CCD geometry

We first summarize the coordinate systems used for formulating the ray tracing problem. For a more comprehensive description of the various coordinate systems of the mission, we refer to the ``ASC Coordinate System'' . The coordinate systems we will use below are:

• Chip Physical Coordinates (CPC), which give the physical position of an event on the active surface of the CCD: X_CPC, Y_CPC, Z_CPC, in mm. The Y_CPC, Z_CPC axes describe the plane of the CCD, with origin in its lower-left corner. The X_CPC axis completes a right-handed set;
• Local Science Instrument (LSI). This system is fixed for each instrument in the SIM. The origin is in the instrument, the +X axis runs toward the mirror aperture, the +Z axis coincides with the upward translation direction of the instrument table. The Y axis completes a right-handed system.

Note that, since the output from SAOSAC is provided in the XRCF coordinate system, a transformation of the event coordinates into LSI will be necessary.

 

Figure 6.9:  Locations and orientations of chips chosen for ACIS flight focal plane.

While the LSI is unique for the instrument, every CCD in both ACIS-I and ACIS-S has its own CPC system, where the plane of the CCD defines the (Y_CPC, Z_CPC) plane. This is illustrated in Figure 3 of the ``ASC Coordinate System'' . To transform from CPC to LSI we need a rotation and a translation, so that a generic point r on the plane is described in the LSI system by:  

$${\bf r = p_0} + Y_{CPC}{\bf e_Y} + Z_{CPC}{\bf e_Z}$$ (56)

where ${\bf p_0}$ is the origin of the CPC coordinates (the lower-left corner of the chip being refered to; this is shown as pixel (1,1) in Fig. 6.9.) and e_Y, e_Z are the unit vectors of the CPC Y, Z axes. The latter, as well as p₀, are determined from the coordinates of the CCD corners in LSI coordinates, specifically, from Eq. (15) and Table 4 of the ``ASC Coordinate System'' .