Look at the raw shifts as seen in the first step of Cocoa for 3.8T data. Bear in mind that the disks bend, and the ME+3 and ME+2 stations are on the same disk--one cantilevered up and the other cantilevered down.
| Name | .5*(U+D)-mid | sign*(.5*(U+D)-mid) | .5*(L+R)-mid |
| DCOPS_MEp4_transfer_1_OUT | -1.32365 | -1.32365 | -0.28055 |
| DCOPS_MEp3_transfer_1_OUT | 3.08275 | 3.08275 | 2.2526 |
| DCOPS_MEp2_transfer_1_OUT | 1.5046 | 1.5046 | 2.8822 |
| DCOPS_MEp1_transfer_1_OUT | 2.4424 | 2.4424 | 8.61085 |
| DCOPS_MEp4_transfer_2_IN | -0.0875 | 0.0875 | -0.362 |
| DCOPS_MEp3_transfer_2_IN | -5.22424 | 5.22424 | 1.2839 |
| DCOPS_MEp2_transfer_2_IN | -3.77675 | 3.77675 | 2.131 |
| DCOPS_MEp1_transfer_2_OUT | 9.04995 | 9.04995 | 8.4498 |
| DCOPS_MEp4_transfer_3_OUT | -0.53955 | -0.53955 | -0.1342 |
| DCOPS_MEp3_transfer_3_OUT | 5.9464 | 5.9464 | -0.1873 |
| DCOPS_MEp2_transfer_3_OUT | 4.18015 | 4.18015 | 3.13985 |
| DCOPS_MEp1_transfer_3_IN | -4.20283 | 4.20283 | 8.21575 |
| DCOPS_MEp4_transfer_4_IN | 0.70725 | -0.70725 | -1.12795 |
| DCOPS_MEp3_transfer_4_IN | -5.41152 | 5.41152 | 0.77895 |
| DCOPS_MEp2_transfer_4_IN | -3.6835 | 3.6835 | 0.62995 |
| DCOPS_MEp1_transfer_4_IN | -2.4009 | 2.4009 | 4.6905 |
| DCOPS_MEp4_transfer_5_OUT | 0.38065 | 0.38065 | -0.7438 |
| DCOPS_MEp3_transfer_5_IN | -6.61964 | 6.61964 | 2.91575 |
| DCOPS_MEp2_transfer_5_OUT | 4.64955 | 4.64955 | 2.26265 |
| DCOPS_MEp1_transfer_5_OUT | 2.5906 | 2.5906 | 7.15335 |
| DCOPS_MEp4_transfer_6_IN | -0.32815 | 0.32815 | -0.97065 |
| DCOPS_MEp3_transfer_6_IN | -6.29824 | 6.29824 | 3.6235 |
| DCOPS_MEp2_transfer_6_IN | -4.8384 | 4.8384 | 2.37545 |
| DCOPS_MEp1_transfer_6_OUT | 5.84415 | 5.84415 | 4.8923 |
The average L/R for a position is independent of the orientation of the DCOPS. Averaging loses information about the tilt of the laser beam, but that's not a concern here. Notice that the position increases the farther from the laser the sensor is, which is consistent with tilts in the laser direction. These tilts vary with transfer point, and of course are not indicative of anything important, since the tilts were adjusted. They are 3.41, 3.38, 3.20, 2.23, 3.03, and 2.25 mrad respectively.
The average U/D (adjusted for DCOPS orientation) is more interesting, since it allows us to get rough estimates of the disk rotations. If the laser is directed down the line accurately, the shifts represent real shifts in the disk position. Imagine for the sake of estimation that the transfer plates are precisely where they are supposed to be and the lasers are directed straight down the middle. Then the average position for each disk in U/D (adjusted) represents an approximation for the rotation of that disk. Obviously YE+3 should have no rotation, since the lasers are mounted on it, so that gives us an estimate of the error involved.
The fact that the lasers are not directly perfectly is partly compensated for by the fact that these misdirections are random, to first order.
This gives a rotation for YE+3 of -.25mrad, for YE+2 of 0.64mrad, and for YE+1 of 0.61mrad. Disk rotation would be YE+1=-.61, YE+2=-.64, YE+3=.25mrad, the first 2 of which agree with photogrammetry
If I regard each shift in U/D as a vector and sum them (multiplying by the appropriate unit vector for each position), the positions turn out to be
| Name | dX mm | dY mm | rotZ mrad |
| YE+1 | -0.85 | 0.48 | 0.61 |
| YE+2 | 0.34 | -0.35 | 0.64 |
| YE+3 | 0.18 | -0.01 | -0.25 |
Obviously these are very coarse approximations--not trustworthy. But they can be used to estimate the size of the displacements.
I can do the same thing with the L/R numbers, and so for comparison
| Name | U/D dX mm | L/R dX mm | U/D dY mm | L/R dY mm |
| YE+1 | -0.85 | 0.30 | 0.48 | 0.77 |
| YE+2 | 0.34 | 0.44 | -0.35 | -0.24 |
| YE+3 | 0.18 | 0.05 | -0.01 | 0.20 |
The YE+2 numbers are consistent, but not the YE+1.
| Name | dX mm | dY mm | rotZ mrad |
| YE+1 | 0.85 | -0.48 | -0.61 |
| YE+2 | -0.34 | 0.35 | -0.64 |
| YE+3 | -0.18 | 0.01 | 0.25 |
Modified 28-May-2009 at 9:13
http://hep.physics.wisc.edu/~jnb/cms/27May2009
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