Soft X-ray Imager aboard Hitomi (ASTRO-H)

The Soft X-ray Imager (SXI) is an imaging spectrometer using charge-coupled devices (CCDs) aboard the Hitomi X-ray observatory. The SXI sensor has four CCDs with an imaging area size of $31~{\rm mm} \times 31~{\rm mm}$ arranged in a $2 \times 2$ array. Combined with the X-ray mirror, the Soft X-ray Telescope, the SXI detects X-rays between $0.4~{\rm keV}$ and $12~{\rm keV}$ and covers a $38^{\prime} \times 38^{\prime}$ field-of-view. The CCDs are P-channel fully-depleted, back-illumination type with a depletion layer thickness of $200~\mu{\rm m}$. Low operation temperature down to $-120~^\circ{\rm C}$ as well as charge injection is employed to reduce the charge transfer inefficiency of the CCDs. The functionality and performance of the SXI are verified in on-ground tests. The energy resolution measured is $161$-$170~{\rm eV}$ in full width at half maximum for $5.9~{\rm keV}$ X-rays. In the tests, we found that the CTI of some regions are significantly higher. A method is developed to properly treat the position-dependent CTI. Another problem we found is pinholes in the Al coating on the incident surface of the CCDs for optical light blocking. The Al thickness of the contamination blocking filter is increased in order to sufficiently block optical light.

microcalorimeter array of the SXS covers only a small FoV of 3 ′ × 3 ′ and the imaging capability is limited. The SXI, with its large FoV and small pixels, plays a complimentary role.
We developed the SXI based on our experiences through the development of the X-ray CCD cameras for astronomical use, the SIS on ASCA, 12 the XIS on Suzaku, 13 and the SSC on MAXI. 14,15 One of the major improvements of the SXI from those CCD cameras is a thicker (200 µm) depletion layer. Another improvement is lower (−120 • C) operation temperature to mitigate radiation damage effects. It is known that operation temperature of −120 • C or lower results in lower charge transfer inefficiency (CTI), 16 which was actually demonstrated by Chandra ACIS 17 and XMM-Newtion EPIC-MOS. 18 To further decrease CTI, we employ a charge injection technique similar to that developed for Suzaku XIS. 19 In this paper, we describe the design and data processing of the SXI. Data taken during onground tests are shown to present its pre-launch performance. We report on in-orbit performance of the SXI in a separate paper. 20 Figure 1 is a block diagram of the SXI system. The SXI consists of the sensor part (SXI-S) which includes CCDs, analog electronics (the Video Boards and SXI-S-FE) and mechanical coolers (SXI-S-1ST), the pixel processing electronics (SXI-PE), the digital electronics (SXI-DE), and the cooler driver (SXI-CD). The spacecraft has a backup digital electronics box, X-MDE (eXtra Mission Digital Electronics). X-MDE can act as any of the digital electronics for the scientific instruments aboard the spacecraft, including SXI-DE, in case of a failure. The SXI-S is placed at the focus of SXT-I on the base panel of the spacecraft whereas the other components are installed on the side panels. The power for the SXI system is supplied by the Power Control Unit (PCU) of the spacecraft whose output voltage ranges from 32 V to 52 V. The voltage is then regulated inside SXI-PE, DE and CD. The whole SXI system consumes a power of ∼ 85 W. The power lines to SXI-PE, DE and CD consume about 25 W, 10 W, and 50 W, respectively. The SXI system communicates with the spacecraft bus based on the SpaceWire protocol. 21 SXI-PE, DE and CD are connected with spacecraft's SpaceWire network via routers.

Camera Body
We show external views and a photograph of SXI-S in Figs. 2 and 3, respectively. The camera body (SXI-S-BDY), made of Al alloy, consists of a hood (SXI-S-HOOD), a bonnet (SXI-S-BNT), a camera housing (SXI-S-HSG), and a base plate (SXI-S-BP). Inside the hood, there are five baffles to block stray light X-rays. SXI-S-BP is mounted 10 cm above the base panel of the spacecraft with seven shafts made of Ti alloy. The shafts are designed so that the thermal expansion or contraction of SXI-S does not distort the base panel of the spacecraft, which is critical for the alignment. Also, the design helps to reduce heat exchange between SXI-S and the spacecraft via conduction. The whole camera body is covered by multi-layer insulators to shut out heat exchange with spacecraft via radiation. Heat generated in SXI-S is transferred to radiators by two heat pipes attached to SXI-S-BP.
The camera body works as a radiation shield for the CCDs. Radiation damage results in increase of dark current and of CTI of the CCDs. In the case of a satellite in a low-earth orbit such as Hitomi, most of the radiation damage is due to protons trapped in the South Atlantic Anomaly (SAA). In order to stop SAA protons, we need to have a shield of 10 g cm −2 corresponding to an Al thickness of 37 mm. Although a thicker body works better for shielding CCDs against SAA protons and also against unfocused X-rays, it results in higher instrumental backgrounds due to secondary particles. We did an optimization study based on Monte Carlo simulations 22,23 and chose to have a shield thickness of 35 mm for most parts of the camera body. The surface of the inner side of the camera body is coated with Au over Ni plating to block Al-K fluorescence lines induced by cosmic rays. The Au layer has a thickness of 2 µm to sufficiently absorb fluorescence lines from the underlying Ni layer.
Four CCDs are installed on the cold plate made of Au-coated AlN inside the camera body. The cold plate is supported by six posts made of Torlon R polyamide-imide to achieve good thermal insulation from the camera body. Two heaters are glued to the cold plate for temperature control. The Video Boards, which digitize signals output by the CCDs, are also installed inside the body for better noise performance. In order to prevent contamination of the X-ray incident surface of the CCDs by outgas from the Video Boards, the space inside the camera body is physically divided into two: the upper room for the CCDs and the lower room for the Video Boards. Each room is directly connected to outside the spacecraft through vent pipes (SXI-S-VP).

CCD
The sensors used in the SXI are fully-depleted, back-illuminated CCDs named Pch-NeXT4 that we developed with Hamamatsu Photonics K.K. [24][25][26][27][28] We summarize the specifications of Pch-NeXT4 in Tab. 1 and present its schematic view in Fig. 4. Pch-NeXT4 is the first P-channel CCD utilized for X-ray astronomy. The development was done also in collaboration with the National Astronomical Observatory of Japan, which was developing CCDs with similar specifications for the Hyper Suprime-Cam (HSC) of the Subaru Telescope. 29 We applied a different treatment to the incident surface of the device from that used for the HSC CCDs to achieve better responses to soft X-rays. 28 Quantum efficiency (QE) of the CCD is plotted as a function of incident X-ray energy in Fig. 5. The n-type substrate with high resistivity enables a thick (200 µm) depletion layer, resulting in high QE for the hard X-ray band whereas the back-illumination (BI) configuration enhances QE in the soft X-ray band. The BI CCD is also advantageous for high resistance to micrometeoroid damage. 30 The imaging area of Pch-NeXT4 has a 24 µm × 24 µm pixel size and 1280 × 1280 pixels, which yields an imaging area size of 30.72 mm × 30.72 mm. Since we nominally apply onchip 2 × 2 binning, the effective pixel size and pixel format are 48 µm × 48 µm and 640 × 640, respectively. In what follows, we refer to the 24 µm×24 µm and 48 µm×48 µm pixels as physical and logical pixels, respectively. The Suzaku XIS team demonstrated that the CTI increased by radiation damage can be restored by using a charge injection technique. 19 Pch-NeXT4 also has charge-injection capability. 16 We can inject artificial charges from the gates attached to the top of each column. We inject charges into every 160th physical row in each frame. The CTI could be restored more if we inject charges to more rows. Charge injection rows, however, cannot be used in observations. The frequency of charge injection rows was determined based on the balance between the CTI restoration and the loss of the effective rows. The amount of injected charges is controlled so that signals from the charge injection rows are saturated but charge leakage to leading and trailing rows is negligible. In order to block optical light, the incident surface of the CCD is coated with the Optical Blocking Layer (OBL), 31 a 100-nm thick Al layer over a 20-nm thick SiO 2 layer. The optical light transmission of the OBL is in the order of 10 −5 . Each CCD has four readout nodes (Fig. 4). We read out a half of the imaging area (a segment) from one of the nodes. We nominally read out signals from the nodes A and C and use the nodes B and D as a redundant option.
We show a photograph of the actual flight CCDs in Fig. 6 and a schematic layout of the CCD array in Fig. 7. The Pch-NeXT4 chips are arranged in a 2 × 2 array. The typical spacing between the chips is ∼ 700 µm according to the measurement described in §6.1. Since the CCD packages are installed directly on the flat cold plate, they are almost co-planer and their tilts are negligible. The aim point of the SXT is offset from the array center to prevent targets from falling into the gap between the CCDs. Combined with the SXT, the imaging areas correspond to a 38 ′ × 38 ′ FoV. The frame-store regions are covered with 3-mm thick Al shields coated with Au to block focused X-rays. The CCD signals are carried to the Video Boards through flexible printed circuits. For gain monitoring, two 55 Fe sources are installed into the bonnet and illuminate a corner of each CCD.

Video Board
The primary function of the Video Board is analog-to-digital conversion of CCD signals by ∆Σ modulation. The main components of the Video Board are four analog ASICs, MND02, 32      a field-programmable gate array (FPGA), RTAX2000 by Microsemi. The MND02 chip has four channels and each channel contains a preamplifier, a 5-bit digital-to-analog converter (DAC), and two ∆Σ modulators. The gain of the preamplifier is adjustable between 0.6 and 10 in nine steps. Pulse height is obtained by subtracting a floating level voltage from a signal level voltage of a CCD signal. Even with no signal charges, the voltage difference becomes non-zero. The DAC is for canceling out this offset. In this way, we can make most of the input signal range of the ∆Σ modulators which convert an analog signal to a digital 155-bit stream. The ASIC has two modulators per channel, which are operated alternately to achieve a high pixel rate. The FPGA sends control signals to MND02, and converts the bit stream into 12-bit pulse height data by a decimation filter. The digitized frame data are then sent to SXI-PE for further processing. One board processes signals from two CCDs and thus the SXI has two boards in the camera body. Each of the readout nodes of the CCD is fed to a pair of channels of different ASICs, which ensures redundancy. Taking advantage of the connection, we nominally average the two outputs to improve the readout noise as we demonstrated with prototype hardware. 34 This method is effective since the noise generated in the ASICs is not negligible.

Front-end Electronics (FE)
SXI-S-FE is composed of four CCD Driver Boards, each of which is connected to one of the four CCDs, and is mounted on SXI-S-BP next to the camera housing (Fig. 2). The driver boards generate analog clocks and biases for the CCDs and supply them to the CCDs via the Video Boards. The back-bias voltage for the CCD substrate, for which we typically apply 35 V, is also generated in SXI-S-FE using a Cockroft-Walton charge pump voltage multiplier. The high and low level voltages of the clocks are determined by outputs from on-board DACs and the two levels are switched according to digital timing signals sent from SXI-PE. The voltage levels for the bias lines are also controlled by DACs. SXI-S-FE measures voltage levels of the clock and bias lines and outputs them to SXI-PE as housekeeping (HK) data after analog-to-digital conversion and multiplexing. Two of the four Driver Boards also take responsibility as temperature control electronics (TCE) for the CCDs (Fig. 1). Each of them measures temperatures of two CCDs and outputs current to one of the heaters attached to the cold plate.

Cooling System
Single-stage Stirling coolers, SXI-S-1ST, are used to cool the CCDs to the operation temperature. The SXI has two Stirling coolers. Only one of them is operated in orbit, and the other is for standby redundancy. The cooler consists of a cold head, a compressor, and a capillary tube to connect them. The cold heads and compressors are installed into SXI-S-HSG and on SXI-S-BP, respectively. Active balancers are inside the cold heads to reduce vibration induced along the drive axis. The cold finger of each cooler is connected to the cold plate with a Cu flexure structure. This design ensures higher thermal conductivity while less vibration is transferred from the cold fingers to the cold plate and the difference of thermal expansion can be absorbed. SXI-S-1ST is controlled and monitored independently of the camera by SXI-CD. In nominal operations, we supply a constant power to SXI-S-1ST and stabilize the CCD temperature at a targeted temperature by changing the heater current with a propotional-integral-derivative (PID) controller implemented in the on-board software of SXI-DE ( §5.2).

Contamination Blocking Filter (CBF)
The low-energy QE of the XIS aboard the Suzaku satellite decreased after the launch because of the accumulation of contaminating material on the optical blocking filter. 13 Since the filter was placed close to the cold CCD surface, the filter was colder than the other parts of the spacecraft and thus adsorbed the contaminant. This experience led us to the design of the SXI in which the CBF 35 is placed on top of the hood. The CBF is a 200-nm thick polyimide film with a stainless steel mesh support. Al is vapor-deposited on both sides of the film. The temperature of the CBF is kept at ∼ 25 • C by heaters attached to SXI-S-HOOD.

SXI Pixel Process Electronics (SXI-PE)
SXI-PE consists of a Power Supply Unit (PSU) and two Mission I/O (MIO) boards (Fig. 1). The PSU generates DC voltages for SXI-S and the MIO boards from the spacecraft's bus power line. The MIO boards are developed to be commonly used for all the scientific instruments aboard Hitomi. Each of the MIO boards has two FPGAs (RTAX2000) and an SDRAM. One of the FPGAs is called SpaceWire FPGA, which provides an interface for SpaceWire communication and also an interface for the SDRAM. A user-specific logic is implemented on the other FPGA, UserFPGA.
One MIO board takes care of two CCDs. One of the MIO boards can provide clock signals to the other board to avoid possible interferences. The functions of SXI-PE are CCD clock pattern generation, CCD data processing, autonomous HK data collection from SXI-S-FE, and control of the DACs of SXI-S-FE in response to directions by SXI-DE.

CCD Clock Pattern Generation
SXI-PE provides SXI-S-FE with digital timing signals, based on which analog CCD clocks are generated. A microcode program loaded to SXI-PE determines the clock pattern and a four-bit pixel code for each pixel read out. The pixel code specifies the attributes of the pixel, for example, if it is an imaging area pixel or is an under/over-clock pixel. The architecture of the microcode program is similar to that used for Suzaku XIS. The timing signals are synchronized with a 10 MHz clock and thus we can assign the logical levels of each signal in every 0.1 µs. In all the clocking modes described below, the vertical transfer time is 28.8 µs per physical pixel row for the transfer from the imaging area to the frame-store region (hereafter fast transfer), and is 5.24 ms per logical pixel row for the transfer in the frame-store region (hereafter slow transfer). The readout time is 14.4 µs per logical pixel. Listed in Tab. 2 are the clocking modes we planned to support for in-orbit observations. When observing bright sources, we can reduce the probability of pile-up by a window option, a burst option, and their combination. Schematic drawings of the window option and burst option are presented in Figs. 8 and 9. In the window option, a limited number of rows of the imaging area are read out, which results in shorter and frequent readout. We read out 80 out of 640 logical pixel rows with the 1/ 8 window option. Although the rows outside the specified window are also transferred to the frame-store region, they are binned on-chip into a single row in the output serial register and then this row is flushed and ignored. The burst option is for partial readout in time, and only a small fraction of the frame cycle is used as the effective exposure time. In the burst option with an exposure time of t exp , the CCD is first exposed for a duration of (4 s − t exp ). The CCD imaging area is cleared of charges accumulated during this period by transferring them to the bottom row of the imaging area. Then, an effective exposure of t exp is started. After this exposure, accumulated charges are transferred to the frame-store region, and are read out in the same manner as in the clocking modes without the burst option. We support two burst options with t exp = 1.9396 s and t exp = 0.0606 s.

CCD Data Processing
Another major role of SXI-PE is processing CCD signals. SXI-PE receives raw, digitized data from the Video Boards of SXI-S. According to settings written in registers, outputs from designated channels of the ASICs are selected and averages of signals from the same CCD readout nodes are calculated. Then, the pixel codes are appended to the data from each pixel by referring to information written in the microcode. Dark level is estimated and subtracted from the raw frame data before further data processing. Dark levels are different for each pixel and can be also time-variable. SXI-PE, therefore, calculates dark levels for each individual pixel and updates them for every frame. If dark-subtracted pulse height (hereafter PH) is between the lower and upper thresholds for dark update, the dark level (Dark) is replaced by Dark + PH/h, where h is a parameter called "History Parameter" whose default and nominally used value is 8. This parameter determines how promptly the dark level estimation reacts to the changes of PH. This algorithm, which was comprehensively verified with prototype hardware, allows us not only to improve accuracy of the dark estimation as the frame cycle continues but also to follow gradual changes of the dark level with time. Pixels are flagged as hot pixels if their dark levels are higher than a preset threshold. The dark calculation and the hot pixel list can be initialized by sending a command. We planned to do so at the beginning of each observation.
After the dark level subtraction, the UserFPGA program searches for X-ray event candidates in the one-dimensional pixel data stream. If PH of a pixel is between the lower and upper thresholds for event detection and the PH is higher than that of the adjacent left pixel and higher than or equal to that of the adjacent right pixel, the pixel is regarded as the event candidate center pixel. The event candidate list as well as the frame data is then sent to SXI-DE, where more detailed data processing is performed. Although only a crude extraction of event candidates is possible with this simple logic implemented in SXI-PE, this makes the data processing later in SXI-DE efficient.

SXI Digital Electronics (SXI-DE)
SXI-DE has a CPU board called SpaceCard and a PSU to supply DC power to it (Fig. 1). Similarly to the MIO boards, the SpaceCard boards are commonly used for all the scientific instruments aboard the spacecraft. SXI-DE interfaces the SXI system with the spacecraft's bus system, receiving commands from the Satellite Management Unit (SMU) and sending telemetry such as event data and HK data to the Data Recorder (DR) and the SMU. Also, SXI-DE performs further CCD data processing and monitor/control the whole SXI system except for the Stirling coolers, SXI-S-1ST, which is under the control of SXI-CD. In what follows, we will describe the CCD data processing and how SXI-DE controls the current through the heaters attached to the cold plate for CCD temperature control.

CCD Data Processing
Firstly, the average PH of horizontal overclocked (HOC) pixels of the row is subtracted from PH from imaging area pixels so that we can remove the effect of short-time variability which cannot be followed by the dark level calculation. Then, three kinds of filters, area discrimination, surround filtering, and 3 × 3 local maximum filtering, are applied to further limit the amount of data. The area discrimination restricts imaging area regions for X-ray event search. The regions are defined as rectangles in the imaging area, and pixels either inside or outside the regions are excluded from the event identification process. For example, a very bright source in the FoV can be masked to avoid telemetry saturation. The surrounding filtering is for discarding charged particle background events in which generated charges are shared by a number of pixels along the track of the particles. This filter examines PH from the eight pixels surrounding the event center pixel. If the number of pixels whose PH exceeds a threshold is more than a preset number, the event is removed from the event list. The threshold and the number of pixels can be set by a command. The 3 × 3 local maximum filtering extracts events whose center pixel in the 3 × 3 pixel island has PH larger than the other eight pixels. This filtering is necessary since the SXI-PE data processing only compares PH of 3 × 1 pixels in the same row, and thus the same event may be double counted in adjacent rows.
Event candidates which passed through all the filters are sent to the DR and then to ground stations as event data. The data include information on the location of the event and PH of 5 × 5 pixels. Here data from inner 3 × 3 pixels and data from outer 16 pixels of the 5 × 5 pixel island are divided into two separate packets. Since the latter packets have lower priority, they may not be sent to the ground. Therefore, 3 × 3 data include hit patterns of the outer 16 pixels indicating which pixels have PH larger than a threshold. Both 3 × 3 and 5 × 5 event data are compressed in SXI-DE to reduce the telemetry size.

Heater Current Control
To keep the CCD temperature constant, the SXI-DE software controls the heater attached to the cold plate on the basis of the PID algorithm. With a frequency of 1 Hz, the CCD temperature is sampled and the heater current is adjusted to keep the temperature stabilized at a targeted value. If we define P i and ∆T i as the power dissipated in the heater and the difference between the targeted temperature and current temperature after the i-th iteration, respectively, and f as the frequency of the iteration, 1 Hz, the PID algorithm yields the equation where K p , K i , and K d are constants called the proportional gain, the integral gain, and the derivative gain, respectively. In on-ground tests, we found an interference between the heater control line and CCD readout electronics. When the heater current was decreased or increased as rapid as 0.05 A s −1 , anomalies of PH appeared as show in Fig. 10. We tuned the parameters to suppress the changing rate of the heater current so that we can avoid the interference. In Fig. 11, we plot the CCD temperature and heater current as a function of time taken in an on-ground test after the parameter optimization.
6 On-ground Data Processing and Pre-launch Performance

Coordinate Assignment
A sky coordinate is assigned to each photon based on information on attitude of the spacecraft. In this process, we must accurately know the relative rotation angle and position of each CCD on the cold plate. We obtained the information by analyzing a shadow image of the mesh shown in Fig. 12. The mesh is made of stainless steel and has a thickness of 0.1 mm. We placed the mesh 7 mm above the surface of the CCDs and illuminated them with Mn-Kα and Kβ X-rays from an 55 Fe source placed 202 mm above the CCDs. In the analysis described below, we use two coordinate systems, the ACT and MESH coordinates, whose definitions are shown in Figs. 7 and 12, respectively. We first measured the rotation angle (θ) of the ACT coordinate of each CCD with respect to the Mesh coordinate. We projected the shadow image along the MESH-X axis with  Fig. 13 is the resultant shadow image of the mesh in the DET coordinate (Fig. 7), which demonstrates the imaging capability of the SXI.

Uniformity of Quantum Efficiency
Analyzing the the X-ray shadow image in Fig. 13, we examined the uniformity of the quantum efficiency. In Fig. 14 (left), we plot X-ray counts detected in regions corresponding to each of the 1.4 mm × 1.4 mm holes of the mesh (Fig. 12) against distance from the 55 Fe source (R), which can be regarded as a point source. The data points follow well a ∝ R −2 relation. We show the distribution of the residuals from the ∝ R −2 curve in Fig. 14 (right). The distribution can be fit by a Gaussian with σ = 0.038. Considering the fact that the data points in Fig. 14 (left) typically have statistical errors of ≈ 3.0%, we conclude that the spatial variation of the quantum efficiency across the CCDs at the Mn-Kα and Kβ energies is at a √ 3.8 2 − 3.0 2 ∼ 2% level.

Charge Trail and CTI Corrections
When charges are transferred in a CCD, a part of the charges may be left behind the pixels. We need to correct data for the effect called charge trail, otherwise the event is assigned a wrong grade, which leads to a misidentification of the event as a background. The charge trail correction is    Fig. 13. Each data point represents X-ray counts accumulated in regions corresponding to each of the 1.4 mm × 1.4 mm holes of the mesh (Fig. 12). The red curve indicates the function A/R 2 , where the normalization A is determined by fitting the data points. (right) Distribution of the residuals of the data from the red curve in the left panel. The red curve is the best-fit Gaussian.
performed by using the method described by Nobukawa et al. 36 We note that different corrections should be applied between data taken with and without the window option because of different fast to slow vertical transfer number ratios between the two cases.
We then apply CTI corrections. 1 In Fig. 15, we plot PH of 5.9 keV monochromatic X-rays as a function of ACTY. Because of the charge injection, a sawtooth shape appears in the plot. As demonstrated by Nobukawa et al., 36 the periodic shape can be fit by a function that considers injected charges filling traps and their re-emission, and PH can be corrected for the CTI. Data taken with the flight CCDs are generally well reproduced by the same function. However, we found that the function fails to fit data from some regions of the CCDs. We show examples in Fig. 16. The CTI of some regions is significantly higher than the other locations of the CCDs. The locations of the anomaly coincide with those with higher dark level as shown in Fig. 17. The method by Nobukawa et al. 36 assumes all the parameters are uniform in a segment, and needs to be modified to reproduce the position-dependent CTI.
In order to take into account the CTI anomaly, we modified the correction method as follows. The relation between PH after the charge trail correction (PH) and CTI-corrected PH (PH 0 ) can be written as The parameter Y {0,1,2,3,4} is a vertical transfer number with the definitions below.
where c {f,a,s}0 , p {f,a,s} , τ {f,a,s} , and ∆Y are the normalization, probability that a trap is filled by injected charges, de-trapping timescales of the charges in the unit of a transfer number, and difference of ACTY between the pixel considered and its preceding charge injection row. Please note that traps between the pixel and the charge injection row are not filled when the vertical transfer starts. That is why we have c f 0 and c a0 instead of c f and c a in the third and fifth factors of Eq. (2). Let us explain in the following with an example shown in Fig. 18, in which a CTI anomaly region is located between two charge injection rows. The lower and upper boundaries of the CTI anomaly are at ACTY = A 1 and ACTY = A 2 , respectively, and the charge injection rows are at ACTY = I 0 , · · · , I i , I i+1 , · · · . If we operate the CCD with the full-window option and consider a pixel with ACTY = Y, the definition above gives Y 0 = 640 − (Y 1 + Y 2 + Y 3 ) and Y 4 = Y. We can obtain Y 1 , Y 2 , and Y 3 for each of the three cases below. Case 1: Here PH 0, 5.9 keV is PH 0 at 5.9 keV, which is set to 982 ch. The index β {f,a,s} was determined using the F-Kα line at 0.68 keV and Ge-Kα line at 9.9 keV in addition to the 5.9 keV line. The indices are all in the range between 0.4 and 0.8. Figure 19 shows 55 Fe spectra from CCD1 Segment CD before and after the CTI correction. We applied the same grade selection as that used for Suzaku XIS, and extracted events with grades 0, 2, 3, 4, and 6. The energy resolution at 5.9 keV was improved from 194.2 ± 0.8 eV to 170.0 ± 0.7 eV in FWHM. The energy resolution was estimated by fitting the peak with a single Gaussian. Energy resolution of all the segments of the flight CCDs are summarized in Tab. 3.

Detector Response
Following the studies reported in literature, 13,37 we modeled the CCD response as presented in Fig. 20. We decomposed the response to monochromatic X-rays with five components: a primary peak, a secondary peak, a constant tail, a Si-K fluorescence peak, and a Si escape peak. We can interpret them as follows.
Primary peak A Gaussian centered at the energy of the incident X-ray. This component corresponds to events in which an X-ray is absorbed and generated charges are fully detected.  Secondary peak A Gaussian whose center energy is slightly lower than the primary peak. In this case, signal charges are split into more than one pixel, and a part of the charges are not detected since the PH is lower than the split threshold.
Constant When an X-ray is absorbed close to the interface between the depletion layer and the oxide layer and only a part of the charges are collected, the event constitutes this component.
Si-K fluorescence peak The peak is attributed to events in which an X-ray is absorbed in the depletion layer away from the corresponding pixel or in an inactive part of the CCD such as the oxide layer, and then the escaped Si fluorescence X-ray photon is detected in the pixel. Si escape peak This is the case in which an X-ray is absorbed and then the Si fluorescence X-ray escapes from the pixel.
In Fig. 21, we show spectra taken in an on-ground test overlaid with the model curves convolved with the response function. We determined parameters for each of the above components based on data taken in on-ground tests as well as Monte Carlo simulations. We modeled the constant to primary peak intensity ratio according to Monte Carlo simulations as already reported elsewhere. 38 The secondary peak to primary peak intensity ratio is phenomenologically modeled to fit on-ground test results. The ratio decreases with energy: 0.12 at 0.68 keV and 0.066 at 5.9 keV. We took into account the spatial variation of the energy resolution in each CCD. This is particularly important to reproduce spectra from the CTI-anomaly regions since energy resolution there is also worse than that of the other regions. We evaluated FWHM of the primary peak in each region of the CCDs using F-Kα, Ge-Lα, Mn-Kα, and Ge-Kα lines. The energy resolution maps at the F-Kα and Mn-Kα line energies are presented in Fig. 22.

Optical and Ultraviolet Light Blocking
X-ray CCDs are sensitive also to optical and ultraviolet (UV) photons, and thus the SXI has OBL and CBF to block them. The SXI is required to perform an observation even with a star as bright as an apparent magnitude of 1.0 in the FoV. This leads to an optical light transmission of < 10 −5 as a requirement. In the UV band, the most stringent requirement comes from the HeII line emission at 30.4 nm (= 40.8 eV) through resonance scattering of sunlight in the geocorona. The intensity of the emission, ∼ 10 7 photons cm −2 s −1 sr −1 , demands a transmission of < 10 −2 at the wavelength.
We measured the transmission of optical light through the OBL using a prototype CCD, confirming that the OBL satisfied the requirement for the optical transmission of < 10 −5 . During on-ground tests of the flight hardware, however, we found a number of pinholes in the OBL developing with time. Fig. 23 shows dark frames from one of the four CCDs illuminated by optical light from an LED, taken about a year apart. At the time of the latter measurement, 3-5% of the pixels have pinholes, and the optical transmission was estimated to be ∼ 100-1000 times higher at those pixels. We, therefore, changed the specifications of the CBF so that optical light can be blocked by the CBF instead of the OBL. We vapor-deposited Al on both sides of the CBF with thicknesses  of 80 nm and 40 nm in the new design whereas only one side was coated with 30-nm thick Al in the original design. We confirmed that the optical transmission of the CBF is < 10 −5 through measurements of samples equivalent to the flight model. UV photons at 40.8 eV are mainly absorbed by 200-nm thick polyimide layer of the CBF. We measured UV transmission of the CBF in the energy range between 38 eV and 60 eV using the same samples as those used for the optical transmission measurement. The transmission obtained is ∼ 3 × 10 −4 , ∼ 6 × 10 −4 , and ∼ 2 × 10 −2 at 38 eV, 40 eV, and 60 eV, respectively, which satisfies the above mentioned requirement.

Summary
Hitomi SXI is an imaging spectrometer, covering the energy range between 0.4 keV and 12 keV. The sensors of the SXI are fully-depleted, back-illuminated CCDs with a 200 µm-thick depletion layer. We arrange the CCDs in a 2 × 2 array. The total imaging area size is ∼ 60 mm × 60 mm, which corresponds to a FoV of 38 ′ × 38 ′ . The CCDs can be cooled by Stirling coolers down to −120 • C so that we can mitigate CTI due to in-orbit radiation damage. To achieve even lower CTI, we adopt a charge injection technique similar to that used for Suzaku XIS. SXI-PE and SXI-DE perform on-board data processing such as dark subtraction and event extraction. SXI-PE also generates CCD clock patterns which can be programmed flexibly by using microcodes. Onground tests confirm the imaging and spectroscopic capability of the SXI. The energy resolution is measured to be 161-170 eV in FWHM for 5.9 keV X-rays. During the tests, we found two problems. One is that CTI of some regions of the CCDs are found to be significantly higher. We developed a method to properly correct for the position-dependent CTI. The other problem is the pinholes in the OBL. We increased the Al thickness of the CBF so that optical light can be blocked by the CBF instead of the OBL.