1 Introduction In order to extend the high-sensitivity and low-background of focusing telescopes into the hard X-ray band (E ο > 10 kev), future exper

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1 Measured Reflectance 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, 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, Grenoble CEDEX, France Future astronomical X-ray telescopes, including the balloon-borne High-Energy Focusing Telescope (HEFT) and the Constellation-X Hard X-ray Telescope (Con-X HXT) plan to incorporate depthgraded multilayer coatings in order to extend sensitivity into the hard X-ray (10 ο < E ο < 80keV) band. In this paper, we present measurements of the reflectance in the kev energy range of a cylindrical prototype nested optic taken at the European Synchrotron Radiation Facility (ESRF). The mirror segments, mounted in a single bounce stack, are coated with depthgraded W/Si multilayers optimized for broadband performance up to 69.5 kev (W K-edge). These designs are ideal for both the HEFT and Con-X HXT applications. We compare the measurements to model calculations to demonstrate that the reflectivity can be well described by the intended power law distribution of the bilayer thicknesses, and that the coatings are uniform at the 5% level over the mirror surface. Finally, we apply the measurements to predict effective areas achievable for HEFT and Con-X HXT using these W/Si designs. Key words: Multilayers Hard X-ray Telescopes, Synchrotron Radiation, Preprint submitted to Elsevier Preprint 15 February 2000

2 1 Introduction In order to extend the high-sensitivity and low-background of focusing telescopes into the hard X-ray band (E ο > 10 kev), future experiments, including the balloon-borne High-Energy Focusing Telescope (HEFT) and the Constellation-X Hard X-ray Telescope (Con-X HXT) plan to incorporate depth graded multilayer coatings. Compared to metal surfaces, multilayers can increase the maximum incidence angle (referred to as the graze angle) for which significant reflectivity is achieved. For standard metal coatings, this angle decreases approximately inversely with photon energy, making systems of reasonable focal length impractical, and in addition resulting in very small fields of view. Depth-graded multilayers utilize Bragg reflection to increase the mirror graze angle over a broad energy band[1,2]. By utilizing alternating layers of low and high index of refraction materials, with the bilayer thickness varying over a wide range, the Bragg condition can be satisfied at a given incidence angle for a range of photon energies. Typically the thinnest bilayers (which reflect the highest energy X-rays) are deposited first, so as to minimize absorption due to the overlying coatings. We have presented designs, optimized for broadband reflectance and Field Of View(FOV), for Wolter I (and conical approximation) astronomical hard X-ray telescopes[3]. These designs are based on a power law distribution of bilayer thicknesses[4]. Depth graded multilayers based on the power law design have been fabricated on test flats, and characterized over a broad range of energies[5]. Other(nonpower law) designs have also been developed and characterized at soft X-ray energies X-rays[6]. Recently, prototype thin mirror segments from the HEFT project have been coated and characterized at soft X-ray energies below 10 kev[7]. This characterization has allowed the hard X-ray reflectance to be calculated theoretically by using models of the multilayer structures derived from the soft X-ray data, assuming that no additional scattering is introduced at higher X-ray energies. In this paper, we present the first detailed measurements 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 kev. We present model fits to the data in order to characterize the multilayer structure. We also studied the coating uniformity as a function of the azimuthal angle on the optic. Finally, we present effective area and FOV calculations for HEFT and the Con-X HXT based on these hard X-ray reflectance measurements. 2

3 2 Mirror and prototype geometry Both HEFT and the Con-X HXT will adopt a Wolter-I or conical approximation X-ray mirror geometry. In this configuration, thin, nested shells are arranged in a two-reflection system. The on-axis graze angle of each shell is determined by = r=4f, where r is the shell radius, and f is the telescope focal length. The optics can be either constructed as full figures of revolution, or divided into segments. The optimum multilayer design depends on the graze angle, and the coating will therefore ideally be different on each shell. As a matter of practicality, we divide the shells into ten graze angle ranges, and optimize a coating for each range. Mao et al.(1999)[3] describes the optimization technique in detail. Table 1 HEFT multilayer design mirror angular range radial range d min [νa] d max [νa] c N group [mrad] [cm] D D D D D D D D D D Table 1 summarizes the multilayer parameters for each on axis graze angle range. The distribution of bilayer thicknesses is described by a power law[4], where the thickness of the i'th bilayer, d i,isgiven by d i =a=(b + i) c. Here a,b and c are constants, and i ranges from 1 to N, with N being the layer closest to the substrate. Each design is completely characterized by the minimum bilayer thickness, d min =d N, the maximum bilayer thickness, d max =d 1, the ratio between the thickness of the heavy element to the bilayer thickness,, the power index, c and the number of bilayers, N. The values of the parameters in Table 1 result from the optimization performed for the HEFT telescopes. The total thickness of any of the optimized coatings in Table 1 does not exceed 1.1 μm [3]. HEFT and Con-X HXT have different target energy bands:

4 kev; and 5 70 kev respectively, and mirror geometries (due to the different focal lengths). This however results in only slightly different multilayer designs, and therefore the parameters in Table 1 are applicable to both. The prototype optic consists of a stack of five quadrant mirror segments in a single reflection cylindrical geometry.we fabricated the mirror substrates used in the prototype by thermally forming glass into cylindrical segments. The glass forming process and mounting technique, described in detail in Hailey et al.(2000) and Craig et al.(2000)[8,9], was developed for HEFT, and is also being considered for use on the Con-X HXT. A separate characterization of the prototype imaging properties demonstrate Half Power Diamater of the one bounce optic at both soft and hard X-ray energies[10]. The mirror segment radii are 8.3, 8.4, 8.5, 8.6 and 8.7 cm. Each of the five mirror segments is coated with a different multilayer design, optimized for a different graze angle range. The five mirror segments are denoted D1, D2, D3, D4 and D5 and the exact specification 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 the cylinder axis of 20 cm. The glass optics were coated with the depth-graded W/Si multilayers in a planar magnetron sputtering system. We describe the deposition parameters and detailed calibration of the coatings in Windt et al.(2000)[11]. 3 Experimental arrangement and reflectance data 3.1 Experimental details To characterize the reflectance of the prototype optic in the energy range of interest we used X-ray beams, tuned to selected monochromatic energies, generated at one of two beamlines at the European Synchrotron Radiation Facility (ESRF). The X-ray beams illuminated the segments along the length of the cylindrical axis. To measure azimuthal variations, we mounted the optic in a ring, which provided precise azimuthal rotation. A similar arrangement, using the same ring in combination with a beam expander, was used for the ground calibration of the SODART X-ray telescopes[12]. Guard slits placed in front of the prototype unit allowed us to vary the size of the illuminated spot. For each beam energy we measured the reflectance as a function of incidence angle on the optic. We aligned the incidence angle by using the mirror segment itself as a shadow for the beam. We estimate systematic misalignments of this angle to be less than 0.2 milliradians. We used beam energies ranging from kev, produced at two separate beamlines. The first beamline we used, referred to as BM5 by ESRF, provided 4

5 energies of 18 kev, 28 kev and 34 kev, selected using a detuned double reflection Si(111) monochromator in reflection geometry. In addition, we used a 54 kev beam selected using the Si(333)-reflection together with an absorber to eliminate the 111-reflection. At the second beamline, designated ID15A by ESRF, we used a double reflection Si(311)monochromator in Laue geometry to 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 reflectivity features due to the finite energy bandwidth of the beam is unobservable for the energies listed above. We determined the angular collimation of the beam, typically 0.07 milliradians, in each case by the intrinsic rocking curve width of the monochromator reflection and/or by the width of slits placed in front of and behind the monochromator. We measured the reflected beam as well as the normalizing direct beam using a pin diode. At BM5 we used the synchrotron ring current to monitor the decay of the intensity during the measurement. At ID15A we used a separate beam monitoring pin diode in front of the prototype to keep track of the decay of the beam intensity. All data sets were, however, taken in the matter of minutes to an hour, and we noticed little variation in the beam intensity. 3.2 Reflectance data In Figures 1 and 2 we show the reflectance as a function of incidence angle for two different multilayer designs, D3 and D4. We have plotted data taken at several different energies on a single plot, scaling each successive curve by a factor of ten in order to separate them (the bottom plot clearly corresponding to the actual reflectance). We show error bars where they are bigger than the plotting symbol, and we have connected the data points to guide the eye. As can be seen by the indicated value of mirror segment azimuth angle, ffi, all data were taken close to zero (corresponding to the center of the mirror segment). Since the coating parameters may vary with azimuth angle (see x 3.3), direct comparison between energies requires comparing data at similar azimuth angles. In order to illustrate the energy dependence of absorption in the multilayers, we plot in Figures 3 and 4 the same data as well as data taken at 80 kev, 90 kev, 115 kev,158 kev and 170 kev as a function of the reciprocal lattice vector q. The reciprocal lattice vector is defined by q=4ßsin( )/, where is the angle of incidence and is the wavelength. The advantage of plotting the data taken as a function of q is that X-rays reflected from a layer pair of given thickness line up at the same reciprocal lattice 5

6 Fig. 1. Measured reflectivity of mirror segment D3 at energies from 18 kev to 170 kev. The line between data points is a guide for the eye. Data sets has been shifted by a factor of 10 for clarity.. The ffi-values at which the data are taken are indicated. Fig. 2. Measured reflectivity of mirror D4 at energies from 18 kev to 158 kev. The line between the data points is a guide for the eye. Data sets are shifted by a factor of 10 for clarity. The ffi-values at which the data are taken are indicated in the plot. vector for all energies. As expected, the reflectivity curve becomes flatter, and the reflectivity at a given q increases(provided q is larger than the value corresponding to the critical angle for total external reflection and smaller than 6

7 Fig. 3. Reflectivity data from mirror segment D3 plotted versus reciprocal lattice vector q. The line between data points is a guide for the eye. The data sets are shifted a factor of 10 for clarity and the energy and ffi-value for each data set is indicated. The effect of the K-absorption edge of W is clearly visible in the 80 kev data. At 170 kev the reflectivity has completely recovered and high reflectivity is measured out to ca. 3 times the critical angle. that at which the reflectivity drops due to the smallest bilayer) as energy increases and absorption becomes less important. Immediately above the W-K absorption edge the reflectivity suffers dramatically (as seen in the 80 kev and 90 kev data). By 115 kev, however, absorption is again small enough that the reflectivity is almost completely recovered. 3.3 Uniformity measurements Although depth-graded multilayers designed for broad band reflectance have a wide range of bilayer thicknesses in each coating, it is still important that the uniformity of the thickness distribution over the optic not deviate so much that coating is no longer optimal. For the HEFT design in particular, a 5% change of the bilayer thicknesses across the mirror surfaces will not significantly reduce the throughput or FOV of the telescopes[13]. The mirror segments in the current prototype consist of 90 ffi segments, and these were coated using a planar magnetron deposition system[14] not specifically designed to ensure uniformity perpendicular to the optical axis of cylindrically curved optics. The mirror module design being developed for HEFT and Con-X HXT will employ 60 ffi segments, and the HEFT mirror segments 7

8 Fig. 4. Reflectivity data from mirror segment D4 plotted versus reciprocal lattice vactor q, The line between the data points is a guide for the eye. The data sets are shifted a factor of 10 for clarity and the energy and ffi-value for each data set are indicated. As in figure 2 the effect of the K-absorption edge of W is clearly visible in the 90 kev data. At 158 kev the reflectivity has completely recovered and high reflectivity is measured out to ca 3 times the critical angle. will be coated in a system at the Danish Space Research Institute(DSRI) designed to achieve coating uniformity for cylindrically curved optics. The current prototype therefore represents a non optimal case in regard to azimuthal uniformity, but it allows us to measure the uniformityover a larger range than will ultimately be required. Figures 5 and 6 show the measured reflectivity of mirror segment D3 taken at 34 kev (Figure 5) and 54 kev (Figure 6) at a number of azimuth angles between -35 ffi and +35 ffi. We have again shifted different data sets by factors of 10 to separate them. The reflectance is essentially constant over this range, with a small degradation visible only at the edges. A variation in the angle where the reflectance 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 function of azimuthal position. To quantify this, we determined the minimum bilayer thickness for each value of ffi at 34 kev by fitting a model to the data (see below). Figure 7 shows the result, with estimated uncertainty. The thickness variation is small up to ±30 ffi from ffi = 0, but changes rapidly after that. Finally, it can be seen from the figures that the variations are not symmetric around ffi = 0 due to a systematic shift resulting from asymmetric mounting of the optics during coating. 8

9 Fig. 5. The measured reflectivity for different ffi-values ranging from -35 ffi to +35 ffi. The data are from mirror segment D3 and taken at 34 kev. The data points are connected by a line as a guide for the eye and the data sets are shifted by a factor of 10 for clarity It is quite clear from these results that the bilayer thickness varies by 5% in the 60 ffi segment around the symmetry point. This is within the required tolerance, however we expect to improve this further with more optimal coating geometries[15]. 4 Modeling of the reflectance data In order to characterize the multilayer coatings we have fit a model to the data that allows us to determine the basic parameters: minimum bilayer thickness (d min ), maximum bilayer thickness (d max ), interface widths (ff), and a small systematic misalignment of the graze angle on the order of 0.2 milliradian or less. We took the ratio of high to low index of refraction material,, as well as the distribution of bilayer thicknesses and number of bilayers to be the nominal values determined in a systematic calibration of the deposition system made just prior to coating. d min is well constrained for each data set, however d max cannot be well-determined. We therefore fit d min, and forced d max to vary by the same percentage. We assumed a constant value of ff, independent of layer. By fitting the data in this manner, we are able to calculate the reflectance over the full range of energies and graze angles relevant to HEFT and Con-X HXT. 9

10 Fig. 6. The measured reflectivity for different ffi-values ranging from -35 ffi to +35 ffi. The data are from mirror segment D3 and taken at 54 kev. The data points is connected by a line to guide the eye and the data sets are shifted by a factor of 10 for clarity Fig. 7. Deduced minimum bilayer thicknesses versus ffi from 34 kev data from mirror segment D3. The variation is small and is near 5% in a 60 ffi segment around the symmetry top point. In the modeling we used an X-ray reflectivity code for multilayered structures written by P.H.Mao[3]. The optical constants used in the code were obtained 10

11 from the websites of L.Kissel and P.M.Bergstrom, Jr. at Lawrence Livermore National Laboratories ( div/scattering/asf.html) and by J.H.Hubbell and S.M.Seltzer at the National Institute of Standards and Technology( 4.1 Data and model for small ffi Figures 8 10 show reflectance near the center of the optic (ffi indicated on the plot) 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 center of the optic, the minimum bilayer thickness should be close to the nominal value, and the value derived by fitting should be independent of energy. This is in fact the case (see Table 2). The uncertainty in d min is 0.25 νa, due almost entirely to residual alignment errors. The small discrepancy between the d min values obtained at the different energies for the same mirror segmentis consistent with this uncertainty. In addition, d min varies as a result of the range in azimuth angles (ffi=-8 ffi to ffi=+5 ffi ), as shown in Figure 7. From Figure 7 this variation is on order 0.2 νa. Fig. 8. Data and model as described in the text for all mirror segments at 34 kev and ffi=+5 ffi. The full line is the model calculation We found that a value of the interface widths, ff, of 4.5 νa fit the majority of these data well, and this is used in the model calculations shown in Figures 8, 9 and 10. The feature of the data providing the tightest constraint on ff is the reflectance after the sharp drop due to the minimum bilayer thickness. The reflectance here is due to second order reflections in the graded multilayer 11

12 Fig. 9. Data and model as described in the text for mirror segments D1, D2, D3 and D4 at 65 kev and ffi=-8 ffi. The full line is the model calculation Fig. 10. Data and model as described in the text for mirror segment D3at170keV and ffi=-8 ffi and mirror segment D4at158keV and ffi=-8 ffi. The full line is the model calculation stack, and (to the extent that c and are correct) this level determines ff. We do observe some small variation in how well this level is fit by a single ff. This could indicate small variations of ff (ο νa) with mirror segment and/or energy, however we see no consistent trend in the data. Considering the 12

13 Table 2 Modelled minimum bilayer thicknesses Mirror segment ffi Energy d min [νa] deg kev D D D D D D D D D D D extended energy range, our results are in good agreement with ff = 4.3 νa that we obtained previously from modelling 8 kev data from DSRI, and 28 kev data 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 must adjust the minimum bilayer thickness from the nominal value. Figure 11 shows the reflectance compared to model calculations for mirror segment D3atffi= 30 ffi ; 17 ffi ; +17 ffi and +30 ffi. We find that ff = 4.5 νa fits the ffi = 17 ffi and ffi = +17 ffi data well, however a slight increase to ff = 5.0 νa is required for ffi = ±30 ffi. 5 Effective area predictions for HEFT and the Con-X HXT The characterization of the depth-graded multilayers at hard X-ray/soft gammaray energies and comparison to model calculations demonstrates that a single, consistent set of parameters can describe the reflectance over this energy range. This is further demonstrated in Figures 12 and 13, which show the reflection versus energy at a graze angle of 2.2 mrad and 0.9 mrad. 13

14 Fig. 11. Data and model as described in the text for mirror segment D3at34keV and ffi-values -30 ffi,-17 ffi,+17 ffi,+30 ffi. The full line is the model calculation Fig. 12. Data and model as described in the text for mirror D3 versus energy at a graze angle of 2.2 mrad which is the center of the on axis graze angle range for this multilayer 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 confidently use the models to predict the effective area for the HEFT and Con-X HXT. To do this we have used the optimized multilayer design shown in Table 1 with 14

15 Fig. 13. Data and model as described in the text for mirror D3 versus energy at a graze angle of 0.9 mrad. Error bar is smaller than data point if not shown. The full line is the model calculation. the interface width of ff = 4:5 νa derived from the measurements. We have not included any variation in the coating parameters as a function of azimuth position, since this will only have a negligible effect on reflectance for the 60 ffi segments planned for the flight mirrors. Figures 14 and 15 show the calculations for the two telescope geometries. Table 3 summarizes the mirror parameters for each assuming that they are both made from thermally slumped 0.3 mm thin glass. For HEFT wehave included the effect of absorption in the residual atmosphere at 3.5 g/cm 2 expected for the balloon observations. For both telescopes, the W/Si multilayers provide large effective area up to the W-K absorption edge at 69.5 kev. For the mirror parameters shown in Table 3, Con-X HXT can exceed the 1500 cm 2 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 prototype nested formed glass optics provide good reflectance in the energy range from a few 69.5 kev. Previous measurements of multilayers on realistic substrates have been limited to low energy (typically the 8 kev Cu K-alpha line). It is important to note that different lengthscales in the roughness and in- 15

16 Fig. 14. Calculated effective area for the HEFT telescopes based on the model derived from the reflectance measurements and the optimization of the multilayer design as presented in Table 1. The area is calculated for on-axis, 1 mrad off axis, 2 mrad off axis and 3 mrad off-axis. Table 3 HEFT and Con-X HXT telescope parameters HEFT Con-X HXT Focal length 6 m 10 m No of modules No of shells per module 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 is not obvious that extrapolating over this large an energy interval is valid. Our high-energy measurements demonstrate, however, that similar results are obtained to those found at low-energy, implying that the roughness is due to lengthscales smaller than those probed at high-energy, leading to the energyindependence in the multilayer model parameters. Applying the multilayer model derived from the data to HEFT and Con-X HXT, we find that large effective area can be achieved up to the K-edge. Finally, the data taken at 170 kev, as well as other high energy data from specialized graded W/Si coatings[11,17], show that this far above the W 16

17 Fig. 15. Calculated effective area for the Con-X HXT telescopes based on the model derived from the reflectance measurements and the optimization of the multilayer design as presented in Table 1. The area is calculated for on-axis, 1 mrad off-axis, 2 mrad off-axis and 3 mrad off-axis. K-edge, the effects of absorption are minimal, and good reflectance can be achieved. Using a model incorporating Compton scattering, we are able to accurately predict the performance. This demonstrates that it is possible to design grazing-incidence mirrors for operation at energies up to 200 kev, or possibly even greater, using W/Si coatings. 7 Acknowledgments We are grateful to Manuel S. Del Rio, Michael Ohler and Robert Hustache for their expert technical assistance during the measurements. 17

18 References [1] F.E. Christensen, A. Hornstrup, N.J. Westergaard, H.W. Schnopper, J.L. Wood and K. Parker. A graded d-spacing multilayer telescope for high energy X- ray astronomy," in Multilayer and grazing incidence X-ray/EUV optics, R.B. Hoover, editor, Proc. SPIE 1546, (1992). [2] K.D. Joensen, F.E. Christensen, H.W. Schnopper, P. Gorenstein, J. Susini, P. Hoghoj, R. Hustache, J.L. Wood, and K. Parker. Medium-sized grazing incidence high-energy X-ray telescopes employing continuously graded multilayers," in X-Ray Detector Physics and Applications, R.B. Hoover, editor, Proc. SPIE 1736, (1993). [3] P.H. Mao, F.A. Harrison, D.L. Windt, F.E. Christensen Optimization of graded multilayer designs for astronomical X-ray telescopes" Applied Optics 38, (1999). [4] K.D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, and F.E. Christensen. Design of grazing-incidence multilayer supermirrors for hard-x-ray reflectors," Applied Optics 34, (1995). [5] K.D. Joensen Design, Fabrication and Characterization of Multilayers for Broad-band, Hard X-ray Astrophysics Instrumentation" Ph.D thesis, Copenhagen University(1995) [6] K. Yamashita, H. Kunieda, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, T. Okajima, Y. Hidaka, S. Ichimaru, S. Takahashi, A. Goto, H. Kito, Y. Tsusaka, K. Yokoyama, and S. Takeda. New design concept of Multilayer Supermirrors for Hard X-ray Optics," in X-ray Optics, Instruments, and Missions II, A.B.C.Walker and R.B. Hoover, editors, Proc. SPIE 3766, (1999). [7] A.M. Hussain, F.E. Christensen, M.A. Jimenez-Garate, W.W. Craig, C.J. Hailey, T.R. Decker, M. Stern, D.L. Windt, P.H. Mao, F.A. Harrison, G. Pareschi, M.S. Del Rio, A. Souvorov, A.K. Freund, R. Tucoulou, A. Madsen, C. Mammen X-ray scatter measurements from Thermally slumped thin glass substrates for the HEFT hard X-ray Telescopes," in X-ray Optics, Instruments and Missions II, A.B.C. Walker and R.B. Hoover, editors, Proc. SPIE 3766, (1999). [8] C.J. Hailey, S. Abdali, F.E. Christensen, W.W. Craig, T.R. Decker, F.A. Harrison, and, M.J. Garate. Substrates and mounting techniques for the High Energy Focusing Telescope (HEFT)," in EUV, X-ray and Gamma- Ray Instrumentation for Astronomy VIII, O.H.Siegmund and M.A. Gummin, editors, Proc. SPIE 3114, (1997). [9] W.W. Craig, F.E. Christensen, T.R. Decker, C.J. Hailey, F.A. Harrison, M.A. Jimenez-Garate. Investigation of substrates and mounting techniques for the High Energy Focusing Telescope(HEFT)," in Proc. SPIE, 3445, (1998) 18

19 [10] W.W. Craig, F.E. Christensen, C.J. Hailey, F.A. Harrison, A.M. Hussain, M.A. Jimenez-Garate, P.H. Mao, D.L. Windt Hard X-ray imaging Performance of Thermally Formed Glass Optics" submitted to Science, (2000) [11] D.L. Windt, F.E. Christensen, W.W. Craig, C.J. Hailey, F.A. Harrison, M.A. Jimenez-Garate, R. Kalaynaraman, P.H. Mao, Growth, Structure and performance of depth-graded W/Si Multilayers for hard X-ray optics," Submitted to J. Appl. Physics, (2000) [12] F.E. Christensen, B. Madsen, A. Hornstrup, P.F. Frederiksen, S. Abdali, N.J. Westergaard, J. Polny, C.B. Joergensen, P. Jonassen, X-ray Calibration of the SODART flight telescopes," in Proc. SPIE, 3113, (1997). [13] P.H. Mao, F.A. Harrison, Y.Y. Platonov, D. Broadway, B. DeGroot, F.E. Christensen, W.W. Craig, C.J. Hailey, Development of grazing incidence multilayer mirrors for hard X-ray focusing telescopes," in Proc. SPIE, 3114, (1997) [14] D.L. Windt, W.K. Waskiewicz, in J. Vac.Sci Technology, B 12, (1994). [15] D.M. Broadway, Y.Y. Platonov, L.A. Gomez Achieving desired thickness gradients on flat and curved substrates," in X-ray Optics, Instruments and Missions II, A.B.C. Walker and R.B. Hoover, editors Proc. SPIE 3766, (1999). [16] F.A. Harrison, W.R. Cook, F.E. Christensen, O. Citterio, W.W.Craig, N. Gehrels, P.Gorenstein, J.E. Grindlay, C.J. Hailey, R.A. Kroeger, H. Kunieda, A.M. Parsons, R. Petre, S.E. Romaine, B.D. Ramsey, J. Tueller,M. Ulmer, M.C. Weisskopf, D.L. windt. Technology Development for the Constellation- X hard X-ray telescope," in EUV X-ray, and Gamma-ray Instrumentation for Astronomy X, O.H. Siegmund and K.A. Flanagan, editors, Proc. SPIE 3765, in print. [17] D.L. Windt, F.E. Christensen, W.W. Craig, C.J. Hailey, F.A. Harrison, M.A. Jimenez-Garate, P.H. Mao, X-ray Multilayers for use at energies above 100 kev." to be published in X-ray Optics, Instruments and Missions, J. Trumper, B. Aschenbach, editors, Proc. SPIE 4012, (2000). 19