5. X-Ray Telescopes (XRTs)

Astro-E2 has five light-weight thin-foil X-Ray Telescopes (XRTs). The XRTs have been developed jointly by NASA/GSFC, Nagoya University, Tokyo Metropolitan University, and ISAS/JAXA. These are grazing-incidence reflective optics consisting of compactly nested, thin conical elements. Because of the reflectors' small thickness, they permit high density nesting and thus provide large collecting efficiency with a moderate imaging capability in the energy range of 0.2-12 keV, all accomplished in telescope units under 20 kg each.

Four XRTs onboard Astro-E2 (XRT-I) are used on the XIS, and the other XRT (XRT-S) is for the XRS. They are arranged on the Extensible Optical Bench (EOB) on the spacecraft in the manner shown in Figure 5.1. Because of the different space requirement in the spacecraft for the micro-calorimeter, the XRT-S is different in terms of focal lengths than that of the 4 XRT-I's. Consequently, the number of the reflectors and their angular placement are also different. The external dimensions of the 5 XRTs, however, are the same (See Table 5.1, which also includes a comparison with the ASCA telescopes).

Figure 5.1: Layout of the 5 XRTs on the Astro-E2 spacecraft.

Table 5.1: Telescope Dimensions and Parameters of XRT

	Astro-E2 XRT-I	Astro-E2 XRT-S	ASCA
Number of telescopes	4	1	4
Focal length	4.75 m	4.5 m	3.5 m
Inner Diameter	118 mm	119 mm	120 mm
Outer Diameter	399 mm	400 mm	345 mm
Height	279 mm	279 mm
Mass/Telescope	19.5 kg	18.5 kg	9.8 kg
Number of nested shells	175	168	120
Reflectors/Telescope	1400	1344	960
Geometric area/Telescope	873 cm$^2$	887 cm$^2$	558 cm$^2$
Reflecting surface	Gold	Gold	Gold
Substrate material	Aluminum	Aluminum	Aluminum
Substrate thickness	155 $\mu$m	155 $\mu$m	127 $\mu$m
Reflector slant height	101.6 mm	101.6 mm	101.6 mm

The angular resolutions of the XRTs range from $1.5'$ to $2.3'$, expressed in terms of half-power diameter, which is the diameter within which half of the focused X-ray is enclosed. The angular resolution does not significantly depend on the energy of the incident X-ray in the energy range of Astro-E2, 0.2-12 keV. The effective areas are typically 440 cm$^{2}$ at 1.5 keV and 250 cm$^{2}$ at 8 keV. The focal lengths are 4.75 m for the XRT-I and 4.5 m for the XRT-S. Individual XRT quadrants have their component focal lengths deviated from the design values by a few cm. The optical axes of the quadrants of each XRT are aligned within 2' from the mechanical axis. The field of view for all 5 XRTs is about 17' at 1.5 keV and 13' at 8 keV. (see also Table 2.1)

5.1 Basic Components of XRT

The Astro-E2 X-Ray Telescopes (XRTs) consist of closely nested thin-foil reflectors, reflecting X-ray at small grazing angles. An XRT is a cylindrical structure, having the following layered components: 1. a thermal shield at the entrance aperture to help maintain a uniform temperature; 2. a pre-collimator mounted on metal rings for stray light elimination; 3. a primary stage for the first X-ray reflection; 4. a secondary stage for the second X-ray reflection; 5. a base ring for structural integrity and interface with the EOB of the spacecraft. All these components, except the base rings, are constructed in 90 segments. Four of these quadrants are coupled together by interconnect-couplers and also by the top and base rings (Figure 5.2). The telescope housings are made of aluminum for an optimal strength to mass ratio. Each reflector consists of a substrate also made of aluminum and an epoxy layer that couples the reflecting gold surface to the substrate.

Including the alignment bars, collimating pieces, screws and washers, couplers, retaining plates, housing panels and rings, each XRT consists of over 4000 mechanically separated parts (4112 for XRT-I and 4028 for XRT-S). In total, nearly 7000 qualified reflectors were used and over 1 million cm$^{2}$ of gold surface was coated.

Figure 5.2: An Astro-E2 X-Ray Telescope

5.1.1 Reflectors

In shape, each reflector is a 90 segment of a section of a cone. The cone angle is designed to be the angle of on-axis incidence for the primary stage and 3 times that for the secondary stage. They are 101.6 mm in slant length and with radii extending approximately from 60 mm at the inner part to 200 mm at the outer part. The reflectors are nominally 178 m in thickness. All reflectors are positioned with grooved alignment bars, which hold the foils at their circular edges. There are 13 alignment bars at each face of each quadrant, separated at approximately 6.4 apart.

To properly reflect and focus X-ray at grazing incidence, the precision of the reflector figure and the smoothness of the reflector surface are important aspects. Since polishing of thin reflectors is both impractical and expensive, reflectors in Astro-E2 XRTs acquire their surface smoothness by a replication technique and their shape by thermo-forming of aluminum. In the replication method, metallic gold is deposited on extrusion glass mandrel (``replication mandrel''), of which the surface has sub-nanometer smoothness over a wide spatial frequency, and the substrate is subsequently bonded with the metallic film with a layer of epoxy. After the epoxy is hardened, the substrate-epoxy-gold film composite can be removed from the glass mandrel and the replica acquires the smoothness of the glass. The replica typically has 0.5 nm rms roughness in the mm or smaller spatial scale, which is sufficient for excellent reflectivity at incident angle less than the critical angle. The Astro-E2 XRTs are designed with on-axis reflection at less than critical angle, which is approximately inversely proportional to X-ray energy.

In the thermo-forming of the substrate, pre-cut, mechanically rolled aluminum foils are pressed onto a precisely shaped ``forming mandrel'', which is not the same as the replication mandrel. The combination is then heated until the aluminum softened. The aluminum foils acquire the figure of the properly shaped mandrel after cooling and release of pressure. In Astro-E2 XRTs, conical approximation of the Wolter-I type geometry is used. This approximation fundamentally limits the angle resolution achievable. More significantly, the combination of the figure error in the replication mandrels and the imperfection in the thermo-forming process (to about 4 micrometers in the low frequency components of the figure error in the axial direction) limits the angular resolution to about 1 minute of arc.

5.1.2 Pre-collimator

The pre-collimator, which blocks off stray light that otherwise would enter the detector at a larger angle than intended, consists of concentrically nested aluminum foils similar to that of the reflector substrates. They are shorter, 22mm in length, and thinner, 120 micrometers in thickness. They are positioned in a fashion similar to that of the reflectors, by 13 grooved aluminum plates at each circular edge of the pieces. They are installed on top of their respective primary reflectors along the axial direction. Due to their smaller thickness, they do not significantly reduce the entrance aperture in that direction more than the reflectors already do. Pre-collimator foils do not have reflective surfaces (neither front nor back). The relevant dimensions are listed in Table 5.2.

Table 5.2: Design Parameters for Pre-collimator

	XRT-I	XRT-S
Number of Collimators	4	1
Height	32 mm	32 mm
Blade Substrate	Aluminum	Aluminum
Blade Thickness	120 $\mu$m	120 $\mu$m
Blade Height	22 mm	22 mm
Height from Blade Top to Reflector Top	30 mm	30 mm
Number of nested shells	175	168
Blade/Telescope	700	672
Mass/Collimator	2.7 kg	2.7 kg

5.1.3 Thermal Shields

The Astro-E2 XRTs are designed to function in a thermal environment of 20 7.5 C. The reflectors, due to its composite nature and thus its mismatch in coefficients of thermal expansion, suffer from thermal distortion that degrades the angular resolution of the telescopes in temperature outside this range. Thermal gradient also distorts the telescope in a larger scale. Even though sun shields and other heating elements on the spacecraft help in maintaining a reasonable thermal environment, thermal shields are integrated on top of the pre-collimator stage to provide the needed thermal control.

Figure 5.3: A thermal shield.

5.2 XRT Performance

Important parameters of the performance of the XRTs include the total effective area and its energy dependence, as well as the angular resolution, field of view, and stray light rejection.

5.2.1 Effective Area

The XRTs have a total collective area of more than 2000 cm$^{2}$ at low X-ray energies. The high collecting efficiency of the Astro-E2 XRTs is made possible by the thin-foil reflectors and a compact design. In fact, only 20% of the active aperture is lost to the thickness of the reflector themselves. An addition of 8% is blocked by the alignment structures (and a smaller fraction to the gap between quadrant housings). Nearly 900 cm$^{2}$ of geometric collecting area for each telescope remains usable for X-ray reflection, from which effective area of typically 440 cm$^{2}$ is obtained at 1.5 keV and 250 cm$^{2}$ at 8 keV. See Figure 5.4 for a graphical representation of effective area as a function of energy.

Figure 5.4: The predicted effective area of a quadrant of the Astro-E2 XRT-Is compared to measurements taken at particular energies for three different XRTs.

5.2.2 Angular Resolution

The angular resolution, traditionally measured in terms of half-power diameter, depends significantly on the proper axial curvature of the reflectors and their proper focusing from the distributed set of reflectors. On the other hand, due to the development of the replication method and its improvement, the micro-roughness is not as significant a factor as the geometric factors, such as slope errors, for resolution degradation. The average value of angular resolution of Astro-E2 XRTs is about 1.9' (half-power diameter) and is nearly independent of X-ray energy. Half-power diameter is derived from the encircled energy function, which is a function of the total power enclosed within a radius. An example of an encircled energy function and the point spread function are shown in Figure 5.5(a) & (b).

Figure 5.5: (a) Encircled Energy Function at Ti-K (4.5 keV) and Cu-K (8.0 keV). (b) Point Spread Function for the same energies. .

5.2.3 Optical Axes

Optical axis is defined as the direction of maximum throughput. It is defined for each quadrant of an XRT and the combination represents that of the telescope. These directions for individual quadrants, by design, are to coincide with the mechanical axis of the telescope system. Any mismatch of optical axes within the telescope or mismatch of the combined direction to that of the mechanical axis will lower the throughput for on-axis sources. However, the image position on the detector will not shift due to the nature of double reflections. The optical axes of individual quadrants were adjusted during quadrant integration and are generally within 1' of the nominal direction.

5.2.4 Focal Length

Focal length is defined as the distance of the image plane at which the image is most concentrated (having the smallest half-power diameter, for example). It is defined for individual quadrants and their combination represents the overall performance for an XRT. (For individual quadrant, it can also be measured effectively as the distance at which the image is symmetrical about the image center.) Focal length is ``built-in'' at the quadrant level and cannot be adjusted once the quadrant is built. The error in focal length of the quadrants in an XRT thus manifests itself in the degradation of the angular resolution, since the image plane is fixed at the detector position. Error in focal length is intimately related to that of the angular resolution and it is primarily affected by the relative error of reflector positioning at the 2 edges of the reflectors. It also has dependence on the location of reflectors (inner vs. outer). For the Astro-E2 XRTs, the focal lengths are typically within several cm of the nominal values. The angular resolution shown in §5.2.2 was measured at nominal focal distance and thus has already absorbed the error of focal length.

5.2.5 Field of View and Stray Light

Off-axis X-rays far out the field of view may not follow the intended light path but still enter the detector. Such ghost image can come from single reflection at the secondary stage, or it may be formed after making a backside reflection at the primary reflector, even though the backside of a reflector is not very reflective. To eliminate such stray light from entering the detector, a set of collimating blades is used to block off large angle reflection. Figure 5.6 shows an example of the elimination of stray light with the collimator action.

Figure 5.6: Stray light images of the spare quadrant in the field of view of the XIS at $45'$ off aixs. The [Left] and [Right] panels correspond to the images at Al-K (1.49 keV) before and after the pre-collimator installation, respectively. In each panel the right side is dominated by a stray light component from ``secondary-only reflection'' while the left side is by dominated by ``backside reflection.'' The stray flux is reduced by two orders of magnitude after the pre-collimator installation. The small filled circles in both images are identified as background particles, i.e., cosmic rays.