6. X-Ray Telescopes (XRT)

Suzaku 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 0.2-12keV, all accomplished in telescope units under 20kg each.

Four XRTs on-board Suzaku are used for the XIS (XRT-I), and the remaining XRT is for the XRS (XRT-S). XRT-S is no longer functional. The XRTs are arranged on the Extensible Optical Bench (EOB) on the spacecraft in the manner shown in Fig. 6.1. The external dimensions of the 4 XRT-Is are the same (see Table 6.1, which also includes a comparison with the ASCA telescopes).

Figure 6.1: Layout of the XRTs on the Suzaku spacecraft.

Table 6.1: Telescope dimensions and parameters of XRT-I.

	Suzaku XRT-I	ASCA
Number of telescopes	4	4
Focal length	4.75m	3.5m
Inner diameter	118mm	120mm
Outer diameter	399mm	345mm
Height	279mm	220mm
Mass per telescope	19.5kg	9.8kg
Number of nested shells	175	120
Reflectors per telescope	1400	960
Geometric area per telescope	873cm$^2$	558cm$^2$
Reflecting surface	gold	gold
Substrate material	aluminum	aluminum
Substrate thickness	155$\mu$m	127$\mu$m
Reflector slant height	101.6mm	101.6mm

The angular resolutions of the XRTs range from $1.\!'8$ to $2.\!'3$, expressed in terms of half-power diameter, which is the diameter within which half of the focused X-rays are enclosed. The angular resolution does not significantly depend on the energy of the incident X-rays in the energy range of Suzaku, 0.2-12keV. The effective areas are typically 440cm$^{\rm 2}$ at 1.5keV and 250cm$^{\rm 2}$ at 8keV. The focal length of the XRT-I is 4.75m. Actual focal lengths of the individual XRT quadrants deviate from the design values by a few cm. The optical axes of the quadrants of each XRT are aligned to within 2$^{\prime}$ from the mechanical axis. The field of view for the XRT-Is is about 17$^{\prime}$ at 1.5keV and 13$^{\prime}$ at 8keV (see also Table 3.1).

6.1 Basic XRT Components

The Suzaku 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 interfacing 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 (Fig. 6.2). 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-I consists of over 4112 mechanically separated parts. In total, nearly 7000 qualified reflectors were used and over 1 millioncm$^{\rm 2}$ of gold surface was coated.

Figure 6.2: A Suzaku X-ray telescope.

6.1.1 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 101.6mm in slant length, with radii extending approximately from 60mm at the inner part to 200mm 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 the face of each quadrant, separated by $\sim$6.4 .

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 Suzaku 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 an extrusion glass mandrel (``replication mandrel''), the surface of which 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 0.5nm rms roughness at mm or smaller spatial scales, which is sufficient for excellent reflectivity at incident angles less than the critical angle. The Suzaku XRTs are designed with on-axis reflection at less than the 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 softens. The aluminum foils acquire the shape of the properly shaped mandrel after cooling and release of pressure. In the Suzaku XRTs, the conical approximation of the Wolter-I type geometry is used. This approximation fundamentally limits the angular resolution achievable. More significantly, the combination of the shape error in the replication mandrels and the imperfection in the thermo-forming process (to about 4$\mu$m in the low frequency components of the shape error in the axial direction) limits the angular resolution to about 1$^{\prime}$.

6.1.2 Pre-Collimator

The pre-collimator, which blocks stray light that otherwise would enter the detector at a larger angle than intended, consists of concentrically nested aluminum foils, similar to those of the reflector substrates. They are shorter, 22mm in length, and thinner, 120$\mu$m 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 6.2.

Table 6.2: Design parameters for the pre-collimator.

	XRT-I
Number of collimators	4
Height	32mm
Blade substrate	aluminum
Blade thickness	120$\mu$m
Blade height	22mm
Height from blade top to reflector top	30mm
Number of nested shells	175
Blades per telescope	700
Mass per collimator	2.7kg

6.1.3 Thermal Shields

The Suzaku XRTs are designed to function in a thermal environment of 20 7.5 C. The reflectors, due to their composite nature and thus their mismatch in coefficients of thermal expansion, suffer from thermal distortion that degrades the angular resolution of the telescopes for temperatures outside this range. Thermal gradients also distort the telescope on 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 6.3: A thermal shield.

6.2 In-Flight Performance

In this section we describe the in-flight performance and calibration of the Suzaku XRTs. There are no data to verify the in-flight performance of the XRT-S, therefore we hereafter concentrate on the four XRT-I modules (XRT-I0 through I3) which focus incident X-rays on the XIS detectors. Several updates of the XRT-related calibration were made in July 2008.

6.2.1 Focal Positions

A point-like source, MCG$-$6-30-15, was observed at the XIS aim point during 2005 August 17-18. Fig. 6.4 shows the focal position of the XRT-Is, that the source is found at on the XISs, when the satellite points at it using the XIS aim point. The focal positions are located close to the detector center with a deviation of 0.3mm from each other. This implies that the fields of view of the XISs coincide to within $\sim0.\!'3$.

Figure 6.4: Focal positions on the XISs when the satellite points at MCG$-$6-30-15 using the XIS aim point.

6.2.2 Optical Axis

The maximum transmission of each telescope module is achieved when a target star is observed along the optical axis. The optical axes of the four XRT-I modules are, however, expected to scatter in an angular range of $\sim$1$'$. Accordingly, we have to define the axis to be used for real observations that provides a reasonable compromise among the four optical axes. We hereafter refer to this axis as the observation axis.

In order to determine the observation axis, we have first searched for the optical axis of each XRT-I module by observing the Crab nebula at various off-axis angles. The observations of the Crab nebula were carried out in 2005 and 2006. Hereafter all the off-axis angles are expressed in the detector coordinate system DETX/DETY (see ftp://heasarc.gsfc.nasa.gov/suzaku/doc/xis/suzakumemo-2006-39.pdf.

By fitting a model comprising of a Gaussian plus a constant to the count rate data as a function of the off-axis angle, we have determined the optical axis of each XRT-I module. The result is shown in Fig. 6.5.

Figure 6.5: Locations of the optical axis of each XRT-I module in the focal plane determined from the observations of the Crab nebula in 2005 August-September. This figure implies that the image on each XIS detector becomes brightest when a target star is placed at the position of the corresponding cross. The dotted circles are drawn every $30''$ in radius from the XIS-default position (see text).

Since the optical axes moderately scatter around the origin, we have decided to adopt it as the default observation axis for XIS-oriented observations. Hereafter we refer to this axis as the XIS-default orientation, or equivalently, the XIS-default position. The optical axis of the XRT-I0 shows the largest deviation of $\sim1.\!'3$ from the XIS-default position. Nevertheless, the efficiency of the XRT-I0 at the XIS-default position is more than 97%, even at 8-10keV, the highest energy band (see Fig. 6.10). The optical axis of the HXD PIN detector, on the other hand, deviates from this default by $\sim$5$'$ in the negative DETX direction (see for example, the instrument paper at ftp://heasarc.gsfc.nasa.gov/suzaku/doc/hxd/suzakumemo-2006-37.pdf). Because of this, the observation efficiency of the HXD PIN at the XIS-default orientation is reduced to $\sim$93% of the on-axis value. We thus provide another default pointing position, the HXD-default position, for HXD-oriented observations, at $(-3.\!'5, 0')$ in DETX/DETY coordinates. At the HXD-default position, the efficiency of the HXD PIN is nearly 100%, whereas that of the XIS is $\sim$88% on average.

6.2.3 Effective Area

In-flight calibration of the effective area has been carried out with version 2.1 processed data of the Crab nebula both at the XIS- and HXD-default positions. The observations were carried out in 2005 September 15-16. The data were taken in the normal mode with the 0.1s burst option in which the CCD is exposed during 0.1s out of the full-frame read-out time of 8s, in order to avoid the event pile-up and the telemetry saturation. The exposure time of 0.1s is, however, comparable to the frame transfer time of 0.025s. As a matter of fact, the Crab image is elongated in the frame-transfer direction due to so-called the out-of-time events, as shown in Fig. 6.6.

Figure 6.6: The source- and background-integration regions overlaid on the Crab images taken with XIS1 at the XIS-default position (left) and the HXD-default position (right) on 2005 September 15-16. The images are elongated in the frame-transfer direction due to the out-of-time events (see text). In order to cancel these events, the background regions with a size of 126 by 1024 pixels each are taken at the left and right ends of the chip for the XIS-default position, and a single region with a size of 252 by 1024 pixels is taken at the side far from the Crab image for the HXD-default position. The remaining source-integration region has a size of 768 by 1024 pixels, or $13.\!'3\times17.\!'8$. The background subtraction is carried out after area-size correction.

Accordingly, the background-integration regions with a size of 126 by 1024 pixels are taken at the left and right ends of the chip for the XIS-default position, perpendicularly to the frame-transfer direction, as shown in the left panel of Fig. 6.6. For the observation at the HXD-default position, the image center is shifted from the XIS-default position in the direction perpendicular to the frame-transfer direction for XIS0 and XIS3. Hence we can adopt the same background-integration regions as those of the XIS-default position for these two XIS modules. For XIS1 and XIS2, on the other hand, the image shift occurs in the frame-transfer direction, as shown in the right panel of Fig. 6.6. We thus take a single background-integration region with a size of 252 by 1024 pixels at the far side from the Crab image for the HXD-default position of these two detectors. As a result, the remaining source-integration region has a size of 768 by 1024 pixels, or $13.\!'3\times17.\!'8$ for all the cases, which is wide enough to collect all the photons from the Crab nebula.

After subtracting the background, taking into account the sizes of the regions, we have fitted the spectra taken with the four XIS modules with a model composed of a power law undergoing photoelectric absorption using xspec Version 11.2. For the photoelectric absorption, we have adopted the model phabs with the cosmic metal abundances of Anders & Grevesse (1989, Geochim. Cosmochim. Acta, 53, 197). First, we let all parameters vary independently for all the XIS modules. The results are summarized for the XIS/HXD nominal positions separately in Table 6.3 and are shown in Fig. 6.7.

Table 6.3: Best-fit parameters of the power law model fits to the Crab spectra taken on 2005 September 15-16.

Sensor ID	$N_{\rm H}$	Photon Index	Normalization	Flux	$\chi^2_\nu$ (d.o.f.)
XIS-default position
XIS0	0.311$\pm$0.015	2.077$\pm$0.017	9.38 $^{+0.24}_{-0.23}$	2.086	1.02 (89)
XIS1	0.294$\pm$0.014	2.085$\pm$0.017	9.73 $^{+0.23}_{-0.22}$	2.141	1.59 (89)
XIS2	0.282$\pm$0.015	2.065$\pm$0.017	9.29 $^{+0.23}_{-0.22}$	2.134	1.34 (89)
XIS3	0.304$\pm$0.015	2.082$\pm$0.017	9.33 $^{+0.24}_{-0.23}$	2.062	1.34 (89)
PIN	0.3 (fix)	2.101$\pm$0.008	11.41$\pm$0.26	2.464	0.74 (72)
HXD-default position
XIS0	0.304$\pm$0.018	2.079$\pm$0.021	9.13 $^{+0.27}_{-0.26}$	2.025	1.28 (89)
XIS1	0.295$\pm$0.016	2.111$\pm$0.021	9.59 $^{+0.27}_{-0.26}$	2.030	0.86 (89)
XIS2	0.282$\pm$0.016	2.070$\pm$0.019	9.54 $^{+0.26}_{-0.25}$	2.151	1.22 (89)
XIS3	0.301 $^{+0.017}_{-0.016}$	2.085$\pm$0.019	9.29$\pm$0.25	2.043	1.19 (89)
PIN	0.3 (fix)	2.090$\pm$0.009	10.93$\pm$0.27	2.400	0.82 (72)

Figure 6.7: Power-law fit to the Crab spectra of all four XIS modules taken at the XIS-default position. All the parameters are allowed to vary independently for each XIS module. The fit is carried out in the 1.0-10.0keV band, excluding the 1.5-2.0keV interval where large systematic uncertainties associated with the Si K-edge remain. This energy range is retrieved after the fit.

For the fit, we have adopted the ARFs and RMFs generated using CALDB 2008-07-09. These ARFs are made for a point source, whereas the Crab nebula is slightly extended ($\sim$2$'$). We thus have created ARFs by utilizing the ray-tracing simulator (Misaki et al. 2005, Appl. Opt., 44, 916) with a Chandra image as input, and have confirmed that the difference of the effective area between these two sets of ARFs is less than 1%. We have neglected the energy channels below 1keV, above 10keV, and in the 1.5-2.0keV band because of insufficient calibration related to uncertainties of the nature and amount of the contaminant on the OBF and to the Si edge structure (see ftp://heasarc.gsfc.nasa.gov/suzaku/doc/hxd/suzakumemo-2006-35.pdf). Data in the 1.5-2.0keV range are retrieved after the fit and shown in Fig. 6.7.

Toor & Seward (1974, AJ, 79, 995) compiled the results from a number of rocket and balloon measurements available at that time, and derived the photon index and the normalization of the power law of the Crab nebula to be $2.10\pm0.03$ and 9.7photons cm$^{-2}$ s$^{-1}$ keV$^{-1}$ at 1keV, respectively. Overlaying photoelectric absorption with $N_{\rm H} = 3\times10^{21}$cm$^{-2}$, we obtain the flux to be $2.1\times 10^{-8}$erg cm$^{-2}$ s$^{-1}$ in the 2-10keV band. The best-fit parameters of all the XIS modules at the XIS- and HXD-default positions are close to these standard values.

Since the best-fit parameters of the four XIS modules are close to the standard values, we have attempted to constrain the photon index to be the same for all the detectors. The best-fit parameters are summarized in Table 6.4.

Table 6.4: Best-fit parameters of the contemporaneous power-law fits to the Crab spectra taken in 2005 September 15-16.

Sensor ID	$N_{\rm H}$	Photon Index	Normalization	Flux	$\chi^2_\nu$ (d.o.f.)
XIS-default position
XIS0	0.321$\pm$0.009	2.090$\pm$0.006	9.55$\pm$0.10	2.080	1.24 (432)
XIS1	0.298$\pm$0.008		9.79$\pm$0.10	2.14
XIS2	0.302$\pm$0.008		9.72$\pm$0.10	2.13
XIS3	0.311$\pm$0.009		9.43$\pm$0.10	2.06
PIN	0.3 (fix)		11.06$\pm$0.11	2.42
HXD-default position
XIS0	0.307$\pm$0.011	2.086$\pm$0.007	9.19 $^{+0.12}_{-0.11}$	2.019	1.13 (432)
XIS1	0.277$\pm$0.009		9.28$\pm$0.11	2.11
XIS2	0.298$\pm$0.010		9.74$\pm$0.11	2.21
XIS3	0.300$\pm$0.010		9.28$\pm$0.15	2.11
PIN	0.3 (fix)		10.80$\pm$0.01	2.45

The hydrogen column density (0.28-0.32) $\times 10^{22}$cm$^{-2}$ and the photon index 2.09$\pm$0.01 are consistent with the standard values.

6.2.4 Vignetting

The vignetting curves calculated by the ray-tracing simulator are compared with the observed intensities of the Crab nebula at various off-axis angles in Figs. 6.8-6.10.

Figure 6.8: Count rates of the Crab pointings offset in DETX (left) and DETY (right) in the 2-10keV band. Red and green symbols correspond to the data during 2005 and 2006, respectively. The solid line corresponds to the output of the ray-tracing simulator xissim. The bottom panels show the ratios of the data to the simulator output.

Figure 6.9: The same as Fig.6.8 but in the 3-6keV band.

Figure 6.10: The same as Fig.6.8 but in the 8-10keV band.

We have utilized the data of the Crab nebula taken during 2005 August and 2006 August. In the figures, we have drawn the vignetting curves for the energy bands 2-10keV, 3-6keV and 8-10keV. To obtain this, we first assume the spectral parameters of the Crab nebula to be a power law with $N_{\rm H}=0.33\times 10^{22}$cm$^{-2}$, photon index$=$2.09, and normalization$=$9.845photons cm$^{-2}$ s$^{-1}$ keV$^{-1}$ at 1keV. These values are the averages of the four detectors at the XIS-default position (Table 6.4). We then calculate the count rate of the Crab nebula on the entire CCD field of view in $0.\!'5$ steps in both the DETX and DETY directions using the ray-tracing simulator. Note that the abrupt drop of the model curves at $\sim$8$'$ is due to the source approaching the detector edge. On the other hand, the data points provide the real count rates in the corresponding energy bands within an aperture of $13.\!'3$ by $17.\!'8$. Note that the aperture adopted for the observed data can collect more than 99% of the photons from the Crab nebula, and hence the difference of the integration regions between the simulation and the observation does not matter. Finally, we re-normalize both the simulated curves and the data so that the count rate of the simulated curves at the origin becomes equal to unity.

These figures roughly show that the effective area is calibrated within $\sim$5% over the XIS field of view, except for the 8-10keV band of XIS1. The excess of these XIS1 data points at the XIS-default position has already been seen in Fig. 6.7 (see also Table 6.3).

6.2.5 Angular Resolution

As shown in Serlemitsos et al. (2007), verification of the imaging capability of the XRTs has been made with the data of SS Cyg in quiescence taken on 2005 November 2 01:02UT-23:39UT. The total exposure time was 41.3ks. SS Cyg is selected for this purpose because it is a point source and moderately bright (3.6, 5.9, 3.7, and 3.5counts s$^{-1}$ for XIS0 through XIS3), and hence, it is not necessary to care about pile-up even at the image core. In Fig. 6.11, we give the images of all the XRT-I modules thus obtained. The HPD is obtained to be $1.\!'8$, $2.\!'3$, $2.\!'0$, and $2.\!'0$ for XRT-I0, 1, 2, and 3, respectively.

In Fig. 6.11, we also show corresponding images produced by the updated ``new'' simulator xissim (version 2008-04-05). The simulator has been tuned for each quadrant. Therefore, the simulated images look different from quadrant to quadrant. More local or spiky structures seen in the observed images, however, are not reproduced.

In Fig. 6.12, we show Point Spread Functions (PSFs) using the data shown in Fig. 6.11 before smoothing. Note that the core shape within $0.\!'2$ is not tuned at all. The core broadening is mainly due to the attitude error of the satellite control (Uchiyama et al. 2007). In Fig. 6.13, we show encircled energy functions (EEFs). The reproducibility of the EEF is important when extracting spectra from a circular region with a given radius. In the new simulator, the EEF of the simulations coincides with that of the observed data to within 4% for radii from 1$'$ to 6$'$.

Figure 6.11: Images of the four XRT-I modules in the focal plane: SS Cyg (left) and simulation (right). All the images are binned to 2$\times$2 pixels and then smoothed with a Gaussian with a sigma of 3 pixels, where the pixel size is 24$\mu$m. The Fe55 events were removed from the SS Cyg image.

XIS0

XIS1

XIS2

XIS3

Figure 6.12: PSF of the four XRT-I images. The lower panels show the ratio between the observed and simulated data.

Figure 6.13: EEF of the four XRT-I images. The EEF is normalized to unity at the edge of the CCD chip (a square of $17'\!.8$ on the side). The lower panels show the ratio between the observed and simulated data.

6.2.6 Stray Light

Studies of the stray light were carried out with Crab nebula off-axis pointings during 2005 August 22 - September 16 for a range of off-axis angles. An example of a stray light image is shown in the right panel of Fig. 6.14.

Figure 6.14: Focal plane images formed by stray light. The left and middle panels show simulated images of a monochromatic point-like source of 4.51keV located at $(-20', 0')$ in (DETX, DETY) without and with the pre-collimator, respectively. The radial dark lanes are the shadows of the alignment bars. The right panel is the in-flight stray image of the Crab nebula in the 2.5-5.5keV energy band located at the same off-axis angle. The unit of the color scale of this panel is counts per 16 pixels over the entire exposure time of 8428.8s. The count rate from the whole image is 0.78$\pm$0.01counts s$^{-1}$ including background. Note that the intensity of the Crab nebula measured with XIS3 at the XIS-default position is 458$\pm$3counts s$^{-1}$ in the same 2.5-5.5keV band. All images are binned to 2$\times$2 pixels and then smoothed with a Gaussian with a sigma of 2 pixels, where the pixel size is 24$\mu$m.

This image is taken with the XIS3 in the 2.5-5.5keV band with the Crab nebula offset at $(-20', 0')$ in (DETX, DETY). The left and central panels show simulated stray light images without and with the pre-collimator, respectively, of a monochromatic point source of 4.5keV being located at the same off-axis angle. The ghost image seen in the left half of the field of view is due to ``secondary reflection''. Although ``secondary reflection'' cannot completely be diminished at the off-axis angle of $20'$, the center of the field of view is nearly free of stray light. The semi-circular bright region in the middle panel, starting at (DETX, DETY)$=$ $(-8'\!'9, +6'\!'5)$, running through $\sim$($0', 0'$), where the image becomes fainter, and ending up at $(-8'.9, -6'.5)$, originates from the innermost secondary reflector, because the space between the innermost reflector and the inner wall of the telescope housing is much larger than the reflector-reflector separation. This semi-circular bright region is only marginally visible in the real Crab nebula image in the right panel. Another remarkable difference between the simulation and the real observation is the location of the brightest area; in the simulation, the left end of the image (DETX $^<_{\sim} -7'.5$, $\vert\mbox{DETY}\vert ^<_{\sim} 3'$) is relatively dark whereas the corresponding part is brightest in the Crab nebula image. These differences originate from relative alignments among the primary and secondary reflectors, and the blades of the pre-collimator, which are to be calibrated by referring to the data of the stray light observations in the near future.

Figure 6.15: Mosaic images of offset observations of the Crab taken in 2005.

XIS0

XIS1

XIS3

Figure 6.16: Same as figure 6.15, but taken in 2010.

XIS0

XIS1

XIS3

Overall, in-flight stray light observations of the Crab were carried out with off-axis angles of $20'$ (4 pointings), $50'$ (4 pointing) and $120'$ (4 pointing) in 2005 autumn. Follow-up observations covering more offset angles of $50'$ (4 pointing) , $65'$ (8 pointing) were made in 2010 autumn. Examples of mozaic images made with the offset observations in SKY coordinate are shown in Figures 6.15 and 6.16. The stray images differ from offset to offset and from azimuth to azimuth in the XRT coordinate. It also strongly depends on energy.

Figure 6.17 shows the measured and simulated angular responses of the XRT-I at 1.5 and 4.5keV up to 2$^\circ$. The effective area is normalized to 1 at the on-axis position. The integration area corresponds to the detector size of the XIS ( $17.\!'8\times17.\!'8$). The plots are necessary to plan observations of diffuse sources or faint emissions near bright sources, such as outskirts of cluster of galaxies, diffuse objects in the Galactic plane, SN 1987A, etc.. The four solid lines in the plots correspond to raytracing simulations for the different detectors, while the crosses are the normalized effective area using the Crab pointings. For example, the effective area of the stray light at 1.5keV is $\sim$10$^{-3}$ at off-axis angles smaller than 70$'$ and $<10^{-3}$ at off-axis angles larger than 70$'$. The measured stray light flux is in agreement with that of the simulations to within an order of magnitude. The solution of the solid lines is incorporated into the xissim and the xissimarfgen tools using CALDB 2008-06-02.

Figure 6.17: Angular responses of the XRT-I at 1.5 (left) and 4.5keV (right) up to 2$^\circ$. The effective area is normalized to 1 at the on-axis position. The integration area is corresponding to the detector size of the XISs ( $17.\!'8\times17.\!'8$). The four solid lines in the plots correspond to different detector IDs. The crosses are the normalized effective area using the Crab pointings.

For feasibility studies of XIS data analyses of faint objects near bright sources, proposers are encouraged to simulate observations using xissim in order to determine whether the stray light flux might dominate that of the faint object or not. Proposers who do observe a target heavily suffering from stray light contamination need to handle the data with special care regarding calibration errors. Faint objects in the Galactic center and plane often suffer from stray light contamination from bright X-ray stars, and the flux of the outskirts of galaxy clusters, widely extended over the detector field of view, is sometimes dominated by stray light from the bright core.

Observers can avoid contamination from stray light if they choose the roll and offset angles properly. Fig. 6.18 shows a schematic diagram of the stray light patterns for a stray light source at an azimuth angle of $\alpha$ and an offset angle of $R$. The square in Fig. 6.18 corresponds to the XIS field of view. The nominal position is located within 1 arcmin from the optical axis of the XIS system within a couple of arcmins. The XIS field of view near to and far from a stray light source is contaminated by stray light of the ``Secondary-reflection component'' and the ``Backside component'', respectively (Mori et al. 2005, PASJ 57, 245). On the other hand the near and far sides are free from the ``Backside component'' and the ``Secondary-reflection component'', respectively. There is another stray light free region corresponding to the ``Quadrant Boundary'' with a cone angle of 12.8 deg at an azimuth angle of 45 deg with 90 deg pitch. Observers can thus choose between three kinds of the ``stray light free'' regions. Fig. 6.19 shows pointing positions targeting these three kinds of stray light free regions, marked in white: the ``Quadrant Boundary'' region (top), the `` Secondary-reflection component free'' region (middle) and the ``Backside component free'' region (bottom).

1. Quadrant Boundary:
   If an azimuth angle of 45, 135, 225, or 315 deg is possible, the target at the XIS nominal position will fall into the stray light free region of the Quadrant Boundary. The integrated radius $r$ which is free from stray light can be expected to be $\sim6.8 \frac{R}{1{\rm deg}}$ arcmin. The radius has an uncertainty of a couple of arcmins due to the misalignments between the optical axis and the nominal position.

2. Secondary-reflection component free region:
   The Backside component is important in the energy band below 1.5keV. It arises from scattering at the aluminum surface of the backside of the primary reflector. Therefore, if the stray light source is heavily absorbed below 1.5keV or the interesting energy band of the target is limited to above 1.5keV, it is recommended to locate the target in the secondary-reflection component free region. The recommended pointing position offset in this case is:

   $\Delta$ DET-X $= - (r+2)$ $\sin\alpha$ [arcmin]
   $\Delta$ DET-Y $= - (r+2)$ $\cos\alpha$ [arcmin].

   Note that the offset direction is towards the near side of the stray light source. The margin of 2 arcmin corresponds to the misalignment between the optical axis and the nominal position. The Backside component appears within an offset angle $R$ of up to $\sim1.3 (\frac{E}{1.5 {\rm keV}})^{-1} {\rm deg}$ ($E<$1.5keV). If the stray light source is located further away than the critical offset angle, observers can choose the Secondary-reflection component free region, as well.

3. Backside component free region:
   The secondary-reflection component focusses at the middle of the detector only for offset angles of 40-75 arcmin at any energy. Therefore, if the stray source is located within 40 arcmin or further away than 75 arcmin, it is recommended to located the target in the backside component free region. The recommended pointing position offset in this case is:

   $\Delta$ DET-X $= + (r+2)$ $\sin\alpha$ [arcmin]
   $\Delta$ DET-Y $= + (r+2)$ $\cos\alpha$ [arcmin].

   The offset direction is towards the far side of the stray light source.

If observers cannot choose any of the three stray light free regions, the possibility of contamination through stray light exists.

Figure 6.18: Stray patterns for a stray source at an azimuth angle of $\alpha$ and an offset angle of $R$.

Figure 6.19: Pointing positions targeting the three kinds of stray light free regions: the ``Quadrant Boundary'' region (top), the ``Secondary-reflection component free'' region (middle) and the ``Backside component free'' region (bottom).