Coordinates for MARS
Notes prepared by Phil Bones 6.6.2009
There are 4 coordinate frames defined for MARS:
1.
2.
3.
4.
Laboratory frame
Gantry frame
Body frame
Detector frame
1. Laboratory frame
- As defined in Alice’s progress report (with minor corrections).
2. Gantry frame
The gantry coordinate frame (x’, y’, z’) defines the rotation of the gantry with respect to
the fixed laboratory frame by an angle  about the z-axis. The gantry frame is shown in
blue in Figure 2. The coordinates z’ and z’ are identical. The origins of the gantry and
laboratory frames are identical. The y’ axis is defined to be parallel to the axis of the
detector scanning apparatus (see Figure 3).
y’
Detector
scan axis
CoR
x’
dCD
Figure 3: The y’ axis of the gantry frame is defined to be parallel to the detector scan
axis. The x’ coordinate of the detector scan axis = - dCD.
3. Object frame
- As defined in Alice’s progress report, except that a axis is parallel to x axis and b axis
is parallel to y axis and some minor corrections.
4. Detector frame
The detector frame is defined to lie on a plane parallel to the y’-z’ plane within the gantry
frame. Physically the plane corresponds to the effective surface within the Medipix
detector at which photon absorption take place. The plane lies a distance dCD from the y’
axis, i.e. at x’ = - dCD, as shown in Figure 3. For the purposes of defining the
coordinates, the detector scan axis is treated as if it lies on the detector plane even though
it is physically displaced.
The coordinates in the detector frame are in pixels with respect to an arbitrary point
defined as the topmost and leftmost scan position for a particular scanner. Coordinates M
(rows) and N (cols) define positions in pixels within the detector frame in the manner of
MATLAB. A particular Medipix detector location within the frame is defined by the (M,
N) coordinates of its top left pixel. Note that the offset coordinates are not necessarily
integer.
The relative location of the detector frame with respect to the gantry frame must be
obtained by calibration.
y’
N = 1, 2, …
M=
1, 2, …
n = 1, 2, …
(M1, N1)
m=
1, 2, …
1
(M1, N1)
z’
(M2, N2)
2
x’ = - dCD
Figure 4: The detector frame has coordinates measured in pixels number in from (1, 1) in
the top left position as viewed from the detector face side. Individual detector locations
are displaced within the frame. Calibration is required to determine the intercept of the
gantry x’ axis with the detector frame coordinates.