Characterization of the Supermirror Hard-X-Ray Telescope for the InFOCµS Balloon Experiment

Characterization of the supermirror hard-x-raytelescope for the InFOC�S balloon experiment

Takashi Okajima, Keisuke Tamura, Yasushi Ogasaka, Kazutoshi Haga, Seiji Takahashi,Satoshi Ichimaru, Hideo Kito, Shin’ichi Fukuda, Arifumi Goto, Kentaro Nomoto,Hiroyuki Satake, Seima Kato, Yuichi Kamata, Akihiro Furuzawa, Fumie Akimoto,Tsutomu Yoshioka, Kazumasa Kondo, Yoshito Haba, Takeshi Tanaka, Keiichi Wada,Noriyuki Hamada, Murat Hudaverdi, Yuzuru Tawara, Koujun Yamashita,Peter J. Serlemitsos, Yang Soong, Kai-Wing Chan, Scott M. Owens,Fred B. Berendse, Jack Tueller, Kazutami Misaki, Ryo Shibata, Hideyuki Mori, Kei Itoh,Hideyo Kunieda, and Yoshiharu Namba

A hard-x-ray telescope is successfully produced for balloon observations by making use of depth-gradedmultilayers, or so-called supermirrors, with platinum–carbon �Pt�C� layer pairs. It consists of four quad-rant units assembled in an optical configuration with a diameter of 40 cm and a focal length of 8 m. Eachquadrant is made of 510 pieces of coaxially and confocally aligned supermirrors that significantly enhancethe sensitivity in an energy range of 20–40 keV. The configuration of the telescope is similar to the x-raytelescope onboard Astro-E, but with a longer focal length. The reflectivity of supermirrors is of the orderof 40% in the energy range concerned at a grazing angle of 0.2 deg. The effective area of a fully assembledtelescope is 50 cm2 at 30 keV. The angular resolution is 2.37 arc min at half-power diameter 8.0 keV. Thefield of view is 12.6 arc min in the hard-x-ray region, depending somewhat on x-ray energies. We discussthese characteristics, taking into account the figure errors of reflectors and their optical alignment in thetelescope assembly. This hard-x-ray telescope is unanimously afforded in the International FocusingOptics Collaboration for �Crab Sensitivity balloon experiment. © 2002 Optical Society of America

OCIS codes: 110.6770, 230.4170, 340.7440, 340.7470, 340.7480.

1. Introduction

The x-ray telescopes onboard the Einstein andROSAT satellites have successfully carried out x-ray

T. Okajima �[email protected]�, K. Tamura, Y.Ogasaka, K. Haga, S. Takahashi, S. Ichimaru, H. Kito, S. Fukuda,A. Goto, K. Nomoto, H. Satake, S. Kato, Y. Kamata, A. Furuzawa,F. Akimoto, T. Yoshioka, K. Kondo, Y. Haba, T. Tanka, K. Wada,N. Hamada, M. Hudaverdi, Y. Tawara, and K. Yamashita are withthe Department of Physics, Nagoya University, Nagoya, 464-8602,Japan. P. J. Serlemitsos, Y. Soong, K.-W. Chan, S. M. Owens,F. B. Berendse, and J. Tueller are with the NASA Goddard SpaceFlight Center, Greenbelt, Maryland 20771. K. Misaki, R. Shi-bata, H. Mori, K. Itoh, and H. Kunieda are with The Institute ofSpace and Astronautical Science, 3-1-1, Yoshinodai, Sagamihara,Kanagawa 229-8510, Japan. Y. Namba is with the Department ofMechanical Engineering, Chubu Unuversity, 1200, Matsumoto-cho, Kasugai, Aichi 487, Japan.

Received 26 November 2002; revised manuscript received 8 May2002.

0003-6935�02�255417-10$15.00�0© 2002 Optical Society of America

imaging observations on a variety of astronomicalobjects in the soft-x-ray region below a few kiloelec-tron volts.1,2 The high-throughput x-ray telescopesonboard ASCA �Advanced Satellite for Cosmologyand Astrophysics3� have made it possible to expandthe high-energy limit to 10 keV by employing tightlynested thin-foil mirrors with grazing angles of 0.3–0.7 deg. Subsequent further progress was made bythe Chandra and XMM-Newton satellites.4,5 How-ever, they were not able to extend the high-energylimit further by the use of grazing-incidence x-rayconfigurations. The application of total external re-flection for grazing-incidence optics at higher ener-gies becomes impractical owing to the very long focallengths necessary to achieve a large collecting area.Consequently observations in the hard-x-ray regionabove 10 keV have been carried out by means oflarge-area nonimaging detectors or a combination ofcoded masks and position-sensitive detectors. Fo-cusing optics improves angular resolution and back-ground reduction by orders of magnitude comparedwith a nonfocusing instrument.

1 September 2002 � Vol. 41, No. 25 � APPLIED OPTICS 5417

Hard-x-ray observations are important in investi-gating objects strongly obscured by the absorption ofneutral gas and nonthermal emissions from the star-forming region, the supernova remnants, active ga-lactic nuclei, clusters of galaxies, and so on.Imaging observations with high sensitivity have notyet been achieved in spite of the demands in astron-omy.

The most promising development for hard-x-raytelescopes is the use of Bragg reflection from periodicstructures, complementing the total external reflec-tion. Multilayers have the advantage of enhancingreflectivity in a narrow energy band beyond the crit-ical energy. To broaden the sensitive energy band,multilayers stacked with graded periodic lengths d,so-called supermirrors, have been introduced.6 At afixed grazing angle a gradual change in layer-pairthickness shifts the peak energy to be enhanced,while the reflectivity depends on the number of layerpairs. After intensive studies,7 a design methodcalled the block method was proposed, that used mul-tiple periodic Pt�C multilayers each with a differentperiodic thickness. This method has the great ad-vantages of minimizing the number of layer pairs andyielding a flat response over a wide energy range.Yamashita et al.8 demonstrated the performance of ahard-x-ray focusing telescope that uses 10 sets of su-permirrors designed by the block method.

The International Focusing Optics Collaborationfor �Crab Sensitivity �InFOC�S� is a collaborationbetween Nagoya University and NASA’s GoddardSpace Flight Center �GSFC� and have launched aseries of balloon flights with multiple hard-x-ray tele-scopes onboard. The first of these flights took placeJuly 2001 at the National Science Balloon Facility inPalestine, Texas with the first multilayer-basedWolter I style x-ray telescope ever used for astronom-ical imaging and a new solid-state cadmium zinc tel-luride �CdZnTe� pixel detector9 as the focal planeinstrument. The aims of InFOC�S are to observecelestial objects such as active galactic nuclei, super-nova remnants, and clusters of galaxies in the hard-x-ray band.

The first InFOC�S mirror consists of 2040 Pt�Csupermirror foils. In the supermirror foils producedat Nagoya University the multilayer coating is depos-ited on previously replicated Pt-coated aluminumfoils, whereas those produced at GSFC were directlyreplicated multilayers. The foils were integratedinto their quadrant housings at their respective in-stitutions, and the four quadrants were mated to-gether at GSFC. In this paper we present the x-raycharacteristics of individual supermirrors and theperformance of the integrated quadrants that wereproduced at Nagoya University. We describe the de-sign of the optical system in Section 2 and the fabri-cation and reflectivity measurements of thesupermirrors in Section 3. We present a character-ization of the supermirror hard-x-ray telescope inSection 4 and discuss its performance compared withthe results of ray-tracing simulations in Section 5.Finally we summarize the characteristics of the tele-

scope and the developments for future hard-x-raytelescopes.

2. Design of the Optical System

We have chosen the optical configuration of the hard-x-ray telescope made of conical thin-foil mirrors �170�m thick�, which is similar to the Astro-E XRT.This configuration is suitable for the hard-x-ray tele-scope that needs extremely small grazing-incidenceoptics with large-aperture efficiency. However, theAstro-E XRT has a focal length of 4.75 m correspond-ing to grazing angles from 0.18 to 0.6 deg, whichlimits the sensitive energy region to less than 10 keV.The longer focal length of 8 m will extend the energyrange to �20 keV while decreasing the grazing anglesto 0.107–0.358 deg. We have optimized the designparameters for a diameter of 40 cm and a focal lengthof 8 m. In this configuration the number of nestedmirror shells is 255 and the aperture efficiency is55%. To enhance the sensitivity beyond 20 keV, wemust introduce supermirrors.

The lower energy limit of x rays is defined to be 20keV by absorption in the residual atmosphere at aballoon altitude of 40 km ��3 g�cm2�. The upperlimit of the energy band is chosen to be 40 keV at agrazing angle of 0.36 deg, given by the minimum d ofa multilayer of 2.5 nm. Therefore the energy bandfor the InFOC�S balloon experiment is 20–40 keV.In this section we describe the design of the super-mirrors and telescope in these conditions.

A. Supermirror Design

The design of supermirrors used for a hard-x-ray tele-scope must satisfy many requirements, such as �1�high reflectivity in the 20–40-keV band with a graz-ing angle of 0.107–0.358 deg to get a large effectivearea for the telescope, �2� a flat and broad energyresponse, and �3� a small number of layer pairs N toshorten the time of the mass-production process.After intensive research of multilayers, we selected acombination of platinum and carbon for thispurpose.10,11

Figure 1 shows the calculated reflectivity of a Pt�Csupermirror �thick solid curve� at a grazing angle of0.183 deg as designed by the block method.8 Plati-num and carbon are stacked as a top �vacuum side�and bottom �substrate side� layer within each layer,respectively. Thin curves show the reflectivity ofeach multilayer block stacked with different sets of dand N.

Broad peaks from left to right correspond to valuesof �d�nm�, N� � �10.6, 1�, �6.6, 2�, �5.9, 4�, �4.9, 8�, �4.3,11�, and �3.8, 15� stacked in order from the reflectingsurface toward the substrate. The total energy re-sponse of a supermirror is derived from the superpo-sition of reflectivities of individual multilayer blocks.The peak reflectivity of deeper blocks has to be grad-ually increased to get a flat response because of at-tenuation by the upper blocks. For the energy rangeconcerned, values of d and N for each block are thusdetermined, so that the reflectivity curve of eachblock is continuously connected to that of the adja-

5418 APPLIED OPTICS � Vol. 41, No. 25 � 1 September 2002

cent one without gaps or unnecessary overlaps. An-other key parameter is a thickness ratio � of theheavy element dH to d. The maximum reflectivity ofthe first-order Bragg reflection peaks for � around 0.5and gradually decreases toward both sides. Wehave adopted � � 0.4 to make use of the first-orderBragg reflection for the deepest five multilayers,whereas � � 0.63 for the outermost bilayer �10.6, 1�for high reflectivity by total external reflection. The� value of the top block was determined by trading offbetween enhancing the total external reflection andminimizing the attenuation for deeper multilayers.The most suitable thickness of the Pt layer �d ��corresponds to the penetration depth Z1�e at the crit-ical energy Ec for a fixed grazing angle. This resultsin the smooth connection of reflectivity between theBragg reflection and the total external reflection, asshown in Fig. 1.

B. Telescope Design

We have adopted the replication technique that wasspecially developed for the Astro-E XRT to transferthe smooth surface of a glass mandrel onto a thin-aluminum-foil substrate. The replication techniquewas described by Soong et al.12 and Serlemitsos andSoong.13 The design uses two-stage conical and co-axial mirror shells that approximate the nestedWolter type I optics. Figure 2 shows the fabricatedsupermirrors and a quadrant of the InFOC�S tele-scope prepared by the Nagoya group. After the dep-osition of supermirrors on the thin-foil substrates, thesupermirrors were assembled into mirror housing.

As mentioned above, grazing angles of 255 pieces ofnested mirror shells range from 0.107 to 0.358 deg.These mirrors with different grazing angles are trun-cated into 13 different sets of supermirrors that arecoated with identical design parameters within eachset. The grazing angles in each group vary by less

than 10% of the mean value. As such we can use thesame block design for each foil in the group and stillget a large effective area for the full telescope withoutany reductions from shifts in the Bragg peak posi-tions. Special care was taken to make use of totalexternal reflection at small grazing angles. The crit-ical angle c and Ec is defined by

c�degrees� � 1.651

� ��ƒ1

A �1/ 2 1Ec�kiloelectron volts�

,

(1)

where � �grams per cubic centimeter� is the density ofthe surface material, f1 is the atomic scattering fac-tor, A is the atomic weight. So, for a grazing angle of0.23 deg, the critical energy is Ec � 20 keV. In thedesign for the 1st to 10th group a bilayer with thethickness of a platinum layer of Z1�e was additionallystacked on top of multilayers. Design parametersfor all 13 groups are shown in Table 1. Figure 1corresponds to the calculated reflectivities of the 6thgroup.

Fig. 1. Thick solid curve represents calculated reflectivity of thesixth group of supermirrors at a graying angle of 0.183 deg. Thinlines are the reflectivity of each block in the multilayer stack. Ontop of them a thick platinum layer is deposited to provide totalexternal reflection to as great as 55 keV. The parameters of eachblock are presented in Table 1 as the sixth group supermirror.

Fig. 2. �a� Fabricated supermirrors and �b� a quadrant of theInFOC�S telescope prepared by the Nagoya group. The totalnumber of supermirrors is 1020 for two quadrants. The radii ofthin-foil mirrors range from 60 to 200 mm. Their height andthickness are 100 mm and 170 �m, respectively. Supermirrorsare assembled into housing, following the Wolter type I configura-tion. The height of the housing is 230 mm and the outer radius is220 mm. The assembled supermirrors are seen on top of thehousing.


The effective areas of all 13 groups of mirror shellsare shown in Fig. 3. The thick curve indicates thesum of them, that is, the ideal total effective area ofthe full telescope. The energy range covered by eachgroup is somewhat different, but the 20–40-keVband is fully covered by all groups. The contributionof each group to the total effective area is almostequal in the region of interest. A total effective areaof more than 100 cm2 in the 20–40-keV band is pre-dicted.

Two quadrants were fabricated at Nagoya Univer-sity and the other two at GSFC. The reflectors wereproduced in two ways: �1� supermirror deposition bythe Nagoya team onto prereplicated platinum-foilsubstrates made by the GSFC team and �2� direct

replication of supermirrors deposited onto glass man-drels by the GSFC team. The direct replication ofsupermirrors is a newly developed technique by bothgroups.14,15 In this paper, we focus on the fabrica-tion and performance of the Nagoya quadrants. Acharacterization of the GSFC quadrants will be pre-sented by Berendse et al.16

3. Fabrication and Characterization of Supermirrors

A. Deposition of Supermirrors

Two sets of dc magnetron sputtering systems areused for the deposition on the inner surfaces of cylin-drical foil mirror substrates with radii of curvature of60–200 mm and a height of 100 mm. One system isspecially designed to deposit multilayers onto the in-ner surfaces of conical mirror substrates.11 It hastwo 10-cm-diameter disk-type targets facing eachother, as shown in Fig. 4. The argon plasma is con-fined in the cylindrical volume between them so thatthe mirrors are free from damage caused by plasmas.A mask is mounted in front of the mirror substrate tocontrol the flow of sputtered material and to keep thethickness of the deposited layers uniform across the

Table 1. Parameters of Each Group of Supermirror

Group Grazing Angles �deg.� Ntot �d�nm�, N, ��a

1 0.105–0.125 25 �13.0,1,0.6�,�8.0,1�,�7.1,3�,�6.3,4�,�5.8,6�,�5.0,10�2 0.125–0.131 25 �13.0,1,0.6�,�8.0,1�,�7.1,3�,�6.3,4�,�5.8,6�,�5.0,10�3 0.131–0.144 25 �13.0,1,0.6�,�8.0,1�,�7.1,3�,�6.3,4�,�5.8,6�,�5.0,10�4 0.144–0.158 38 �12.0,1,0.6�,�7.1,3�,�6.0,5�,�5.3,7�,�4.9,10�,�4.3,12�5 0.158–0.174 38 �12.0,1,0.6�,�7.1,3�,�6.0,5�,�5.3,7�,�4.9,10�,�4.3,12�6 0.174–0.192 41 �10.6,1,0.63�,�6.6,2�,�5.9,4�,�4.9,8�,�4.3,11�,�3.8,15�7 0.192–0.210 41 �10.6,1,0.63�,�6.6,1�,�6.0,4�,�5.1,7�,�4.5,8�,�4.0,9�,�3.6,11�8 0.210–0.232 40 �9.3,1,0.59�,�6.3,1�,�5.6,3�,�5.0,5�,�4.5,7�,�4.0,10�,�3.5,13�9 0.232–0.256 50 �8.3,1,0.54�,�6.3,1�,�5.2,5�,�4.5,7�,�3.9,10�,�3.5,12�,�3.2,14�

10 0.256–0.281 50 �7.4,1,0.57�,�5.4,1�,�4.8,3�,�4.3,4�,�4.0,5�,�3.7,8�,�3.4,10�,�3.1,18�11 0.281–0.308 63 �5.8,2�,�4.5,5�,�3.8,8�,�3.4,12�,�3.1,16�,�2.9,20�12 0.308–0.339 63 �5.8,2�,�4.5,5�,�3.8,8�,�3.4,12�,�3.1,16�,�2.9,20�13 0.339–0.356 65 �5.2,3�,�4.2,6�,�3.7,8�,�3.4,10�,�3.1,16�,�2.9,22�

Note: Each line in the fourth column presents parameters of stacked multilayers in order from the reflecting surface toward thesubstrate.

a If � is not shown, � � 0.4.

Fig. 3. Effective areas, thin curves, of each mirror group and,thick solid curve, of a full telescope. Among the 13 groups theinner 10 groups have an outermost platinum layer as thick as the1�e penetration depth of x rays at the designated energy for eachfoil, and their effective areas have a smooth continuation to lowerenergy. The outer three groups dip at 15 keV, since total externalreflection by a single platinum layer is no longer effective. Allgroups show almost the same effective area in the 20–40-keVband.

Fig. 4. Schematic view of the dc magnetron sputtering system:Left, sputtering system with two disk-type sputtering targets fac-ing each other. An argon plasma is created between the twotargets; substrates rotate around the sputter sources during dep-osition. Right, another sputtering system that has a linear sput-ter target facing a fixed substrate.


surface of the foils to within �2%. The depositionrates of platinum and carbon are 0.16 and 0.06 nm�son the surface of the substrate, respectively. Thethickness is controlled by the rotation speed of thesubstrate around the sputtering target.

Another dc sputtering system has two large planartargets �75 mm 250 mm�, one for each material,that face the substrate �Fig. 4�. The nonuniformityalong the vertical and azimuthal directions of thesubstrate is �2.5% and �5%, respectively. The dep-osition rates of platinum and carbon are 0.34 and 0.12nm�s on the surface of substrate, respectively. Thethickness of the layers is controlled by the depositiontime incorporated with the shutter mechanism. Thedeposition for 1020 foils was completed within �9months.

B. Reflectivity Measurements of Supermirrors

We characterized each supermirror thus fabricatedby measuring x-ray reflectivity as a function of graz-ing angles and energies with the x-ray beamline atNagoya University. The x rays are produced by aconventional rotating anode x-ray tube with a tung-sten anode and a removable Ge�220� double-crystalmonochromator. The x-rays are collimated to 0.1mm 1 mm in the horizontal and vertical directions.The W-L 1 line �8.4 keV� is used for monochromaticreflectivity versus angle measurement. The contin-uum x rays are used to measure the broadband re-flectivity at fixed grazing angles. The reflectedbeam intensity and spectra are measured with a 3mm 3 mm 2 mm thick CdZnTe solid-state detec-tor that has a detection efficiency of almost 100% inthe 10–100-keV range and an energy resolution of 3%at 30 keV.

The surface of the foil mirror substrate is replicatedfrom smooth glass mandrels with a surface rough-ness is less than 0.5 nm. Also the interfacial rough-ness of the layer pairs significantly reduces thereflectivity from the ideal, depending on the relativethickness of each layer pair d. The Debye–Waller�DW� factor is introduced to express the roughness �throughout this paper. It is defined by

R � R0 exp��2�md

��2� , (2)

where R is the measured reflectivity, Ro is the idealreflectivity, and m is the order of the Bragg reflection.The DW factor can be obtained by comparing themeasured reflectivity at the Bragg peak with theideal one.

Figures 5�a�, 5�b�, and 5�c� show examples of themeasured reflectivity of supermirrors of group 3, 7,and 11 mentioned in Table 1. These measurementsare done with the continuum x rays in a broad energyband. The reflectivity in the 20–40-keV region isshown to be more than 40% at grazing angles of lessthan 0.2 deg. At grazing angles of �0.3 deg thereflectivities are reduced but are still more than 20%.Although the broadband measurements are vital toproving the performance of our supermirrors, the

critical parameters of a supermirror are more clearlyevaluated from the measurements of monochromaticreflectivity versus angle. Figure 5�d� shows an ex-ample of the measured result of the 6th group withthe angular scan by using the W-L 1 line. The pro-file of the reflectivity fits the calculated one well with� � 0.4 nm. A quarter of all supermirrors wereevaluated by this method. Several samples of su-permirrors were measured with the monochroma-tized hard x rays at 25–50 keV at a synchrotronradiation facility.17 The roughness distribution isderived by the reflectivity measurements and shownin Fig. 6. The average � obtained during productionwas 0.38 � 0.05 nm, and 95% of the measured data iswithin the range of 0.30–0.50 nm. This proves thatour fabricated supermirrors are of sufficient qualityfor use in a hard-x-ray telescope in the 20–40-keVband.

After completion of the segmented 1020 foil mir-rors, we assembled them in quadrants by using thesame techniques developed for the Astro-E XRT.18

4. Evaluation of the telescope

The performance of x-ray telescopes with supermir-rors installed is evaluated in terms of �1� effectivearea, �2� field of view, and �3� image quality �angularresolution�. We performed each of these measure-ments on each of the Nagoya quadrants with thex-ray beamline at the Institute of Space and Astro-nautical Science �ISAS�.

A. Measuring System

Continuum x rays to as great as 50 keV are producedfrom the tungsten anode of the x-ray generator. Thex-ray beam is collimated by a movable slit to 0.2mm 2.0 mm in the horizontal and vertical direc-tions, yielding a beam divergence of 1.2 arc sec 12arc sec. A NaI scintillation detector with a 25.4-mm-diameter aperture, and a 17.3% energy resolu-tion at 22 keV is used to collect the focused radiation.We cannot use the CdZnTe detector used in the indi-vidual foil measurements because it is smaller thanthe focused spot of a full quadrant. To illuminatethe entire aperture of a quadrant uniformly with thenarrow pencil beam, we perform raster scans of thex-ray beam by moving the telescope and detector syn-chronously. Note that a beamwidth of 2 mm in thevertical direction is effective in reducing the numberof raster scans and hence speeds up the measuringprocess while covering the entire geometric area ofthe quadrant. As noted above the beam divergencein the vertical direction is 12 arcsec and does notcontribute significantly to the measurement of theeffective area. Further details of the beamline sys-tem at ISAS and measuring methods for telescopesare described by Kunieda et al.19 and Shibata et al.20

Our measuring method is similar to the case ofAstro-E XRT except for the x-ray energies, the focalplane detector, and its focal length. In the Astro-Ecase the focal plane detector was placed at a focallength of 4.5–4.75 m away from the telescope. Inthis experiment, although the focal length of the mir-


ror was 8 m, the focal plane detector was placed 4 maway from the mirror owing to the physical con-straints of our vacuum chambers. To compensate,we moved the detector at half of the speed of themirror during scans. Placing the detector at onlyhalf of the focal length did yield an image twice aslarge as that at the nominal focal plane, but thiseffect can be compensated for during data processing.

B. Measurement of Quadrants

1. Effective AreaIn Fig. 7 the open circles show the measured value ofa quadrant multiplied by a factor of 4 to estimate theeffective area of a full telescope. The dashed andsolid curves show the calculated, ideal effective areawith interfacial roughnesses of 0.0 and 0.38 nm.The latter value is the average value obtained by thereflectivity measurements mentioned in Section 3.

Fig. 5. Measured reflectivity of supermirrors, dots with error bars, deposited on prereplicated foil substrates. �a�–�c�, Reflectivity versusenergy at grazing angles of 0.138, 0.190, and 0.295 deg, respectively: Overlaid dashed curves, best-fit reflectivity with parameters of the3rd, 7th, and 11th group in Table 1 and interfacial roughnesses of 0.35, 0.40, and 0.43 nm �DW�, respectively. The calculation includesthe CdZnTe detector response that has an energy resolution of 3% at 30 keV. �d� Reflectivity of a 6th group supermirror measured at 8.4keV �W-L 1�: Overlaid curve, calculated with an interfacial roughness of 0.45 nm �DW�. The parameters are summarized in Table 1.

Fig. 6. Histogram of the distribution of the interfacial roughnessof fabricated supermirrors derived from measurements of the re-flectivity of 250 production supermirrors. The average value of theinterfacial roughness is 0.38 � 0.05 nm.


The effective areas are estimated to be 66, 50, and 27cm2 at 20, 30, and 40 keV, respectively. Those val-ues are smaller than the nominal by 34%, 37%, and44%, respectively. The reasons for these reductionsare discussed in Section 5.

2. Field of ViewWe measured the angular response of the effectivearea �the vignetting function�, which is expressed asa function of the off-axis angles. The vignettingfunction fits the Lorentzian curve well, and theFWHM is used to define the field of view. We mea-sured the angular response in the sensitive �1� andinsensitive �2� directions of each quadrant �see Fig.8�. Figure 9 shows the vignetting function at 20, 30,and 40 keV for both directions. For the sensitiveand insensitive directions, the field of view is 6.5 and

24.5 arc min, respectively, and shows a weak depen-dence on x-ray energies. The angular response ofthe full telescope is the sum of responses for the twodirections. The field of view of the full telescope isderived to be 12.6 arc min in the hard-x-ray region.

3. Image QualityWe also measured the intensity distribution with theCuK 1 x-ray line �8.04 keV� in the on-axis direction ofthe telescope. An x-ray CCD camera �with a windowsize of 25.4 mm 25.4 mm� was used as the focalplane detector. The beam size was set to 0.5 mm 0.5 mm, yielding a beam divergence of 3.4 arc sec.This is small enough to obtain an accurate half-powerdiameter �HPD� without compensating for the beamdivergence. The top panel of Fig. 10 is the contour

Fig. 7. On-axis effective area of the full-x-ray telescope: opencircles, measured effective area of one quadrant multiplied by afactor of 4; dashed and solid curves, calculated values with inter-facial roughnesses of 0 and 0.38 nm, respectively. The measuredeffective area is lower than the calculation by �40%. Squares,results of ray-tracing simulation with an interfacial roughness of0.38 nm. This model calculation method was developed for theAstro-E XRT calibration, including alignment and surface figureerrors.

Fig. 8. Schematic view of the configuration for the off-axis mea-surements.

Fig. 9. Vignetting functions of a quadrant measured with hard xrays: squares, triangles, and circles, data at 20, 30, and 40 keV,respectively. �a�, �b� Sensitive �1� and insensitive �2� directions,respectively: solid curves, Lorentzian functions fitted to the mea-sured data. The FWHM of each function for the sensitive direc-tion is 7.7, 6.5, and 5.2 arc min for 20, 30, and 40 keV, respectively.For the insensitive direction the FWHM is 25.8, 24.4, and 23.2 arcmin for 20, 30, and 40 keV, respectively.


map of a quadrant on a logarithmic scale. The bot-tom panel shows the encircled energy function �EEF�,which is the fraction of photons within a circle cen-tered at the peak of the distribution. From this wesee that the angular resolution is 2.37 arc min, HPD.

We also measured the effective area at 8.04 keVwith a NaI scintillation detector and a proportionalcounter. The effective areas are consistent with oneanother among those taken with three detectors.The effective area at 8.04 keV is estimated to be 333cm2 for the full telescope. This area is smaller thanthe ideal value by a factor of 29%.

5. Discussion

A. Effective Areas

As shown in Fig. 7 the measured effective area is 71%at 8.04 keV and 63% at 30 keV relative to the nomi-nal. The nominal values are derived from the prod-uct of the geometric area and the reflectivity of eachsupermirror with an average interfacial roughness of0.38 nm. To investigate the reasons for this loss, weperformed detailed reflectivity measurements of eachpair of reflectors aligned in the optical configuration.

The CuK 1 beam was collimated to 0.05 mm 4.0mm in the horizontal and the vertical directions, re-spectively. The beam size is much smaller than theprojected width of each reflector, so we can measurethe reflectivity in the central part of each pair of foils.When the beam illuminates the edges of either foil,some photons are lost owing to misalignment andslope errors. The beam spot is stepped in 0.05-mmincrements along the radial direction of the quadrant,stopping for a 3-s exposure at each position. By com-paring the total reflected intensity at each step withthat of an incident beam, we can map the local vari-ation of the relative effective area.

Figure 11 shows the results of this measurement.The number of reflected photons expected from idealshells is shown by the dashed lines. Although thepeak counts for each reflector are close to the ideal,the regions where each foil reflects well are somewhatnarrower. As the radius and grazing angles becomesmaller, the peak counts significantly deviate fromthe expected values and the region of good reflectionbecomes much narrower. This result shows that thephotons are lost mostly at the edges of the foils. Webelieve that, owing to figure errors, misalignmentand shadowing by adjacent foils are the primarycauses of the reduction seen above.

We found that the fractional loss of the effectivearea is 21% in the local scanning measurement.This is still smaller than the 29% reduction found inthe raster scan of the full quadrant at 8.04 keV.This discrepancy is explained by the large distortionat the azimuthal ends of each foil where the fractionalloss is found to be 40%.

We performed a ray-tracing simulation of the ef-fective area, taking into account figure errors of thin-foil mirrors and misalignment of assembled foils.

Fig. 10. Top, on-axis look-down image; bottom, EEF of a quadrantmeasured at CuK 1 �8.04 keV� with a beam size of 0.5 mm 0.5mm. The contours in the left plot are drawn on a logarithmicscale. The large distortion of the image is primarily caused by theedge shape of mirror shells. The EEF is derived by counting thenumber of photons within a circle of arbitrary radius comparedwith the total number of photons in a 10-arc min radius.

Fig. 11. Results of local reflectivity measurements. Abscissa,radial position of the beam; ordinate, number of reflected photonswith a 3-s exposure at every stop. Data for inner, middle, andouter reflectors are shown in panels from top to bottom: solidlines with error bars are data points; dashed lines are expectednumber of photons for ideal foil. The loss of the effective areas is46%, 23%, and 15% from top, middle, to bottom, respectively.


In these calculations, we used scattering parametersderived during calibration of the Astro-E XRTs.21

Misalignment of foils is caused by the free play of foilsin the support grooves. Foils 170 �m thick can movein the alignment grooves by �13.2 �m, yielding avariation in the on-axis incident angle of as much as0.9 arc min. On the other hand, figure errors in thereflecting surfaces can also cause fluctuation of thelocal incident angles along each foil. This was eval-uated by measuring the reflected x-ray beam profileas a function of the scattering angle s. The scatter-ing profile I�s� can be expressed by a combination ofGaussian, exponential, and Lorentzian functions:

I�s� � Ngau exp��s

2

2�gau2 �

� Nexp exp��s��exp

� �Nlo

1 � �22

�lo�2 . (3)

The best-fit parameters are summarized in Table 2.Taking these errors into account, we plotted the

result of this ray-tracing simulation with solidsquares at 20, 30, and 40 keV in Fig. 7. It turns outthat the contributions of the figure error and mis-alignment to the reduction in effective area are 20%and 11% at 8 keV and 22% and 15% at 30 keV,respectively. The simulated data points are consis-tent with the measured effective area at lower ener-gies. Only the value at 40 keV is a little larger thanthe measured data. Since the energy response ofsupermirrors drops steeply at around 40 keV, thisdifference can be explained by the 5% deviations inthe layer-pair thickness of the supermirror coatings,as mentioned in Subsection 3.A.

The reduction factor of the effective area at 8.0 keVis 29% compared with 20% for Astro-E XRT becauseour telescope has smaller grazing angles �0.1–0.35deg� than those of Astro-E XRT �0.18–0.6 deg�. Atthe smallest grazing angles �0.1–0.18 deg� figure andalignment errors cause the largest reduction of 44%,as indicated by the ray-trace results and the localreflectivity measurements in Fig. 10.

B. Image Quality

In the conical approximation to the Wolter I geome-try, we approximate the hyperboloid and paraboloidsurfaces by a conical shape. Owing to this approxi-mation, the image of a pointlike x-ray source locatedat infinity has a minimum size of 22 arc sec, HPD.However, this does not significantly contribute to themeasured angular resolution of 2.37 arc min, HPD.

The mirror substrates were fabricated by the rep-

lication method; then supermirrors were deposited onthe surface. According to the calibration of Astro-EXRT, the measured angular resolution of a fully as-sembled mirror is typically �2 arc min, HPD, whichis consistent with the results of quadrants of ourhard-x-ray telescope. This result means that thedeposition of supermirrors does not significantly af-fect image quality.

The measurement of the image quality of theInFOC�S quadrant was carried out only with soft xrays �8.04 keV�. In the previous experiment8 thepoint-spread function of the central core in the soft-x-ray band was not different from that in hard energybands, although the scattering tails were slightlyhigher for hard x rays. The angular resolution inhard x rays was larger than that in soft x rays by�20%. Thus the angular resolution of the InFOC�Smirror in the hard-x-ray band is expected to be �2.8arc min. The hard-x-ray image quality will be con-firmed by postflight calibration.

6. Summary

The InFOC�S hard-x-ray telescope has been fullyassembled with platinum–carbon multilayer super-mirrors. These supermirrors were designed by theblock method to obtain a flat response in the 20–40-keV band, while minimizing the number of layerpairs on each foil. The platinum thickness of theoutermost layer was tuned to the penetration depthat the grazing angle and the critical energy where thesupermirror was designed to maximize the contribu-tion from total external reflection. X-ray measure-ments of a sample of production supermirrorsconfirmed that the reflectivity was more than 40%are great as 40 keV at grazing angles smaller than 0.2deg, whereas the reflectivity was at least 20% to asgreat as a grazing angle of 0.3 deg. The reductionrate of these measured reflectivity to ideal valuescould be attributed to an average interfacial rough-ness of 0.38 � 0.05 nm.

We carried out effective-area, field of view, andimage-quality measurements of quadrants of the su-permirror hard-x-ray telescope at the ISAS 30-mbeamline. The effective area was 66, 50, and 27 cm2

at 20, 30, and 40 keV, respectively. The field of viewwas 12.6 arc min in the hard-x-ray region, and theangular resolution was 2.37 arc min at CuK 1 �8.04keV�. The reduction in the effective area of 30–44%from the designed value was explained by the figureerrors of reflector surfaces and misalignment of eachreflector based on the modeling of the Astro-E XRT.

Further improvements in the effective area andimage quality will be made by improving the foilfigure and the accuracy of reflector alignment. Wealso plan to improve the interfacial roughness to bet-ter than 0.30 nm to provide higher reflectivity be-cause future hard-x-ray missions are being designedfor an energy band as great as and beyond 100 keV.

This research was supported in part by a grand inaid of Specially Promoted Research contract07102007 from the Ministry of Education, Culture,

Table 2. Best-Fit Parameters of Reflected X-Ray Beam Profile Model

Function Parameters

Gaussian Ngau � 0.25 �gau � 0.65Exponential Nexp � 0.25 �exp � 1.11Lorentzian Nlo � 2.85 10�3 �lo � 2.50


Sports, Science and Technology. T. Okajima ac-knowledges the Japan Society for the Promotion ofScience for the support of his fellowship. The au-thors thank the team of engineers and technicians atthe GSFC for carrying out the actual work of theproduction of the foil substrates. The authors alsothank the current and former students of NagoyaUniversity who have been involved in the researchand development of the supermirror hard-x-ray tele-scope.

References1. R. Giacconi, G. Branduardi, U. Briel, A. Epstein, D. Fabricant,

E. Feigelson, W. Forman, P. Gorenstein, J. Grindlay, H. Gur-sky, F. R. Harnden, Jr., J. P. Henry, C. Jones, E. Kellogg, D.Koch, S. Murray, E. Schreier, F. Seward, H. Tananbaum, K.Topka, L. Van Speybroeck, S. S. Holt, R. H. Becker, E. A. Boldt,P. J. Serlemitsos, G. Clark, C. Canizares, T. Markert, R. Nov-ick, D. Helfand, and K. Long, “The Einstein �HEAO-2� X-rayObservatory,” Astrophys. J. 230, 540–550 �1979�.

2. B. Aschenbach, “X-ray telescopes,” Rep. Prog. Phys. 48, 579–628 �1986�.

3. P. J. Serlemitsos, L. Jalota, Y. Soong, H. Kunieda, Y. Tawara,Y. Tsusaka, H. Suzuki, Y. Sakima, T. Yamazaki, H. Yoshioka,A. Furuzawa, K. Yamashita, H. Awaki, M. Itoh, Y. Ogasaka, H.Honda, and Y. Uchibori, “The x-ray telescope onboard ASCA,”Publ. Astron. Soc. Jpn. 47, 105–114 �1995�.

4. M. C. Weisskopf and S. L. O’dell, “Calibration of the AXAFobservatory: overview,” in Grazing Incidence and MultilayerX-Ray Optical Systems, R. B. Hoover and A. B. Walker, eds.,Proc. SPIE 3113, 2–17 �1997�.

5. F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C.Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M.Santos, N. Schartel, D. Texier, and G. Vacanti, “XMM-NewtonObservatory. I. The spacecraft and operations,” Astron. As-trophys. 365, L1–L6 �2001�.

6. K. D. Joensen, P. Hoghoj, F. E. Christensen, P. Gorenstein, J.Susini, E. Ziegler, A. K. Freund, and J. L. Wood, “Multilayeredsupermirror structures for hard-x-ray synchrotron and astro-physics instrumentation,” in Multilayer and Grazing IncidenceX-Ray�EUV Optics II, R. B. Hoover and A. B. Walker, eds.,Proc. SPIE 2011, 360–372 �1994�.

7. K. Yamashita, K. Akiyama, K. Haga, H. Kunieda, G. S. Lodha,N. Nakajo, N. Nakamura, T. Okajima, K. Tamura, and Y.Tawara, “Fabrication and characterization of multilayer su-permirrors for hard-x-ray optics,” J. Synchrotron Radiat. 5,711–713 �1998�.

8. K. Yamashita, P. J. Serlemitsos, J. Tueller, S. D. Barthelmy,L. M. Bartlett, K.-W. Chan, A. Furuzawa, N. Gehrels, K. Haga,H. Kunieda, P. Kurczynski, G. Lodha, N. Nakajo, N. Naka-mura, Y. Namba, Y. Ogasaka, T. Okajima, D. Palmer, A. Par-sons, Y. Soong, C. M. Stahl, H. Takata, K. Tamura, Y. Tawara,and B. J. Teegarden, “Supermirror hard-x-ray telescope,” Appl.Opt. 37, 8067–8073 �1998�.

9. W. H. Baumgartner, J. Tueller, S. Barthelmy, H. Krimm, F.Birsa, and L. Ryan, “The CZT pixellated detectors on theInFOC�S hard-x-ray telescope,” in New Century of X-ray As-tronomy, H. Kunieda and H. Inoue, eds., ASP Conf. Ser. 251,520–521 �2001�.

10. Y. Tawara, K. Yamashita, H. Kunieda, K. Haga, K. Akiyama,A. Furuzawa, Y. Terashima, and P. J. Serlemitsos, “Multilayersupermirror coating for hard-x-ray telescope,” in Multilayerand Grazing Incidence X-Ray�EUV Optics III, R. B. Hooverand A. B. Walker, eds., Proc. SPIE 2805, 236–243 �1996�.

11. K. Tamura, K. Yamashita, H. Kunieda, Y. Tawara, A. Fu-ruzawa, K. Haga, G. Lodha, N. Nakajo, N. Nakamura, T. Oka-jima, O. Tsuda, P. J. Serlemitsos, J. Tueller, R. Petre, Y.Ogasaka, Y. Soong, and K.-W. Chan, “Development of balloon-borne hard-x-ray telescopes using a multilayer supermirror,”in Grazing Incidence and Multilayer X-Ray Optical Systems, R.Hoover and A. B. Walker, eds., Proc. SPIE 3113, 285–292�1997�.

12. Y. Soong, L. Jalota, P. J. Serlemitsos, “Conical thin foil x-raymirror fabrication via surface replication,” in X-Ray and Ex-treme Ultraviolet Optics, R. B. Hoover and A. B. Walker, eds,Proc. SPIE 2515, 64–69 �1995�.

13. P. J. Serlemitsos and Y. Soong, “Foil x-ray mirrors,” Astrophys.Space Sci. 239, 177–196 �1996�.

14. A. Furuzawa, K. Yamashita, H. Kunieda, Y. Tawara, K.Tamura, K. Haga, N. Nakamura, N. Nakajo, H. Takata, T.Okajima, Y. Ogasaka, G. S. Lodha, and Y. Namba, “Replicationof a multilayer supermirror,” in X-Ray Optics, Instruments,and Missions, R. B. Hoover and A. B. Walker, eds., Proc. SPIE3444, 569–575 �1998�.

15. S. M. Owens, T. Okajima, Y. Ogasaka, F. Berendse, and P. J.Serlemitsos, “Multilayer coated thin foil mirrors forInFOC�S,” in X-Ray Optics, Instruments, and Missions III,J. E. Truemper and B. Aschenbach, eds., Proc. SPIE 4012,619–625 �2000�.

16. F. Berendse, S. M. Owens, P. J. Serlemitsos, J. Tueller, K.-W.Chan, Y. Soong, H. Krimm, W. H. Baumgartner, Y. Ogasaka,K. Tamura, T. Okajima, Y. Tawara, K. Yamashita, K. Misaki,and H. Kunieda, “Production and performance of the InFOC�S20–40-keV graded multilayer mirror,” submitted to Appl. Opt.

17. T. Okajima, S. Ichimaru, K. Tamura, K. Haga, Y. Ogasaka, S.Takahashi, S. Fukuda, H. Kitou, A. Gotou, Y. Tawara, K.Yamashita, Y. Tsusaka, S. Takeda, and H. Kunida, “The X-raymeasurement of the supermirror using synchrotron radiation,”in Advances in X-Ray Optics, A. K. Freund, T. Ishikawa, A. M.Khounsary, D. C. Mancini, A. G. Michette, and S. Oestreich,eds., Proc. SPIE 4145, 53–60 �2000�.

18. H. Kunieda, M. Ishida, T. Endo, Y. Hidaka, H. Honda, K.Imamura, J. Ishida, M. Maeda, K. Misaki, R. Shibata, A. Fu-ruzawa, K. Haga, Y. Ogasaka, T. Okajima, Y. Tawara, Y.Terashima, M. Watanabe, K. Yamashita, T. Yoshioka, P. J.Serlemitsos, Y. Soong, and K.-W. Chan, “X-ray telescope on-board Astro-E: optical design and fabrication of thin foil mir-rors,” Appl. Opt. 40, 553–564 �2001�.

19. H. Kunieda, Y. Tsusaka, H. Suzuki, Y. Ogasaka, H. Awaki, Y.Tawara, K. Yamashita, T. Yamazaki, M. Itoh, T. Kii, F.Makino, Y. Ogawara, H. Tsunemi, K. Hayashida, S. Nomoto,M. Wada, E. Miyata, and I. Hatsukade, “Thirty-meter x-raypencil beam line at the Institute of Space and AstronauticalScience,” Jpn. J. Appl. Phys. 32, 4805–4813 �1993�.

20. R. Shibata, M. Ishida, H. Kunieda, T. Endo, H. Honda, K.Misaki, J. Ishida, K. Imamura, Y. Hidaka, M. Maeda, Y.Tawara, Y. Ogasaka, A. Furuzawa, M. Watanabe, Y. Ter-ashima, T. Yoshioka, T. Okajima, K. Yamashita, P. J. Ser-lemitsos, Y. Soong, and K.-W. Chan, “X-ray telescope onboardAstro-E. II. Ground-based x-ray characterization,” Appl. Opt.40, 3762–3783 �2001�.

21. K. Misaki, H. Kunieda, M, Ishida, T. Endo, Y. Hidaka, H.Honda, K. Imamura, J. Ishida, M. Maeda, R. Shibata, H. Mori,K. Itoh, A. Furuzawa, K. Haga, Y. Ogasaka, T. Okajima, Y.Tawara, Y. Terashima, M. Watanabe, K. Yamashita, T. Yo-shioka, P. J. Serlemitsos, Y. Soong, and K.-W. Chan, “X-raytelescope onboard Astro-E. III. Guideline to performance im-provements and optimization of ray-tracing program,” to besubmitted to Appl. Opt.


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