26
5.2
Acquiring the Motion Matrix
During the Motion Matrix acquisition, each motor is moved, one-at-a-time and in
both directions then returned back to where it started. The resulting beam
movement is measured along the
X
and
Y
axes on each camera and this is used to
construct the 4x4 Motion Matrix shown below. Each element A
mn
in the matrix
describes the motion resulting from the Motor movement from the
m
th
motor (i.e.,
four motors: Picomotor for horizontal motion on first Mirror Mount or MM
1,x
,
MM
1,y
, MM
2,x
, MM
2,y
) along the nth camera axis (i.e., four axes: the x axis on
Camera 1 or Cam
1,x
, Cam
1,y
, Cam
2,x
, Cam
2,y
).
For example, the motion along the x-axis of Camera 1 due to the x-axis Picomotor
on Mirror Mount 1 is given by ΔCam 1,x which is obtained according to
However, this actuation will also move the beam along the y-axis of Mirror
Mount 1, the x-axis of Mirror Mount 2, and the y-axis of Mirror Mount 2.
Lock Single Step Equation
Determines the movement for each motor from the
difference between the current beam positions and the
Target beam positions
MM1X
MM1Y
MM2X
MM2Y
MM1X
MM1Y
MM2X
MM2Y
CAM1X
CAM1Y
CAM2X
CAM2Y
CAM1X
CAM1Y
CAM2X
CAM2Y
gain
. A
-1
CAM1X
CAM1Y
CAM2X
CAM2Y
MM1X
MM1Y
MM2X
MM2Y
A
11
A
12
A
13
A
14
A
21
A
22
A
23
A
24
A
31
A
32
A
33
A
34
A
41
A
42
A
43
A
44
Movement Matrix A
CAM1X
CAM1Y
CAM2X
CAM2Y
MM1X
0
A
11
A
12
A
13
A
14
A
21
A
22
A
23
A
24
A
31
A
32
A
33
A
34
A
41
A
42
A
43
A
44
0
0
CAM1X = A11 .
MM1X
CAM1X
MM1X
A11 =
CAM1Y
MM1X
A21 =
CAM2X
MM1X
A31 =
CAM2Y
MM1X
A41 =
CAM1X
CAM1Y
CAM2X
CAM2Y
MM1X
0
A
11
A
12
A
13
A
14
A
21
A
22
A
23
A
24
A
31
A
32
A
33
A
34
A
41
A
42
A
43
A
44
0
0
CAM1X = A11 .
MM1X
CAM1X = A11 .
MM1X
CAM1X
MM1X
A11 =
CAM1X
MM1X
A11 =
CAM1Y
MM1X
A21 =
CAM2X
MM1X
A31 =
CAM2X
MM1X
A31 =
CAM2Y
MM1X
A41 =
CAM2Y
MM1X
A41 =
