovesmm toroidal grat-ing optimized for the UV range A toroidal mirror focuses the monochromatic radiation on thesample placed in the experimental chamber together with the detector fixed in the θ minus 2θ config-uration As sources different lamps have been coupled with the facility an home made hollowcathode filled with different gases a deuterium and a Hg lamps A Channel Electron Multiplier(CEM AMPTEK MD501) working in photon counting mode has been adopted for the EUV testwhile a PhotoMultiplier (PM Hamamatsu 6352) for the FUV(see table 1)

The beam probe provided by the reflectometer is polarized by the optical components of thereflectometer itself therefore to obtain all the information necessary for a full knowledge of thePHEBUS subsystem components the probe beam has been fully characterized with a dedicatedexperimental session The method adopted is the same reported in (Garoli [9]) and the results areexpressed in term of the polarization degree f = |ETE|2minus|ETM|2

|ETE|2+|ETM|2as reported in table 1

Then the measurements have been performed in two different positions of the test chamberrotated 90 to each other giving Rmg

up and Rmgdown respectively

Rmgupdown =

Signalmgupdown

Signaldirectupdown

(41)

ndash 5 ndash

2012 JINST 7 P10023

Table 1 Sources Polarization Degree of the illumination system amp Detectors Hollow Cathode Lamp(HCL) Deuterium Lamp (DL) Mercury Lamp (Hg) Channel Electron Multiplier Ampektron MD-501(CEM) Photomultiplier Hamamatsu 6352 (PMT)

λ (nm) Source Polarization Degree (f) Detector304 HCL-He 040 CEM461 HCL-Ne 048 CEM584 HCL-He 053 CEM744 HCL-Ne 059 CEM919 HCL-Ar 073 CEM1025 HCL-He 085 CEM1066 HCL-Ar 082 CEM1216 DL HCL-He 090 CEM1233 DL HCL-He 090 CEM1400 DL 091 CEM1600 DL 092 CEM2540 Hg -038 PMT2654 Hg -068 PMT2800 Hg -082 PMT2960 Hg -070 PMT3022 Hg -075 PMT3127 Hg -063 PMT

where Signalmgupdown and Signaldirect

updown are the reflectedrefracted and the direct signal The average

of the two values corresponds to the throughput for unpolarized light Rmgun To determine the

relevant parameters (equations (36) (37) (38) and (39)) of the the Phebus associated MuellerMatrix the term Rmg

T MT E must be calculated accordingly to the following equation starting fromthe experimental data

RmgT MT E =

Rmgup +Rmg

down2

plusmnRmg

up minusRmgdown

2 f(42)

The phase shift Φm (equation (35)) has been derived by a combination of experimental data theirfitting and proper simulations The method is resumed in the following steps

bull Experimental measure of Rmgup and Rmg

down

bull Determination of Rmgun from Rmg

up and Rmgdown averaging

bull Fitting of Rmgun with a simulation software (optimization of optical constant and roughness

via IMD software in case of SiC mirror optimization of grooves parameters via PC GrateSoftware demo version in case of the gratings)

bull Recovering of RmgT MT E curves by simulation and consequent determination of the phase

shifts Φm

The RmgT MT E results of FM optical subsystems are reported in figure 4 5 and 6

ndash 6 ndash

2012 JINST 7 P10023

Figure 4 shows the results obtained for the SiC mirror and relative fitting The characteri-zazion have been performed over the whole Phebus working range since the mirror is shared bythe two gratings and the two channels In the range from 304 nm to 1216 nm the fitting havebeen computed by using the experimental optical constants provided by D Windt (Windt [10])and finely adjusting the roughness surface (σ=21 nm) and the roughness of the substrate (σ=1nm) As it can be seen a very good match has been obtained by simulations with this proce-dure In the range from 1233 to 160 nm experimental optical constants are available in licteratureonly for two wavelenghts (132 and 149 nm) and beyond 200 nm (Fernandez-Perea [11] Larru-quert [12]) and only in case of a SiC layers deposited by sputtering or Pulsed Laser Deposition(PLD)(Monaco [13] Monaco [14]) In the FUV range threfore the fitting has involved also theoptical constants starting from (Fernandez-Perea [11] Larruquert [12]) below 200 nm and (Pa-lik [15]) for longer wavelengths The unavailability of the optical constants beyond 1216 nm hasjustified the small mistmacth that still persists between simulations and value derived by experimen-tal measurements (figure 5) Nevertheless it is important to underline that for the purpose of thiswork the need has been finding a combination of roughnessesoptical costants that allows a goodfit of the experimental data and not the determination of each specific parameter indipendently

In the case of the EUV grating the fittings and then the simulations have been computed withPC Grate Software demo version the input parameters (20 nm depth 2726 groovesmm land toperiod ratio cd=045) are taken from the gratingrsquos specifications provided by the manufacturingcompany Jobin Yvon The substrate is Al the coating is Pt with an interlayer of Cr interposed theoptical constants used are those provided with the software and are very well known in the EUVspectral range It is worth to be noticed that the theoretical curve is perfectly compatible with theexperimental data (figure 5)

Analogous procedure has been followed for the FUV grating 517 nm depth 1603 groovesmmand cd=056 have been used as input parameters on the PC Grate Software In this case the exper-imental data are slightly higher than the those simulated by the fitting parameters (figure 6) Thediscrepancy can be attributed to differences between the optical constants used in the calculus andactual ones and mostly in the modelling of the groove profile

5 Results and discussions

The Mueller parameters M00M01M02 and M03 of PHEBUS have been experimentally determinedat different scan angles θ In figure 7 and 8 the coefficient values are reported for three selectedcases being θ = 090 and θ = 45 In the case of θ = 090 the M02 and M03 calculatedparameters are zero as can be deduced from equations (38) and (39) while at θ = 45 a non zerocontribution is reported in figure 8 again formula (38) and (39) tell that these are the maximumvalues obtainable Nevertheless the value of M02 and M03 in this case are still at least one orderlower than M01 at each wavelength (figure 8) so the equation (35) can be re-written according tothe following approximation

Soutput0 asymp ηd(M00Sinput

0 +M01Sinput1 ) (51)

The complete response of the instrument has been therefore determined for each wavelengthand each scanning angle The results take into account the roles of the optical subsystems which

ndash 7 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

when there is a series of optical components In general these dependencies are not expressed inthe calibration of optical instruments being sometimes neglected in name of rdquothe normal incidenceconfigurationrdquo usually adopted The importance of this approach is even more dramatic if the in-strument as in the case of PHEBUS is provided by a scanning system which changes dynamicallythe mutual position of the optical elements In the present analysis the Mueller Matrix has beenexperimentally determined by characterizing the optical components for the nominal incidence an-gle which actually is defined by following the optical path of the chief ray of the central field ofview of the instrument The full field of view and aperture and the curvature of the optical surfacesthat geometrically affect the optical path of the beam resulting in the local variation of the angle ofincidence of the entering rays with respect to the chief ray must be taken into account during theradiometric simulation tool as a secondary effects

The model that has been built allows the determination of the Mueller Matrix for any positionof the scanning system resulting therefore in a very flexible tool for the data analysis The futureexperimental sessions dedicated to the full instrument efficiency measurement and the etenduedetermination will be interpreted as an experimental verification of the model proposed with forselected position of the scanning system

The first part of the manuscript is devoted to the instrument by defining the optical design andthe basic characteristics of the optics then it moves to the description of the method supportedby a Mueller formalism recall The theory will be fundamental to select and drive the proper mea-surements and the consequent experimental results modeling The Mueller parameters of PHEBUShave been finally determined and critically discussed in light of PHEBUS instrument configurationand theoretical predictions

2 PHEBUS optical configuration

PHEBUS (see figure 1) is a French led spectrometer implemented in a cooperative project involvingJapan Russia and Italy It consists of two distinct channels working in the EUV (55-155 nm) andFUV (145-315 nm) spectral ranges with an extension for two extra visible lines at 4047 nm and4228 nm (Chassefiere [1]) The paraxial field of view of the instrument is 2 by 01 The opticalscheme (see figure 2) includes two drawing blocks the collecting and the spectrometer parts

The collector one is composed of the straylight rejection baffle the primary mirror and theentrance slit The mirror is a Silicon Carbide (SiC) off-axis parabola 50 incidence angle and 170mm focal length The SiC has been chosen for its efficiency performances in the whole 55 - 315 nmspectral range and for its mechanical and thermal properties The coating has been manufacturedby CVD process The nominal surface roughness has been specified as 05 nm RMS in orderto minimize the straylight inside the instrument The mirror is positioned at the baffle exit andaccommodated inside a scanner rotating mechanism The main function of the scanner mechanismis to point the spectrometerrsquos toward the selected line-of-sight selected in order to provide thewhole coverage of the Merury exosphere The spectrometer is instead composed by two channelsthe EUV and the FUV one Two holographic gratings share the same mechanical mount and areaccommodated in front of the slit The light is then diffracted and collected by two Multi ChannelPlates (MCPs) detectors The aberration corrected holographic gratings of PHEBUS are made ofaluminum covered by platinum coating The holograph process has been adopted in order to obtaina Variable Line Space Gratings with a mean groove density of 1600 groovesmm for the FUV

ndash 2 ndash

2012 JINST 7 P10023

Figure 1 PHEBUS inner view The light incoming from the baffle impinges on the off-axis parabolic mirrorand is focused on the entrance slit

Figure 2 PHEBUS optical layout The spectrometer consists of two distinct channels working in the EUVand FUV respectively with a common collecting part

and 2700 groovesmm for the EUV one respectively The groove profiles are laminar ion-etchedoptimized for the respective spectral range

3 Matrix Mueller formalism

A block diagonal Mueller matrix is associated to each optical component at each wavelength

Mmg =

|rmg

TM |2+|rmgTE |2

2|rmg

TM |2minus|rmgTE |2

2 0 0|rmg

TM |2minus|rmgTE |2

2|rmg

TM |2+|rmgTE |2

2 0 00 0 real(rmg

TM rmgTE ) image(rmg

TM rmgTE )

0 0 minusimage(rmgTM rmg

TE ) real(rmgTM rmg

TE )

(31)

ndash 3 ndash

2012 JINST 7 P10023

such matrix can be easily derived by considering the gratings and the mirror as a combination ofa polarizer and a phase retarder (Fundamentals of Photonics [5] Polarized Light [6]) The termsrmg

T MT E (rmgT MT E are the complex conjugates) are respectively the Fresnel reflection (efficiency for

the grating) coefficients of the TM and TE components of the electric fields Since |rmgT MT E |

2 =

RmgT MT E the Mueller parameters will depend on the reflectanceefficiency of the optical components

and correspondent phase shift Φm = φ mTMminusφ m

TE The scanning system is described by the rotationmatrix reported below

Ms =

1 0 0 00 cos2θ sin2θ 00 minussin2θ cos2θ 00 0 0 1

(32)

where θ is the scan angle By combining the matrices (31) and (32) the Mueller Matrix Massociated to the spectrometer can be derived

M = MgtimesMstimesMm =

M00 M01 M02 M03

M10 M11 M12 M13

M20 M21 M22 M23

M30 M31 M32 M33

(33)

From a general point of view the matrix M is an operator acting on the polarization state of thelight described by the Stokes vectors

S =

S0

S1

S2

S3

=

|ETM|2 + |ETE|2

|ETM|2minus|ETE|2

2real(ETEETM)2image(ETEETM)

(34)

where ET MT E are the T MT E component of the electric field

If we assume Sinput and Soutput are the Stokes vectors associated to the incoming light and tothe beam impinging the detector (Polarized Light [6]) the relationship

Soutput = MtimesSinput

can be written The detectors used to collect the radiation are MCPs In general the quantumdetection efficiency ηd associated to them depends on the polarization state of the incoming lightand on the bias angle in the first stack (Tomc [7] Yoshioka [2] Yoshioka [8]) In this respect somepreliminar analysis have been done and a fully characterization will be carried on during the propercalibration activities

Then taking into account the efficiency of the MCP at fixed wavelenght and polarization stateof the light the detected signal is the following

Soutput0 = ηd(M00Sinput

0 +M01Sinput1 +M02Sinput

2 +M03Sinput3 ) (35)

ndash 4 ndash

2012 JINST 7 P10023

Figure 3 The normal incidence reflectometer at CNR-IFN UOS Padova It consists of a Johnson-Onakamonochromator with a 600 groovesmm toroidal grating optimized for the UV range

and the relevant terms of the M Mueller matrix of the spectrometer are the coefficients of thefirst row

M00 =Rg

TM +RgTE

2Rm

TM +RmTE

2+

RgTMminusRg

TE2

RmTMminusRm

TE2

cos2θ (36)

M01 =Rg

TM +RgTE

2Rm

TMminusRmTE

2+

RgTMminusRg

TE2

RmTM +Rm

TE2

cos2θ (37)

M02 = RmTMRm

TERg

TMminusRgTE

2cosΦ

msin2θ (38)

M03 = minusRmTMRm

TERg

TMminusRgTE

2sinΦ

msin2θ (39)

4 Experimental

The experimental characterization of the PHEBUS Flight Model (FM) optical subsystems has beenperformed by using the normal incidence reflectometer (see figure 3) at CNR-IFN UOS Padova(Garoli [9]) It consists of a Johnson-Onaka monochromator with a 600 groovesmm toroidal grat-ing optimized for the UV range A toroidal mirror focuses the monochromatic radiation on thesample placed in the experimental chamber together with the detector fixed in the θ minus 2θ config-uration As sources different lamps have been coupled with the facility an home made hollowcathode filled with different gases a deuterium and a Hg lamps A Channel Electron Multiplier(CEM AMPTEK MD501) working in photon counting mode has been adopted for the EUV testwhile a PhotoMultiplier (PM Hamamatsu 6352) for the FUV(see table 1)

The beam probe provided by the reflectometer is polarized by the optical components of thereflectometer itself therefore to obtain all the information necessary for a full knowledge of thePHEBUS subsystem components the probe beam has been fully characterized with a dedicatedexperimental session The method adopted is the same reported in (Garoli [9]) and the results areexpressed in term of the polarization degree f = |ETE|2minus|ETM|2

|ETE|2+|ETM|2as reported in table 1

Then the measurements have been performed in two different positions of the test chamberrotated 90 to each other giving Rmg

up and Rmgdown respectively

Rmgupdown =

Signalmgupdown

Signaldirectupdown

(41)

ndash 5 ndash

2012 JINST 7 P10023

Table 1 Sources Polarization Degree of the illumination system amp Detectors Hollow Cathode Lamp(HCL) Deuterium Lamp (DL) Mercury Lamp (Hg) Channel Electron Multiplier Ampektron MD-501(CEM) Photomultiplier Hamamatsu 6352 (PMT)

λ (nm) Source Polarization Degree (f) Detector304 HCL-He 040 CEM461 HCL-Ne 048 CEM584 HCL-He 053 CEM744 HCL-Ne 059 CEM919 HCL-Ar 073 CEM1025 HCL-He 085 CEM1066 HCL-Ar 082 CEM1216 DL HCL-He 090 CEM1233 DL HCL-He 090 CEM1400 DL 091 CEM1600 DL 092 CEM2540 Hg -038 PMT2654 Hg -068 PMT2800 Hg -082 PMT2960 Hg -070 PMT3022 Hg -075 PMT3127 Hg -063 PMT

where Signalmgupdown and Signaldirect

updown are the reflectedrefracted and the direct signal The average

of the two values corresponds to the throughput for unpolarized light Rmgun To determine the

relevant parameters (equations (36) (37) (38) and (39)) of the the Phebus associated MuellerMatrix the term Rmg

T MT E must be calculated accordingly to the following equation starting fromthe experimental data

RmgT MT E =

Rmgup +Rmg

down2

plusmnRmg

up minusRmgdown

2 f(42)

The phase shift Φm (equation (35)) has been derived by a combination of experimental data theirfitting and proper simulations The method is resumed in the following steps

bull Experimental measure of Rmgup and Rmg

down

bull Determination of Rmgun from Rmg

up and Rmgdown averaging

bull Fitting of Rmgun with a simulation software (optimization of optical constant and roughness

via IMD software in case of SiC mirror optimization of grooves parameters via PC GrateSoftware demo version in case of the gratings)

bull Recovering of RmgT MT E curves by simulation and consequent determination of the phase

shifts Φm

The RmgT MT E results of FM optical subsystems are reported in figure 4 5 and 6

ndash 6 ndash

2012 JINST 7 P10023

Figure 4 shows the results obtained for the SiC mirror and relative fitting The characteri-zazion have been performed over the whole Phebus working range since the mirror is shared bythe two gratings and the two channels In the range from 304 nm to 1216 nm the fitting havebeen computed by using the experimental optical constants provided by D Windt (Windt [10])and finely adjusting the roughness surface (σ=21 nm) and the roughness of the substrate (σ=1nm) As it can be seen a very good match has been obtained by simulations with this proce-dure In the range from 1233 to 160 nm experimental optical constants are available in licteratureonly for two wavelenghts (132 and 149 nm) and beyond 200 nm (Fernandez-Perea [11] Larru-quert [12]) and only in case of a SiC layers deposited by sputtering or Pulsed Laser Deposition(PLD)(Monaco [13] Monaco [14]) In the FUV range threfore the fitting has involved also theoptical constants starting from (Fernandez-Perea [11] Larruquert [12]) below 200 nm and (Pa-lik [15]) for longer wavelengths The unavailability of the optical constants beyond 1216 nm hasjustified the small mistmacth that still persists between simulations and value derived by experimen-tal measurements (figure 5) Nevertheless it is important to underline that for the purpose of thiswork the need has been finding a combination of roughnessesoptical costants that allows a goodfit of the experimental data and not the determination of each specific parameter indipendently

In the case of the EUV grating the fittings and then the simulations have been computed withPC Grate Software demo version the input parameters (20 nm depth 2726 groovesmm land toperiod ratio cd=045) are taken from the gratingrsquos specifications provided by the manufacturingcompany Jobin Yvon The substrate is Al the coating is Pt with an interlayer of Cr interposed theoptical constants used are those provided with the software and are very well known in the EUVspectral range It is worth to be noticed that the theoretical curve is perfectly compatible with theexperimental data (figure 5)

Analogous procedure has been followed for the FUV grating 517 nm depth 1603 groovesmmand cd=056 have been used as input parameters on the PC Grate Software In this case the exper-imental data are slightly higher than the those simulated by the fitting parameters (figure 6) Thediscrepancy can be attributed to differences between the optical constants used in the calculus andactual ones and mostly in the modelling of the groove profile

5 Results and discussions

The Mueller parameters M00M01M02 and M03 of PHEBUS have been experimentally determinedat different scan angles θ In figure 7 and 8 the coefficient values are reported for three selectedcases being θ = 090 and θ = 45 In the case of θ = 090 the M02 and M03 calculatedparameters are zero as can be deduced from equations (38) and (39) while at θ = 45 a non zerocontribution is reported in figure 8 again formula (38) and (39) tell that these are the maximumvalues obtainable Nevertheless the value of M02 and M03 in this case are still at least one orderlower than M01 at each wavelength (figure 8) so the equation (35) can be re-written according tothe following approximation

Soutput0 asymp ηd(M00Sinput

0 +M01Sinput1 ) (51)

The complete response of the instrument has been therefore determined for each wavelengthand each scanning angle The results take into account the roles of the optical subsystems which

ndash 7 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Figure 1 PHEBUS inner view The light incoming from the baffle impinges on the off-axis parabolic mirrorand is focused on the entrance slit

Figure 2 PHEBUS optical layout The spectrometer consists of two distinct channels working in the EUVand FUV respectively with a common collecting part

and 2700 groovesmm for the EUV one respectively The groove profiles are laminar ion-etchedoptimized for the respective spectral range

3 Matrix Mueller formalism

A block diagonal Mueller matrix is associated to each optical component at each wavelength

Mmg =

|rmg

TM |2+|rmgTE |2

2|rmg

TM |2minus|rmgTE |2

2 0 0|rmg

TM |2minus|rmgTE |2

2|rmg

TM |2+|rmgTE |2

2 0 00 0 real(rmg

TM rmgTE ) image(rmg

TM rmgTE )

0 0 minusimage(rmgTM rmg

TE ) real(rmgTM rmg

TE )

(31)

ndash 3 ndash

2012 JINST 7 P10023

such matrix can be easily derived by considering the gratings and the mirror as a combination ofa polarizer and a phase retarder (Fundamentals of Photonics [5] Polarized Light [6]) The termsrmg

T MT E (rmgT MT E are the complex conjugates) are respectively the Fresnel reflection (efficiency for

the grating) coefficients of the TM and TE components of the electric fields Since |rmgT MT E |

2 =

RmgT MT E the Mueller parameters will depend on the reflectanceefficiency of the optical components

and correspondent phase shift Φm = φ mTMminusφ m

TE The scanning system is described by the rotationmatrix reported below

Ms =

1 0 0 00 cos2θ sin2θ 00 minussin2θ cos2θ 00 0 0 1

(32)

where θ is the scan angle By combining the matrices (31) and (32) the Mueller Matrix Massociated to the spectrometer can be derived

M = MgtimesMstimesMm =

M00 M01 M02 M03

M10 M11 M12 M13

M20 M21 M22 M23

M30 M31 M32 M33

(33)

From a general point of view the matrix M is an operator acting on the polarization state of thelight described by the Stokes vectors

S =

S0

S1

S2

S3

=

|ETM|2 + |ETE|2

|ETM|2minus|ETE|2

2real(ETEETM)2image(ETEETM)

(34)

where ET MT E are the T MT E component of the electric field

If we assume Sinput and Soutput are the Stokes vectors associated to the incoming light and tothe beam impinging the detector (Polarized Light [6]) the relationship

Soutput = MtimesSinput

can be written The detectors used to collect the radiation are MCPs In general the quantumdetection efficiency ηd associated to them depends on the polarization state of the incoming lightand on the bias angle in the first stack (Tomc [7] Yoshioka [2] Yoshioka [8]) In this respect somepreliminar analysis have been done and a fully characterization will be carried on during the propercalibration activities

Then taking into account the efficiency of the MCP at fixed wavelenght and polarization stateof the light the detected signal is the following

Soutput0 = ηd(M00Sinput

0 +M01Sinput1 +M02Sinput

2 +M03Sinput3 ) (35)

ndash 4 ndash

2012 JINST 7 P10023

Figure 3 The normal incidence reflectometer at CNR-IFN UOS Padova It consists of a Johnson-Onakamonochromator with a 600 groovesmm toroidal grating optimized for the UV range

and the relevant terms of the M Mueller matrix of the spectrometer are the coefficients of thefirst row

M00 =Rg

TM +RgTE

2Rm

TM +RmTE

2+

RgTMminusRg

TE2

RmTMminusRm

TE2

cos2θ (36)

M01 =Rg

TM +RgTE

2Rm

TMminusRmTE

2+

RgTMminusRg

TE2

RmTM +Rm

TE2

cos2θ (37)

M02 = RmTMRm

TERg

TMminusRgTE

2cosΦ

msin2θ (38)

M03 = minusRmTMRm

TERg

TMminusRgTE

2sinΦ

msin2θ (39)

4 Experimental

The experimental characterization of the PHEBUS Flight Model (FM) optical subsystems has beenperformed by using the normal incidence reflectometer (see figure 3) at CNR-IFN UOS Padova(Garoli [9]) It consists of a Johnson-Onaka monochromator with a 600 groovesmm toroidal grat-ing optimized for the UV range A toroidal mirror focuses the monochromatic radiation on thesample placed in the experimental chamber together with the detector fixed in the θ minus 2θ config-uration As sources different lamps have been coupled with the facility an home made hollowcathode filled with different gases a deuterium and a Hg lamps A Channel Electron Multiplier(CEM AMPTEK MD501) working in photon counting mode has been adopted for the EUV testwhile a PhotoMultiplier (PM Hamamatsu 6352) for the FUV(see table 1)

The beam probe provided by the reflectometer is polarized by the optical components of thereflectometer itself therefore to obtain all the information necessary for a full knowledge of thePHEBUS subsystem components the probe beam has been fully characterized with a dedicatedexperimental session The method adopted is the same reported in (Garoli [9]) and the results areexpressed in term of the polarization degree f = |ETE|2minus|ETM|2

|ETE|2+|ETM|2as reported in table 1

Then the measurements have been performed in two different positions of the test chamberrotated 90 to each other giving Rmg

up and Rmgdown respectively

Rmgupdown =

Signalmgupdown

Signaldirectupdown

(41)

ndash 5 ndash

2012 JINST 7 P10023

Table 1 Sources Polarization Degree of the illumination system amp Detectors Hollow Cathode Lamp(HCL) Deuterium Lamp (DL) Mercury Lamp (Hg) Channel Electron Multiplier Ampektron MD-501(CEM) Photomultiplier Hamamatsu 6352 (PMT)

λ (nm) Source Polarization Degree (f) Detector304 HCL-He 040 CEM461 HCL-Ne 048 CEM584 HCL-He 053 CEM744 HCL-Ne 059 CEM919 HCL-Ar 073 CEM1025 HCL-He 085 CEM1066 HCL-Ar 082 CEM1216 DL HCL-He 090 CEM1233 DL HCL-He 090 CEM1400 DL 091 CEM1600 DL 092 CEM2540 Hg -038 PMT2654 Hg -068 PMT2800 Hg -082 PMT2960 Hg -070 PMT3022 Hg -075 PMT3127 Hg -063 PMT

where Signalmgupdown and Signaldirect

updown are the reflectedrefracted and the direct signal The average

of the two values corresponds to the throughput for unpolarized light Rmgun To determine the

relevant parameters (equations (36) (37) (38) and (39)) of the the Phebus associated MuellerMatrix the term Rmg

T MT E must be calculated accordingly to the following equation starting fromthe experimental data

RmgT MT E =

Rmgup +Rmg

down2

plusmnRmg

up minusRmgdown

2 f(42)

The phase shift Φm (equation (35)) has been derived by a combination of experimental data theirfitting and proper simulations The method is resumed in the following steps

bull Experimental measure of Rmgup and Rmg

down

bull Determination of Rmgun from Rmg

up and Rmgdown averaging

bull Fitting of Rmgun with a simulation software (optimization of optical constant and roughness

via IMD software in case of SiC mirror optimization of grooves parameters via PC GrateSoftware demo version in case of the gratings)

bull Recovering of RmgT MT E curves by simulation and consequent determination of the phase

shifts Φm

The RmgT MT E results of FM optical subsystems are reported in figure 4 5 and 6

ndash 6 ndash

2012 JINST 7 P10023

Figure 4 shows the results obtained for the SiC mirror and relative fitting The characteri-zazion have been performed over the whole Phebus working range since the mirror is shared bythe two gratings and the two channels In the range from 304 nm to 1216 nm the fitting havebeen computed by using the experimental optical constants provided by D Windt (Windt [10])and finely adjusting the roughness surface (σ=21 nm) and the roughness of the substrate (σ=1nm) As it can be seen a very good match has been obtained by simulations with this proce-dure In the range from 1233 to 160 nm experimental optical constants are available in licteratureonly for two wavelenghts (132 and 149 nm) and beyond 200 nm (Fernandez-Perea [11] Larru-quert [12]) and only in case of a SiC layers deposited by sputtering or Pulsed Laser Deposition(PLD)(Monaco [13] Monaco [14]) In the FUV range threfore the fitting has involved also theoptical constants starting from (Fernandez-Perea [11] Larruquert [12]) below 200 nm and (Pa-lik [15]) for longer wavelengths The unavailability of the optical constants beyond 1216 nm hasjustified the small mistmacth that still persists between simulations and value derived by experimen-tal measurements (figure 5) Nevertheless it is important to underline that for the purpose of thiswork the need has been finding a combination of roughnessesoptical costants that allows a goodfit of the experimental data and not the determination of each specific parameter indipendently

In the case of the EUV grating the fittings and then the simulations have been computed withPC Grate Software demo version the input parameters (20 nm depth 2726 groovesmm land toperiod ratio cd=045) are taken from the gratingrsquos specifications provided by the manufacturingcompany Jobin Yvon The substrate is Al the coating is Pt with an interlayer of Cr interposed theoptical constants used are those provided with the software and are very well known in the EUVspectral range It is worth to be noticed that the theoretical curve is perfectly compatible with theexperimental data (figure 5)

Analogous procedure has been followed for the FUV grating 517 nm depth 1603 groovesmmand cd=056 have been used as input parameters on the PC Grate Software In this case the exper-imental data are slightly higher than the those simulated by the fitting parameters (figure 6) Thediscrepancy can be attributed to differences between the optical constants used in the calculus andactual ones and mostly in the modelling of the groove profile

5 Results and discussions

The Mueller parameters M00M01M02 and M03 of PHEBUS have been experimentally determinedat different scan angles θ In figure 7 and 8 the coefficient values are reported for three selectedcases being θ = 090 and θ = 45 In the case of θ = 090 the M02 and M03 calculatedparameters are zero as can be deduced from equations (38) and (39) while at θ = 45 a non zerocontribution is reported in figure 8 again formula (38) and (39) tell that these are the maximumvalues obtainable Nevertheless the value of M02 and M03 in this case are still at least one orderlower than M01 at each wavelength (figure 8) so the equation (35) can be re-written according tothe following approximation

Soutput0 asymp ηd(M00Sinput

0 +M01Sinput1 ) (51)

The complete response of the instrument has been therefore determined for each wavelengthand each scanning angle The results take into account the roles of the optical subsystems which

ndash 7 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

such matrix can be easily derived by considering the gratings and the mirror as a combination ofa polarizer and a phase retarder (Fundamentals of Photonics [5] Polarized Light [6]) The termsrmg

T MT E (rmgT MT E are the complex conjugates) are respectively the Fresnel reflection (efficiency for

the grating) coefficients of the TM and TE components of the electric fields Since |rmgT MT E |

2 =

RmgT MT E the Mueller parameters will depend on the reflectanceefficiency of the optical components

and correspondent phase shift Φm = φ mTMminusφ m

TE The scanning system is described by the rotationmatrix reported below

Ms =

1 0 0 00 cos2θ sin2θ 00 minussin2θ cos2θ 00 0 0 1

(32)

where θ is the scan angle By combining the matrices (31) and (32) the Mueller Matrix Massociated to the spectrometer can be derived

M = MgtimesMstimesMm =

M00 M01 M02 M03

M10 M11 M12 M13

M20 M21 M22 M23

M30 M31 M32 M33

(33)

From a general point of view the matrix M is an operator acting on the polarization state of thelight described by the Stokes vectors

S =

S0

S1

S2

S3

=

|ETM|2 + |ETE|2

|ETM|2minus|ETE|2

2real(ETEETM)2image(ETEETM)

(34)

where ET MT E are the T MT E component of the electric field

If we assume Sinput and Soutput are the Stokes vectors associated to the incoming light and tothe beam impinging the detector (Polarized Light [6]) the relationship

Soutput = MtimesSinput

can be written The detectors used to collect the radiation are MCPs In general the quantumdetection efficiency ηd associated to them depends on the polarization state of the incoming lightand on the bias angle in the first stack (Tomc [7] Yoshioka [2] Yoshioka [8]) In this respect somepreliminar analysis have been done and a fully characterization will be carried on during the propercalibration activities

Then taking into account the efficiency of the MCP at fixed wavelenght and polarization stateof the light the detected signal is the following

Soutput0 = ηd(M00Sinput

0 +M01Sinput1 +M02Sinput

2 +M03Sinput3 ) (35)

ndash 4 ndash

2012 JINST 7 P10023

Figure 3 The normal incidence reflectometer at CNR-IFN UOS Padova It consists of a Johnson-Onakamonochromator with a 600 groovesmm toroidal grating optimized for the UV range

and the relevant terms of the M Mueller matrix of the spectrometer are the coefficients of thefirst row

M00 =Rg

TM +RgTE

2Rm

TM +RmTE

2+

RgTMminusRg

TE2

RmTMminusRm

TE2

cos2θ (36)

M01 =Rg

TM +RgTE

2Rm

TMminusRmTE

2+

RgTMminusRg

TE2

RmTM +Rm

TE2

cos2θ (37)

M02 = RmTMRm

TERg

TMminusRgTE

2cosΦ

msin2θ (38)

M03 = minusRmTMRm

TERg

TMminusRgTE

2sinΦ

msin2θ (39)

4 Experimental

The experimental characterization of the PHEBUS Flight Model (FM) optical subsystems has beenperformed by using the normal incidence reflectometer (see figure 3) at CNR-IFN UOS Padova(Garoli [9]) It consists of a Johnson-Onaka monochromator with a 600 groovesmm toroidal grat-ing optimized for the UV range A toroidal mirror focuses the monochromatic radiation on thesample placed in the experimental chamber together with the detector fixed in the θ minus 2θ config-uration As sources different lamps have been coupled with the facility an home made hollowcathode filled with different gases a deuterium and a Hg lamps A Channel Electron Multiplier(CEM AMPTEK MD501) working in photon counting mode has been adopted for the EUV testwhile a PhotoMultiplier (PM Hamamatsu 6352) for the FUV(see table 1)

The beam probe provided by the reflectometer is polarized by the optical components of thereflectometer itself therefore to obtain all the information necessary for a full knowledge of thePHEBUS subsystem components the probe beam has been fully characterized with a dedicatedexperimental session The method adopted is the same reported in (Garoli [9]) and the results areexpressed in term of the polarization degree f = |ETE|2minus|ETM|2

|ETE|2+|ETM|2as reported in table 1

Then the measurements have been performed in two different positions of the test chamberrotated 90 to each other giving Rmg

up and Rmgdown respectively

Rmgupdown =

Signalmgupdown

Signaldirectupdown

(41)

ndash 5 ndash

2012 JINST 7 P10023

Table 1 Sources Polarization Degree of the illumination system amp Detectors Hollow Cathode Lamp(HCL) Deuterium Lamp (DL) Mercury Lamp (Hg) Channel Electron Multiplier Ampektron MD-501(CEM) Photomultiplier Hamamatsu 6352 (PMT)

λ (nm) Source Polarization Degree (f) Detector304 HCL-He 040 CEM461 HCL-Ne 048 CEM584 HCL-He 053 CEM744 HCL-Ne 059 CEM919 HCL-Ar 073 CEM1025 HCL-He 085 CEM1066 HCL-Ar 082 CEM1216 DL HCL-He 090 CEM1233 DL HCL-He 090 CEM1400 DL 091 CEM1600 DL 092 CEM2540 Hg -038 PMT2654 Hg -068 PMT2800 Hg -082 PMT2960 Hg -070 PMT3022 Hg -075 PMT3127 Hg -063 PMT

where Signalmgupdown and Signaldirect

updown are the reflectedrefracted and the direct signal The average

of the two values corresponds to the throughput for unpolarized light Rmgun To determine the

relevant parameters (equations (36) (37) (38) and (39)) of the the Phebus associated MuellerMatrix the term Rmg

T MT E must be calculated accordingly to the following equation starting fromthe experimental data

RmgT MT E =

Rmgup +Rmg

down2

plusmnRmg

up minusRmgdown

2 f(42)

The phase shift Φm (equation (35)) has been derived by a combination of experimental data theirfitting and proper simulations The method is resumed in the following steps

bull Experimental measure of Rmgup and Rmg

down

bull Determination of Rmgun from Rmg

up and Rmgdown averaging

bull Fitting of Rmgun with a simulation software (optimization of optical constant and roughness

via IMD software in case of SiC mirror optimization of grooves parameters via PC GrateSoftware demo version in case of the gratings)

bull Recovering of RmgT MT E curves by simulation and consequent determination of the phase

shifts Φm

The RmgT MT E results of FM optical subsystems are reported in figure 4 5 and 6

ndash 6 ndash

2012 JINST 7 P10023

Figure 4 shows the results obtained for the SiC mirror and relative fitting The characteri-zazion have been performed over the whole Phebus working range since the mirror is shared bythe two gratings and the two channels In the range from 304 nm to 1216 nm the fitting havebeen computed by using the experimental optical constants provided by D Windt (Windt [10])and finely adjusting the roughness surface (σ=21 nm) and the roughness of the substrate (σ=1nm) As it can be seen a very good match has been obtained by simulations with this proce-dure In the range from 1233 to 160 nm experimental optical constants are available in licteratureonly for two wavelenghts (132 and 149 nm) and beyond 200 nm (Fernandez-Perea [11] Larru-quert [12]) and only in case of a SiC layers deposited by sputtering or Pulsed Laser Deposition(PLD)(Monaco [13] Monaco [14]) In the FUV range threfore the fitting has involved also theoptical constants starting from (Fernandez-Perea [11] Larruquert [12]) below 200 nm and (Pa-lik [15]) for longer wavelengths The unavailability of the optical constants beyond 1216 nm hasjustified the small mistmacth that still persists between simulations and value derived by experimen-tal measurements (figure 5) Nevertheless it is important to underline that for the purpose of thiswork the need has been finding a combination of roughnessesoptical costants that allows a goodfit of the experimental data and not the determination of each specific parameter indipendently

In the case of the EUV grating the fittings and then the simulations have been computed withPC Grate Software demo version the input parameters (20 nm depth 2726 groovesmm land toperiod ratio cd=045) are taken from the gratingrsquos specifications provided by the manufacturingcompany Jobin Yvon The substrate is Al the coating is Pt with an interlayer of Cr interposed theoptical constants used are those provided with the software and are very well known in the EUVspectral range It is worth to be noticed that the theoretical curve is perfectly compatible with theexperimental data (figure 5)

Analogous procedure has been followed for the FUV grating 517 nm depth 1603 groovesmmand cd=056 have been used as input parameters on the PC Grate Software In this case the exper-imental data are slightly higher than the those simulated by the fitting parameters (figure 6) Thediscrepancy can be attributed to differences between the optical constants used in the calculus andactual ones and mostly in the modelling of the groove profile

5 Results and discussions

The Mueller parameters M00M01M02 and M03 of PHEBUS have been experimentally determinedat different scan angles θ In figure 7 and 8 the coefficient values are reported for three selectedcases being θ = 090 and θ = 45 In the case of θ = 090 the M02 and M03 calculatedparameters are zero as can be deduced from equations (38) and (39) while at θ = 45 a non zerocontribution is reported in figure 8 again formula (38) and (39) tell that these are the maximumvalues obtainable Nevertheless the value of M02 and M03 in this case are still at least one orderlower than M01 at each wavelength (figure 8) so the equation (35) can be re-written according tothe following approximation

Soutput0 asymp ηd(M00Sinput

0 +M01Sinput1 ) (51)

The complete response of the instrument has been therefore determined for each wavelengthand each scanning angle The results take into account the roles of the optical subsystems which

ndash 7 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Figure 3 The normal incidence reflectometer at CNR-IFN UOS Padova It consists of a Johnson-Onakamonochromator with a 600 groovesmm toroidal grating optimized for the UV range

and the relevant terms of the M Mueller matrix of the spectrometer are the coefficients of thefirst row

M00 =Rg

TM +RgTE

2Rm

TM +RmTE

2+

RgTMminusRg

TE2

RmTMminusRm

TE2

cos2θ (36)

M01 =Rg

TM +RgTE

2Rm

TMminusRmTE

2+

RgTMminusRg

TE2

RmTM +Rm

TE2

cos2θ (37)

M02 = RmTMRm

TERg

TMminusRgTE

2cosΦ

msin2θ (38)

M03 = minusRmTMRm

TERg

TMminusRgTE

2sinΦ

msin2θ (39)

4 Experimental

The experimental characterization of the PHEBUS Flight Model (FM) optical subsystems has beenperformed by using the normal incidence reflectometer (see figure 3) at CNR-IFN UOS Padova(Garoli [9]) It consists of a Johnson-Onaka monochromator with a 600 groovesmm toroidal grat-ing optimized for the UV range A toroidal mirror focuses the monochromatic radiation on thesample placed in the experimental chamber together with the detector fixed in the θ minus 2θ config-uration As sources different lamps have been coupled with the facility an home made hollowcathode filled with different gases a deuterium and a Hg lamps A Channel Electron Multiplier(CEM AMPTEK MD501) working in photon counting mode has been adopted for the EUV testwhile a PhotoMultiplier (PM Hamamatsu 6352) for the FUV(see table 1)

The beam probe provided by the reflectometer is polarized by the optical components of thereflectometer itself therefore to obtain all the information necessary for a full knowledge of thePHEBUS subsystem components the probe beam has been fully characterized with a dedicatedexperimental session The method adopted is the same reported in (Garoli [9]) and the results areexpressed in term of the polarization degree f = |ETE|2minus|ETM|2

|ETE|2+|ETM|2as reported in table 1

Then the measurements have been performed in two different positions of the test chamberrotated 90 to each other giving Rmg

up and Rmgdown respectively

Rmgupdown =

Signalmgupdown

Signaldirectupdown

(41)

ndash 5 ndash

2012 JINST 7 P10023

Table 1 Sources Polarization Degree of the illumination system amp Detectors Hollow Cathode Lamp(HCL) Deuterium Lamp (DL) Mercury Lamp (Hg) Channel Electron Multiplier Ampektron MD-501(CEM) Photomultiplier Hamamatsu 6352 (PMT)

λ (nm) Source Polarization Degree (f) Detector304 HCL-He 040 CEM461 HCL-Ne 048 CEM584 HCL-He 053 CEM744 HCL-Ne 059 CEM919 HCL-Ar 073 CEM1025 HCL-He 085 CEM1066 HCL-Ar 082 CEM1216 DL HCL-He 090 CEM1233 DL HCL-He 090 CEM1400 DL 091 CEM1600 DL 092 CEM2540 Hg -038 PMT2654 Hg -068 PMT2800 Hg -082 PMT2960 Hg -070 PMT3022 Hg -075 PMT3127 Hg -063 PMT

where Signalmgupdown and Signaldirect

updown are the reflectedrefracted and the direct signal The average

of the two values corresponds to the throughput for unpolarized light Rmgun To determine the

relevant parameters (equations (36) (37) (38) and (39)) of the the Phebus associated MuellerMatrix the term Rmg

T MT E must be calculated accordingly to the following equation starting fromthe experimental data

RmgT MT E =

Rmgup +Rmg

down2

plusmnRmg

up minusRmgdown

2 f(42)

The phase shift Φm (equation (35)) has been derived by a combination of experimental data theirfitting and proper simulations The method is resumed in the following steps

bull Experimental measure of Rmgup and Rmg

down

bull Determination of Rmgun from Rmg

up and Rmgdown averaging

bull Fitting of Rmgun with a simulation software (optimization of optical constant and roughness

via IMD software in case of SiC mirror optimization of grooves parameters via PC GrateSoftware demo version in case of the gratings)

bull Recovering of RmgT MT E curves by simulation and consequent determination of the phase

shifts Φm

The RmgT MT E results of FM optical subsystems are reported in figure 4 5 and 6

ndash 6 ndash

2012 JINST 7 P10023

Figure 4 shows the results obtained for the SiC mirror and relative fitting The characteri-zazion have been performed over the whole Phebus working range since the mirror is shared bythe two gratings and the two channels In the range from 304 nm to 1216 nm the fitting havebeen computed by using the experimental optical constants provided by D Windt (Windt [10])and finely adjusting the roughness surface (σ=21 nm) and the roughness of the substrate (σ=1nm) As it can be seen a very good match has been obtained by simulations with this proce-dure In the range from 1233 to 160 nm experimental optical constants are available in licteratureonly for two wavelenghts (132 and 149 nm) and beyond 200 nm (Fernandez-Perea [11] Larru-quert [12]) and only in case of a SiC layers deposited by sputtering or Pulsed Laser Deposition(PLD)(Monaco [13] Monaco [14]) In the FUV range threfore the fitting has involved also theoptical constants starting from (Fernandez-Perea [11] Larruquert [12]) below 200 nm and (Pa-lik [15]) for longer wavelengths The unavailability of the optical constants beyond 1216 nm hasjustified the small mistmacth that still persists between simulations and value derived by experimen-tal measurements (figure 5) Nevertheless it is important to underline that for the purpose of thiswork the need has been finding a combination of roughnessesoptical costants that allows a goodfit of the experimental data and not the determination of each specific parameter indipendently

In the case of the EUV grating the fittings and then the simulations have been computed withPC Grate Software demo version the input parameters (20 nm depth 2726 groovesmm land toperiod ratio cd=045) are taken from the gratingrsquos specifications provided by the manufacturingcompany Jobin Yvon The substrate is Al the coating is Pt with an interlayer of Cr interposed theoptical constants used are those provided with the software and are very well known in the EUVspectral range It is worth to be noticed that the theoretical curve is perfectly compatible with theexperimental data (figure 5)

Analogous procedure has been followed for the FUV grating 517 nm depth 1603 groovesmmand cd=056 have been used as input parameters on the PC Grate Software In this case the exper-imental data are slightly higher than the those simulated by the fitting parameters (figure 6) Thediscrepancy can be attributed to differences between the optical constants used in the calculus andactual ones and mostly in the modelling of the groove profile

5 Results and discussions

The Mueller parameters M00M01M02 and M03 of PHEBUS have been experimentally determinedat different scan angles θ In figure 7 and 8 the coefficient values are reported for three selectedcases being θ = 090 and θ = 45 In the case of θ = 090 the M02 and M03 calculatedparameters are zero as can be deduced from equations (38) and (39) while at θ = 45 a non zerocontribution is reported in figure 8 again formula (38) and (39) tell that these are the maximumvalues obtainable Nevertheless the value of M02 and M03 in this case are still at least one orderlower than M01 at each wavelength (figure 8) so the equation (35) can be re-written according tothe following approximation

Soutput0 asymp ηd(M00Sinput

0 +M01Sinput1 ) (51)

The complete response of the instrument has been therefore determined for each wavelengthand each scanning angle The results take into account the roles of the optical subsystems which

ndash 7 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Table 1 Sources Polarization Degree of the illumination system amp Detectors Hollow Cathode Lamp(HCL) Deuterium Lamp (DL) Mercury Lamp (Hg) Channel Electron Multiplier Ampektron MD-501(CEM) Photomultiplier Hamamatsu 6352 (PMT)

λ (nm) Source Polarization Degree (f) Detector304 HCL-He 040 CEM461 HCL-Ne 048 CEM584 HCL-He 053 CEM744 HCL-Ne 059 CEM919 HCL-Ar 073 CEM1025 HCL-He 085 CEM1066 HCL-Ar 082 CEM1216 DL HCL-He 090 CEM1233 DL HCL-He 090 CEM1400 DL 091 CEM1600 DL 092 CEM2540 Hg -038 PMT2654 Hg -068 PMT2800 Hg -082 PMT2960 Hg -070 PMT3022 Hg -075 PMT3127 Hg -063 PMT

where Signalmgupdown and Signaldirect

updown are the reflectedrefracted and the direct signal The average

of the two values corresponds to the throughput for unpolarized light Rmgun To determine the

relevant parameters (equations (36) (37) (38) and (39)) of the the Phebus associated MuellerMatrix the term Rmg

T MT E must be calculated accordingly to the following equation starting fromthe experimental data

RmgT MT E =

Rmgup +Rmg

down2

plusmnRmg

up minusRmgdown

2 f(42)

The phase shift Φm (equation (35)) has been derived by a combination of experimental data theirfitting and proper simulations The method is resumed in the following steps

bull Experimental measure of Rmgup and Rmg

down

bull Determination of Rmgun from Rmg

up and Rmgdown averaging

bull Fitting of Rmgun with a simulation software (optimization of optical constant and roughness

via IMD software in case of SiC mirror optimization of grooves parameters via PC GrateSoftware demo version in case of the gratings)

bull Recovering of RmgT MT E curves by simulation and consequent determination of the phase

shifts Φm

The RmgT MT E results of FM optical subsystems are reported in figure 4 5 and 6

ndash 6 ndash

2012 JINST 7 P10023

Figure 4 shows the results obtained for the SiC mirror and relative fitting The characteri-zazion have been performed over the whole Phebus working range since the mirror is shared bythe two gratings and the two channels In the range from 304 nm to 1216 nm the fitting havebeen computed by using the experimental optical constants provided by D Windt (Windt [10])and finely adjusting the roughness surface (σ=21 nm) and the roughness of the substrate (σ=1nm) As it can be seen a very good match has been obtained by simulations with this proce-dure In the range from 1233 to 160 nm experimental optical constants are available in licteratureonly for two wavelenghts (132 and 149 nm) and beyond 200 nm (Fernandez-Perea [11] Larru-quert [12]) and only in case of a SiC layers deposited by sputtering or Pulsed Laser Deposition(PLD)(Monaco [13] Monaco [14]) In the FUV range threfore the fitting has involved also theoptical constants starting from (Fernandez-Perea [11] Larruquert [12]) below 200 nm and (Pa-lik [15]) for longer wavelengths The unavailability of the optical constants beyond 1216 nm hasjustified the small mistmacth that still persists between simulations and value derived by experimen-tal measurements (figure 5) Nevertheless it is important to underline that for the purpose of thiswork the need has been finding a combination of roughnessesoptical costants that allows a goodfit of the experimental data and not the determination of each specific parameter indipendently

In the case of the EUV grating the fittings and then the simulations have been computed withPC Grate Software demo version the input parameters (20 nm depth 2726 groovesmm land toperiod ratio cd=045) are taken from the gratingrsquos specifications provided by the manufacturingcompany Jobin Yvon The substrate is Al the coating is Pt with an interlayer of Cr interposed theoptical constants used are those provided with the software and are very well known in the EUVspectral range It is worth to be noticed that the theoretical curve is perfectly compatible with theexperimental data (figure 5)

Analogous procedure has been followed for the FUV grating 517 nm depth 1603 groovesmmand cd=056 have been used as input parameters on the PC Grate Software In this case the exper-imental data are slightly higher than the those simulated by the fitting parameters (figure 6) Thediscrepancy can be attributed to differences between the optical constants used in the calculus andactual ones and mostly in the modelling of the groove profile

5 Results and discussions

The Mueller parameters M00M01M02 and M03 of PHEBUS have been experimentally determinedat different scan angles θ In figure 7 and 8 the coefficient values are reported for three selectedcases being θ = 090 and θ = 45 In the case of θ = 090 the M02 and M03 calculatedparameters are zero as can be deduced from equations (38) and (39) while at θ = 45 a non zerocontribution is reported in figure 8 again formula (38) and (39) tell that these are the maximumvalues obtainable Nevertheless the value of M02 and M03 in this case are still at least one orderlower than M01 at each wavelength (figure 8) so the equation (35) can be re-written according tothe following approximation

Soutput0 asymp ηd(M00Sinput

0 +M01Sinput1 ) (51)

The complete response of the instrument has been therefore determined for each wavelengthand each scanning angle The results take into account the roles of the optical subsystems which

ndash 7 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Figure 4 shows the results obtained for the SiC mirror and relative fitting The characteri-zazion have been performed over the whole Phebus working range since the mirror is shared bythe two gratings and the two channels In the range from 304 nm to 1216 nm the fitting havebeen computed by using the experimental optical constants provided by D Windt (Windt [10])and finely adjusting the roughness surface (σ=21 nm) and the roughness of the substrate (σ=1nm) As it can be seen a very good match has been obtained by simulations with this proce-dure In the range from 1233 to 160 nm experimental optical constants are available in licteratureonly for two wavelenghts (132 and 149 nm) and beyond 200 nm (Fernandez-Perea [11] Larru-quert [12]) and only in case of a SiC layers deposited by sputtering or Pulsed Laser Deposition(PLD)(Monaco [13] Monaco [14]) In the FUV range threfore the fitting has involved also theoptical constants starting from (Fernandez-Perea [11] Larruquert [12]) below 200 nm and (Pa-lik [15]) for longer wavelengths The unavailability of the optical constants beyond 1216 nm hasjustified the small mistmacth that still persists between simulations and value derived by experimen-tal measurements (figure 5) Nevertheless it is important to underline that for the purpose of thiswork the need has been finding a combination of roughnessesoptical costants that allows a goodfit of the experimental data and not the determination of each specific parameter indipendently

In the case of the EUV grating the fittings and then the simulations have been computed withPC Grate Software demo version the input parameters (20 nm depth 2726 groovesmm land toperiod ratio cd=045) are taken from the gratingrsquos specifications provided by the manufacturingcompany Jobin Yvon The substrate is Al the coating is Pt with an interlayer of Cr interposed theoptical constants used are those provided with the software and are very well known in the EUVspectral range It is worth to be noticed that the theoretical curve is perfectly compatible with theexperimental data (figure 5)

Analogous procedure has been followed for the FUV grating 517 nm depth 1603 groovesmmand cd=056 have been used as input parameters on the PC Grate Software In this case the exper-imental data are slightly higher than the those simulated by the fitting parameters (figure 6) Thediscrepancy can be attributed to differences between the optical constants used in the calculus andactual ones and mostly in the modelling of the groove profile

5 Results and discussions

The Mueller parameters M00M01M02 and M03 of PHEBUS have been experimentally determinedat different scan angles θ In figure 7 and 8 the coefficient values are reported for three selectedcases being θ = 090 and θ = 45 In the case of θ = 090 the M02 and M03 calculatedparameters are zero as can be deduced from equations (38) and (39) while at θ = 45 a non zerocontribution is reported in figure 8 again formula (38) and (39) tell that these are the maximumvalues obtainable Nevertheless the value of M02 and M03 in this case are still at least one orderlower than M01 at each wavelength (figure 8) so the equation (35) can be re-written according tothe following approximation

Soutput0 asymp ηd(M00Sinput

0 +M01Sinput1 ) (51)

The complete response of the instrument has been therefore determined for each wavelengthand each scanning angle The results take into account the roles of the optical subsystems which

ndash 7 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Figure 4 SiC entrance mirror Experimental measurements of Rmun together with theoretical trend Rm

T MT Ehave been obtained from the experimental measurements by knowing the polarization degree f

Figure 5 EUV grating Experimental data are and theoretical trend are shown in the graph The simulationhas been obtained by PC Grate Software

affect the efficency and phase of the incidence beam if we consider that both mirror and gratingswork at an incidence angle far from the normal one the effect is of course very pronunciated Onthe contrary the model built shows that the instrument response only partially depends on the sourcepolarization status since Sinput

2 and Sinput3 do not enter in the approximation 51 In order to estime

the relative importance of the Sinput0 and Sinput

1 parameters we have calculated the Soutput0 assuming

ndash 8 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Figure 6 FUV grating The data obtained by the experimental measurements are shown togheter with thesimulated trend

ηd = 1 for a different set of Stokes parameters being

Sinput =

1Xi

00

where Xi varies from 0 to 1 with a step of 01 (figure 9) this set of Stokes vectors describes differentsource status ranging from a completely unpolarized one to a completely linearly polarized one Ifthe polarization factor of the source is less than 20 (ie S = (10200)T ) the calculated Soutput

0shows that can be approximated to

Soutput0 asympM00Sinput

0 +C (52)

where C is a correction factor lower than 10 In this case the recovering of the intensity ofthe input source can be obtained by knowing M00 with an error lower than 10 according to thevalue reported in figure 9 For higher polarization factor the formula (51) contains two unknownparameters and therefore it is not possible to derive a full knowledge of the entering source Asalready recall in the introduction this model has been built for the chief ray of the central field ofview For the complete radiometric model it will be necessary to take into account the optical pathassociated to each ray entering to the system

6 Conclusions

A method based on the Mueller Matrix formalism has been adopted to fully determine the pure ef-ficiency of PHEBUS spectrometer by using the experimental throughputs of the optical subsystemsand the simulations Right now the PHEBUS data could be understood by applying the proposed

ndash 9 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Figure 7 M00 and M01 PHEBUS parameters at θ = 0 and θ = 90 respectively The empty symbols referto θ = 0 while the black ones to θ = 90 In both cases M00 = M01 = 0

Figure 8 The Mueller parameters of PHEBUS at θ = 45

approach In fact the Mueller parameters have been determined at different scan angles It hasalso been studied the theoretical response of the instrument for different polarization status of theincoming light ranging from a completely unpolarized one to a completely linearly polarized oneIf the polarization factor of the source is less than 20 its intensity can be obtained by means ofthe first Mueller parameter with an error lower than 10

ndash 10 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

Figure 9 Soutput0 has been calculated for different Stokes parameters describing different sources status

ranging from a completely unpolarized one to a completely linearly polarized one

Acknowledgments

This paper is supported by the Italian Space Agency (contract ASIINAF nI022100) for theBepiColombo mission

References

[1] E Chassefiere et al PHEBUS A double ultraviolet spectrometer to observe Mercuryrsquos exospherePlanet Space Sci 58 (2010) 201

[2] K Yoshioka et al Development of the EUv detector for the BepiColombo mission Adv Space Res41 (2008) 1392

[3] R Killen et al Expected emission from Mercuryrsquos exosphere species and their ultraviolet-visiblesignatures Astrophys J Suppl 181 (2009) 351

[4] E Buenzli et al Polarization models for Rayleigh scattering planetary atmospheres Earth MoonPlanets 105 (2009) 153

[5] BEA Saleh and MC Teich Fundamentals of photonics John Wiley amp Sons Inc Hoboken USA(2007)

[6] D Goldstein Polarized light Marcel Deker Inc New York USA (1993)

[7] J Tomc et al Variations in the polarization sensitivity of microchannel plates with photon incidenceangle and wavelength in the VUV Appl Opt 23 (1984) 656

[8] K Yoshioka et al Optical performance of PHEBUSEUV detector onboard BepiColombo AdvSpace Res 49 (2012) 1265

[9] D Garoli et al Reflectance measurements and optical constants in the extreme ultraviolet-vacuumultraviolet regions for SiC with a different C7Si ratio Appl Opt 45 (2006) 5642

ndash 11 ndash

2012 JINST 7 P10023

[10] DL Windt et al Optical constants for thin films of C diamond Al Si and CVD SiC from 24 Ato1216 A Appl Opt 27 (1988) 279

[11] M Fernandez-Perea et al In situ reflectance and optical constants of ion-beam-sputtered SiC films inthe 584 to 1492 nm region Appl Opt 48 (2009) 4698

[12] JI Larruquert et al Self-consistent optical constants of SiC thin films J Opt Soc Am A 28 (2011)2348

[13] G Monaco et al Silicon carbide thin films for EUV and soft X-ray applications in the 584 to1492 nm region Eur Phys J 169 (2009) 159

[14] G Monaco et al Synthesis of heteroepytaxial 3C-SiC by means of PLD Appl Phys A 105 (2011)225

[15] ED Palik et al Handbook of optical constants of solids Elsevier (1998)

ndash 12 ndash