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A study of 8.5μ m microchannel plate X-ray optics
Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
A study of 8.5 lm microchannel plate X-ray optics A.N. Brunton *, A.P. Martin , G.W. Fraser , W.B. Feller X-ray Astronomy Group, Space Research Centre, Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK Nova Scientixc Inc., 54 Main Street, Sturbridge, MA 01566, USA Received 16 February 1999
Abstract We have investigated the X-ray focusing properties of microchannel plates (MCPs) with square channels of side length 8.5 lm. Both planar and spherically slumped MCPs (radius of curvature R "0.5m) have been examined. We have observed foci of 7 K and 14 K FWHM, respectively. In addition, we have measured the 8 keV X-ray re#ectivity of channel surfaces which have been subjected to a variety of chemical treatments. These re#ectivities are found to correspond closely to theoretical values calculated by a simple two-layer model of the MCP re#ecting surfaces. The inferred values of surface roughness for those MCPs thermally annealed at 4303C is &11 As , about a factor of two better than previously measured. 1999 Elsevier Science B.V. All rights reserved. Keywords: Microchannel plates; X-ray optics; X-ray astronomy; X-ray re#ectivity; X-ray telescopes
Introduction `Slumpeda square pore microchannel plates (MCPs), in which the axes of many channels point to a common centre of curvature, have been proposed as wide "eld soft (0.1}3 keV) X-ray optics for astronomy [1,2], providing a means to realise Angel's `Lobster-Eyea X-ray telescope geometry [3]. MCPs of larger channel aspect ratio (500:1 rather than 50:1) can also be used as hard X-ray optics, making possible a focusing telescope for the 2}50 keV band [4]. MCP X-ray optics may also be used in the laboratory as #ux collimators or `relay lensesa, for example in X-ray #uorescence analysis [5]. * Corresponding author. Tel.: #44-116-252-3882; fax: #44116-252-2464.. E-mail address: [email protected] (A.N. Brunton)
The angular resolution of an MCP X-ray optic is, in principle, only limited by the channel size D and, the distance of the image plane from the optic, l . G The FWHM width of the central, `truea, focus is equal to tan\(D/l )"tan\(2D/R ) in the case G of a slumped optic. In practice, the focus is broadened by misalignments and distortions of the channels and by micro-roughness of the re#ecting surfaces [6]. To date, only MCPs with very large (200 lm) channels have produced images in which the channel size makes a signi"cant contribution to the width of the focus [7]. In Section 2, below, we describe the focusing properties of two MCPs supplied by Nova Scienti"c Inc. They have square channels of side length 8.5 lm, packed in a square array of pitch 12 lm. The "rst MCP (designated MCP 1) is #at and provides the sharpest focus reported to date in such a small-pore optic. The second plate (MCP 2) has
0168-9002/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 2 6 3 - 6
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Table 1 Basic characteristics of the MCP optics used in focusing and re#ectivity measurements. All the MCPs are made from Corning 8161 glass, composition: Si O Pb K, o"4.0 g/cm Plate number
1
2
3A
3B
3C
3D
Channel size D (lm) Channel pitch p (lm) Open area fraction A Active area (mm) Channel length ¸ (mm) ¸/D Figure
8.5 12 0.5
8.5 12 0.5
8 12 0.44
8 12 0.44
8 12 0.44
8 12 0.44
0.34 40 Slumped
0.8 100 Flat
0.8 100 Flat
0.8 100 Flat
0.8 100 Flat
21;21 0.51 60 Flat
21;21
been spherically slumped to a radius of 0.5 m and has been used to image a distant point source } the "rst test of an MCP `X-ray telescopea. This radius of curvature is appropriate to a wide "eld of view `all sky monitora [2]. In Section 3 we report X-ray re#ectivity measurements made on a set of four similar MCP test pieces (MCPs 3A}D), which had been subjected to di!ering post-etch surface treatments. These synchrotron measurements show good agreement with a simple model of the re#ecting surface where the bulk, lead silicate composition glass is covered by a &400 As overlayer of silica. Table 1 summarises the geometric properties of all the optics described in this paper.
2. X-ray focusing 2.1. Inyuence of MCP channel geometry The MCPs discussed here were cut from a boule manufactured by a quadruple-draw process from Corning 8161 lead silicate glass. A previous report [8] describes the performance of earlier MCPs cut from this boule. Scanning electron microscope (SEM) images showed the channel array to be regular with good fusion of the multi-"bres and multi-multi-"bres. Few of the distorted channels previously seen at multi-"bre boundaries [6] were present. These initial optics, however, performed poorly in X-rays. An `aggressive etcha had successfully increased their open area fraction to A "85% by removing some cladding glass as well as core glass. Unfortunately, due to the relative
inaccessibility of the channel corners, the etch had not progressed as rapidly there, leading to rounded channel vertices and hence to poor focusing. The acid etch used for MCP1 was, although modi"ed, still a little strong, leading to moderate vertex radiusing. We estimate that less than 10% of the channel perimeter is curved (cf. &20% for the earlier MCPs). This optic has an open area fraction of A "50%. The etching of the slumped plate, MCP 2, using a further modi"cation of the #at plate etch, was near perfect, resulting in very square channels. We believe that, in this case, the broadening of the focus due to rounded corners [6] is negligible. During the manufacture of these MCPs, prior to the "nal draw, the entire multi-multi-multi or boule structure is encased in a glass sheath, which shrinks down, bonds with and encapsulates the boule as the draw progresses. When individual MCPs are sliced from the boule, this capsule appears as a solid `rima about 3 mm wide around the active area. It was found that at some time after slumping, perhaps a week, the rim could separate from the plate, in which case internal stresses are released and the plate is grossly deformed from its correct spherical curvature. Thus, while the #at plate discussed below had its rim attached, the rim of the curved one had been ground away prior to slumping. 2.2. Planar MCP (MCP 1) Images in `point to pointa focusing mode were obtained by illuminating the #at plate with the CLRC Rutherford Appleton Laboratory [9]
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repetitive laser plasma source [10]. The source of X-rays is a point-like (10 lm diameter) &10K plasma, generated by a picosecond-pulsed 248 nm excimer laser focused onto an aluminium tape target. The bulk of the 25 lJ/shot X-ray energy is concentrated in an Al XII line at 1.59 keV. An image (Fig. 1) of the cruxiform MCP focus was recorded on Kodak DEF X-ray "lm, protected from visible and UV light emitted from the plasma by a 1 lm polypropylene "lter coated with 0.2 lm aluminium. The source-optic and optic-image distances were l "l "300 mm. A Quantrad [11] 100-PIN-125 Si(Li) X-ray diode with a 10 lm beryllium "lter was used as a #ux monitor. The developed "lm was scanned using a JoyceLoebl MkIIIc microdensitometer with a numerical aperture of 0.25. Fig. 2 shows a typical scan along a cross arm, incorporating the central peak. After exposure by a single shot of the laser, the developed "lm had a peak optical density of approximately two, therefore the calibration curves of
Rockett et al. [12] were used. The peak has a breadth of 2 mrad"7 K FWHM and the maximum focusing gain (ratio of intensities measured with and without the MCP present) was 65, determined by a careful calculation incorporating the relevant solid angles, #ux distribution from the source and transmission of ambient gas (1 bar helium) and "lters [13]. 2.3. Slumped MCP (MCP 2) Previous investigations of slumped MCP optics have been con"ned to `beam expandera experiments [8,14], in which the optic is used to convert the diverging beam from a point-like source at its focus into a quasi-parallel output beam. Recently, we have commissioned a 20 m X-ray beam-line, to examine the performance of MCP optic telescopes focusing parallel X-rays. An electron-bombardment X-ray source with a copper anode was "ltered with aluminised Lexan and collimated to give
Fig. 1. 1.59 keV X-ray image recorded on Kodak DEF X-ray "lm with the #at MCP in point-to-point focusing mode. The length of the cross-arms is +8 mm from centre to end.
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
Fig. 2. Microdensitometer scan across horizontal cross-arm of 1.59 keV point-to-point focused X-ray image (Fig. 1).
a 2 mm (equivalent to 0.3 K at the optic) diameter spot emitting 0.93 keV Cu L X-rays. MCP 2 was mounted in a large chamber containing both the three-axis, stepper motor driven optic carriage and a large area (10;10 cm) two stage microchannel plate focal plane detector. [15]. The entire beamline was evacuated (pressure (10\ mbar) by a single liquid helium cryo-pump at the detector end of the beamline. MCP 2, with an aspect ratio ¸/D"40, had a nominal slump radius of 0.5 m (Table 1). The plate curvature was investigated using a Surfcom [16] stylus pro"lometer (see Section 3, below) and the radius of curvature found to be +543 mm. MCP 2 was installed in the beamline such that l +19.5 m and l +0.25 m. The quality of the fo cus was then optimised by motor driving the MCP carriage along the optic axis. Fig. 3 shows the best image obtained, with the focus slightly o! axis to suppress the di!use image component [17]. Fig. 3 was obtained at l "0.253 m corresponding to a slump radius of R "0.499 m once the "nite source-optic distance is accounted for. Fig. 4 shows a 1.5 mm wide slice along the cross-arm extending
359
Fig. 3. Image formed with R "0.5 m slumped MCP focus ing a 19.5 m distant source.
Fig. 4. 1.5 mm width slice along horizontal cross-arm of slumped MCP image (Fig. 3).
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A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365 Table 2 Pro"lometer slump radii Plate number
Orientation
Radius (mm)
Error$(mm)
2
1 2
537 549
16 16
2A
1 2
505 497
15 15
2B
1 2
491 495
15 15
2C
1 2
546 540
16 16
Fig. 5. Variation of focus FWHM with position along the optic axis.
to the bottom right in Fig. 3. The central, true, focus has a 13 K ;15 K FWHM and the focusing gain is 5.5, determined, in this case, solely from the digitised detector signals. The complete image incorporates an unimpeded reference beam (not visible in the Fig. 3) which reaches the detector via an aperture in the optic mounting structure. Fig. 5, used for focus optimisation, shows the variation of true focus FWHM with MCP position along the optic axis.
3. Measurement of slump pro5le We have made extensive use of Surfcom [16] stylus pro"lometers to "nd the slump pro"les of MCP optics. The slumped plate, MCP 2, was characterised, along with three nominally identical optics (designated MCPs 2A}C), by orthogonal pro"lometer scans, each parallel to a side of the plate and passing through its centre. We estimate that each scan was central and parallel with the sides of the plate to within 0.5 mm over the 20 mm traverse. Circles were "tted to datasets from the Surfcom chart recorder to determine the best "t slump radii. The results are listed in Table 2 and the pro"les and "tted curves are shown in Fig. 6. Fig. 7 shows the geometrical construction used to determine the errors in the radii. The radius of curvature and the
Fig. 6. Orthogonal Surfcom scans across MCP 2. The two "tted radii are indicated.
saggital depth, y, are related by R "(y#x/y) (1) where 2x is the side length of the MCP. The dominant error (in y) is $1.25 lm. We may then plot minimum and maximum radius curves using this error (Fig. 7) to yield the overall maximum error in the measurement technique of $3%.
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Table 3 Post etch treatments. Plates B}D also had extra cleaning after etching compared to plate A
Fig. 7. Construction required to calculate radius of MCP curvature from saggital depth y and MCP side length 2x. Method of "nding error from maximum and minimum radius circles is also indicated.
For each plate, the radii of the two orthogonal arcs are close in value; well within experimental error. However, there appear to be two distinct pairs in the set of four MCPs, the "rst with radii at, or very near, 500 mm and the second with radii of about 540 mm. The reason for this grouping is not clear. The X-ray tested plate, MCP 2, shows a clear discrepancy between the mechanical slump radius and the radius obtained from X-ray measurement (0.543 m vs. 0.499 m). This discrepancy indicates that, during slumping, the channels have not exactly followed the external "gure of the optic and, as a result, they are no longer normal to the surface. This points to an area where further work is required to perfect the manufacturing process.
4. Re6ectivity (MCPs 3A}D) 4.1. Synchrotron measurements We have made X-ray re#ectivity measurements on this set of four MCPs, which were subjected, by the manufacturers Nova Scienti"c Inc., to the various post-etch treatments listed in Table 3. These plates were externally similar to MCPs 1 and 2 described above and were made by the same process from the same Corning 8161 glass. They were cut, however, from a second boule and have somewhat
MCP
Treatment
3A 3B 3C 3D
Hydrogen reduction 4303C Hydrogen reduction 4303C Air bake 4303C Vacuum bake 2503C
poorer channel alignment, though perfectly adequate for the re#ectivity measurements described below. There has been some evidence [18] that hydrogen reduction reduces surface roughness; 4303C is the annealing temperature of 8161 glass [19]. Measurements were made on beamline 9.3 of the Daresbury Synchrotron Radiation Source [20] at an energy of 8 keV. Line 9.3 is illuminated by a 5T multipole wiggler and has 3 mrad horizontal angle of acceptance. X-ray wavelength is selected by means of a water cooled, double Si(220) crystal, harmonic rejecting monochromator. Work in this energy range may be carried out in air. The beamline is shown schematically in Fig. 8. The various motors to adjust positions and tilts are driven in steps of 1 lm or 0.0013, respectively. The entrance slit is "xed in position but the tungsten exit beam stop can be driven up and down. A 0.25 mm;3 mm area of each MCP was illuminated by stopping down the beam. The argon/helium "lled ion chambers preceding and following the MCP were operated at 1bar total pressure with 50 and 360 mbar partial pressures of argon respectively. They were cross-calibrated without an MCP present, which allows us to ignore absorption of X-rays by the air and ion chamber windows. An MCP was inserted with the beam stop driven out of the optical path and the signal from the rear ion chamber maximised. This con"rmed the estimate of channel plate open area fraction, previously measured by SEM, as 44%. We then established the `straight througha position to an accuracy of &0.0013 by progressively tilting the MCP and recording a symmetrical `rocking curvea with the zero tilt (maximum transmission) position in the centre.
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Fig. 8. Schematic of beam-line 9.3 of the Daresbury SRS.
We measured re#ectivity as a function of angle at constant energy of 8 keV. For each MCP a pair of measurements was necessary. As the critical grazing angle at 8 keV is less than the `transmission anglea h "tan\(D/¸) of the MCP, the optic pro duced both a re#ected and an unre#ected beam. First, by removing the beam stop, we measured the summed intensity of the two beams. We then drove the beam stop up until it intercepted the transmitted beam and measured the re#ected beam alone. Using the following analysis we calculated the re#ectivity, independent of the MCP geometry. We have F "(F /R#F )/A (2) where R is the re#ectivity, F is the #ux incident on the MCP, F is the re#ected #ux and F is the unre#ected #ux. In terms of the ion chamber currents: kI$"(I0/R#I0)/A (3) where I$ is the front ion chamber current, I0 is the contribution to the rear ion chamber current due to the re#ected X-rays and I0 is the contribution to the rear ion chamber current due to the unre#ected X-rays. k is the ratio of the currents in the rear and front ion chambers with no MCP present. Our two datasets (with and without beam-stop) give I0 and I0#I0"I0 , respectively. Hence, Eq. (3) yields, in > terms of measurable quantities: R"I0/(kI$A #I0!I0 ). (4) > Fig. 9 plots re#ectivity against angle at an energy of 8 keV for MCPs 3A}D. Apart from plate 3D the re#ectivity curves are very similar. There are bumps visible in the steep part of the curves which are `Kiessig fringesa [21,22] resulting from the struc-
ture of the MCP re#ecting surfaces. Fig. 10 illustrates this e!ect. Kiessig fringes occur when X-rays are re#ected from a layered mirror (e.g. gold deposited on a glass substrate) to form an X-ray mirror. At certain combinations of layer thickness, angle and energy, rays can penetrate the layer, re#ect from the substrate surface, penetrate the layer once again and, at the detector, interfere with rays re#ected directly from the layer surface to give apparently anomalous re#ectivity values. This, of course, is the principle employed in multilayer X-ray mirrors. In the production of functioning MCP electron multipliers the basic MCP glass (in this case Corning 8161) undergoes a series of chemical processes, of which the most important are etching of the MCP to remove the core glass and hydrogen "ring to reduce, hence activate, the surface. This treatment leads to a variation in glass composition with depth below the channel surface. Several authors have reported composition versus depth pro"les for activated MCP glass using Auger electron spectroscopy [23}25], ESCA [24] or secondary ion mass spectrometry (SIMS) [26]. These authors agree, qualitatively, on the surface and sub-surface structure (Fig. 10). At the surface is a very thin (& mono-layer) region, rich in the alkali metals. Below this is a lead free region, 100}500 As thick. Below this is a thick semiconducting region where some of the lead oxide has been reduced to metallic lead; in this region the overall elemental composition appears to be that of the bulk glass. From the perspective of X-ray re#ectivity there are, therefore, two important layers: the silica like leaddepleted region and the bulk glass composition region beneath it. We have successfully "tted the re#ectivity of these MCPs to theoretical curves based on this two-layer model, having previously reported a model based upon a more complex
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
363
Fig. 9. Re#ectivity vs. angle at an X-ray energy of 8 keV for optics 3A,B,C,D. Solid lines } "tted curves from the simple layered re#ector model with the parameters noted in Table 4.
layered mirrors using the formulae of Parratt [28]. For plane parallel interfaces between homogeneous layers, (n!1,n,n#1) the re#ectivity coe$cient is
R #F L L> L\ L R "a L\ L L\ R F #1 L L> L\ L where Fig. 10. Layered structure of MCP surface forms Kiessig fringes. Layers are: (1) air, (2) alkali metal monolayer, (3) leaddepleted silica layer, (4) bulk MCP glass.
gradation of lead content with depth into the channel surface [22]. 4.2. Reyectivity model The computer programme Rex [27] was used to "t the data. This code calculates the re#ectivity of
(5)
f !f F " L\ L (6) L\ L f #f L\ L f "( !2d !2ib) . (7) L L Here d and b are the real and imaginary refractive index decrements and is the grazing angle. The quantity a is the amplitude reduction factor at half L the perpendicular depth d L a "exp(!ip f d /2). (8) L L L The refractive index decrements d, b were obtained from the database of Cromer and Liberman [29] according to the method of Henke [30].
364
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
Surface roughness is accounted for using the scalar theory of Beckmann and Spizzichino [31]. Here the Fresnel coe$cient is modi"ed by a Debye}Waller factor to give:
Table 4 Values of free parameters derived from least-squares minima MCP
3A
3B
3C
3D
(9) FH "F exp[! (4ppsin /j)] L\ L L\ L where p is the rms surface roughness and j is the X-ray wavelength. It is necessary to account for the instrumental resolution, in this case dominated by the divergence introduced by channel misalignments to the beam re#ected from the MCP. These misalignments have successfully been modelled by a Gaussian distribution [6]. The Rex programme simulates the e!ect of beam divergence by calculating an averaged re#ectivity for a given beam pro"le. Least squares "tting to the data was carried out with layer thickness, rms interface and surface roughnesses and beam divergence as free parameters. The least squares minima for the three plates (3A}3C) were very similar, though plate 3B appears to have a somewhat thicker silica layer. The main di!erence between the "ts to these three datasets and that of MCP D, with poorer re#ectivity, was an increased surface roughness in the latter case. Table 4 summarises the "tted values, which appear entirely reasonable in the context of previously published work [6,7,22}26,32}35]. Only two of the MCPs described here (3A,3B) have been subjected to the full activation treatment while the other two have not been hydrogen "red. One of the non-reduced MCPs yielded a very similar re#ectivity curve to the reduced ones. The explanation for this is that the lead-free region develops during the etching process (common to all MCPs) in which the acid etchant leaches lead away from the near-surface region [26]. As already noted, plate 3D exhibited poorer re#ectivity than the other optics. Plates 3A}3C were all subjected to post etch thermal treatments which raised them to the glass annealing temperature of 4303C, while plate 3D was only heated to 2503C. We believe that heating to 4303C caused some annealing which smoothed the re#ecting surfaces. A temperature of 2503C was not su$cient for such annealing to occur leading to a poorer surface "nish in plate 3D. Indeed, the di!erence in re#ectivity between plates A}C and plate D was success-
RMS surface roughness (As ) RMS interface roughness (As ) Layer thickness (As ) Instrumental resoultion
11.3 25.5 359 0.0363
11.7 19.1 448
11.0 21.8 352
17.6 21.8 444
fully simulated by altering the roughness parameter in our model (Table 4). The value derived for rms surface roughness (&11 As ) on the annealed MCPs is about a factor of two better than that previously reported for a plate subjected to a weak acid polishing etch [18]. Fig. 9 compares measured and calculated re#ectivity against angle curves. It is clear from this work that bi-layered re#ecting surfaces adequately account for the shape of the curves. We suspect, however, that certain simpli"cations in our method are responsible for the small residual discrepancies between measured and theoretical plots. The "rst of these is the approximation of a homogeneous, lead free, surface layer when the literature suggests considerable intermixing of the two layers leading to a steady lead concentration gradient from the surface to the bulk glass [22]. The second is the simple Gaussian beam divergence and Debye}Waller roughness treatment. In fact, some radiation will be scattered due to the surface roughness, hence, modifying the beam pro"le in a non-Gaussian way.
5. Conclusions We have demonstrated X-ray focusing with 8.5 lm channel MCP optics. The focus had a 7 K FWHM width and the intensity gain was 65. We have further demonstrated the focusing of a distant source with a similar optic, slumped to a radius of 0.5 m. In this case the focus was broader } 14 K FWHM. The broadening must be caused by an imperfect slumping technique introducing distortion into the optic. The imperfection of the slumping process has been quanti"ed by measuring the radii of several optics using a contact pro"lometer. The four optics vary from the correct radius
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
by 25 mm rms. We have also shown that the slump radius determined for one MCP by X-ray measurements is almost perfect but di!ers by 43 mm from the slump radius obtained by the pro"lometer. The re#ectivity of MCP optics at an X-ray energy of 8 keV corresponds closely to theoretical values suggested by a simple layered mirror model. Fitting the experimental data to this model indicates that the etched surfaces are already quite smooth (&17 As ) and that heating to a temperature of 4303C causes annealing which improves the roughness to &11 As } a value comparable to that of conventional X-ray optics. Further, the "ts indicate that the, lead depleted, silica-like surface layers have thicknesses in the range 350}450 As , in accord with published work [23}26]. Acknowledgements The authors gratefully acknowledge the assistance of Edmond Turcu, Nic Lisi, Ric Allott and sta! of the CLRC Central Laser Facility and the help provided by Andy Dent of the CLRC Daresbury Lab. Thanks are due to the technical sta! in the Leicester University workshop, in particular Nick Boldra. The authors would also like to thank Ray Tomlinson of Advanced Metrology Systems, Leicester; the authors of the Rex analysis programme, Paul White of Nova Scienti"c Inc. and Andrew Peele of NASA Goddard Space Flight Centre. APM acknowledges "nancial support from the UK PPARC and Photonis SAS through a CASE studentship and GWF acknowledges the award of time to use the RAL laser plasma source and beamline 9.3 of the Daresbury SRS. References [1] G.W. Fraser, J.E. Lees, J.F. Pearson, M.R. Sims, K. Roxburgh, Proc. SPIE 1546 (1991) 41. [2] W.C. Priedhorsky, A.G. Peele, K.A. Nugent, Mon. Not. R. Astron. Soc. 279 (1996) 733. [3] J.R.P. Angel, Astrophys. J. 233 (1979) 364. [4] R. Willingale, G.W. Fraser, A.N. Brunton, A.P. Martin, Experimental Astronomy 8 (1998) 281. [5] A.P. Martin et al., X-Ray Spectrometry 28 (1999) 64. [6] A.N. Brunton, G.W. Fraser, J.E. Lees, I.C.E. Turcu, Appl. Opt. 36 (1997) 5461.
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[7] A. Peele, K.A. Nugent, A.V. Rode, K.Gabel, M.C. Richardson, R.Strack, W.Siegmund, Proc. SPIE 2515 (1995) 14. [8] A.N. Brunton, G.W. Fraser, J.E. Lees, W.B. Feller, P.L. White, Proc. SPIE 2519 (1995) 40. [9] Central Laser Facility, CLRC Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, U.K. [10] I.C.E. Turcu et al., Proc. SPIE 2015 (1994) 243. [11] Quantrad Corporation, Torrance, CA 90502, U.S.A. [12] P.D. Rockett, C.R. Bird, C.J. Hailey, D. Sullivan, D.B. Brown, P.G. Burkhalter, Appl. Opt. 24 (1985) 2536. [13] I.C.E. Turcu, A.N. Brunton, G.W. Fraser, J.E. Lees, Proc. SPIE 2523 (1995) 102. [14] G.W. Fraser, A.N. Brunton, J.E. Lees, D.L. Emberson, Nucl. Instr. and Meth. A 334 (1993) 579. [15] J.E. Lees, J.F. Pearson, Nucl. Instr. and Meth. A 384 (1997) 410. [16] Surfcom pro"lometer, Advanced Metrology Systems Ltd., 2 Pomeroy Drive, Oadby, Leicester, UK. [17] H.N. Chapman, K.A. Nugent, S.W. Wilkins, Rev. Sci. Instrum. 62 (1991) 1542. [18] G.W. Fraser, A.N. Brunton, J.E. Lees, J.F. Pearson, R. Willingale, D.L. Emberson, W.B. Feller, M. Stedman, J. Haycocks, Proc. SPIE 2011 (1993) 215. [19] J.D. Mackenzie, MCP glass analysis studies, Final Technical Report, Materials Department, Univ. California at Los Angeles, 1977. [20] CLRC, Daresbury Laboratory, Warrington, Cheshire WA4 4AD, UK. [21] H. Kiessig, Ann. Physik 10 (1931) 769. [22] A. Peele, G.W. Fraser, A.N. Brunton, A.P. Martin, R.M. Rideout, W. Zhang, N. White, R. Petre, Proc. SPIE 3444 (1998) 404. [23] G.E. Hill, Adv. Electron. Electron Phys. 40A (1976) 153. [24] S.H. Siddiqui, J. Appl. Phys. 48 (1977) 3053. [25] B. Prac\ ek, M. Kern, Appl. Surf. Sci. 70/71 (1993) 169. [26] A.M. Then, C.G. Pantano, J. Non-Cryst. Solids 120 (1990) 178. [27] T.A. Crabb, P.N. Gibson, K.J. Roberts, Comput. Phys. Commun. 3 (1993) 441. [28] L.G. Parratt, Phys. Rev. 95 (1954) 1593. [29] D.T. Cromer, D. Liberman, Relativistic Calculation of Anomolous Scattering Factors for X-rays, LASL Report LA-4403 Los Alamos Laboratory, 1970. [30] B.L. Henke, in: Topical Conf. on Low-energy X-ray Diagnostics, AIP Conf. Proc. 75 (1981) 146. [31] P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon Press, Oxford, 1963. [32] P. Kaaret, P. GeissbuK hler, A. Chen, E. Glavinas, Appl. Opt. 31 (1992) 7339. [33] A.V. Rode, H.N. Chapman, K.A. Nugent, S.W. Wilkins, Laser Interactions and Related Phenomena, vol. 10, Plenum Press, New York, 1992, p. 111. [34] H.N. Chapman, K.A. Nugent, S.W. Wilkins, A.V. Rode, Proc. SPIE 1741 (1992) 40. [35] H.N. Chapman, K.A. Nugent, S.W. Wilkins, Appl. Opt. 32 (1993) 6333.
A study of 8.5 lm microchannel plate X-ray optics A.N. Brunton *, A.P. Martin , G.W. Fraser , W.B. Feller X-ray Astronomy Group, Space Research Centre, Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK Nova Scientixc Inc., 54 Main Street, Sturbridge, MA 01566, USA Received 16 February 1999
Abstract We have investigated the X-ray focusing properties of microchannel plates (MCPs) with square channels of side length 8.5 lm. Both planar and spherically slumped MCPs (radius of curvature R "0.5m) have been examined. We have observed foci of 7 K and 14 K FWHM, respectively. In addition, we have measured the 8 keV X-ray re#ectivity of channel surfaces which have been subjected to a variety of chemical treatments. These re#ectivities are found to correspond closely to theoretical values calculated by a simple two-layer model of the MCP re#ecting surfaces. The inferred values of surface roughness for those MCPs thermally annealed at 4303C is &11 As , about a factor of two better than previously measured. 1999 Elsevier Science B.V. All rights reserved. Keywords: Microchannel plates; X-ray optics; X-ray astronomy; X-ray re#ectivity; X-ray telescopes
Introduction `Slumpeda square pore microchannel plates (MCPs), in which the axes of many channels point to a common centre of curvature, have been proposed as wide "eld soft (0.1}3 keV) X-ray optics for astronomy [1,2], providing a means to realise Angel's `Lobster-Eyea X-ray telescope geometry [3]. MCPs of larger channel aspect ratio (500:1 rather than 50:1) can also be used as hard X-ray optics, making possible a focusing telescope for the 2}50 keV band [4]. MCP X-ray optics may also be used in the laboratory as #ux collimators or `relay lensesa, for example in X-ray #uorescence analysis [5]. * Corresponding author. Tel.: #44-116-252-3882; fax: #44116-252-2464.. E-mail address: [email protected] (A.N. Brunton)
The angular resolution of an MCP X-ray optic is, in principle, only limited by the channel size D and, the distance of the image plane from the optic, l . G The FWHM width of the central, `truea, focus is equal to tan\(D/l )"tan\(2D/R ) in the case G of a slumped optic. In practice, the focus is broadened by misalignments and distortions of the channels and by micro-roughness of the re#ecting surfaces [6]. To date, only MCPs with very large (200 lm) channels have produced images in which the channel size makes a signi"cant contribution to the width of the focus [7]. In Section 2, below, we describe the focusing properties of two MCPs supplied by Nova Scienti"c Inc. They have square channels of side length 8.5 lm, packed in a square array of pitch 12 lm. The "rst MCP (designated MCP 1) is #at and provides the sharpest focus reported to date in such a small-pore optic. The second plate (MCP 2) has
0168-9002/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 2 6 3 - 6
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357
Table 1 Basic characteristics of the MCP optics used in focusing and re#ectivity measurements. All the MCPs are made from Corning 8161 glass, composition: Si O Pb K, o"4.0 g/cm Plate number
1
2
3A
3B
3C
3D
Channel size D (lm) Channel pitch p (lm) Open area fraction A Active area (mm) Channel length ¸ (mm) ¸/D Figure
8.5 12 0.5
8.5 12 0.5
8 12 0.44
8 12 0.44
8 12 0.44
8 12 0.44
0.34 40 Slumped
0.8 100 Flat
0.8 100 Flat
0.8 100 Flat
0.8 100 Flat
21;21 0.51 60 Flat
21;21
been spherically slumped to a radius of 0.5 m and has been used to image a distant point source } the "rst test of an MCP `X-ray telescopea. This radius of curvature is appropriate to a wide "eld of view `all sky monitora [2]. In Section 3 we report X-ray re#ectivity measurements made on a set of four similar MCP test pieces (MCPs 3A}D), which had been subjected to di!ering post-etch surface treatments. These synchrotron measurements show good agreement with a simple model of the re#ecting surface where the bulk, lead silicate composition glass is covered by a &400 As overlayer of silica. Table 1 summarises the geometric properties of all the optics described in this paper.
2. X-ray focusing 2.1. Inyuence of MCP channel geometry The MCPs discussed here were cut from a boule manufactured by a quadruple-draw process from Corning 8161 lead silicate glass. A previous report [8] describes the performance of earlier MCPs cut from this boule. Scanning electron microscope (SEM) images showed the channel array to be regular with good fusion of the multi-"bres and multi-multi-"bres. Few of the distorted channels previously seen at multi-"bre boundaries [6] were present. These initial optics, however, performed poorly in X-rays. An `aggressive etcha had successfully increased their open area fraction to A "85% by removing some cladding glass as well as core glass. Unfortunately, due to the relative
inaccessibility of the channel corners, the etch had not progressed as rapidly there, leading to rounded channel vertices and hence to poor focusing. The acid etch used for MCP1 was, although modi"ed, still a little strong, leading to moderate vertex radiusing. We estimate that less than 10% of the channel perimeter is curved (cf. &20% for the earlier MCPs). This optic has an open area fraction of A "50%. The etching of the slumped plate, MCP 2, using a further modi"cation of the #at plate etch, was near perfect, resulting in very square channels. We believe that, in this case, the broadening of the focus due to rounded corners [6] is negligible. During the manufacture of these MCPs, prior to the "nal draw, the entire multi-multi-multi or boule structure is encased in a glass sheath, which shrinks down, bonds with and encapsulates the boule as the draw progresses. When individual MCPs are sliced from the boule, this capsule appears as a solid `rima about 3 mm wide around the active area. It was found that at some time after slumping, perhaps a week, the rim could separate from the plate, in which case internal stresses are released and the plate is grossly deformed from its correct spherical curvature. Thus, while the #at plate discussed below had its rim attached, the rim of the curved one had been ground away prior to slumping. 2.2. Planar MCP (MCP 1) Images in `point to pointa focusing mode were obtained by illuminating the #at plate with the CLRC Rutherford Appleton Laboratory [9]
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repetitive laser plasma source [10]. The source of X-rays is a point-like (10 lm diameter) &10K plasma, generated by a picosecond-pulsed 248 nm excimer laser focused onto an aluminium tape target. The bulk of the 25 lJ/shot X-ray energy is concentrated in an Al XII line at 1.59 keV. An image (Fig. 1) of the cruxiform MCP focus was recorded on Kodak DEF X-ray "lm, protected from visible and UV light emitted from the plasma by a 1 lm polypropylene "lter coated with 0.2 lm aluminium. The source-optic and optic-image distances were l "l "300 mm. A Quantrad [11] 100-PIN-125 Si(Li) X-ray diode with a 10 lm beryllium "lter was used as a #ux monitor. The developed "lm was scanned using a JoyceLoebl MkIIIc microdensitometer with a numerical aperture of 0.25. Fig. 2 shows a typical scan along a cross arm, incorporating the central peak. After exposure by a single shot of the laser, the developed "lm had a peak optical density of approximately two, therefore the calibration curves of
Rockett et al. [12] were used. The peak has a breadth of 2 mrad"7 K FWHM and the maximum focusing gain (ratio of intensities measured with and without the MCP present) was 65, determined by a careful calculation incorporating the relevant solid angles, #ux distribution from the source and transmission of ambient gas (1 bar helium) and "lters [13]. 2.3. Slumped MCP (MCP 2) Previous investigations of slumped MCP optics have been con"ned to `beam expandera experiments [8,14], in which the optic is used to convert the diverging beam from a point-like source at its focus into a quasi-parallel output beam. Recently, we have commissioned a 20 m X-ray beam-line, to examine the performance of MCP optic telescopes focusing parallel X-rays. An electron-bombardment X-ray source with a copper anode was "ltered with aluminised Lexan and collimated to give
Fig. 1. 1.59 keV X-ray image recorded on Kodak DEF X-ray "lm with the #at MCP in point-to-point focusing mode. The length of the cross-arms is +8 mm from centre to end.
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
Fig. 2. Microdensitometer scan across horizontal cross-arm of 1.59 keV point-to-point focused X-ray image (Fig. 1).
a 2 mm (equivalent to 0.3 K at the optic) diameter spot emitting 0.93 keV Cu L X-rays. MCP 2 was mounted in a large chamber containing both the three-axis, stepper motor driven optic carriage and a large area (10;10 cm) two stage microchannel plate focal plane detector. [15]. The entire beamline was evacuated (pressure (10\ mbar) by a single liquid helium cryo-pump at the detector end of the beamline. MCP 2, with an aspect ratio ¸/D"40, had a nominal slump radius of 0.5 m (Table 1). The plate curvature was investigated using a Surfcom [16] stylus pro"lometer (see Section 3, below) and the radius of curvature found to be +543 mm. MCP 2 was installed in the beamline such that l +19.5 m and l +0.25 m. The quality of the fo cus was then optimised by motor driving the MCP carriage along the optic axis. Fig. 3 shows the best image obtained, with the focus slightly o! axis to suppress the di!use image component [17]. Fig. 3 was obtained at l "0.253 m corresponding to a slump radius of R "0.499 m once the "nite source-optic distance is accounted for. Fig. 4 shows a 1.5 mm wide slice along the cross-arm extending
359
Fig. 3. Image formed with R "0.5 m slumped MCP focus ing a 19.5 m distant source.
Fig. 4. 1.5 mm width slice along horizontal cross-arm of slumped MCP image (Fig. 3).
360
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365 Table 2 Pro"lometer slump radii Plate number
Orientation
Radius (mm)
Error$(mm)
2
1 2
537 549
16 16
2A
1 2
505 497
15 15
2B
1 2
491 495
15 15
2C
1 2
546 540
16 16
Fig. 5. Variation of focus FWHM with position along the optic axis.
to the bottom right in Fig. 3. The central, true, focus has a 13 K ;15 K FWHM and the focusing gain is 5.5, determined, in this case, solely from the digitised detector signals. The complete image incorporates an unimpeded reference beam (not visible in the Fig. 3) which reaches the detector via an aperture in the optic mounting structure. Fig. 5, used for focus optimisation, shows the variation of true focus FWHM with MCP position along the optic axis.
3. Measurement of slump pro5le We have made extensive use of Surfcom [16] stylus pro"lometers to "nd the slump pro"les of MCP optics. The slumped plate, MCP 2, was characterised, along with three nominally identical optics (designated MCPs 2A}C), by orthogonal pro"lometer scans, each parallel to a side of the plate and passing through its centre. We estimate that each scan was central and parallel with the sides of the plate to within 0.5 mm over the 20 mm traverse. Circles were "tted to datasets from the Surfcom chart recorder to determine the best "t slump radii. The results are listed in Table 2 and the pro"les and "tted curves are shown in Fig. 6. Fig. 7 shows the geometrical construction used to determine the errors in the radii. The radius of curvature and the
Fig. 6. Orthogonal Surfcom scans across MCP 2. The two "tted radii are indicated.
saggital depth, y, are related by R "(y#x/y) (1) where 2x is the side length of the MCP. The dominant error (in y) is $1.25 lm. We may then plot minimum and maximum radius curves using this error (Fig. 7) to yield the overall maximum error in the measurement technique of $3%.
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361
Table 3 Post etch treatments. Plates B}D also had extra cleaning after etching compared to plate A
Fig. 7. Construction required to calculate radius of MCP curvature from saggital depth y and MCP side length 2x. Method of "nding error from maximum and minimum radius circles is also indicated.
For each plate, the radii of the two orthogonal arcs are close in value; well within experimental error. However, there appear to be two distinct pairs in the set of four MCPs, the "rst with radii at, or very near, 500 mm and the second with radii of about 540 mm. The reason for this grouping is not clear. The X-ray tested plate, MCP 2, shows a clear discrepancy between the mechanical slump radius and the radius obtained from X-ray measurement (0.543 m vs. 0.499 m). This discrepancy indicates that, during slumping, the channels have not exactly followed the external "gure of the optic and, as a result, they are no longer normal to the surface. This points to an area where further work is required to perfect the manufacturing process.
4. Re6ectivity (MCPs 3A}D) 4.1. Synchrotron measurements We have made X-ray re#ectivity measurements on this set of four MCPs, which were subjected, by the manufacturers Nova Scienti"c Inc., to the various post-etch treatments listed in Table 3. These plates were externally similar to MCPs 1 and 2 described above and were made by the same process from the same Corning 8161 glass. They were cut, however, from a second boule and have somewhat
MCP
Treatment
3A 3B 3C 3D
Hydrogen reduction 4303C Hydrogen reduction 4303C Air bake 4303C Vacuum bake 2503C
poorer channel alignment, though perfectly adequate for the re#ectivity measurements described below. There has been some evidence [18] that hydrogen reduction reduces surface roughness; 4303C is the annealing temperature of 8161 glass [19]. Measurements were made on beamline 9.3 of the Daresbury Synchrotron Radiation Source [20] at an energy of 8 keV. Line 9.3 is illuminated by a 5T multipole wiggler and has 3 mrad horizontal angle of acceptance. X-ray wavelength is selected by means of a water cooled, double Si(220) crystal, harmonic rejecting monochromator. Work in this energy range may be carried out in air. The beamline is shown schematically in Fig. 8. The various motors to adjust positions and tilts are driven in steps of 1 lm or 0.0013, respectively. The entrance slit is "xed in position but the tungsten exit beam stop can be driven up and down. A 0.25 mm;3 mm area of each MCP was illuminated by stopping down the beam. The argon/helium "lled ion chambers preceding and following the MCP were operated at 1bar total pressure with 50 and 360 mbar partial pressures of argon respectively. They were cross-calibrated without an MCP present, which allows us to ignore absorption of X-rays by the air and ion chamber windows. An MCP was inserted with the beam stop driven out of the optical path and the signal from the rear ion chamber maximised. This con"rmed the estimate of channel plate open area fraction, previously measured by SEM, as 44%. We then established the `straight througha position to an accuracy of &0.0013 by progressively tilting the MCP and recording a symmetrical `rocking curvea with the zero tilt (maximum transmission) position in the centre.
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A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
Fig. 8. Schematic of beam-line 9.3 of the Daresbury SRS.
We measured re#ectivity as a function of angle at constant energy of 8 keV. For each MCP a pair of measurements was necessary. As the critical grazing angle at 8 keV is less than the `transmission anglea h "tan\(D/¸) of the MCP, the optic pro duced both a re#ected and an unre#ected beam. First, by removing the beam stop, we measured the summed intensity of the two beams. We then drove the beam stop up until it intercepted the transmitted beam and measured the re#ected beam alone. Using the following analysis we calculated the re#ectivity, independent of the MCP geometry. We have F "(F /R#F )/A (2) where R is the re#ectivity, F is the #ux incident on the MCP, F is the re#ected #ux and F is the unre#ected #ux. In terms of the ion chamber currents: kI$"(I0/R#I0)/A (3) where I$ is the front ion chamber current, I0 is the contribution to the rear ion chamber current due to the re#ected X-rays and I0 is the contribution to the rear ion chamber current due to the unre#ected X-rays. k is the ratio of the currents in the rear and front ion chambers with no MCP present. Our two datasets (with and without beam-stop) give I0 and I0#I0"I0 , respectively. Hence, Eq. (3) yields, in > terms of measurable quantities: R"I0/(kI$A #I0!I0 ). (4) > Fig. 9 plots re#ectivity against angle at an energy of 8 keV for MCPs 3A}D. Apart from plate 3D the re#ectivity curves are very similar. There are bumps visible in the steep part of the curves which are `Kiessig fringesa [21,22] resulting from the struc-
ture of the MCP re#ecting surfaces. Fig. 10 illustrates this e!ect. Kiessig fringes occur when X-rays are re#ected from a layered mirror (e.g. gold deposited on a glass substrate) to form an X-ray mirror. At certain combinations of layer thickness, angle and energy, rays can penetrate the layer, re#ect from the substrate surface, penetrate the layer once again and, at the detector, interfere with rays re#ected directly from the layer surface to give apparently anomalous re#ectivity values. This, of course, is the principle employed in multilayer X-ray mirrors. In the production of functioning MCP electron multipliers the basic MCP glass (in this case Corning 8161) undergoes a series of chemical processes, of which the most important are etching of the MCP to remove the core glass and hydrogen "ring to reduce, hence activate, the surface. This treatment leads to a variation in glass composition with depth below the channel surface. Several authors have reported composition versus depth pro"les for activated MCP glass using Auger electron spectroscopy [23}25], ESCA [24] or secondary ion mass spectrometry (SIMS) [26]. These authors agree, qualitatively, on the surface and sub-surface structure (Fig. 10). At the surface is a very thin (& mono-layer) region, rich in the alkali metals. Below this is a lead free region, 100}500 As thick. Below this is a thick semiconducting region where some of the lead oxide has been reduced to metallic lead; in this region the overall elemental composition appears to be that of the bulk glass. From the perspective of X-ray re#ectivity there are, therefore, two important layers: the silica like leaddepleted region and the bulk glass composition region beneath it. We have successfully "tted the re#ectivity of these MCPs to theoretical curves based on this two-layer model, having previously reported a model based upon a more complex
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
363
Fig. 9. Re#ectivity vs. angle at an X-ray energy of 8 keV for optics 3A,B,C,D. Solid lines } "tted curves from the simple layered re#ector model with the parameters noted in Table 4.
layered mirrors using the formulae of Parratt [28]. For plane parallel interfaces between homogeneous layers, (n!1,n,n#1) the re#ectivity coe$cient is
R #F L L> L\ L R "a L\ L L\ R F #1 L L> L\ L where Fig. 10. Layered structure of MCP surface forms Kiessig fringes. Layers are: (1) air, (2) alkali metal monolayer, (3) leaddepleted silica layer, (4) bulk MCP glass.
gradation of lead content with depth into the channel surface [22]. 4.2. Reyectivity model The computer programme Rex [27] was used to "t the data. This code calculates the re#ectivity of
(5)
f !f F " L\ L (6) L\ L f #f L\ L f "( !2d !2ib) . (7) L L Here d and b are the real and imaginary refractive index decrements and is the grazing angle. The quantity a is the amplitude reduction factor at half L the perpendicular depth d L a "exp(!ip f d /2). (8) L L L The refractive index decrements d, b were obtained from the database of Cromer and Liberman [29] according to the method of Henke [30].
364
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Surface roughness is accounted for using the scalar theory of Beckmann and Spizzichino [31]. Here the Fresnel coe$cient is modi"ed by a Debye}Waller factor to give:
Table 4 Values of free parameters derived from least-squares minima MCP
3A
3B
3C
3D
(9) FH "F exp[! (4ppsin /j)] L\ L L\ L where p is the rms surface roughness and j is the X-ray wavelength. It is necessary to account for the instrumental resolution, in this case dominated by the divergence introduced by channel misalignments to the beam re#ected from the MCP. These misalignments have successfully been modelled by a Gaussian distribution [6]. The Rex programme simulates the e!ect of beam divergence by calculating an averaged re#ectivity for a given beam pro"le. Least squares "tting to the data was carried out with layer thickness, rms interface and surface roughnesses and beam divergence as free parameters. The least squares minima for the three plates (3A}3C) were very similar, though plate 3B appears to have a somewhat thicker silica layer. The main di!erence between the "ts to these three datasets and that of MCP D, with poorer re#ectivity, was an increased surface roughness in the latter case. Table 4 summarises the "tted values, which appear entirely reasonable in the context of previously published work [6,7,22}26,32}35]. Only two of the MCPs described here (3A,3B) have been subjected to the full activation treatment while the other two have not been hydrogen "red. One of the non-reduced MCPs yielded a very similar re#ectivity curve to the reduced ones. The explanation for this is that the lead-free region develops during the etching process (common to all MCPs) in which the acid etchant leaches lead away from the near-surface region [26]. As already noted, plate 3D exhibited poorer re#ectivity than the other optics. Plates 3A}3C were all subjected to post etch thermal treatments which raised them to the glass annealing temperature of 4303C, while plate 3D was only heated to 2503C. We believe that heating to 4303C caused some annealing which smoothed the re#ecting surfaces. A temperature of 2503C was not su$cient for such annealing to occur leading to a poorer surface "nish in plate 3D. Indeed, the di!erence in re#ectivity between plates A}C and plate D was success-
RMS surface roughness (As ) RMS interface roughness (As ) Layer thickness (As ) Instrumental resoultion
11.3 25.5 359 0.0363
11.7 19.1 448
11.0 21.8 352
17.6 21.8 444
fully simulated by altering the roughness parameter in our model (Table 4). The value derived for rms surface roughness (&11 As ) on the annealed MCPs is about a factor of two better than that previously reported for a plate subjected to a weak acid polishing etch [18]. Fig. 9 compares measured and calculated re#ectivity against angle curves. It is clear from this work that bi-layered re#ecting surfaces adequately account for the shape of the curves. We suspect, however, that certain simpli"cations in our method are responsible for the small residual discrepancies between measured and theoretical plots. The "rst of these is the approximation of a homogeneous, lead free, surface layer when the literature suggests considerable intermixing of the two layers leading to a steady lead concentration gradient from the surface to the bulk glass [22]. The second is the simple Gaussian beam divergence and Debye}Waller roughness treatment. In fact, some radiation will be scattered due to the surface roughness, hence, modifying the beam pro"le in a non-Gaussian way.
5. Conclusions We have demonstrated X-ray focusing with 8.5 lm channel MCP optics. The focus had a 7 K FWHM width and the intensity gain was 65. We have further demonstrated the focusing of a distant source with a similar optic, slumped to a radius of 0.5 m. In this case the focus was broader } 14 K FWHM. The broadening must be caused by an imperfect slumping technique introducing distortion into the optic. The imperfection of the slumping process has been quanti"ed by measuring the radii of several optics using a contact pro"lometer. The four optics vary from the correct radius
A.N. Brunton et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 356}365
by 25 mm rms. We have also shown that the slump radius determined for one MCP by X-ray measurements is almost perfect but di!ers by 43 mm from the slump radius obtained by the pro"lometer. The re#ectivity of MCP optics at an X-ray energy of 8 keV corresponds closely to theoretical values suggested by a simple layered mirror model. Fitting the experimental data to this model indicates that the etched surfaces are already quite smooth (&17 As ) and that heating to a temperature of 4303C causes annealing which improves the roughness to &11 As } a value comparable to that of conventional X-ray optics. Further, the "ts indicate that the, lead depleted, silica-like surface layers have thicknesses in the range 350}450 As , in accord with published work [23}26]. Acknowledgements The authors gratefully acknowledge the assistance of Edmond Turcu, Nic Lisi, Ric Allott and sta! of the CLRC Central Laser Facility and the help provided by Andy Dent of the CLRC Daresbury Lab. Thanks are due to the technical sta! in the Leicester University workshop, in particular Nick Boldra. The authors would also like to thank Ray Tomlinson of Advanced Metrology Systems, Leicester; the authors of the Rex analysis programme, Paul White of Nova Scienti"c Inc. and Andrew Peele of NASA Goddard Space Flight Centre. APM acknowledges "nancial support from the UK PPARC and Photonis SAS through a CASE studentship and GWF acknowledges the award of time to use the RAL laser plasma source and beamline 9.3 of the Daresbury SRS. References [1] G.W. Fraser, J.E. Lees, J.F. Pearson, M.R. Sims, K. Roxburgh, Proc. SPIE 1546 (1991) 41. [2] W.C. Priedhorsky, A.G. Peele, K.A. Nugent, Mon. Not. R. Astron. Soc. 279 (1996) 733. [3] J.R.P. Angel, Astrophys. J. 233 (1979) 364. [4] R. Willingale, G.W. Fraser, A.N. Brunton, A.P. Martin, Experimental Astronomy 8 (1998) 281. [5] A.P. Martin et al., X-Ray Spectrometry 28 (1999) 64. [6] A.N. Brunton, G.W. Fraser, J.E. Lees, I.C.E. Turcu, Appl. Opt. 36 (1997) 5461.
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