Measured Re ectance of Graded Multilayer Mirrors

Designed for Astronomical Hard X-ray Telescopes

Finn E.Christensen a James M. Chakan b William W. Craig c

Charles J. Hailey c Fiona A. Harrison b Veijo Honkimaki d

Mario A. Jimenez-Garate c Peter H. Mao b David L. Windt c

Eric Ziegler d

a Danish Space Research Institute, Juliane Maries Vej 30, Copenhagen,DK-2100,

Denmark

b Space Radiation Laboratory, 220-47 California Institute of Technology,

Pasadena, CA 91125, USA

c Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027,

USA

d European Synchrotron Radiation Facility , B.P.200-F , 38043 Grenoble CEDEX,

France

Future astronomical X-ray telescopes, including the balloon-borneHigh-Energy Focusing Telescope (HEFT) and the Constellation-XHard X-ray Telescope (Con-X HXT) plan to incorporate depth-graded multilayer coatings in order to extend sensitivity into thehard X-ray (10

�

< E�

< 80keV) band. In this paper, we presentmeasurements of the re ectance in the 18 { 170 keV energyrange of a cylindrical prototype nested optic taken at the Eu-ropean Synchrotron Radiation Facility (ESRF). The mirror seg-ments, mounted in a single bounce stack, are coated with depth-graded W/Si multilayers optimized for broadband performance upto 69.5 keV (W K-edge). These designs are ideal for both the HEFTand Con-X HXT applications. We compare the measurements tomodel calculations to demonstrate that the re ectivity can be welldescribed by the intended power law distribution of the bilayerthicknesses, and that the coatings are uniform at the 5% level overthe mirror surface. Finally, we apply the measurements to predicte�ective areas achievable for HEFT and Con-X HXT using theseW/Si designs.

Key words: Hard X-ray Telescopes, Synchrotron Radiation,Multilayers

Preprint submitted to Elsevier Preprint 15 February 2000

1 Introduction

In order to extend the high-sensitivity and low-background of focusing tele-scopes into the hard X-ray band (E �> 10 keV), future experiments, includingthe balloon-borne High-Energy Focusing Telescope (HEFT) and theConstellation-X Hard X-ray Telescope (Con-X HXT) plan to incorporate depthgraded multilayer coatings. Compared to metal surfaces, multilayers can in-crease the maximum incidence angle (referred to as the graze angle) for whichsigni�cant re ectivity is achieved. For standard metal coatings, this angle de-creases approximately inversely with photon energy, making systems of rea-sonable focal length impractical, and in addition resulting in very small �eldsof view.

Depth-graded multilayers utilize Bragg re ection to increase the mirror grazeangle over a broad energy band[1,2]. By utilizing alternating layers of low andhigh index of refraction materials, with the bilayer thickness varying over awide range, the Bragg condition can be satis�ed at a given incidence angle fora range of photon energies. Typically the thinnest bilayers (which re ect thehighest energy X-rays) are deposited �rst, so as to minimize absorption due tothe overlying coatings. We have presented designs, optimized for broadbandre ectance and Field Of View(FOV), for Wolter I (and conical approximation)astronomical hard X-ray telescopes[3]. These designs are based on a power lawdistribution of bilayer thicknesses[4].

Depth graded multilayers based on the power law design have been fabricatedon test ats, and characterized over a broad range of energies[5]. Other(non-power law) designs have also been developed and characterized at soft X-rayenergies X-rays[6]. Recently, prototype thin mirror segments from the HEFT

project have been coated and characterized at soft X-ray energies below 10keV[7]. This characterization has allowed the hard X-ray re ectance to becalculated theoretically by using models of the multilayer structures derivedfrom the soft X-ray data, assuming that no additional scattering is introducedat higher X-ray energies. In this paper, we present the �rst detailed measure-ments of HEFT prototype nested multilayer mirrors in the hard X-ray band. The measurements, taken at the European Synchrotron Radiation Facility(ESRF) in Grenoble, France, spanned the energy range from 18 { 170 keV. Wepresent model �ts to the data in order to characterize the multilayer structure.We also studied the coating uniformity as a function of the azimuthal angle onthe optic. Finally, we present e�ective area and FOV calculations for HEFTand the Con-X HXT based on these hard X-ray re ectance measurements.

2

2 Mirror and prototype geometry

Both HEFT and the Con-X HXT will adopt a Wolter-I or conical approxi-mation X-ray mirror geometry. In this con�guration, thin, nested shells arearranged in a two-re ection system . The on-axis graze angle of each shell isdetermined by � = r=4f , where r is the shell radius, and f is the telescopefocal length. The optics can be either constructed as full �gures of revolution,or divided into segments.

The optimum multilayer design depends on the graze angle, and the coatingwill therefore ideally be di�erent on each shell. As a matter of practicality, wedivide the shells into ten graze angle ranges, and optimize a coating for eachrange. Mao et al.(1999)[3] describes the optimization technique in detail.

Table 1HEFT multilayer design

mirror angular range radial range dmin [�A] dmax [�A] c � N

group [mrad] [cm]

D1 1.67-1.86 4.00-4.46 33.3 297.6 0.225 0.40 150

D2 1.86-2.08 4.46-4.99 29.9 266.6 0.230 0.40 200

D3 2.08-2.32 4.99-5.57 28.7 238.9 0.220 0.40 250

D4 2.32-2.59 5.57-6.22 27.4 214.0 0.225 0.40 250

D5 2.59-2.89 6.22-6.94 26.1 191.8 0.220 0.40 300

D6 2.89-3.22 6.94-7.73 24.7 171.8 0.215 0.40 350

D7 3.22-3.60 7.73-8.64 24.6 153.9 0.200 0.40 350

D8 3.60-4.01 8.64-9.62 24.3 137.9 0.205 0.35 350

D9 4.01-4.48 9.62-10.75 23.7 123.6 0.200 0.35 350

D10 4.48-5.00 10.75-12.0 23.0 110.7 0.195 0.35 350

Table 1 summarizes the multilayer parameters for each on axis graze anglerange. The distribution of bilayer thicknesses is described by a power law[4],where the thickness of the i'th bilayer, di , is given by di=a=(b+ i)c. Here a,band c are constants, and i ranges from 1 to N , with N being the layer closestto the substrate. Each design is completely characterized by the minimumbilayer thickness, dmin=dN , the maximum bilayer thickness, dmax=d1, the ratiobetween the thickness of the heavy element to the bilayer thickness, �, thepower index, c and the number of bilayers, N . The values of the parameters inTable 1 result from the optimization performed for the HEFT telescopes. Thetotal thickness of any of the optimized coatings in Table 1 does not exceed 1.1�m [3]. HEFT and Con-X HXT have di�erent target energy bands: 20 { 70

3

keV; and 5 { 70 keV respectively, and mirror geometries (due to the di�erentfocal lengths). This however results in only slightly di�erent multilayer designs,and therefore the parameters in Table 1 are applicable to both.

The prototype optic consists of a stack of �ve quadrant mirror segments in asingle re ection cylindrical geometry. We fabricated the mirror substrates usedin the prototype by thermally forming glass into cylindrical segments . Theglass forming process and mounting technique, described in detail in Haileyet al.(2000) and Craig et al.(2000)[8,9], was developed for HEFT, and is alsobeing considered for use on the Con-X HXT. A separate characterization of theprototype imaging properties demonstrate 35 00 Half Power Diamater of the onebounce optic at both soft and hard X-ray energies[10]. The mirror segmentradii are 8.3, 8.4, 8.5, 8.6 and 8.7 cm. Each of the �ve mirror segments iscoated with a di�erent multilayer design, optimized for a di�erent graze anglerange. The �ve mirror segments are denoted D1, D2, D3, D4 and D5 and theexact speci�cation of the coatings are given in Table 1. For this prototype,we used 0.3 mm thick DESAG AF45 glass[8], with total length along thecylinder axis of 20 cm. The glass optics were coated with the depth-gradedW/Si multilayers in a planar magnetron sputtering system. We describe thedeposition parameters and detailed calibration of the coatings in Windt et

al.(2000)[11].

3 Experimental arrangement and re ectance data

3.1 Experimental details

To characterize the re ectance of the prototype optic in the energy rangeof interest we used X-ray beams, tuned to selected monochromatic energies,generated at one of two beamlines at the European Synchrotron RadiationFacility (ESRF). The X-ray beams illuminated the segments along the lengthof the cylindrical axis. To measure azimuthal variations, we mounted the opticin a ring, which provided precise azimuthal rotation. A similar arrangement,using the same ring in combination with a beam expander, was used for theground calibration of the SODART X-ray telescopes[12]. Guard slits placed infront of the prototype unit allowed us to vary the size of the illuminated spot.For each beam energy we measured the re ectance as a function of incidenceangle on the optic. We aligned the incidence angle by using the mirror segmentitself as a shadow for the beam. We estimate systematic misalignments of thisangle to be less than 0.2 milliradians.

We used beam energies ranging from 18 { 170 keV, produced at two separatebeamlines. The �rst beamline we used, referred to as BM5 by ESRF, provided

4

energies of 18 keV, 28 keV and 34 keV, selected using a detuned double re- ection Si(111) monochromator in re ection geometry. In addition, we used a54 keV beam selected using the Si(333)-re ection together with an absorberto eliminate the 111-re ection. At the second beamline, designated ID15A byESRF, we used a double re ection Si(311)monochromator in Laue geometryto provide the following energies: 65 keV, 80 keV, 90 keV, 100 kev, 115 keV,158 keV and 170 keV. The spectral purity of the beams was typically 10�4 in�E/E(FWHM). This is small enough that broadening or smearing of re ec-tivity features due to the �nite energy bandwidth of the beam is unobservablefor the energies listed above. We determined the angular collimation of thebeam, typically 0.07 milliradians, in each case by the intrinsic rocking curvewidth of the monochromator re ection and/or by the width of slits placed infront of and behind the monochromator.

We measured the re ected beam as well as the normalizing direct beam using apin diode. At BM5 we used the synchrotron ring current to monitor the decayof the intensity during the measurement. At ID15A we used a separate beammonitoring pin diode in front of the prototype to keep track of the decay of thebeam intensity. All data sets were, however, taken in the matter of minutes toan hour, and we noticed little variation in the beam intensity.

3.2 Re ectance data

In Figures 1 and 2 we show the re ectance as a function of incidence angle fortwo di�erent multilayer designs, D3 and D4.

We have plotted data taken at several di�erent energies on a single plot,scaling each successive curve by a factor of ten in order to separate them (thebottom plot clearly corresponding to the actual re ectance). We show errorbars where they are bigger than the plotting symbol, and we have connectedthe data points to guide the eye. As can be seen by the indicated value of mirrorsegment azimuth angle, �, all data were taken close to zero (corresponding tothe center of the mirror segment). Since the coating parameters may varywith azimuth angle (see x 3.3), direct comparison between energies requirescomparing data at similar azimuth angles. In order to illustrate the energydependence of absorption in the multilayers, we plot in Figures 3 and 4 thesame data as well as data taken at 80 keV, 90 keV, 115 keV ,158 keV and170 keV as a function of the reciprocal lattice vector q. The reciprocal latticevector is de�ned by q=4�sin(�)/�, where � is the angle of incidence and � isthe wavelength.

The advantage of plotting the data taken as a function of q is that X-rays re- ected from a layer pair of given thickness line up at the same reciprocal lattice

5

Fig. 1. Measured re ectivity of mirror segment D3 at energies from 18 keV to 170keV. The line between data points is a guide for the eye. Data sets has been shiftedby a factor of 10 for clarity. . The �-values at which the data are taken are indicated.

Fig. 2. Measured re ectivity of mirror D4 at energies from 18 keV to 158 keV. Theline between the data points is a guide for the eye. Data sets are shifted by a factorof 10 for clarity. The �-values at which the data are taken are indicated in the plot.

vector for all energies. As expected, the re ectivity curve becomes atter, andthe re ectivity at a given q increases(provided q is larger than the value cor-responding to the critical angle for total external re ection and smaller than

6

Fig. 3. Re ectivity data from mirror segment D3 plotted versus reciprocal latticevector q. The line between data points is a guide for the eye. The data sets areshifted a factor of 10 for clarity and the energy and �-value for each data set isindicated. The e�ect of the K-absorption edge of W is clearly visible in the 80 keVdata. At 170 keV the re ectivity has completely recovered and high re ectivity ismeasured out to ca. 3 times the critical angle.

that at which the re ectivity drops due to the smallest bilayer) as energy in-creases and absorption becomes less important. Immediately above the W-Kabsorption edge the re ectivity su�ers dramatically (as seen in the 80 keV and90 keV data). By 115 keV, however, absorption is again small enough that there ectivity is almost completely recovered.

3.3 Uniformity measurements

Although depth-graded multilayers designed for broad band re ectance have awide range of bilayer thicknesses in each coating, it is still important that theuniformity of the thickness distribution over the optic not deviate so much thatcoating is no longer optimal. For the HEFT design in particular, a 5% changeof the bilayer thicknesses across the mirror surfaces will not signi�cantly reducethe throughput or FOV of the telescopes[13].

The mirror segments in the current prototype consist of 90Æ segments, andthese were coated using a planar magnetron deposition system[14] not specif-ically designed to ensure uniformity perpendicular to the optical axis of cylin-drically curved optics. The mirror module design being developed for HEFTand Con-X HXT will employ 60Æ segments, and the HEFT mirror segments

7

Fig. 4. Re ectivity data from mirror segment D4 plotted versus reciprocal latticevactor q, The line between the data points is a guide for the eye. The data sets areshifted a factor of 10 for clarity and the energy and �-value for each data set areindicated. As in �gure 2 the e�ect of the K-absorption edge of W is clearly visiblein the 90 keV data. At 158 keV the re ectivity has completely recovered and highre ectivity is measured out to ca 3 times the critical angle.

will be coated in a system at the Danish Space Research Institute(DSRI) de-signed to achieve coating uniformity for cylindrically curved optics. The cur-rent prototype therefore represents a non optimal case in regard to azimuthaluniformity, but it allows us to measure the uniformity over a larger range thanwill ultimately be required.

Figures 5 and 6 show the measured re ectivity of mirror segment D3 takenat 34 keV (Figure 5) and 54 keV (Figure 6) at a number of azimuth anglesbetween -35Æ and +35Æ. We have again shifted di�erent data sets by factorsof 10 to separate them. The re ectance is essentially constant over this range,with a small degradation visible only at the edges. A variation in the anglewhere the re ectance drops due to the minimum bilayer thickness is, however,clearly visible. This is due to a change in the thickness of all layers as a functionof azimuthal position. To quantify this, we determined the minimum bilayerthickness for each value of � at 34 keV by �tting a model to the data (seebelow). Figure 7 shows the result, with estimated uncertainty. The thicknessvariation is small up to �30Æ from � = 0, but changes rapidly after that .Finally, it can be seen from the �gures that the variations are not symmetricaround � = 0 due to a systematic shift resulting from asymmetric mountingof the optics during coating.

8

Fig. 5. The measured re ectivity for di�erent �-values ranging from -35Æ to +35Æ.The data are from mirror segment D3 and taken at 34 keV. The data points areconnected by a line as a guide for the eye and the data sets are shifted by a factorof 10 for clarity

It is quite clear from these results that the bilayer thickness varies by 5% inthe 60Æ segment around the symmetry point. This is within the required tol-erance, however we expect to improve this further with more optimal coatinggeometries[15].

4 Modeling of the re ectance data

In order to characterize the multilayer coatings we have �t a model to the datathat allows us to determine the basic parameters: minimum bilayer thickness(dmin), maximum bilayer thickness (dmax), interface widths (�), and a smallsystematic misalignment of the graze angle on the order of 0.2 milliradian orless. We took the ratio of high to low index of refraction material, �, as well asthe distribution of bilayer thicknesses and number of bilayers to be the nominalvalues determined in a systematic calibration of the deposition system madejust prior to coating. dmin is well constrained for each data set, however dmax

cannot be well-determined. We therefore �t dmin, and forced dmax to vary bythe same percentage. We assumed a constant value of �, independent of layer.By �tting the data in this manner, we are able to calculate the re ectanceover the full range of energies and graze angles relevant to HEFT and Con-X

HXT.

9

Fig. 6. The measured re ectivity for di�erent �-values ranging from -35Æ to +35Æ.The data are from mirror segment D3 and taken at 54 keV. The data points isconnected by a line to guide the eye and the data sets are shifted by a factor of 10for clarity

Fig. 7. Deduced minimum bilayer thicknesses versus � from 34 keV data from mirrorsegment D3. The variation is small and is near 5% in a 60Æ segment around thesymmetry top point.

In the modeling we used an X-ray re ectivity code for multilayered structureswritten by P.H.Mao[3]. The optical constants used in the code were obtained

10

from the websites of L.Kissel and P.M.Bergstrom, Jr. at Lawrence LivermoreNational Laboratories (http://www-phys.llnl.gov/V div/scattering/asf.html)and by J.H.Hubbell and S.M.Seltzer at the National Institute of Standards andTechnology(http://physics.nist.gov/PhysRefData/XrayMassCoe�/cover/html).

4.1 Data and model for small �

Figures 8 { 10 show re ectance near the center of the optic (� indicated on theplot) compared to our model calculations. We have plotted the data for 34 kev(Figure 8), 65 keV (Figure 9), 158 and 170 keV (Figure 10). Close to the centerof the optic, the minimum bilayer thickness should be close to the nominalvalue, and the value derived by �tting should be independent of energy. Thisis in fact the case (see Table 2). The uncertainty in dmin is 0.25 �A , duealmost entirely to residual alignment errors. The small discrepancy betweenthe dmin values obtained at the di�erent energies for the same mirror segment isconsistent with this uncertainty. In addition, dmin varies as a result of the rangein azimuth angles (�=-8Æ to �=+5Æ), as shown in Figure 7. From Figure 7 thisvariation is on order 0.2 �A.

Fig. 8. Data and model as described in the text for all mirror segments at 34 keVand �=+5Æ. The full line is the model calculation

We found that a value of the interface widths, �, of 4.5 �A �t the majority ofthese data well, and this is used in the model calculations shown in Figures 8, 9and 10. The feature of the data providing the tightest constraint on � is there ectance after the sharp drop due to the minimum bilayer thickness. There ectance here is due to second order re ections in the graded multilayer

11

Fig. 9. Data and model as described in the text for mirror segments D1, D2, D3and D4 at 65 keV and �=-8Æ. The full line is the model calculation

Fig. 10. Data and model as described in the text for mirror segment D3 at 170 keVand �=-8Æ and mirror segment D4 at 158 keV and �=-8Æ. The full line is the modelcalculation

stack, and (to the extent that c and � are correct) this level determines �.We do observe some small variation in how well this level is �t by a single �.This could indicate small variations of � (�0.1-0.3 �A) with mirror segmentand/or energy, however we see no consistent trend in the data. Considering the

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Table 2Modelled minimum bilayer thicknesses

Mirror segment � Energy dmin [�A]

deg keV

D1 +5 34 34.6

D1 -8 65 34.3

D2 +5 34 30.8

D2 -8 65 30.2

D3 +5 34 29.4

D3 -8 65 29.6

D3 -8 170 29.6

D4 +5 34 27.6

D4 -8 65 27.5

D4 -8 158 28.0

D5 +5 34 26.4

extended energy range, our results are in good agreement with � = 4.3 �A thatwe obtained previously from modelling 8 keV data from DSRI, and 28 keVdata from BM5 at ESRF taken on free-standing mirror segments[7].

4.2 Data and model at large azimuth angles

As described previously, to model the data for large azimuth angles we mustadjust the minimum bilayer thickness from the nominal value. Figure 11 showsthe re ectance compared to model calculations for mirror segment D3 at � =�30Æ;�17Æ;+17Æ and +30Æ. We �nd that � = 4.5 �A �ts the � = �17Æ and� = +17Æ data well, however a slight increase to � = 5.0 �A is required for� = �30Æ.

5 E�ective area predictions for HEFT and the Con-X HXT

The characterization of the depth-graded multilayers at hard X-ray/soft gamma-ray energies and comparison to model calculations demonstrates that a single,consistent set of parameters can describe the re ectance over this energy range.This is further demonstrated in Figures 12 and 13, which show the re ectionversus energy at a graze angle of 2.2 mrad and 0.9 mrad.

13

Fig. 11. Data and model as described in the text for mirror segment D3 at 34 keVand �-values -30Æ ,-17Æ ,+17Æ ,+30Æ. The full line is the model calculation

Fig. 12. Data and model as described in the text for mirror D3 versus energy at agraze angle of 2.2 mrad which is the center of the on axis graze angle range for thismultilayer design (see Table 1). Error bar is smaller than data point if not shown.The full line is the model calculation.

The excellent agreement between model and data allow us to con�dently usethe models to predict the e�ective area for the HEFT and Con-X HXT. Todo this we have used the optimized multilayer design shown in Table 1 with

14

Fig. 13. Data and model as described in the text for mirror D3 versus energy at agraze angle of 0.9 mrad. Error bar is smaller than data point if not shown. The fullline is the model calculation.

the interface width of � = 4:5 �A derived from the measurements. We havenot included any variation in the coating parameters as a function of azimuthposition, since this will only have a negligible e�ect on re ectance for the 60Æ

segments planned for the ight mirrors.

Figures 14 and 15 show the calculations for the two telescope geometries.Table 3 summarizes the mirror parameters for each assuming that they areboth made from thermally slumped 0.3 mm thin glass.

For HEFT we have included the e�ect of absorption in the residual atmosphereat 3.5 g/cm2 expected for the balloon observations. For both telescopes, theW/Si multilayers provide large e�ective area up to the W-K absorption edgeat 69.5 keV. For the mirror parameters shown in Table 3, Con-X HXT canexceed the 1500 cm2 at 45 keV target[16] using W/Si coatings on formed glass.

6 Conclusions

We have demonstrated that depth graded W/Si multilayers applied to proto-type nested formed glass optics provide good re ectance in the energy rangefrom a few { 69.5 keV. Previous measurements of multilayers on realistic sub-strates have been limited to low energy (typically the 8 keV Cu K-alpha line).It is important to note that di�erent lengthscales in the roughness and in-

15

Fig. 14. Calculated e�ective area for the HEFT telescopes based on the modelderived from the re ectance measurements and the optimization of the multilayerdesign as presented in Table 1. The area is calculated for on-axis, 1 mrad o� axis,2 mrad o� axis and 3 mrad o�-axis.

Table 3HEFT and Con-X HXT telescope parameters

HEFT Con-X HXT

Focal length 6 m 10 m

No of modules 14 12

No of shells per module 72 149

Minimum Radius 4 cm 3 cm

Maximum Radius 12 cm 20 cm

Shell length 20 cm 25 cm

terface widths are important at high-energy compared to at 8 keV, so it isnot obvious that extrapolating over this large an energy interval is valid. Ourhigh-energy measurements demonstrate, however, that similar results are ob-tained to those found at low-energy, implying that the roughness is due tolengthscales smaller than those probed at high-energy, leading to the energy-independence in the multilayer model parameters. Applying the multilayermodel derived from the data to HEFT and Con-X HXT, we �nd that largee�ective area can be achieved up to the K-edge.

Finally, the data taken at 170 keV, as well as other high energy data fromspecialized graded W/Si coatings[11,17], show that this far above the W

16

Fig. 15. Calculated e�ective area for the Con-X HXT telescopes based on the modelderived from the re ectance measurements and the optimization of the multilayerdesign as presented in Table 1. The area is calculated for on-axis, 1 mrad o�-axis,2 mrad o�-axis and 3 mrad o�-axis.

K-edge, the e�ects of absorption are minimal, and good re ectance can beachieved. Using a model incorporating Compton scattering, we are able toaccurately predict the performance. This demonstrates that it is possible todesign grazing-incidence mirrors for operation at energies up to 200 keV, orpossibly even greater, using W/Si coatings.

7 Acknowledgments

We are grateful to Manuel S. Del Rio, Michael Ohler and Robert Hustache fortheir expert technical assistance during the measurements.

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