Ground-based x-ray calibration of the Astro-H/Hitomi soft x-ray telescopes

Abstract. We present the summary of the on-ground calibration of two soft x-ray telescopes (SXT-I and SXT-S), developed by NASA’s Goddard Space Flight Center (GSFC), onboard Astro-H/Hitomi. After the initial x-ray measurements with a diverging beam at the GSFC 100-m beamline, we performed the full calibration of the x-ray performance, using the 30-m x-ray beamline facility at the Institute of Space and Astronautical Science of Japan Aerospace Exploration Agency in Japan. We adopted a raster scan method with a narrow x-ray pencil beam with a divergence of ∼15″. The on-axis effective area (EA), half-power diameter, and vignetting function were measured at several energies between 1.5 and 17.5 keV. The detailed results appear in tables and figures in this paper. We measured and evaluated the performance of the SXT-S and the SXT-I with regard to the detector-limited field-of-view and the pixel size of the paired flight detector, i.e., SXS and the SXI, respectively. The primary items measured are the EA, image quality, and stray light for on-axis and off-axis sources. The accurate measurement of these parameters is vital to make the precise response function of the ASTRO-H SXTs. This paper presents the definitive results of the ground-based calibration of the ASTRO-H SXTs.


Introduction
Astro-H is a joint Japan Aerospace Exploration Agency (JAXA)/NASA x-ray satellite launched on February 17, 2016. [1][2][3][4] The Astro-H has several instruments to cover a wide energy range from a few hundred eV to 600 keV. It is equipped with two soft x-ray telescopes (SXTs) covering up to about 15 keV. 5,6 One of the two SXTs is for the soft x-ray spectroscopy (SXS: x-ray microcalorimeter detector) for high-resolution spectroscopy. The detector-limited field-of-view (FoV) of the SXS is 3.05 arc min 2 , comprising 6 × 6 pixels. The other SXT is for the soft x-ray imaging (SXI: x-ray CCD detector) for general x-ray spectroscopy. The detector-limited FoV of the SXI is very wide and 38 arc min 2 , comprising 1280 × 1280 pixels.
The Astro-H SXTs are designed on the same basis as those built for the telescopes (XRT-Is) onboard Suzaku, launched in 2007. 7 In order to achieve high throughput within a limited weight allowance, as many aluminum foils as possible, each of which is 101.6 mm long and is 0.15 to 0.31 mm thick, are nested within geometrical constraints. Each telescope consists of 203 nested shells of segmented thin-foil reflectors with a 200-nm gold, epoxy-replicated mirror surfaces, installed in primary and secondary mirror housings. The weight is 43 kg∕telescope, which is very light for the achieved effective area (EA). On the other hand, it is difficult to retain all the reflectors in the ideal shapes required by the original Wolter-I optics. We approximated both the primary and secondary reflectors by cones.
The design parameters of the SXT-I and SXT-S are identical and summarized in Table 1. The system requirements are listed in Table 2. Each SXT is composed of the identically designed four "quadrants." Each quadrant comprises primary and secondary housings, which contain reflectors. The reflectors in each housing are supported by seven alignment bars on the top and bottom sides. The precollimator is installed for stray-light protection, which consists of coaxially nested cylindrical aluminum blades placed above each reflector. 8 A thermal shield is attached in front of the precollimator to stabilize the thermal environment of the SXTs. 9 The shield is made of Al-coated 0.2 μm thick polyimide film (PI) to ensure a large EA in the soft energy band. Figure 1 shows the photos of the Astro-H SXT flight-models. The SXTs were developed at NASA/GSFC. The full details on the design concept, expected performance, fabrication, and interface to the satellite are described in Refs. 5 and 10.
On ground, two measurement methods have been applied for the calibration of the telescope. One is the diverging beam illuminating the full aperture of the telescope (e.g., Ref. 11), where as the other is the raster scan with the pencil beam (e.g., Ref. 12). The full-aperture-illumination with the diverging beam with a long distance source such as the MSFC's XRCF facility and the Panter facility well works to calibrate the image of a high-angular-resolution "arc sec" telescope, such as the Chandra HRMA (e.g., Ref. 13) and the XMM-Newton telescope (e.g., Ref. 11). The pencil-beam raster scan gives a precise solution for the EA calibration since the diverging angle of the beam is quite small, typically tens of arc secs are much smaller than the telescope vignetting. The EA taken with the raster scan method is known as well consistent with that obtained in orbit (e.g., Refs. 7 and 14). Also, the image with an "arc min" angular resolution can be made with the scan (e.g., Ref. 15).
The initial ground calibration was performed at the 100-m beamline at NASA/GSFC, using a diverging beam, and the angular resolutions at 8.0 keV were determined to be 1.1 0 and 1.0 0 in a half-power diameter (HPD) for SXT-I and SXT-S, respectively. 16 We later conducted the comprehensive ground calibration at the 30-m x-ray beam facility at the Institute of Space and Astronautical Science (ISAS)/JAXA, Japan. We adopted a raster scan method with a narrow x-ray pencil beam with a divergence of 15 00 .
In this paper, we report the summary of the ground calibration of the Astro-H SXTs at ISAS/JAXA. In Sec. 2, we describe the measurement system at ISAS. The results of the EA, image quality, and stray light are presented in Secs. 3, 4, and 5, respectively. We also compare the results with those of the Suzaku XRT-Is.
2 Measurement Setup Figure 2 shows a schematic view of the x-ray beam facility at ISAS/JAXA. The measurements are carried out by scanning the SXT aperture with a parallel narrow x-ray beam as follows. To archive high parallelism, we place an x-ray generator at one end of the system and collimate the beam with the slit placed 27 m away from the x-ray source. The resultant beam is highly parallel with the size of 2 mm 2 , and the beam divergence is square, ∼15 00 on each side. To illuminate the entire aperture of the SXT by the fixed x-ray pencil beam, SXTs and detectors are moved synchronously. In addition, thin metal filters and double-crystal monochromator are installed in the beam path in order to obtain monochromatic x-rays.
The same ISAS facility has been also used for the calibration of the x-ray telescopes of Suzaku. The measurement system for Astro-H is almost identical except for two minor changes; the chamber of the sample stage is larger and longer, and the image detector was renewed for the Astro-H calibration. For the focal plane detectors, charge-coupled device (CCD) and proportional counter (PC) are used. The FoV of the CCD is 17.1 0 × 15.9 0 (1240 × 1152 pixels) at the distance of 5.6 m. The size of the PC is 12 mmΦ (7.4 0 at 5.6 m). The CCD is used for investigating the image quality, whereas the PC is used for the EA. The details of the raster scan and beam facility are described in Refs. 17-19.
The coordinate system is defined as in Fig. 2. The x-axis is defined to align with the x-ray beam direction. The z-axis is perpendicular to the ground, with the positive direction being upward. The y-axis is on the horizontal plane, and so the three axes form a right-hand coordinate system. The EA and the image quality are measured with raster scan at each quadrant. The four quadrants in each telescope are named Q1, Q2, Q3, and Q4. In this paper, a quadrant coupled with the measured configuration of the coordinates is referred to as QnðAEAÞ, where n is the quadrant number of 1 to 4 and A is either Y or Z for the axis; for example, Q1ðþZÞ means the Q1 with the positive Z-axis configuration. Mass of a telescope ∼20 kg ∼43 kg A dummy frame with the same shape of the thermal shield is installed at the measurement. The thermal shield is a forwardend component of the SXT that plays a role in the thermal shielding to the space. A structure of the frame obstruct a large fraction of the photons at the end sectors and less at the others. The dummy frame has no film or mesh. The mesh works as a neutral density filter in x-rays, whereas the film with the constant thickness uniformly absorbs incoming x-rays. The reduction of the EA due to the film or the mesh is not included in our measurements but was then modeled in our calculation. The errors quoted in this paper are at 1σ confidence level for one parameter of interest.

Effective Area
The EA S eff ðEÞ is given by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 6 3 ; where v y and h z are the scanning speed in the y direction and the scanning pitch in the z direction, respectively, I is the photon count rate of the incident beam, and C scan is the number of the collected photons from all the raster scan paths. In the typical setting, v y ¼ 4 mm∕s and h z ¼ 4 mm. The beam size is 2 × 2 mm, and the divergence of the beam is about 15". The aperture of the focal plane detector of the PC is a 12 mmΦ (7.4 0 ) circle. Roughly 3% of the reflected photons fall outside this 7.4 0 diameter circle, irrespective of the energy (see the later section about the image quality calibration), a factor which is not corrected in the tables and figures presented in this section.

Optical Axis Distribution
First, we determined the optical axis of the SXTs for the x-ray calibration with Ti-K 4.5 keV. We measured the EA for all the quadrants at off-axis angles of θ y , θ z ¼ −4 0 , 0, þ4 0 from the approximate optical axis of the whole telescope with optical parallel beams. The peaks fitted with the three-point data of θ y and θ z directions are defined as the optical axis on the respective coordinate axis. Figure 3 shows the results for the quadrant axis and the whole-telescope axis. The distribution of the measured optical axes among the quadrants is ∼30 00 wide. The distribution in the SXT-S is narrower than that in the SXT-I.

On-Axis Effective Area
We measured the EA of the quadrants of the SXT-I and SXT-S at the whole-telescope axis (on-axis) with seven energies (Al-K 1.5 keV, Ti-K 4.5 keV, Cu-Kα 8.0 keV, Pt-Lα 9.4 keV, Pt-Lβ 11.1 keV, Pt-Lγ 12.9 keV, and Mo-K 17.5 keV). Figure 4 and Table 3 summarize the results. For comparison, those of the Suzaku XRT-I are also included. The characteristics of the EA are found to vary significantly from quadrant to quadrant. For example, Q4ðþYÞ of SXT-I and Q3ð−ZÞ for SXT-S have a relatively low EA, irrespective of x-ray energies. We find that the EA is ∼80% of the ideal value irrespective of the energy (Fig. 4). The ideal value is calculated with the design parameters and the reflectivity with the roughness of 4 Å. We adopted the Debye-Waller model for the reflectivity calculation and coded the formula by the Debye-Waller. During the calculation, we refer to the optical constant of the HENKE table. The total EA of the SXT-S is slightly larger than that of the SXT-I by ∼2%. The loss of ∼20% is not due to the test configuration on ground but due to deficiency of the telescope modeling. Misaki et al. 20 discussed the cause of the deficiency for the ASTRO-E XRTs. The cause of the loss will be in part due to the nonperfect shape of each reflector in which some fraction of the reflected xrays with a large angle due to the figure error hits the back of the inner reflector. The similar loss is also occurred with nonperfect positioning of the reflector. The loss of ∼20% in the SXT EA can be qualitatively explained with a similar cause with the ASTRO-E XRTs.
Compared with the XRT-Is of Suzaku, the EA of the SXTs is larger by factors of ∼1.3 and ∼1.5 at 1.5 and 8.0 keV, respectively. This improvement is mainly due to the scale up of the diameter from 40 to 45 cm and of the focal length from 4.75 to 5.6 m.
Considering the EA of a telescope, the distribution of the quadrant axes is important. We measured the EA at each quadrant axis at 4.5 keV and show the results in Table 4. The sum of the EA of the quadrant is almost the same as the EA of the full telescope. This result implies that the optical axes of the four quadrants in SXT-I and SXT-S are well co-aligned.

Off-Axis Effective Area (SXT-I)
The SXT-I is for the SXI detector, which has a large detectorlimited FoV (38 0 × 38 0 ). We measured the angular response at wide off-axis angles. First, we measured the EA at off-axis angles from −4 0 to 4 0 , scanning the full-telescope, at 4.5 keV. The measurement points of two directions (θ y and θ z ), where the telescope is accordingly tilted to incident x-rays, are shown in Fig. 5. The data are fitted with a Lorentzian function with a fullwidth at half-maximum (FWHM) of 15.8 0 . The residual in the best-fit results is found to be a few percent irrespective of the tilted direction.
Next, we measured the EA at wide off-axis angles up to 32 0 , scanning the quadrant Q1ðþZÞ at the multiple energies (1.5, 4.5, 8.0, 9.4, 11.1, 12.9, and 17.5 keV). Figure 6 shows the result. The data are found to be well fitted with the model of a Lorentzian function but not with a Gaussian model. The residual to the best-fit model is typically 5% at smaller off-axis angles and energies, whereas it increases toward larger off-axis angles or larger energies [ Fig. 6(c)]. The SXT FoV is 15.7 0 in FWHM at 1.5 keV, decreasing with higher x-ray energies, and is 6.2 0 at 17.5 keV. The vignetting width in full width at 90% maximum of the EA is within 5.2 0 and 2.1 0 at 1.5 and 17.5 keV, respectively. Although the vignetting measurement was made only for one quadrant and one direction, the vignetting of the whole telescope must be in the similar shape because the tilt directions are    intermediate between θ y and θ z , or between steeper and flatter angular responses.

Off-Axis Effective Area (SXT-S)
We measured angular responses at a small off-axis angle at various tilt directions for the SXT-S. It is because the focal-plane detector SXS is so small that the FoV of the SXS system is limited by the detector size. First, we measured the EA at off-axis angles from −4 0 to 4 0 , scanning the full-telescope, at 4.5 keV. Figure 7(a) shows the results for the two tilt directions (θ y and θ z ). We then fitted the data with a Lorentzian model and found the best-fit Lorentzian width to be 16.0 0 in FWHM, which is the same value as that for the SXT-I (Fig. 5). The residual in fitting is ∼1%. Next, we measured the EA at 1 0 off-axis angle for four tilting points at energy bands of 1.5, 4.5, 8.0, 9.4, and 11.1 keV [ Fig. 7(b)]. The residual to the best-fit model is typically a few percent, with an increasing trend toward larger energies. Finally, we measured the EA at 1 0 and 2 0 off-axis angles for eight tilting points at 4.5 keV [ Fig. 7(c)]. The residual is ∼1%. From these results, we conclude that the narrow vignetting in the SXS FoV has a small scattering of 1% to 2%, regardless of the tilt directions and x-ray energies.

Image Quality
In this section, we present the measured results of the imaging capability of the Astro-H SXT-I and SXT-S.

On-Axis
The detailed results are described in Refs. 21 and 22. To summarize, the obtained HPDs of the full-telescope in the 1.5 to 17.5 keV band are 1.25 0 to 1.47 0 and 1.19 0 to 1.35 0 for the SXT-I and SXT-S, respectively. The angular resolution is almost independent of the x-ray energy but is marginally worse at higher energies. The trend is especially notable for the Q3ð−ZÞ quadrant of the SXT-I. More detailed measurement has been carried out with the spot scan in order to examine this trend further, as reported in Refs. 21 and 22. By contrast, the angular resolution of the XRT-Is of Suzaku was 1.7 0 to 1.9 0 (HPD). The significant improvement in the angular resolutions from Suzaku to Astro-H comes primarily from the improvement in precision in the shape of the reflecting surface and reflector positions. 5 The image quality with the Suzaku XRT-Is showed a large scatter from telescope to telescope due to a gravitation effect. 23 However, we find from the measurement of the rotation of the telescope of Q1ð−ZÞ that the gravitation effect causes no change in the optical axes or the image quality of the Astro-H SXTs. This improvement may be due to the fact that the reflectors are glued to the alignment bars in the Astro-H SXTs, whereas they were not in the Suzaku SXTs.

X-Ray Scattering into the SXS FoV
Because of the narrow detector-limited FoV of the SXS and the moderate angular resolution of the SXT-S, a significant fraction of the photons collected by the SXT-S does not fall onto the SXS even when the target source is located at the center of the SXS FoV. Figure 8 shows a SXT-S/SXS image of a point-like source located at the center of the FoVof the SXS. We estimated the EA for the SXS and its ratio to the EA with the circular FoV of a  Table 5 at six energy bands. We find the ratio to be ∼90% and to hardly depend on the energy (91% to 88% at 1.5 to 17.5 keV). The fact that a significant fraction of the collected photons misses the SXS detector-limited FoV means that a significant amount of the flux from a source just outside the detector's FoV. We estimated the amount of the contamination, from sources at three off-axis angles of 3 0 , 4.5 0 , and 8.6 0 . For the 3 0 off-axis image, the source is shifted from the on-axis in the perpendicular direction to the SXS, and for the 4.5 0 and 8.6 0 , the sources are shifted in the diagonal direction, as demonstrated in Fig. 9. In the cases of 3 0 and 4.5 0 off-axis sources at 4.5 keV, we placed the off-axis source at four different positions, rotated for 90 deg, and measured the EA for each configuration. Table 6 shows the resultant EAs with the off-axis sources.
The 4.5-keV EA due to sources outside the detector FoV is 7.4 to 10.5 and 2.2 to 2.8 cm 2 at off-axis angles of 3 0 and 4.5 0 , respectively, and hence to slightly depend on the off-axis angle. These EAs correspond to ∼2% and ∼0.6% of the on-axis EA, respectively. The ratio of the EA to that of on-axis sources does not depend on the energy with errors ∼0.5%. The EA for a highly off-axis source at an off-axis angle of 8.6 0 is ∼0.1% of the on-axis EA.

Large Off-Axis in the SXI FoV
The SXI has a large detector-limited FoVof 38 0 × 38 0 , and thus, the images at off-axis angles more than the half width of the SXI FoV should be investigated. Figure 10 shows images at off-axis angles between −4.5 0 and 27 0 , where the positive is defined as in the direction of (DET-X, DET-Y) = (þ1∕ ffiffi ffi 2 p , þ1∕ ffiffi ffi 2 p ). The EA and image quality (HPD) for the off-axis sources with the off-angles are tabulated in Table 7. We find that the image shrinks along the tilting direction and its opposite, the EA becomes smaller, and HPD becomes larger, as the off-axis angle increases, presumably because of the vignetting effect. Above 13.5 0 of off-axis angle, a fan-shaped stray-light structure appears in the opposite side of the tilting direction to the image center. The surface brightness of the stray-light structure is ∼10 −3 of that of image center. The details are described in the next section.

Stray Light
Although the FoV of the SXTs is ∼16 0 in FWHM (Secs. 3.2 and 3.3), x-rays from outside of the FoV can reach the focal plane without experiencing the double reflection as they should be in the ideal Wolter-I type optics, because the thin-foil-nested mirrors used in the SXTs do not completely block the light paths of those kinds. The component makes a ghost image and is referred to as "stray light." In order to cut off the stray light as much as possible, a "precollimator" is installed on the top of each SXT. 8 The precollimator is composed of a thin and conical blade attached in front of the each primary reflector. The blade effectively blocks the light pass with an incident angle of about 30 0 or larger on the plane (or radial) direction. The precollimator    significantly reduces the light pass of the nondouble reflection in the mirror modules. In order to calibrate the stray lights, we, in advance, examined the light pass of the strays using the ray-tracing code. We then pick up three cases and made measurements as given as follows. The first and second is picked up for the SXT-I/SXI system while the third is for the SXT-S/SXS. The image clearly shows a ring-like stray-light structure with the radius of 18 0 around the image center. This stray is constructed by the photons reflected by only the innermost secondary reflectors and is identified as the unique stray pass at onaxis. Its surface brightness is very low and ∼10 −5 of that of the image center.

30 0 Off-Axis in the SXI Detector-Limited FoV
Due to the time limitation, we carried out the measurement at two representative off-axis angles of AE30 0 only. The stray light at the other off-axis angles is then deduced via ray-tracing simulation, which is calibrated with the AE30 0 off-axis angle data.
First, we took images, irradiating x-rays on only one quadrant at off-axis angles of AE30 0 at 1.5 keV. In this measurement, the detector was placed at a distance of 3.733 m from the telescope (2∕3 of the focal length) in order to reduce the number of  mosaic mapping, and images were taken at three or four offset positions from the telescope's on-axis focus in order to cover the entire SXI FoV. Figures 12(a) and 12(b) show the resultant images at the offaxis angles of þ30 0 and −30 0 , respectively. In the þ30 0 off-axis image, we identify some stray light components [e.g., the secondary-mirror single reflection, the direct component (no reflection), the backside-of-the-mirror reflection, and the precollimator reflection]. In the þ30 0 off-axis image, the backside-of-the-mirror reflection and precollimator reflection are marginally visible. We also estimate the EAs at the circular regions indicated in Fig. 12 (1S, 2S, 1B, and 2B), and list them in Table 8. Among them, the 2S region is found to be brightest with the EA of ∼0.59 cm 2 , which is ∼10 −3 of the on-axis EA of the full telescope. This region is dominated by the secondarymirror single reflection component.
Next, we constructed an image, combining four images to cover the SXI FoV, each of which was illuminated for the entire telescope aperture at an off-axis angle of 30 0 [ Fig. 12(c)].
The illuminating x-ray beam is tilted toward one of the boundaries of the quadrants. The detector was placed at the focal point (5.6 m from the telescope). We find in the resultant image only the direct component within the FoV. The other stray-light components are absent in the image, presumably because there are no reflectors or precollimators at the quadrant boundary.   EA of the SXT-I at an off-axis angle of AE30 0 at 1.5 keV at several regions (see Fig. 12 for region IDs).