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Calibration Access and Data Handbook

Spatial coordinate systems

The CAL makes use of the following spatial coordinate systems

• PIXCOORD0: Telemetry-related CCD pixel coordinate system
  A pair of two integer numbers $telX$/$telY$ specifies a pixel position on the currently defined CCD chip (state variable $ccdChipId$) which is read out through one of two nodes (state variable $ccdNodeId$). Pixels outside the actual image area of the chip (over/underscan pixels) are taken into account and are counted as ordinary pixels. The pixel closest to the readout node is designated as (0/0). If a readout window is defined PIXCOORD0 coordinates are relative to the lower left corner of that window.

• PIXCOORD1: Node-oriented CCD pixel coordinate system
  A pair of two integer numbers - referred to as $rawX$/$rawY$ in the following - specifies a pixel position on the currently defined CCD chip (state variable $ccdChipId$) which is read out through one of two readout nodes (state variable $ccdNodeId$). The pixel coordinate system is, thus, node-oriented. Example: Pixel position (123/456) on the central EMOS1 chip readout through the primary node corresponds to pixel $(600-123+1=478/456)$ on the same chip read-out through the redundant node. CCD pixel coordinates are in the range $[1, max_x] \times [1, max_y]$ where $max_x$, $max_y$ are the number of available pixels in X/Y for the current instrument.

  In the case of OM the notion of raw pixels is identical to centroided pixels. The size of the detector in centroided pixels is $2048\times2048$.

  Over- and/or underscan pixels are no longer considered. PIXCOORD1 is no longer relative to any defined readout window.

• CHIPCOORD: Node-free CCD pixel coordinate systemThe CHIPCOORD system is identical to the PIXCOORD1 system except for the removal of the node-orientation. All pixel coordinates are referred to the primary/first readout node.

• CAMCOORD1/CAMCOORD2: Camera reference systems
  A triple of three real numbers ($xmm$/$ymm$/$zmm$) specifies a physical location in the camera system in units of mm from the origin of a right-handed, Cartesian reference system. The origin in CAMCOORD1 is the geometrical center of the camera (center of central chip for MOS/RGS/OM and center of chip wafer for EPN), in CAMCOORD2 it is the point where the optical axis of the telescope in front of the the camera intersects the focal plane. For RGS1 the CAMCOORD1 and CAMCOORD2 systems are identical.

  The alignments of the CAMCOORD1/2 $+X$ and $+Y$ axes with respect to the PIXCOORD1 (see Sect. 2.1) and the SACCOORD (see Sect. 2.1) frames for all cameras are as specified in the following table:

  Camera unit(s)	alignment of CAMCOORD1/2 axes in PIXCOORD1 frame	$+X_{CC1/2}$ aligned with axis in SACCOORD frame	$+Y_{CC1/2}$ aligned with axis in SACCOORD frame
  EMOS1/2	$+X$/$+Y$ axes aligned with the respective axes of primary node of central CCD	$+Y_{SC}$/$+Z_{SC}$	$-Z_{SC}$/$+Y_{SC}$
  EPN	$+X$/$+Y$ axes aligned with respective PIXCOORD1 axes of CCDs 7-12 in quadrants 2/3	$-Z_{SC}$	$-Y_{SC}$
  RGS1/2	$+X$/$+Y$ axes aligned with $+X$/$-Y$ PIXCOORD1 axes	$+Z_{SC}$ rotated by $7.333^{\circ }$	$+Y_{SC}$
  OM	$+X$/$+Y$ axes aligned with $-X$/$+Y$ PIXCOORD1 axes	$+Z_{SC}$	$+Y_{SC}$

• SACCOORD: Spacecraft reference system
  A triple of three real numbers ($xmm$/$ymm$/$zmm$) specifies a physical location in the satellite in units of mm from the origin of the right-handed, Cartesian spacecraft reference system which is defined as follows:
  • The origin is located in the center of the circle inscribing the optical axes of the three mirror modules in the plane of the mirror support platform which faces the focal plane assembly.
  • The $+X$ axis is perpendicular to the mirror support platform, pointing positively towards the focal plane assembly, i.e., along the direction of incoming X-rays. Please note that the $-X$ axis corresponds to the viewing direction of the telescope (not taking the effect of boresight misalignment into account).

  • The $+Z$ is defined by the point where the optical axis of mirror module 3 (which is in front of the EPN camera) intersects the mirror support platform and the origin. $+Z$ is pointing positively away from mirror module 3 (and the optical monitor) and is perpendicular to the solar panels.

  • The $+Y$ axis completes the right-handed orthogonal coordinate frame.

• TELCOORD: Telescope coordinate system
  A right-handed Cartesian reference system whose +X axis is defined by the optical axis of the telescope in front of the currently set instrument (state variable $instrument$) along the direction of incoming photons. The +Y and +Z axes are aligned with the respective axes of the SACCOORD (see Sect. 2.1) frame. The origin lies in the mirror support platform, so, in front of the telescope when looking from the sky along the +X axis.

  A pair of two real angles $(\theta, \phi)$ represents a position in the +Y/+Z plane. The $\theta$ angle signifies the angular deviation from the X-axis, i.e., $\theta=0$ is the on-axis case corresponding to $Y=Z=0$. $\phi$ is the azimuthal angle measured in the mathematically positive sense (anti-clockwise) from the +Z-axis when looking along the +X axis. Please note: If the TELCOORD system is translated to the focal plane the mirror inversion effect has to be considered.
  The units for $\theta$ and $\phi$ are arcsecs and radians respectively.
  Example: $(600, \pi/2)$ specifies a point being 10 arcmin off the optical axis with an azimuth of +90 degrees away from the spacecraft +Z-axis, i.e., on the spacecraft +Y-axis. In the CAMCOORD2 (see Sect. 2.1) system of EMOS1 this approximatley refers to the mid-point of CCD 6 and for EMOS2 is refers to the mid-point between CCDs 7 and 2 respectively.

• ROWCOORD: Rowland coordinate system
  ROWCOORD is a RGS-specific coordinate system where the two angles $\beta$ and $\chi$ designate an event position in the dispersion and cross-dispersion direction respectively. $(\beta/\chi) =(3.228^{\circ}/0)$ are the ROWCOORD coordinates of the central pixel of CCD 5 (M-point). $\beta$ increases positively in the direction of increasing dispersion. $\chi$ increases in the direction of the CAMCOORD1 (see Sect. 2.1) $+Y$ axis. Please note: $\beta$/$\chi$ designate the non-aspect corrected dispersion/cross-dispersion angles in the frame of the RGA. $\beta$/$\chi$ are defined with respect to the RGA-G point and the center of the mirror module respectively.

Please note: A pixel location in the CHIPCOORD system is given by two integer numbers. When converting any such CHIPCOORD pixel location to the CAMCOORD1 frame the corresponding physical location is that of the center of the pixel.

The following figures illustrate the alignment of the PIXCOORD1/CAMCOORD1/CAMCOORD2 and SACCOORD reference system with respect to each other for the six cameras. The last figure is a schematic overview of all available coordinate systems in the CAL and the provided paths of conversions between them.

Figure 1: Alignment of the CAMCOORD1/2 frames with respect to the PIXCOORD1 and SACCORD frames for the EMOS1 and EMOS2 cameras. Please note that the two CAMCOORD frames are identical because the telescopes' optical axes intersect the cameras in their centers.

Figure 2: Alignment of the CAMCOORD1/2 frames with respect to the PIXCOORD1 and SACCORD frames for the EPN camera. Please note that the CAMCOORD2 frame is offset from the CAMCOORD1 frame by about (4mm/2mm) in the $-Z$ and $-Y$ SACCOORD direction respectively. The optical axis of mirror module 3 in front of EPN intersects the camera plane in the origin of CAMCOORD2.

Figure 3: Alignment of the CAMCOORD1 frame with respect to the PIXCOORD1 and SACCORD frames for the RGS camera units. Please note that strictly speaking CAMCOORD2 does not exists for RGS, however, it is formally equivalent to CAMCOORD1. The CAMCOORD1 $X/Y$ plane is rotated by $7.333^{\circ }$ with respect to the SACCOORD $Y/Z$ plane around the $+Y_{CC1}$ axis. Increasing values of the CAMCOORD1 $X$ coordinate correspond to decreasing dispersion, i.e., increasing energy (decreasing wavelength).

Figure 4: Alignment of the CAMCOORD1/2 frames with respect to the PIXCOORD1 and SACCORD frames for the OM camera.