2.1.

Basic Concept Design and Physical Characteristics

The CAMS consists of two identical units. Each unit measures the lateral displacement ($X/Y$), and in combination, the rotation of the HXI plate relative to the fixed optical bench (FOB). The positioning of the CAMS units on the satellite is shown in Fig. 1. Each CAMS consists of a laser and detector module (CAMS-LD) and a target module (CAMS-T). The CAMS-LD modules are installed on the top plate of the FOB next to the HXTs. The CAMS-T is a passive retroreflector (corner cube mirror) placed on the HXI plate at the end of the EOB 12-m away from the CAMS-LD.

Fig. 1

The location of the CAMS modules on the satellite is shown in the top figure. The positioning of the CAMS-LD on the top plate is shown in the bottom figure, the laser beam apertures are marked by red dots.

The CAMS concept is rather straightforward and shown in Fig. 2. A continuous wave laser beam at 980 nm wavelength generated by a diode laser (3S Photonics 1994 SGP) is launched from the CAMS-LD modules and travels through the interior structure of the satellite. The laser strikes the retroreflector of the CAMS-T and is reflected back to the CAMS-LD. The beam expander in the LD unit reduces the beam size by an expansion ratio $M$. The CMOS imaging detector of $1024\times 1024\text{pixels}$ detects the position of the laser beam. There is a linear relationship between the EOB lateral shift and the laser spot shift that is recorded by the CMOS detector. If the corner cube is displaced in the lateral direction, then the reflected laser spot shift is scaled by a factor of two. The measured shift from the nominal position on the CMOS detector will be scaled down accounting for the beam expander effects.

Fig. 2

(a) The path of the laser through the CAMS module. The laser is emitted from the collimator (4) then is deflected off a beamsplitter (3) and directed toward the corner cube retroreflector (6). The beam is returned through the satellite interior, through the beamsplitter and into the scaling optics (2) before it is recorded on the CMOS detector (1). Other components of the system are the CAMS-LD electronics (5) and the CAMS-T heater and temperature sensor (7). The linearity of the system is depicted in (b). The robustness to tilt in the corner cube is illustrated in (c).

There are several inherent benefits to the CAMS design. The minimal divergence collimated laser beam makes the system less susceptible to background and stray light issues and minimizes concerns with stray laser light affecting other sensors on the satellite. The laser output power of several mW from the CAMS-LD, and the use of narrowband and neutral density filters, are important to overcome any expected solar background interference. In addition to the linearity of the system, it is also highly sensitive to lateral shifts. A $1\text{-}\mu \mathrm{m}$ shift on the detector corresponds to a $2.4\text{-}\mu \mathrm{m}$ shift of the EOB. The measurement is also not sensitive to the tilt of the corner cube around its apex (Fig. 2). Physical characteristics of the CAMS system are provided in Table 1.

Table 1

Physical characteristics of each CAMS unit.

A description of the optical components and module structures can be found in Ref. 6. Images of the CAMS-LD and retroreflector are shown in Fig. 3.

Fig. 3

(a) The components, as delivered for integration with the spacecraft, in their respective housings (CAMS-LD on the left, CAMS-T on the right). Dimensions are given in Table 1. (b) A view of the critical optomechanical components of the CAMS-LD, beamsplitter, and collimator assembly, (c) and of the CAMS-T, corner cube mirror.

The key performance requirement for the CAMS system is the measurement accuracy of the HXI-plate position, which is set to a maximum $3\sigma$-error of $240\mu \mathrm{m}$ (or 4.297 arcsec). The value is driven by the HXI detector pixel size and the expected point spread function of the HXT. The accuracy requirement represents the key challenge for the CAMS development by imposing microradian scale pointing stability on the optical system while operating in a relatively wide temperature range. While there are other factors that contribute to the CAMS measurement error, their combined effect falls outside of the maximum allowance of $240\mu \mathrm{m}$. The most prevalent factor is the flexing of the FOB top plate onto which the CAMS-LD is mounted.

2.2.

TVAC Performance Results

CAMS data were collected throughout spacecraft-level thermal vacuum (TVAC) testing. Restricted by the size of the TVAC chamber, the EOB remained retracted as it would during launch. This provided a unique opportunity to measure the CAMS performance in the absence of flexing since the two modules were hard mounted between the two optical benches supporting them.

Solar lamps and shades were used to control the operational thermal set points. During testing, the shades were returned to the “closed” position in between set points. This created thermal creeping on the solar lamp exposed multilayer insulation. This phenomenon creates stresses within the structure, which are observable in the CAMS data. Figure 4 shows the measured structural distortion of about $12.6\mu \mathrm{m}$ for CAMS-1 and $4.6\mu \mathrm{m}$ for CAMS-2. The CAMS resolution is $1\mu \mathrm{m}$ with an rms measurement noise of $\sim 0.5\mu \mathrm{m}$.

Fig. 4

The spacecraft structural distortions measured in the $X$ and $Y$ directions by (a, b) CAMS-1 and (c, d) CAMS-2 during thermal vacuum testing of the spacecraft. The vertical axis shows the distortion in units of $\mu \mathrm{m}$ in the CAMS coordinate system (Csys). The black circles indicate the results of manual centroid calculations based on images downloaded from CAMS (full image dump).

The black dots superimposed on Fig. 4 relate to the detector raw images that were downloaded to verify that the measurements were not influenced by solar lamp background noise. The data are in the CAMS coordinate system and the units are rotated 90 deg to each other on the FOB.

2.3.

CAMS-LD Alignment on the FOB

The alignment budget for differences between the incident angle of the laser emitted from the CAMS-LD and the satellite $Z$ axis were targeted to be less than 10 arcsec in each lateral direction. The feasibility of achieving the alignment target by shimming the CAMS-LD was initially tested by JAXA with the CAMS engineering model during the Mechanical Interface Check in January 2014.

With the CAMS-LD flight models mounted on the top plate of the FOB, the laser spot position on the detector was measured when the CAMS-T was placed on the middle plate and then on the lower plate of the FOB. The top plate was 1.3 and 3.4 m from the middle and lower plates, respectively. If the CAMS-LD alignment was perfect, then the laser spot would land on the same detector position when the CAMS-T was in either location. Shims were inserted between the CAMS-LD baseplate and the FOB top plate to achieve laser alignment.

After shimming, the laser orientation was measured to be within 15 and 7 arcsec in the $X$ and $Y$ lateral directions with respect to the satellite $Z$ axis for CAMS-1 and CAMS-2 units, respectively.

3.1.

Turn-On and Snapshots

Activities consisted of reviewing the CAMS telemetry commands that needed to be sent to control the CAMS, reviewing telemetry to confirm the health of CAMS, and validating the image snapshot and download process in preparation for the next few days.

Figure 5 is the snapshot images taken on the day launch +10 while the EOB was still stowed, showing that both units survived the launch. The distortions seen in the images were caused by laser beam segmentation on the corner cubes and diffraction on the corner cube center and boundaries between the petals. These distortions were expected to dissipate in the extended EOB configuration. Telemetry indicated the CAMS units were operating within nominal temperature range and there were no errors reported other than saturation of the unit readings in flight module-1. This was fully anticipated and evident in the image [Fig. 5(a)].

Fig. 5

The imaged laser beam spot from (a) CAMS-1 and (b) CAMS-2 with the EOB stowed. The aberration in the images was expected as the EOB was not extended. In addition, the CAMS-1 image is saturated. Pixel values are shown on the axes. The color scale indicates relative intensity.

While the EOB was still stowed, the CAMS measurement deviations were compared with temperature changes in the telescope optics heaters and orbital temperature changes to investigate the influence of temperature variations on-board. Temperature changes in the heaters would occur on timescales of 10 to 20 min whereas orbital temperature fluctuations would occur on $\sim 100\min$ timescales. Figure 6 illustrates how the heater cycling did indeed influence the CAMS measurements by inducing stresses in the FOB top plate onto which CAMS-LD was mounted. Note, the measurements in Fig. 6 were calculated assuming the extended length of the EOB to demonstrate the anticipated full impact of heater cycling on the CAMS measurements. Fluctuations in the displacement on the order of 1 mm are seen in the $X$ and $Y$ directions on timescales consistent with heater cycling. In Fig. 6(d), the absolute accuracy of the system is tested. Here, the value $r12$ is shown, which is the distance between the two units. The measurement is a sanity check to verify that both lasers travel in a parallel path, and nominally, the value of $r12$ should be 600 mm. The effect of heater cycling introduced an uncorrectable error of $\sim 80\mu \mathrm{m}$ rms, corresponding to 1.5 arcsec, and will be further discussed in Sec. 3.4.

Fig. 6

The effect of the telescope optics heater cycle on the CAMS measurements of the EOB position. Lateral translation in (a) $X$ and (b) $Y$, (c) rotation around $Z$ axis, and (d) the distance measured between CAMS-T1 and CAMS-T2 ($r12$, design value is 600 mm) indicating the absolute accuracy. The horizontal axes show timescales in hh:mm format (UTC). A one-mm shift corresponds to 17.19 arcsec angular shift in the focal plane (at HXI) when the EOB is extended.

3.2.

EOB Extension

On day launch +11, the CAMS was used to monitor the deployment of the EOB.⁷ The EOB is an extensible mast structure comprising 23 stages, of which 22 are extensible. After full extension, it becomes 6377 mm in length (689 mm in stowed configuration). The EOB, whose total weight is 42.2 kg, pushes and sustains the HXI plate, which has a mass of $\sim 150\mathrm{kg}$, throughout the extension operation. During EOB extension, the CAMS generated $X/Y$ data pairs with both units. At the same time, the triaxial angular velocities of the spacecraft were monitored with the inertial reference unit (IRU).

Figure 7 shows the calculated EOB translation and rotation based on the combined data from both units. The extension motion can easily be unstable even for small perturbations since the HXI plate is massive and the EOB is not completely stiff. In fact, the HXI plate was sufficiently unstable in the lateral direction that the extension operation was manually suspended on four occasions that were determined by monitoring the CAMS and the IRU data. These delays occurred at 2:17UT, 2:59UT, 3:02UT, and 3:53UT during the extension of the 7th, 14th, 20th, and 23rd stages, respectively. The vibrations damped quickly (within $\sim 30\mathrm{s}$) and the extension process resumed after confirmation that the EOB was sufficiently steady. Even with such careful consideration, the unsteadiness was unexpectedly large during the last extension to the latch point that the rotation rate of one of the four reaction wheels (RWs) exceeded a preset limit and that RW was shut off by the fault detection isolation and reconfiguration (FDIR). Despite such challenges, the EOB was fully extended and the CAMS real-time data proved extremely beneficial in the process.

Fig. 7

EOB calculated translation and rotation based on CAMS measurements during the entire period of EOB deployment (horizontal axis is time). Lateral translation in (a) $X$ and (b) $Y$, (c) rotation around $Z$ axis, and (d) the distance measured between CAMS-T1 and CAMS-T2 ($\mathbf{r}12$, design value is 600 mm) indicating the absolute accuracy. The horizontal axes show timescales in hh:mm format (UTC). A one-mm shift corresponds to 17.19 arcsec angular shift in the focal plane (at HXI) when the EOB is extended.

3.3.

Parameter Adjustment

On day launch +12, after successful EOB deployment, the snapshots in Fig. 8 were obtained and inspected to ensure the laser beams were operating normally. The laser beam shapes were Gaussian, as expected, alleviating concerns prior to launch that interference patterns were observed from both units. The concentric patterns observed in Fig. 8 are effects of laser diffraction on dust particles present in the optical system close to the CAMS detector. This diffraction does not impact the CAMS centroid calculation and measurement. A beam quality factor, returned in the telemetry, matched values obtained during the unit calibration process. The beam quality factor provided by CAMS was used to quantify the quality of the data that go into calculating the centroid. It is based on the Pearson coefficient to compare sampled data points to a Gaussian distribution representing the expected laser beam shape on the detector.

Fig. 8

The CAMS beam shape from each unit taken after the EOB deployment. Pixel values are shown on the axes. The color scale indicates relative intensity.

Based on ground calibration data of the expected return intensity over the detector [Fig. 9(b)] and parameter sensitivity, the detector gain and laser current could be sequentially modified until reaching the desired intensity [blue dots in Fig. 9(a)]. Initially, the returning laser intensity [red dots Fig. 9(a)] was slightly higher compared to the calibration levels. The returning laser intensity was adjusted until it was within the calibration range (i.e., the red dot fell within the blue uncertainty range in Fig. 9).

Fig. 9

(a) Parameters adjustment sequence for CAMS-1 (top) and CAMS-2 (bottom). The red dots indicate the CAMS telemetry measurement of the total intensity parameter. The blue dots are the calibration levels for the current beam location on the FOV with the error bars. (b) The final beam position (white cross) and the beam size (magenta region concentric to the white cross) over the expected intensity distribution maps measured during ground calibration (on the right).

Figure 9(b) shows the expected intensity returned as a function of beam position on the detector. Figure 9(b) indicates the final beam position (white cross) and the beam size (magenta region concentric to the white cross) relative to the detector FOV. The final calibrated image is displayed in Fig. 10 and shows a Gaussian laser beam of similar intensity in each unit.

Fig. 10

The final images acquired by CAMS showing Gaussian laser beams of similar intensity in the (a) CAMS-LD1 and (b) CAMS-LD2. Pixel values are shown on the axes. The color scale indicates relative intensity.

3.4.

Orbital Effects

The CAMS parameter adjustment activities were successfully concluded on launch +13 days.

Snapshots continued to be acquired from both units to evaluate the parameters throughout the day. Due to minimal EOB motion, the same detector area was consistently imaged. Laser beam quality remained nominal throughout the day providing confidence in the parameter selection.

As CAMS telemetry data were cumulated, the effects of night/day cycles on the spacecraft structure became apparent. As shown in Fig. 11, the effect is mostly noticeable in the EOB rotation around the $Z$ axis [Fig. 11(c)] where there is clear delineation between night and day. A sinusoidal oscillation of $\sim 175\mu \mathrm{m}$ (3 arcsec) peak-to-peak amplitude can be seen in the $X$ direction [Fig. 11(a)]. The $Y$ direction exhibits similar oscillations, but is more uneven by what is attributed to the FOB distortions induced by the optics heater cycles. Figure 11(d) shows the calculated distance between the two measurements ($r12$), which should nominally be 600 mm if both lasers travel in an ideal parallel path. After deployment of the EOB, the average value was 600.62 mm indicating very small deviations from the projected, gravity-free, FOB deflections. The variations of this value are due to slight differences in the laser direction from the two CAMS units due to thermal distortion of the FOB top plate.

Fig. 11

Calculated translation and rotation in the EOB based on CAMS measurements during day and night cycles. Lateral translation in (a) $X$ and (b) $Y$, (c) rotation around $Z$ axis, and (d) the distance measured between CAMS-T1 and CAMS-T2 ($\mathbf{r}12$, design value is 600 mm) indicating the absolute accuracy. The horizontal axes show timescales in hh:mm format (UTC). A one-mm shift corresponds to 17.19 arcsec angular shift in the focal plane (at HXI) when the EOB is extended.

Data were scrutinized to explain the higher frequency excursions measured by CAMS. By comparing with the telescope optics heater commands (Fig. 12), correlations with the CAMS data could be confirmed. Heater cycling introduces heat on the FOB top plate, creating stresses, which alter the CAMS-LD laser launch angle. These changes in the launch angle are measured as an EOB deflection on the order of $\sim 100\mu \mathrm{m}$. The effects of heater cycles ultimately limit the accuracy of the CAMS measurements. Although the correlation with heater cycles is evident, it is difficult to accurately distinguish heater-induced displacement in laser launch angle (error) from actual EOB motions.

Fig. 12

Comparison of CAMS-1 raw data in the $X$ direction and the soft x-ray telescope heaters over the same time frame.

4.1.

HXI Astronomical Flight Data

During the limited lifetime of the mission, there were two HXI observations of astronomical objects conducted where the CAMS corrections could be applied and its importance validated. The x-ray observations were of the Crab and the supernova remnant G21.5-0.9. These observations were of significant interest from an instrument calibration point-of-view as the energy distribution in the image is spherical and peaked at the center. The distribution remains constant even when observations are carried out over long periods, therefore any variation would be attributed to spacecraft pointing inaccuracy or movement within the telescope structure.

X-ray observations are composed of discrete photon events associated with a pixel position on the imager and a timestamp for an effective exposure of several hours. JAXA had preprocessed the two datasets to contain average pixel position, pixel count, and spacecraft attitude within a sampling period. When aggregated together and corrected for motion, the images can be reconstructed as shown in Fig. 13.

Fig. 13

(a) Raw HXI-1 and (b) HXI-2 images of the Crab (top) and G21.5-0.9 (bottom). The FOV of HXI sensors corresponds to 9.17 arcmin in angular scale.

Table 3 shows the sampling period for each x-ray source and the average number of photons received. The count rate is significantly lower for G21.5-0.9 resulting in a longer sampling period (hence more time for telescope fluctuations), more scatter, and a greater number of outliers in the centroid measurements. Photons were gathered in the HXI 1/2 coordinate frames, which are rotated $\pm 22.5\mathrm{deg}$ to the spacecraft coordinate system (Fig. 15).

Table 3

X-ray point source data.

4.2.

Flight Data Processing

This section describes the methodology employed in using CAMS data to correct the HXI images. The procedure is based on earlier work⁵ and includes several updates and improvements.

The orientation of the spacecraft body-frame, denoted by SAT, is shown in Fig. 14 along with the main spacecraft structure. Figure 14 identifies the location and orientation of the coordinate frames for both units of the CAMS and HXI. The CAMS measurements are reported in the CAMS-1 and CAMS-2 reference frames. The orientations of these local coordinate frames are defined by the orientation of each alignment cube,⁶ but their origins are the geometrical center of the FOV of each unit.

Fig. 14

CAMS and HXI coordinate frames as viewed looking from the FOB along the EOB. The nominal (as designed) location of each instrument is given in mm as a coordinate pair $(x,y)$ in the SAT coordinate frame, except for the CAMS readings which are in the CAMS local coordinate frames. Red circles represent the center of CAMS-T1 and CAMS-T2 in an undisturbed EOB location. The origin in the CAMS frames are the centers of their field-of-view.

A set of CAMS alignment parameters is required for determining the transformation from the CAMS coordinates to the satellite coordinate system (Table 4).

Table 4

CAMS installation parameters.

Two other frames related to the HXI that are relevant to the data processing are the RAW and ACT coordinate frames (Fig. 15). The ACT (short for active) coordinate frame is a virtual coordinate frame representing the ideal (or nominal) location of the HXI, that is, the location of the HXI when all deformations of the EOB are zero. The RAW coordinate frame is the base sensor frame attached to the HXI. The raw position of photon events observed by the imager is expressed in RAW coordinates, and as such, the RAW frame translates and rotates along with the HXI detectors mounted on the end of the EOB. In the case of zero EOB deformation the ACT, RAW, and HXI frames all have the same orientation but their origins are offset.

Fig. 15

HXI reference frame to spacecraft reference frame.

Prior to applying a CAMS correction to HXI measurements, it is important to ensure that an adequate correction of thermal pointing drifts is applied to the CAMS data themselves. This correction takes into consideration the laser beam displacement caused by temperature variation in the CAMS. Ground-based unit level tests determined linear thermal drift coefficients for correcting the CAMS internal contribution. A contribution to thermally induced laser pointing drift caused by the top plate bending is not included in this correction. The options to implement such a correction were either (i) through on-board processing or (ii) during ground processing. The ground-based approach was selected thus the correction became part of the data processing.

The temperature corrected CAMS readings can be calculated using the following pair of expressions:

Table 5

Thermal correction parameters for CAMS.

Next, the four CAMS measurements are used to estimate three parameters representing the three significant relative motion degrees-of-freedom: the two-dimensional (2-D) planar translation and the rotation about an axis parallel to the bore sight. The data processing algorithm begins by calculating the twist angle ($\gamma$) followed by the planar displacement. Although the CAMS measurements are planar, they are represented as three-dimensional (3-D) position vectors with a zero value in the $z$ direction, i.e., ${\mathbf{r}}_1^{\mathrm{CAMS}1}=[\begin{array}{ccc}{x}_1& y_1& 0\end{array}]$ and ${\mathbf{r}}_2^{\mathrm{CAMS}2}=[\begin{array}{ccc}{x}_2& y_2& 0\end{array}]$ in each local CAMS coordinate frame (denoted with a superscript). The measurement vectors and the twist angle are shown in Fig. 16, along with the original position of the reflected laser beams 1 and 2, and the displaced position denoted with a prime superscript. The position vectors from one laser beam location to the other, ${\mathbf{r}}_{12}$ and ${\mathbf{r}}_{12}^{\prime }$, are combined with a dot product to calculate the twist angle:

Fig. 16

Estimation of roll angle, $\gamma$, using the planar displacement of the two CAMS-T.

It is assumed here that the original reference orientation of the EOB is the nondisturbed nominal orientation, where the targets are located at nominal coordinates. The shifted reading of CAMS must consider a bias (${\mathbf{r}}_{\mathrm{1,2}}^{\mathrm{CAMS}\mathrm{1,2}}$) measured at spacecraft calibration (Table 4). A rotation is necessary to express the CAMS measurements in a common frame such as the SAT frame

For the orientation of the frames in Fig. 16, the following rotations are used:

Once the twist angle is determined, the planar displacement of the EOB is estimated using the centroid position of the CAMS-T1,2 locations. The displacement ($\mathrm{\Delta }\mathbf{r}$) is the difference between a vector pointing to the centroid of the original CAMS-T1,2 locations, ${\mathrm{r}}_{c/m}$, after it has been rotated by the twist angle, $\gamma$, and a vector to the centroid of the displaced CAMS-T1,2 locations, ${\mathbf{r}}_{c/m}^{\prime }$

This step is shown graphically in Fig. 17.

Fig. 17

Illustration of the planar translation, $\mathrm{\Delta }\mathbf{r}$, using the centroid of the original and displaced CAMS-T1,2 locations.

Here a vector pointing to the centroid of any two vectors, ${\mathbf{r}}_1$ and ${\mathbf{r}}_2$, is found using the following relationship:

Expression (6) also takes into consideration that the HXI detectors are elevated 232 mm above the HXI plate and the lateral translational displacement measured by CAMS must be factored. It is found that the higher the HXI detectors are located, the smaller the motion will be if it is caused by bending of the EOB. This does not hold true for the lateral motion associated with the twist angle of the EOB. The rotation associated with twist is preserved without an extra factor. This consideration also means that calculating the HXI detector displacement $\mathrm{\Delta }\mathbf{r}$ in the reference frame centered in the physical axis of the rotation becomes important.

Once the CAMS data are processed using Eqs. (1)–(8), the position of photon events observed by the HXI, ${\mathbf{r}}_{\mathrm{RAW}}$, can be corrected to account for the measured distortion of the EOB relative to the FOB. For this algorithm, the data ${\mathbf{r}}_{\mathrm{RAW}}$ already include any required correction from spacecraft attitude control sensors.

The corrected HXI observation in active coordinates, ${\mathbf{r}}_{\mathrm{ACT}}$, are calculated directly using the calculated displacement vector, $\mathrm{\Delta }\mathbf{r}$, and twist angle, $\gamma$, using the following expression:

The coordinate rotation matrices are

The vectors used in this equation are displayed in Fig. 18.

Fig. 18

2-D-transformation from RAW to ACT coordinates. The blue circle represents the HXI measurement event.

When the data from both sensors are obtained in stable ACT coordinate frames, a rotation and superposition are used to generate the final image data obtained from both sensors in the SAT coordinate frame.