Available on CMS information server CMS NOTE 2001/???

![](media/image1.wmf){width="6.097222222222222in"
height="1.2381944444444444in"}November 19, 2001

Version 4.0

# ISR 2000 EMU Alignment Test Results Using COCOA Reconstruction

D. Eartly, R. Lee, K. Maeshima

####### Fermi National Accelerator Laboratory

#### Abstract

COCOA (CMS Object oriented Code for Optical Alignment) is an Object
Oriented software program designed to study optical components in the
CMS Position Monitoring system by geometrical approximation. The Endcap
Muon Alignment group has utilized COCOA to reconstruct and simulate
measurements made during the June, August, and September 2000 ISR tests
with DCOPS (Digital CCD Optical Positioning System) sensors. In this
note we discuss the results of the 2000 ISR test using a simple COCOA
model with static reference sensors and fixed orientations.

## Software Design 

COCOA was designed by Pedro Arce
([*arce@ifca.unican.es*](mailto:arce@ifca.unican.es)**)** for the study
and use in the CMS Optical Position Monitor System. The software allows
the user to reconstruct the position and angles of optical objects in a
given system as well as propagate associated (RMS) errors. Calculations
in COCOA are based on a non-linear least squares fit model and allow the
user to provide estimations of errors on a model system as well as a set
of actual measurements taken by the system. COCOA then reconstructs the
system based on the errors provided by making variations in the
positions of the modeled components corresponding to how well the errors
are known. The final output of the software supplies the user with the
optimal solutions for the input parameters such that the ideal
measurements modeled by the program come as close as possible to the
real measurements. Errors can be defined as fixed, calibrated, or
unknown. Components set to be fixed are not moved at all, those set to
calibrated are free to be moved within the range of the error, and
unknown quantities are completely free to be moved as the software sees
fit.

## Endcap Muon Position Monitoring System (EMPMS) Reconstruction at CERN ISR Test Hall

The primary goal of the CERN ISR tests is to reconstruct a full scale
mock-up of a Cathode Strip Chamber (CSC) SLM (Straight Line Monitor)
Line and connecting Transfer Line with DCOPS sensors and monitor the
position of the sensor brackets to within 200μm of their expected
positions. The Endcap Muon test project outline describing the
principles of the Endcap Muon Position Monitoring System (EMPMS) can be
found at
<http://home.fnal.gov/~maeshima/alignment/outline/outline.html>.

The implementation of the EMPMS in the CMS detector will allow for the
transfer of Tracker system coordinate information from the Barrel and
LINK alignment system. This transfer is accomplished across the Module
for the Alignment of the Barrel Muon (MAB) interface. Since the location
of the MAB units are referenced to the Tracker coordinate system by the
LINK system, the location of the DCOPS sensors mounted on the MABs is
known. By using these DCOPS sensors as references, the location of other
DCOPS sensors located along the Transfer laser line can be determined.
DCOPS sensors along the SLM line must also be determined from the
location of at least two known DCOPS sensors. The location of the
reference DCOPS sensors in the SLM line are provided by rigidly
connecting these DCOPS sensors to DCOPS sensors located in the Transfer
line. Once the positions of the connecting Transfer line sensors are
determined, the reference sensors on the SLM line become known and the
remaining sensors in the SLM line can be determined. Of course, since
the DCOPS sensors only measure directions perpendicular to the laser
lines, a host of proximity sensors and inclinometers are employed to
determine the spacing between the DCOPS sensors and their angular
orientations.

A full scale model of this arrangement was implemented at the CERN ISR
tunnel which included one Transfer line and SLM line. A sketch
approximating the arrangement of the DCOPS sensors in the ISR tunnel is
shown below in Figure 1. In the figure, DCOPS et2 and et3 are located on
the MABs and sensors et1 and es1 are rigidly connected by a transfer
link plate. Since only one of the MABs (et2) was constructed for the ISR
tests, reference sensors et3 and es10 must be given by photogrammetry.
Reference sensor et2 is specified by the location of the MAB while es1
is found by determining et1 and making a translation across the known
geometry of the transfer plate. The angular orientation and spacing
between the DCOPS sensors along their respective laser lines are given
by photogrammetry.

![](media/image2.jpeg){width="5.993055555555555in"
height="4.699305555555555in"}

**Figure 1: A Schematic Representation of the ISR Setup**

For each of the sensors mounted in the ISR tunnel, the brackets on which
the DCOPS sensors are mounted are defined by three photogrammetry
targets. The photogrammetry targets have a relationship (as established
by FNAL CMM measurements) to the dowel pins upon which the DCOPS sensors
mount. The DCOPS sensors, in turn, have their CCD pixel arrays
calibrated to the mounting points of the dowel pins (See Fig. 2). The
calibration of the first pixel position in each sensor's CCD to the
local dowel pin hole on the sensors circuit board was done by
Northeastern University prior to the start of the ISR tests. The
calibration was done in a manner so that only one measurement was given
per CCD array in the direction of the pixel array. Transverse
measurements were not considered (i.e. the offset of the pixel array
from the axis of the dowel). Figure 2 (below) shows the parameters
calibrated for a flat CCD sensor window. Calibration for bi-directional
CCD windows are identical, however each bi-directional CCD also has an
unmeasured component coming out of or into the page. Errors arising from
the uncalibrated parameters in the dimensions perpendicular to the pixel
array are thought to be negligible (esp. for bi-directional CCD offset
along the beam axis).

![](media/image3.jpeg){width="2.182638888888889in"
height="2.3333333333333335in"}

Figure 2: NEU DCOPS Calibration Parameters D1, D2, D3, and D4

By knowing these calibration parameters, the angular orientation of all
the sensors, the distance between the sensors and the absolute position
of two sensors in each line, all remaining spatial information of the
sensors can be determined and monitored.

#####  {#section .unnumbered}

##### Implementation of COCOA for EMPMS ISR Testing

The DCOPS sensor configuration for EMPMS used in the ISR tests was
implemented with help from Pedro Arce in COCOA version 1.4.0.

The software was essentially used to accomplish two tasks:

1.  Determine the location of the reference dowel positions and
    orientations in the ISR hall for each DCOPS sensor bracket from
    available CERN Photogrammetry and FNAL CMM (Coordinate Measuring
    Machine) data.

2.  Reconstruct the reference dowel positions for each of the DCOPS
    brackets in the laser line based on actual measurements taken by the
    sensors during the ISR test.

The EMPMS employed in the CMS Muon Endcap will not be able to rely on a
photogrametric survey of components in the system. Although the initial
positions and orientations of the DCOPS sensors will be determined by
photogrametery prior to installation of the Endcap into the Barrel, it
is expected that the CSC chamber orientations (and hence the orientation
of the DCOPS) will change significantly in the high magnetic fields
generated by the solenoid. These shifts in sensor orientations will have
to be determined by the EMPMS system. The present COCOA reconstruction
model (Task #2) detailed in this note does not attempt to reconstruct
potential shifts in the orientation of the DCOPS sensors. Rather these
orientations are determined directly from the survey data (Task #1).
Additional studies with COCOA will be needed to understand how these
orientations will be handled.

## Determination of ISR Dowel Positions from Survey Information 

To do a complete reconstruction of the optical sensors, the positions
and orientations of at least two reference sensors in each laser line
have to be known completely as well as the spacing of all the remaining
sensors to be reconstructed. COCOA was used to determine the location
and orientation of every sensor in the ISR test system (Task #1 above)
from survey data. Deriving the location and orientation of all the dowel
pins allows us to establish our two reference sensors for each line as
well as to establish the separation and angular orientation of the
remainder of the sensors. In addition, by specifying all dowel locations
and orientations, we have created a set of reference dowel locations
with which we can compare all future reconstructed measurements.

COCOA was employed to determine the location and orientation of the
sensors by mapping the location of the three Photogrammetry targets on
the bracket as seen by the CERN Survey Group in the ISR hall to the
corresponding CMM measurements measuring the distance between those
targets and the dowel pins. CERN Photogrammetry was done by determining
the relative coordinates the specified targets within a local assembly
area and then patching the assembly coordinates into the global ISR
coordinates using reference socket targets. Initial uncertainties in
CERN Photogrammetry (June 2000) in the ISR hall were quoted as \< 90 μm
within the global ISR coordinate system and \< 30 μm for local assembly
measurements. CMM Measurement uncertainties were quoted as \< 12.7 μm.
An analysis (August 2000) of the distances between individual
photogrammetry targets has shown that the distances are preserved
between CMM and CERN Photogrammetry measurements within understood
errors. The uncertainties estimates provided by the CERN Photogrametry
Group for the placement of the assemblies in the global ISR coordinate
systems were later revised (Dec 2000) to incorporate the relative
uncertainty and correlation of uncertainties within the survey grid.
Final estimations of the uncertainty in SLM sensor placement within the
global ISR grid were generally estimated as \< 180 μm in Y and \< 160 μm
in Z.

  ----------------- ----------------- ----------------- -----------------
  **Sensor**        **X CMS (mm)**    **Y CMS (mm)**    **Z CMS (mm)**

                                                        

  et0               -7334.75          1370.08           9028.48

  et1               -7256.93          1300.19\*         7822.29

  et2               -7327.37          1360.43           6606.56

  et3               -7268.81          1288.83           -6649.45

  et4               -7262.87          1291.97           -9049.56

  es1               -7235.11          1485.99           7914.87

  es2               -6954.62          1474.07           7903.23

  es4               -3436.21          1475.80           7905.06

  es5               -1512.8963        1476.70           7908.22

  es6               1521.42           1478.33           7842.00

  es7               3434.77           1477.26           7840.27

  es9               6953.99           1476.56           7839.43

  es10              7234.93           1545.31           7909.75
  ----------------- ----------------- ----------------- -----------------

\* Location of et1Y was broken by unrecorded adjustment on transfer
plate. See Section VI.D for a discussion of the et1 Y CMS location

.

#### Table 1: Dowel Locations of DCOPS Sensor Brackets (CMS Coordinates) in ISR Hall

The results from COCOA were checked independently on one sensor by the
CERN survey group (by an unknown commercial software package) and on all
sensors by hand calculations (to first order). COCOA matched the CERN
survey group measurements exactly and matched two independent hand
calculations (done by NEU and FNAL) within 50 μm.

+----------------+-----------+---------+--------+---------+---------+
|                | X ISR     | Y ISR   | Z ISR  | X, Y    | Z Error |
|                |           | (mm)    | (mm)   | Error   |         |
|                | \(mm\)    |         |        | (mm)\*  | (mm)\*  |
+----------------+-----------+---------+--------+---------+---------+
| COCOA          | -7268.81  | 1288.83 | -6     | \< 152  | \< 158  |
|                |           |         | 649.45 |         |         |
+----------------+-----------+---------+--------+---------+---------+
| CERN Survey    | -7268.81  | 1288.83 | -6     | unk     | unk     |
| Group          |           |         | 649.45 |         |         |
+----------------+-----------+---------+--------+---------+---------+
| FNAL Hand      | -7268.81  | -       | -6     | \< 155  | \< 164  |
| Calc.          |           | 1288.83 | 649.50 |         |         |
+----------------+-----------+---------+--------+---------+---------+
| NEU Hand Calc. | -7268.81  | -       | -6     | unk     | unk     |
|                |           | 1288.83 | 649.50 |         |         |
+----------------+-----------+---------+--------+---------+---------+

\* Errors in Z are slightly higher since CMM measurements are given in
only local X, Y while CERN PG

are given as global (X, Y, Z).

## Table 2: Comparison of Dowel Locations in ISR Hall for Sensor et3

The results from dowel et3 were typical of the other sensors, except for
those assemblies around the transfer plate where CERN photogrammetry
resolution was degraded to \< 90 μm (local). The total (global) error in
the dowel locations for sensors in this area is typically \< 168 μm.

One of the key advantages of using COCOA to derive the location of dowel
pins in the ISR hall is the accurate determination of the angular
orientation of the sensor. For example, in the Transfer Line all sensors
are placed by COCOA in the ISR hall with their planar normals pointing
along the ISR Z-axis and rotations always performed (in this order)
about the X, Y, and Z ISR axes. Since the sensors are mounted on the
dowels in a manner which matches the sensor face with that of the
bracket and puts the normal of the sensor in line with the dowel pin,
the orientation of the dowel pin is identical with that of the sensor.
Table 2 shows the angular orientation for sensor et3 as determined by
COCOA. Errors in a sensor's angular orientation are determined by the
quadrature of local photogrammetry errors and global rotation of the
photogrametry targets.

  ----------- ---------- ----------- ----------- ------------- -----------
              X Angle    Y Angle     Z Angle     Error X,Z     Error Y
              (mrad)     (mrad)      (mrad)      (mrad)        (mrad)\*

  Sensor et3  -3.93      -6.51       .691        \< 1.77       \< 4.84
  ----------- ---------- ----------- ----------- ------------- -----------

\* Errors about Y are slightly higher for reasons similar to those found
in the position along Z in Table A

## Table 3: Dowel Orientations for Sensor et3 as derived by COCOA

###### COCOA Reconstruction of ISR Test Setup

To reconstruct the Transfer and SLM lines within the framework of COCOA,
the location of reference sensors et2, et3, and es10 were completely
specified by the previously determined survey data. The remaining
sensors had only their angular orientations and positions along the
laser line specified. Variations of sensors et1 and es1 were bound
together by a simulated transfer plate allowing es1 to become a
reference sensor in the SLM line once the position of sensor et1 has
been established by a complete reconstruction of the Transfer line.
Laser sources were only specified by a single coordinate corresponding
to the beginning of the laser line. No objects placed in the simulation
were specified as 'fixed', but rather their positions and orientations
were set within calibration limits or specified as unknown. COCOA was
then set to recalculated and/or determine the location and orientations
of all components based on a supplied set of measurements taken by the
sensors. Our primary interest in the reconstruction was the
determination of the unknown coordinates marking the sensor positions --
those parallel to the X and Y ISR axes for sensors in the Transfer line
and parallel to the Y and Z axes for sensors in the SLM line.

Several of the CCDs on the DCOPS sensors were not illuminated by the
crosshair laser or suffered from poor fits due to highly unsymmetrical
charge distributions and poorly defined signals across the CCD pixel
arrays. These CCDs were not included in the fitting algorithms employed
by COCOA. Often, conditions in our system would change in a manner which
allowed some CCDs to be included in our reconstruction while excluding
others. A First Level Analysis Program was written to determine the
centroid of the charge distribution in all the CCDs. The determination
as to whether a CCD measurement was usable within the reconstruction was
done through a careful examination of the FLAP data and study of FLAP
fit sigma, how closely the FLAP fit matched the raw CCD distribution,
and the actual value of the FLAP fitted mean. A more detailed discussion
of the FLAP program and study of the raw CCD data can be found in a
separate note.

Approximately 2100 measurement events (Transfer + SLM Line measurements)
were processed utilizing this reconstruction method with 750 events
being taken from a July/August run and 1350 events taken from a
September run. In each test period, the number of events using Laser 302
was roughly equal to the number of events utilizing Laser 303. During
the initial examination of the data, some anomalous events were removed
from the dataset. These single events were typically separated by
several hundred microns to more than a millimeter from the main body of
data points. For the following analysis, approximately 10-30 events
total were cut from both the original July and September data sets.

**A. COCOA Reconstruction with References et2, et3, and es10**

The results presented here summarize the reconstruction of Transfer and
SLM Line sensors in the manner described previously. A complete set of
plots detailing the reconstruction of all events taken during the two
test periods can be found separately in Appendix A, Figures 1-21.
Sensors in both the Transfer and SLM laser lines were reconstructed and
plotted as the deviation between their COCOA reconstructed location and
surveyed location as a function of real UNIX time. These distributions
were then projected into histograms and fit with an appropriate function
to obtain a mean location for each test period.

**1. July/August Results**

The COCOA reconstructed location of sensors with et2, et3, and es10
references in the July/August are shown in Appendix A, Figures 1-10.
Figures 3 and 4 show a distribution of reconstructed sensor locations
which was typical of this test period. \[Note: The binning in these
figures is much finer than the actual resolution of the distribution.
This causes the nonphysical banding of data in the Figures. This will be
corrected in an updated report.\]

The distribution of sensor locations along the SLM line reconstructed
from Laser 302 typically fell inside of a 150-180 μm range in Y and a
50-80 μm range in Z. The Laser 302 Y and Z distributions fell within the
systematic errors of the reconstruction. Although the distribution of
reconstructed values of the sensors' Y coordinates seems to indicate a
slight upward drift in several sensors, scaling downward from
approximately 100μm in es2-es5 to 50μm in es6 and es7, the systematic
error associated with each event precludes any definitive correlations.

![](media/image4.wmf){width="6.095138888888889in"
height="3.5506944444444444in"}

**Figure 3 : Typical Distribution of Reconstructed Positions for an SLM
sensor in July/August for Laser 302 Using es10 as the Final Reference
Sensor.** (Bands are non-physical**)**

![](media/image5.wmf){width="6.095138888888889in"
height="3.5506944444444444in"}

**Figure 4 : Typical Distribution of Reconstructed Positions for an SLM
sensor in July/August for Laser 303 Using es10 as the Final Reference
Sensor.** (Bands are non-physical**)**

The characterization of the Laser 303 SLM data in this period is very
similar to that of the Laser 302 data. All events contained in the
distribution of reconstructed values with Laser 303 typically fall
within the systematic errors associated with the reconstruction. The
only exception occurs in a single cluster of events in the Y
distributions near the end of the test period. This apparent 'jump' in
the sensor Y-coordinate locations increases in magnitude with the
distance of the sensor from the transfer plate. The Y coordinates of et1
or the transfer plate (es1) does not show any apparent shift in position
which corresponds to the 'apparent' jump in these sensor positions.
Aside from this extraneous cluster of events, reconstructed sensor
locations typically well inside a 100μm range in Y and 20-40μm range in
Z.

Transfer Line distributions typically fell inside a 60μm range for both
the X and Y coordinate reconstructions with the exception of et4X, which
has a range of 150 μm. The systematic errors exceeded the range of these
distributions in all cases.

**2. September Results**

The complete set of plots showing the reconstruction of all events in
the September test period can be seen in Appendix A, Figures 12-21.
Figures 5 and 6 show a distribution of reconstructed sensor locations
which was typical of this test period.

The reconstruction of sensors in the SLM line using Laser 302 appears to
be unstable for all the events in both Y and Z coordinates for the
beginning of the test period. Rather than a tight distribution of points
contained within the systematic error of the reconstruction, these
initial events are not clustered about any particular value and scatter
randomly across several hundred microns (\>600 μm). This behavior
terminates for all the sensors further into the test period with the
values of the Y reconstruction falling into a 100μm range and Z
reconstruction values into a 100-150μm range for sensors es2-6 and
150-200μm range for sensors es7 and es9. The end of the erratic behavior
in these distributions coincides with the introduction of a new Laser
302 module. With the exception of the Z distributions of sensors es7 and
es9, these distributions fall roughly within the range of values
encompassed by the systematic error.

![](media/image6.wmf){width="6.095138888888889in"
height="3.5506944444444444in"}

**Figure 5: Typical Distribution of Reconstructed Positions for an SLM
sensor in September for Laser 302 Using es10 as the Final Reference
Sensor.** (Bands are non-physical**)**

![](media/image7.jpeg){width="6.097916666666666in" height="3.61875in"}

**Figure 6: Typical Distribution of Reconstructed Positions for an SLM
sensor in September for Laser 303 Using es10 as the Final Reference
Sensor (Sensor es4).** (Bands are non-physical)

Events reconstructed with Laser 303 do not show any of the erratic
behavior associated with the Laser 302 events in the beginning of the
test period. However, like the earlier reconstruction of the July Laser
303 events, the Y distributions of reconstructed events features a
cluster of approximately 50 events which show an apparent jump in the
positions of the SLM sensors. As before, the magnitude of this jump
increases in magnitude with the distance from the transfer plate.
Excluding this cluster of events, the distribution of reconstructed
events in Y is confined within a 120μm region. Events in the
distribution of Z coordinates also fall inside a 100μm range. Both of
the main bodies of these distributions lie well within the systematic
errors.

Reconstruction of events on the Transfer Line show distinct patterns in
X and Y for all sensors except et4 Y. The sensors seem to track each
other in both coordinates, though the entire distribution for both
coordinates (across 150μm in X and Y) fall almost completely inside the
systematic error. As in July, the et4 Y distribution of events is
slightly smeared over wider range (200μm) and slightly exceeds the
systematic error on the sensor reconstruction. It is also entirely
possible that miscalibration of the CCD-dowel relationship or survey
errors could contribute substantially to this deviation.

**3. Discussion of et2, et3, and es10 Reference Sensor Reconstruction**

A summary of the results for all sensors from each test period are given
in Table 4 and Figures 7-9. The reconstruction of SLM Y coordinates is
consistent for both lasers during the two test periods. Furthermore,
both lasers seem to track the locations of the SLM sensor Y locations in
the same manner as the errors on the reconstructed positions overlap
(see Appendix A, Figure 24). A slight drift in the sensor Y locations
can be seen in all four sets of reconstructed data. The fact that the
same drift is evident for both lasers suggests that the placement of the
es10 reference sensor or transfer plate may be different from the
surveyed value.

Reconstruction of SLM sensor Z coordinates with Laser 302 is
inconsistent between the July/August and September test periods. The
Laser 302 September Z coordinate reconstruction matches almost exactly
with the Z coordinate reconstructions done with Laser 303 for both test
periods. An examination of the raw FLAP data from July indicates the
Laser 302 peak in the es10 CCD which should track motions along the Z
coordinates does not respond to small shifts in the orientation of the
laser in the same manner as preceding sensors. Since es10 is a reference
sensor, its inability to track Laser 302 in Z inhibits an accurate
reconstruction of any SLM sensor Z coordinates. Impact on the Laser 302
July/August Y coordinate reconstruction from the inability to track the
Z coordinate is presently being reviewed, though it is thought to be a
second or third order effect. The effect does not appear in the
September data as Laser 302 was replaced early in the test period.
Sensor Z coordinate locations were found to be very close to their
surveyed location, though es5 and es9 show somewhat higher deviations
that the other sensors. No drift is evident in these distributions.

The reconstruction of sensors on the Transfer Line yields the expected
results, with only the X position of et 4 being reconstructed well away
from the surveyed location. Measurements on sensor et4 were restricted
to two CCDs only with the peak on the CCD tracking the laser along the X
axis suffering from a low signal to background ratio. As noted in the
discussion of individual et4 events during the test period, the
distribution of X coordinate reconstructions as a function of time was
slightly more dispersed than those in the Y coordinate indicating some
instability in the signal. The elevated location of the sensor et1 Y
reconstruction can be seen to correspond exactly to the elevation of the
es1 sensor Y location. The calibration of the Transfer Plate was broken
during the photogrametry survey of the system in the ISR hall by moving
the et1 sensor in Y, so this sensor was expected to significantly
deviate from the surveyed location. Since the location of es1 was
unchanged, a series of mechanical measurements between the et1 and es1
brackets was made to establish the new et1-es1 relationship and es1
expected location. These measurements have an estimate error of 500 μm.
Deviations of this measurement from the actual separation of es1 and et1
are therefore expected to show the reconstructed Y coordinate location
of et1 as being different from the calculated Y position of the sensor
and the location of es1 as being askew since the et1-es1 relationship
would be incorrectly specified. Section VI.D. details the problems with
the calibration of the transfer plate.

![](media/image8.wmf){width="6.095138888888889in"
height="3.7090277777777776in"}

Figure 7: Transfer Line Results of COCOA Reconstruction for July/August
and September Runs Using es10 as the Final Reference Sensor. Error bars
indicate total uncertainty in sensor location as determined by COCOA.

<table>
<colgroup>
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 8%" />
<col style="width: 8%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Sensor</strong></td>
<td colspan="2"><h4 id="julyaug">July/Aug</h4>
<h4 id="laser-301">Laser 301</h4></td>
<td colspan="2"><h4 id="statistical-error-july">Statistical Error
(July)</h4></td>
<td colspan="2"><h4 id="sept">Sept° </h4>
<h4 id="laser-301-1">Laser 301</h4></td>
<td colspan="2"><h2 id="statistical-error-sept">Statistical Error
(Sept)</h2></td>
<td colspan="2"><h2 id="systematic-error">Systematic Error</h2></td>
</tr>
<tr class="even">
<td><strong>Xmean (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Xerror (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Xmean (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Xerror (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><p><strong>Xerror</strong></p>
<p><strong>(μm)</strong></p></td>
<td><p><strong>Yerror</strong></p>
<p><strong>(μm)</strong></p></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>et0</strong></td>
<td>-54</td>
<td>39</td>
<td>9</td>
<td>9</td>
<td>-168</td>
<td>32</td>
<td>8</td>
<td>21</td>
<td>133</td>
<td>168</td>
</tr>
<tr class="odd">
<td><strong>et1</strong></td>
<td>26</td>
<td>274</td>
<td>7</td>
<td>7</td>
<td>-125</td>
<td>259</td>
<td>15</td>
<td>13</td>
<td>133</td>
<td>165</td>
</tr>
<tr class="even">
<td><strong>et4</strong></td>
<td>435</td>
<td>-47</td>
<td>28</td>
<td>10</td>
<td>445</td>
<td>-49</td>
<td>23</td>
<td>13</td>
<td>170</td>
<td>158</td>
</tr>
</tbody>
</table>

<table style="width:100%;">
<colgroup>
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Sensor</strong></td>
<td colspan="2"><h4 id="julyaug-laser-302">July/Aug Laser 302</h4></td>
<td colspan="2"><h4 id="statistical-error-july-1">Statistical Error
(July)</h4></td>
<td colspan="2"><h4 id="sept-1">Sept°</h4>
<h4 id="laser-302">Laser 302</h4></td>
<td colspan="2"><h4 id="statistical-error-sept-1">Statistical Error
(Sept)</h4></td>
<td colspan="2"><h4 id="systematic-error-1">Systematic Error</h4></td>
</tr>
<tr class="even">
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><p><strong>Yerror</strong></p>
<p><strong>(μm)</strong></p></td>
<td><p><strong>Zerror</strong></p>
<p><strong>(μm)</strong></p></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>es1</strong></td>
<td>276</td>
<td>13</td>
<td>7</td>
<td>fixed</td>
<td>258</td>
<td>13</td>
<td>15</td>
<td>fixed</td>
<td>165</td>
<td>53</td>
</tr>
<tr class="odd">
<td><strong>es2</strong></td>
<td>143</td>
<td>79</td>
<td>59</td>
<td>5</td>
<td>-25</td>
<td>-453</td>
<td>26</td>
<td>6</td>
<td>198</td>
<td>125</td>
</tr>
<tr class="even">
<td><strong>es4</strong></td>
<td>72</td>
<td>330</td>
<td>28</td>
<td>7</td>
<td>20</td>
<td>-56</td>
<td>13</td>
<td>10</td>
<td>158</td>
<td>110</td>
</tr>
<tr class="odd">
<td><strong>es5</strong></td>
<td>136</td>
<td>569</td>
<td>22</td>
<td>11</td>
<td>74</td>
<td>245</td>
<td>13</td>
<td>17</td>
<td>158</td>
<td>107</td>
</tr>
<tr class="even">
<td><strong>es6</strong></td>
<td>-328</td>
<td>494</td>
<td>12</td>
<td>9</td>
<td>-255</td>
<td>191</td>
<td>9</td>
<td>23</td>
<td>117</td>
<td>109</td>
</tr>
<tr class="odd">
<td><strong>es7</strong></td>
<td>-366</td>
<td>524</td>
<td>11</td>
<td>15</td>
<td>-281</td>
<td>322</td>
<td>11</td>
<td>26</td>
<td>110</td>
<td>116</td>
</tr>
<tr class="even">
<td><strong>es9</strong></td>
<td>-383</td>
<td>638</td>
<td>9</td>
<td>35</td>
<td>-170</td>
<td>380</td>
<td>14</td>
<td>36</td>
<td>114</td>
<td>137</td>
</tr>
</tbody>
</table>

<table style="width:100%;">
<colgroup>
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Sensor</strong></td>
<td colspan="2"><h4 id="julyaug-laser-303">July/Aug Laser 303</h4></td>
<td colspan="2"><h4 id="statistical-error-july-2">Statistical Error
(July)</h4></td>
<td colspan="2"><h4 id="sept-2">Sept°</h4>
<h4 id="laser-303">Laser 303</h4></td>
<td colspan="2"><h4 id="statistical-error-sept-2">Statistical Error
(Sept)</h4></td>
<td colspan="2"><h4 id="systematic-error-2">Systematic Error</h4></td>
</tr>
<tr class="even">
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><p><strong>Yerror</strong></p>
<p><strong>(μm)</strong></p></td>
<td><p><strong>Zerror</strong></p>
<p><strong>(μm)</strong></p></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>es1</strong></td>
<td>276</td>
<td>13</td>
<td>7</td>
<td>fixed</td>
<td>263</td>
<td>13</td>
<td>12</td>
<td>fixed</td>
<td>165</td>
<td>53</td>
</tr>
<tr class="odd">
<td><strong>es2</strong></td>
<td>-262</td>
<td>0</td>
<td>12</td>
<td>8</td>
<td>-300</td>
<td>2</td>
<td>21</td>
<td>9</td>
<td>228</td>
<td>145</td>
</tr>
<tr class="even">
<td><strong>es4</strong></td>
<td>-324</td>
<td>-30</td>
<td>9</td>
<td>8</td>
<td>-245</td>
<td>-27</td>
<td>18</td>
<td>10</td>
<td>188</td>
<td>122</td>
</tr>
<tr class="odd">
<td><strong>es5</strong></td>
<td>-211</td>
<td>214</td>
<td>15</td>
<td>8</td>
<td>-252</td>
<td>215</td>
<td>9</td>
<td>7</td>
<td>147</td>
<td>112</td>
</tr>
<tr class="even">
<td><strong>es6</strong></td>
<td>-369</td>
<td>-15</td>
<td>8</td>
<td>8</td>
<td>-404</td>
<td>-8</td>
<td>5</td>
<td>7</td>
<td>120</td>
<td>104</td>
</tr>
<tr class="odd">
<td><strong>es7</strong></td>
<td>-446</td>
<td>-18</td>
<td>9</td>
<td>6</td>
<td>-457</td>
<td>-24</td>
<td>5</td>
<td>5</td>
<td>111</td>
<td>104</td>
</tr>
<tr class="even">
<td><strong>es9</strong></td>
<td>-605</td>
<td>-271</td>
<td>7</td>
<td>7</td>
<td>-475</td>
<td>-247</td>
<td>4</td>
<td>4</td>
<td>117</td>
<td>117</td>
</tr>
</tbody>
</table>

#### Table 4: Deviation of COCOA Reconstruction of DCOPS Dowel Pin Positions from Expected Survey Location with es10 Survey as Final Reference

° Events fitted in Sept Data correspond to introduction of new laser
diode in SLM line (525+ events). September events taken prior to the
introduction of the new laser (100 events) where typically within
20-150μm of July positions.

\* Transfer plate Y definition was broken by at 1.71 mm ± .5 mm. This is
survey position with estimated movement of transfer plate components.
See Section IV.C for detailed description of problem.

#### 

#### ![](media/image9.wmf){width="6.095138888888889in" height="3.7090277777777776in"}

**Figure 8: SLM Line (Laser 302) Results of COCOA Reconstruction for
July/August and September Runs** **Using es10 as the Final Reference
Sensor.** Error bars indicate total uncertainty in sensor location as
determined by COCOA.

![](media/image10.wmf){width="6.095138888888889in"
height="3.7090277777777776in"}

**Figure 9 : SLM Line (Laser 303) Results of COCOA Reconstruction for
July/August and September Runs Using es10 as the Final Reference
Sensor.** Error bars indicate total uncertainty in sensor location as
determined by COCOA.

**B. COCOA Reconstruction with References et2, et3, and es9**

In an attempt to further study the principles and operation of the
system, a second reconstruction with COCOA was done using the final
reference sensor as es9 rather than es10. Since es9 is only 85mm ahead
of es10 in the SLM line, it is the logical choice for the final
reference sensor to check es10 reconstruction results. Appendix B offers
the output of all COCOA reconstructed points for all sensors in the ISR
hall using es9 as the final reference sensor. Reconstruction of sensors
using es9 as the final reference was done using an incorrect rotation on
es10, hence the reconstructed value of es10 do not match the value of
es10 as it was used in Section V.A for the final reference sensor in the
SLM line. The misorientation in es10 has been shown to have no
significant influence on other SLM sensors in the laser line. A
discussion of the problems encountered with the rotations of es10 is
discussed in Section VI.A.

#####  {#section-3 .unnumbered}

#####  1. July/August Results  {#julyaugust-results .unnumbered}

All the sensors were reconstructed with COCOA in the manner described
previously. All of the reconstructed sensors in the ISR tunnel had their
mean reconstructed positions in the tunnel plotted as a function of real
UNIX time to examine the characteristic behavior of the system. These
plots detailing the distributions of COCOA reconstructed positions are
reproduced in their entirety in Appendix B, Figures 1-10. Samples of
characteristic plots for each SLM laser are given below in Figures 10
and 11.

![](media/image11.wmf){width="5.992361111111111in"
height="3.5083333333333333in"}

**Figure 10: Typical Distribution of Reconstructed Positions for an SLM
sensor in July for Laser 302 Using es9 as the Final Reference Sensor.**
(Bands are non-physical**)**

![](media/image12.wmf){width="5.992361111111111in"
height="3.5083333333333333in"}

**Figure 11: Typical Distribution of Reconstructed Positions for an SLM
sensor in July for Laser 303 Using es9 as the Final Reference Sensor.**
(Bands are non-physical**)**

The distribution of reconstructed means along the CSC layer SLM
typically fell within a 100-140 μm range in Y and a 40-80 μm range in Z
for both lasers 302 and 303. Though both lasers appear to show a slight
drift in the Y distributions, any apparent drift in the data cannot be
resolved outside the systematic errors. All of the distributions appear
to look very similar, with the exception of es10. As discussed in the
review of the COCOA reconstruction of the SLM using es10 as a reference
sensor (Section V.A.), the raw and fitted pixel distributions from FLAP
were found to not track the distributions in the other SLM sensors, so
this result in not unexpected.

The reconstruction of the Transfer line sensors yielded a distribution
of the sensors' mean ISR positions that fell within the systematic error
involved in the COCOA reconstruction. Though no correlations could be
drawn out due to the systematic error, the resulting distributions (in X
and Y) for sensors et0 and et1 looked fairly similar. The distribution
of positions for sensor et4 seemed to mirror those of the other sensors
in Y, but looked random in X. It should be noted that sensor et4 had
only two CCDs (lower and far X ISR) illuminated by the laser and the
preceding reference sensor, et3, did not have its upper CCD (which
tracks X motions) illuminated, thus it was expected that et4's
resolution would be degraded.

##  2. September Results

These plots detailing the distributions of COCOA reconstructed positions
are reproduced in their entirety in Appendix B, Figures 11-21. Sample
plots from the September data set showing the position of a typical
sensor are shown in Figures 12 and 13. The distribution of COCOA
reconstructed positions of the SLM sensors as a function of time all
seem to be continuation of the previous July/August data until there is
a large jump in the Laser 302 Y and Z and Laser 303 Y data. This
apparent jump in sensor positions is most prevalent when the sensors
were reconstructed with Laser 302, though a smaller apparent jump is
observed along the Y axis when the reconstruction was done with Laser
303. The jump appears to coincide exactly with the replacement of Laser
302 and matches a jump in the raw and pixel distributions from FLAP. The
amplitude of the jumps appears to gradually decrease in magnitude from
es2 to es7 as the sensor distance from laser 302 increases. The Z
positions of the SLM sensors do not appear to undergo any significant
changes when reconstructed with Laser 303. Indeed, an examination of
Figures 1-20 in Appendix B shows significant changes between the
July/August SLM sensor positions and September SLM sensor positions -
except in the Z positions associated with Laser 303. Such shifts could
potentially have been caused by disturbing the position or orientation
of the transfer plate during the replacement of the laser; however it is
not yet clear if this was the case. Raw FLAP data is presently being
correlated with the September COCOA reconstruction to further study this
phenomenon. Since the jump in apparent sensor positions was so
significant and occurred early in the September test period, the time
period prior to the jump (containing approximately 120 of 1300 events)
was excluded from the analysis and the July/August test period was
examined separately from the September test period.

![](media/image13.wmf){width="5.992361111111111in"
height="3.5083333333333333in"}

**Figure 12: Typical Distribution of Reconstructed Positions for an SLM
sensor in Sept for Laser 302 Using es9 as the Final Reference Sensor.**
(Bands are non-physical**)**

![](media/image14.wmf){width="5.992361111111111in"
height="3.5083333333333333in"}

**Figure 13: Typical Distribution of Reconstructed Positions for an SLM
sensor in Sept for Laser 303 Using es9 as the Final Reference Sensor.**
(Bands are non-physical**)**

An examination of the remaining September SLM data after the jump shows
that the range of the entire distribution of mean positions for all
sensors (and all lasers) typically fall within the systematic error of
each sensor. The distributions appear to be much tighter than those in
July as reflected by the smaller statistical errors associated with
these events. The Transfer line sensor distributions (again they fall
within the systematic error) appear very similar to those taken in
July/August, though the September distributions are slightly more spread
out. There is no apparent jump in the location of any Transfer line
sensors.

**3. Discussion of et2, et3, and es9 Reference Sensor Reconstruction**

COCOA Reconstruction of the test setup using es9 as the final SLM
reference show the Transfer Line, Laser 302 Z September, and all Laser
303 Z reconstructions remain essentially unchanged from the es10
reconstruction results. The drift in the Y coordinate reconstruction of
the SLM sensors evident in Figure 4 for the es10 reconstruction is no
longer visible. Rather, all of the sensor Y locations now lie roughly
within 200 μm of their surveyed locations (es10 excluded). A slight
shift in the sensor Y reconstructions is now observed between the
July/August and September data and is more prevalent with the Laser 302
reconstruction. A summary of the results for all sensors from each test
period are given in Table 5 and Figures 14-16.

<table>
<colgroup>
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 8%" />
<col style="width: 8%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Sensor</strong></td>
<td colspan="2"><h4 id="julyaug-1">July/Aug</h4>
<h4 id="laser-301-2">Laser 301</h4></td>
<td colspan="2"><h4 id="statistical-error-july-3">Statistical Error
(July)</h4></td>
<td colspan="2"><h4 id="sept-3">Sept° </h4>
<h4 id="laser-301-3">Laser 301</h4></td>
<td colspan="2"><h2 id="statistical-error-sept-3">Statistical Error
(Sept)</h2></td>
<td colspan="2"><h2 id="systematic-error-3">Systematic Error</h2></td>
</tr>
<tr class="even">
<td><strong>Xmean (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Xerror (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Xmean (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Xerror (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><p><strong>Xerror</strong></p>
<p><strong>(μm)</strong></p></td>
<td><p><strong>Yerror</strong></p>
<p><strong>(μm)</strong></p></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>et0</strong></td>
<td>54</td>
<td>39</td>
<td>9</td>
<td>9</td>
<td>-168</td>
<td>31</td>
<td>8</td>
<td>22</td>
<td>&lt; 132</td>
<td>&lt; 168</td>
</tr>
<tr class="odd">
<td><strong>et1</strong></td>
<td>25</td>
<td>-237*</td>
<td>7</td>
<td>7</td>
<td>-123</td>
<td>-257*</td>
<td>15</td>
<td>16</td>
<td>&lt; 133</td>
<td>&lt; 500</td>
</tr>
<tr class="even">
<td><strong>et4</strong></td>
<td>435</td>
<td>-48</td>
<td>27</td>
<td>11</td>
<td>447</td>
<td>49</td>
<td>24</td>
<td>12</td>
<td>&lt; 170</td>
<td>&lt; 158</td>
</tr>
</tbody>
</table>

<table style="width:100%;">
<colgroup>
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Sensor</strong></td>
<td colspan="2"><h4 id="julyaug-laser-302-1">July/Aug Laser
302</h4></td>
<td colspan="2"><h4 id="statistical-error-july-4">Statistical Error
(July)</h4></td>
<td colspan="2"><h4 id="sept-4">Sept°</h4>
<h4 id="laser-302-1">Laser 302</h4></td>
<td colspan="2"><h4 id="statistical-error-sept-4">Statistical Error
(Sept)</h4></td>
<td colspan="2"><h4 id="systematic-error-4">Systematic Error</h4></td>
</tr>
<tr class="even">
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><p><strong>Yerror</strong></p>
<p><strong>(μm)</strong></p></td>
<td><p><strong>Zerror</strong></p>
<p><strong>(μm)</strong></p></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>es1</strong></td>
<td>276*</td>
<td>1</td>
<td>8</td>
<td>fixed</td>
<td>254</td>
<td>13</td>
<td>17</td>
<td>fixed</td>
<td>&lt; 166</td>
<td>&lt; 53</td>
</tr>
<tr class="odd">
<td><strong>es2</strong></td>
<td>205</td>
<td>67</td>
<td>44</td>
<td>6</td>
<td>-18</td>
<td>-471</td>
<td>17</td>
<td>12</td>
<td>&lt; 211</td>
<td>&lt; 125</td>
</tr>
<tr class="even">
<td><strong>es4</strong></td>
<td>202</td>
<td>162</td>
<td>53</td>
<td>7</td>
<td>56</td>
<td>157</td>
<td>6</td>
<td>5</td>
<td>&lt; 167</td>
<td>&lt; 110</td>
</tr>
<tr class="odd">
<td><strong>es5</strong></td>
<td>282</td>
<td>312</td>
<td>27</td>
<td>11</td>
<td>124</td>
<td>101</td>
<td>13</td>
<td>5</td>
<td>&lt; 146</td>
<td>&lt; 107</td>
</tr>
<tr class="even">
<td><strong>es6</strong></td>
<td>-80</td>
<td>106</td>
<td>22</td>
<td>18</td>
<td>-153</td>
<td>-42</td>
<td>10</td>
<td>6</td>
<td>&lt; 121</td>
<td>&lt; 109</td>
</tr>
<tr class="odd">
<td><strong>es7</strong></td>
<td>-68</td>
<td>58</td>
<td>21</td>
<td>17</td>
<td>-156</td>
<td>39</td>
<td>21</td>
<td>17</td>
<td>&lt; 112</td>
<td>&lt; 116</td>
</tr>
<tr class="even">
<td><strong>es10**</strong></td>
<td>985</td>
<td>-932</td>
<td>8</td>
<td>46</td>
<td>771</td>
<td>-684</td>
<td>16</td>
<td>28</td>
<td>&lt; 114</td>
<td>&lt; 137</td>
</tr>
</tbody>
</table>

<table style="width:100%;">
<colgroup>
<col style="width: 10%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td rowspan="2"><strong>Sensor</strong></td>
<td colspan="2"><h4 id="julyaug-laser-303-1">July/Aug Laser
303</h4></td>
<td colspan="2"><h4 id="statistical-error-july-5">Statistical Error
(July)</h4></td>
<td colspan="2"><h4 id="sept-5">Sept°</h4>
<h4 id="laser-303-1">Laser 303</h4></td>
<td colspan="2"><h4 id="statistical-error-sept-5">Statistical Error
(Sept)</h4></td>
<td colspan="2"><h4 id="systematic-error-5">Systematic Error</h4></td>
</tr>
<tr class="even">
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><strong>Ymean (μm)</strong></td>
<td><strong>Zmean (μm)</strong></td>
<td><strong>Yerror (μm)</strong></td>
<td><strong>Zerror (μm)</strong></td>
<td><p><strong>Yerror</strong></p>
<p><strong>(μm)</strong></p></td>
<td><p><strong>Zerror</strong></p>
<p><strong>(μm)</strong></p></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td><strong>es1</strong></td>
<td>276*</td>
<td>1</td>
<td>7</td>
<td>fixed</td>
<td>257</td>
<td>13</td>
<td>15</td>
<td>fixed</td>
<td>&lt; 167</td>
<td>&lt; 53</td>
</tr>
<tr class="odd">
<td><strong>es2</strong></td>
<td>-183</td>
<td>-40</td>
<td>38</td>
<td>8</td>
<td>-231</td>
<td>-41</td>
<td>22</td>
<td>15</td>
<td>&lt; 147</td>
<td>&lt; 146</td>
</tr>
<tr class="even">
<td><strong>es4</strong></td>
<td>-21</td>
<td>6</td>
<td>17</td>
<td>9</td>
<td>198</td>
<td>-2</td>
<td>10</td>
<td>8</td>
<td>&lt; 188</td>
<td>&lt; 123</td>
</tr>
<tr class="odd">
<td><strong>es5</strong></td>
<td>58</td>
<td>291</td>
<td>11</td>
<td>8</td>
<td>-36</td>
<td>284</td>
<td>8</td>
<td>6</td>
<td>&lt; 146</td>
<td>&lt; 113</td>
</tr>
<tr class="even">
<td><strong>es6</strong></td>
<td>19</td>
<td>129</td>
<td>11</td>
<td>9</td>
<td>-102</td>
<td>121</td>
<td>7</td>
<td>6</td>
<td>&lt; 120</td>
<td>&lt; 105</td>
</tr>
<tr class="odd">
<td><strong>es7</strong></td>
<td>17</td>
<td>177</td>
<td>10</td>
<td>17</td>
<td>-96</td>
<td>148</td>
<td>10</td>
<td>17</td>
<td>&lt; 112</td>
<td>&lt; 105</td>
</tr>
<tr class="even">
<td><strong>es10**</strong></td>
<td>1211</td>
<td>-266</td>
<td>7</td>
<td>6</td>
<td>1082</td>
<td>-287</td>
<td>4</td>
<td>5</td>
<td>&lt; 117</td>
<td>&lt; 117</td>
</tr>
</tbody>
</table>

#### Table 5 : Deviation of COCOA Reconstruction of DCOPS Dowel Pin Positions from Expected Survey Location with es9 Survey as Final Reference

° Events fitted in Sept Data correspond to introduction of new laser
diode in SLM line (525+ events). September events taken prior to the
introduction of the new laser (100 events) where typically within
20-150μm of July positions.

\* Transfer plate Y definition was broken by at 1.71 mm ± .5 mm. This is
survey position with estimated movement of transfer plate components.
See Section IV.C for detailed description of problem.

\*\* The orientation of Sensor es10 was found to be incorrect.
Subsequent reconstruction of single events using the corrected
orientation indicates the (Y,Z) location of es10 is closer to (182,
-419) in July and (162, -439) in Sept

![](media/image15.wmf){width="6.095138888888889in"
height="3.7090277777777776in"}

**Figure 14: Transfer Line Results of COCOA Reconstruction for
July/August and September Runs Using es9 as the Final Reference
Sensor.** Error bars indicate total uncertainty in sensor location as
determined by COCOA.

![](media/image16.wmf){width="6.095138888888889in"
height="3.7090277777777776in"}

**Figure 15: SLM Line (Laser 302) Results of COCOA Reconstruction for
July/August and September Runs Using es9 as the Final Reference
Sensor.** Placement of es10 is exaggerated by the misorientation of the
es10 sensor. The corrected orientation was used for the reconstruction
of the SLM shown in Section V.A. See Section VI.A for a more detailed
description of the problem. Error bars indicate total COCOA uncertainty.

##### ![](media/image17.wmf){width="6.095138888888889in" height="3.7090277777777776in"} {#section-4 .unnumbered}

**Figure 16: SLM Line (Laser 303) Results of COCOA Reconstruction for
July/August and September Runs.** Placement of es10 is exaggerated by
the misorientation of the es10 sensor. The corrected orientation was
used for the reconstruction of the SLM shown in Section V.A. See Section
VI.A for a more detailed description of the problem. Error bars indicate
total uncertainty in sensor location as determined by COCOA.

As with the es10 reference sensor reconstruction, a comparison of Figure
15 and 16 shows that the reconstructed Z coordinate positions of several
of the sensors do not overlap (an overlay of Figures 8 and 9 is given in
Appendix B, Figure 24). In particular, the reconstructed means of the
Laser 302 es2, es5, and es10 Z coordinates in September show some
disagreement with corresponding reconstructions using the other lasers.
The discrepancy is, however, much less than with the es10 reconstruction
since most error bars now overlap between the two lasers and test
periods. Since sensor es10's operable CCDs monitoring changes along the
Z axis were found not to track the CCDs in preceding sensors, the es10
result was expected.

##  4. Conclusions

Reconstruction of all DCOPS sensors within 200 μm of the June survey
positions was achieved for most of the sensors in both reconstructions
for both test periods if the errors in the CERN Photogrametry are
considered. The elimination of the drift in the es10 reference sensor Y
coordinate reconstruction by choosing es9 as the reference indicates the
surveyed location of orientation of es10 is incorrect. The shifted
location of es7's Y coordinate between the two reconstructions suggests
the misplacement or impact of an incorrect orientation of es10 is on the
order of 250-350 μm.

Figure 17 indicates that the reconstruction of sensors utilizing es9 as
the final reference indicates that resolution of the entire ISR system
(excluding es10) can be generalized as ∼223µm for the July test period,
∼150µm for the September test period, and ∼187µm across both test
periods. This again compares favorably to the uncertainty in the
photogrammetric location of the dowel pins (σ~y~ =180 μm, σ~z~ =160μm)
with which the reconstructed location of the dowel pins are compared.

![](media/image18.jpeg){width="6.094444444444444in"
height="3.798611111111111in"}

**Figure 17: Summary of Reconstructed SLM and Transfer Sensor Locations
for es9 Reference Reconstruction.** Histograms represent the deviation
of all reconstructed sensor locations from their initial photogrammetry
survey location. Both Laser 302 and 303 reconstructions are included in
the data. The averaged σ for both test periods is 187µm.

The most basic test as to whether or not the system works in a self
consistent manner has been met: the apparent location and relative
positioning of most sensors can be said to remain roughly within the
projected error of the reconstruction independent of the choice of laser
used along the SLM line. This test is much more critical than matching
the reconstructed position of the sensor dowel pins to their surveyed
location since survey errors can be large (\>150 μm along SLM line,
perhaps more in the case of the es10 Y coordinate). Some discrepancies
between reconstructions based on the laser choice are expected since the
sensors participating in the measurements may gain or lose CCDs or see
completely different signal to background ratios. Perhaps more
significantly, the active CCDs on the SLM reference sensors are switched
with choice of lasers due to shadowing effects by preceding sensors.
Thus, two sets of measurements utilizing each laser *with the same
reference CCDs* on the endpoints are not available.

There is also ample evidence to suggest that the reconstructed positions
of the sensors are independent of small variations in the orientation of
the laser. An analysis of the individual CCDs used in the reconstruction
shows several cases in which the angle of the laser seems to suddenly
shift. Figure 18 (below) shows the July distribution of raw centroid
measurements in each CCD of sensor es4. Three distinct jumps in the
location of the laser centroid can be clearly seen. The first jump in
the distribution is approximately 30 pixels (30 pixel = 420μm). Figure
19 (below) shows the reconstructed location of sensor es4 over the same
period of time. There is no indication of any breaks or jumps in the
distribution to suggest any sort of correlation with the jumps in CCD
centroids in Figure 18 (σ~y~ = 10 μm, σ~z~ = 8 μm).

![](media/image19.jpeg){width="6.227083333333334in"
height="4.585416666666666in"}

Figure 18 : Distribution of raw CCD means in es4 during the July/August
Run. Three distinct jumps in the pixel distributions can be seen.

![](media/image20.jpeg){width="5.677083333333333in" height="3.34375in"}

Figure 19 : Distribution of COCOA Reconstructed location of es4 in the
ISR hall during the July/August Run. No jumps in the data are evident.
(Bands are non-physical)

As previously discussed, there does seem to be a clear correlation with
the introduction of a replacement Laser 302 in September with a large
jump in the es9 reconstructed positions of the sensor and the ending of
erratic behavior from those reconstructed with the es10 reference sensor
(see Appendix A, Figure 16). This effect is not entirely understood and
presently under review.

###### Limitations of Reconstruction

Not all sensors in the test hall could be reconstructed within the
desired 200μm. Furthermore, the systematic errors were significant.
Several factors which may have contributed to errors in the COCOA
reconstruction are now addressed.

## A. Determination of Angular Orientations

As discussed, the results presented were determined by fixing the
angular orientation of the unknown sensors in COCOA to their surveyed
orientation. This cannot be done in the final CMS system. Additional
studies are underway to understand how well these angles can be
determined from the COCOA reconstruction of actual CCD measurements and
the impact on this has on the spatial resolution of the system.

COCOA determines the angular orientation of the dowel pins be finding
the minimum error associated with the inverse of the matrix used to
determine the best fit of the CMM data with the CERN survey data. In the
case of es10, two local minima's to this fit occurred unusually close to
each other. Although both minima's yielded slightly different dowel
orientations (\<1.5 degrees), they had identical dowel locations.
Reconstructing with the larger of the two rotations introduced
significant errors in the entire SLM line when es10 was used as the
final SLM reference (see Appendix A, Figure 24) The larger rotation on
es10 introduced errors in only the reconstructed location of es10 when
es9 was used as the final SLM reference. Upon discovery of the second
minima, the reconstruction of all events using the new (smaller
rotation) orientation of es10 as the SLM reference was performed. The
location of es10 in the reconstruction using es9 as the final reference
is the original (larger rotation) value.

## B. Reference et2 MAB Motions

The absolute establishment of the positions of the reference sensors
et2, et3, and es10 are the most critical parameters of the
reconstruction. In the present COCOA simulation, the locations of et3
and es10 are given by photogrammetric measurements taken in June. These
sensors were not moved or repositioned from their mounts until the end
of the September tests. The et2 sensor, however, was installed just
prior to the July tests on a simulated MAB. Though a series of
photogrammetry measurements were taken just prior to the beginning of
the test periods, the MAB could have undergone small shifts in position
and orientation. These small motions of the MAB (if any) were monitored
by the LINK Alignment group. Test data from the EMU and LINK groups are
presently being correlated to better understand possible motions. The
ISR data can be reconstructed with a new COCOA simulation using a
non-static MAB model if motions are supplied by the LINK group.

## C. Calibration of DCOPS Sensors

In principle, the calibration of the sensors taken before the June ISR
tests was to be compared to a recalibration of the sensors upon
completion of the September tests. This measurement was to estimate both
the stability of the sensors during the ISR tests as well as reconfirm
the validity of the original calibration. However, serious problems with
the original calibration and the recalibration were uncovered upon
careful examination of the data, making any definitive estimation of the
sensor calibration at the time of installation impossible. The sensors
have since been recalibrated a third time and this data is being
examined. However, the new set of calibrated data is being estimated as
valid with a maximal uncertainty of 100 μm.

Instability in the mount points of the CCDs in each sensor is clearly
insignificant in the flat CCD windows by construction. The
bi-directional sensor windows may exhibit some instability, particularly
after handling and installation of filter tapes on the window. Errors in
the Reconstruction due to these instabilities have not yet been
investigated.

It is expected that a better understanding of the calibration process in
the coming months will significantly drop the error associated with the
calibrated parameters. A calibration of the parameters perpendicular to
the pixel arrays is also planned.

## D. Calibration of Transfer Plate

The transfer plate fixes the relationship of sensors et1 and es1 and
allows for the reconstruction of the SLM line (which uses es1 and es10
as reference sensors). Since et1 is determined from the Transfer line
reconstruction (using et2 and et3 as reference sensors), it is essential
that relationship on the transfer plate is specified precisely - as
errors in the definition of this relationship will be compounded with
errors from the derived position of et1.

Unfortunately, after the CERN photogrammetry of the transfer plate
components, the relationship between es1 and et1 was accidentally broken
by someone making an unrecorded adjustment to plate. It is assumed that
such adjustments were only made to the slide which mounts the et1
sensor. This difference appeared after the survey of the photogrammetry
targets on these sensors was done. Based on the subsequent measurements
with a micrometer, it is thought that the et1 sensor was lowered
approximately 1.71 mm ± .5mm in Y CMS only. The transfer plate was
secured in its final position and sent to FNAL for additional CMM
measurements to determine the precise magnitude of the displacement.

The transfer plate was measured again at FNAL by CMM on February 6,
2001. It was determined at this time that the vertical (Y CMS)
separation between the et1 and es1 reference dowel pins was 187.198 mm ±
.030 mm. Since the adjustable slide on the transfer plate moves only the
et1 sensor, the 'true location' of et1 can be inferred from the CERN
Photogrammetry location of es1 and the CMM separation of the dowel pin
to be 1298.792 mm ± .153 mm in Y CMS.

## E. Additional Fit Parameters (Shadowing, Poor Centroids)

Not all sensors in the ISR tunnel were able acquire usable data from all
four of their CCDs due to either a malfunction on the DCOPS board or the
shadowing of the laser line by preceding sensor windows. As a result,
COCOA reconstructed the laser lines using only two or three CCDs on
these particular sensors. Fortunately, sensors with two unusable CCDs
had at least one vertical and horizontal CCD operable allowing for a
reconstruction of the dowel location in the requisite two dimensions.
Reference sensors et2, et3, and es10 had three usable CCDs and reference
sensor es1 had all four CCDs working. However, July Run 458 showed
sensor et2 with only two operable CCDs. This introduced significant
errors in the Reconstruction. For example, the et1 sensor reconstructed
positions along the X axis showed very large deviations exceeding 200μm
between successive events. This error was propagated across the transfer
plate and introduced significant variations between events on the SLM
line as well. By contrast, with the more typical readout of three CCDs
on et2, reconstructed positions of et1 typically fell well within a
range of 100 μm. Fit and reconstruction problems were also induced by
very poor laser distributions in individual CCDs.

Since reference sensors et2, et3 and es10 each had a shadowed CCD, it
seems plausible that successfully illuminating all four CCDs on these
reference sensors would improve the accuracy and precision of the
overall reconstruction. This issue is presently being studied with an
idealized simulation model of the EMU system.

## F. Redundancy of Second Measurements in SLM Line

Events reconstructed thus far have utilized SLM Laser 302 (with the beam
running toward the es9 reference) or Laser 303 (with the beam running
toward reference sensor es1) separately. Since data with either SLM
laser is taken synchronously with the Transfer line, events
reconstructed with Laser 302 have no direct correlation to those
reconstructed with Laser 303. If SLM Laser 302 and 303 data could be
taken very close in time, the tracking and resolution of the sensors
within short time frames could be greatly improved by incorporating both
sets of SLM data into a single reconstruction of the system. Simulations
modeling the reconstruction of single events using both Laser 302 and
303 data as near simultaneous measurements are underway.

## G. First Level Analysis of CCD Data

The processing of raw data from the DAQ included the determination of
the mean pixel location of the charge distribution formed by the
incident laser. This mean was later entered into COCOA as a starting
point for a reconstructed measurement. A detailed study of the raw
charge distribution in the CCDs and the determination of the mean value
have been presented separately. The conclusion of this study is that the
mean value of the charge distribution can be determined in the ISR
within 1 pixel (\<14 μm of rms error) under repeated, short term
measurements. The studies examining medium and long term resolutions are
thought to be limited by the stability of the laser diode. It should be
emphasized that the spatial stability of the laser lines for time
periods exceeding the integration time of the CCDs is not a requirement
for a successful Reconstruction of the system. However, abnormalities in
raw CCD data have not yet been correlated to the abnormalities in the
reconstructed data.

Additional work has been done carefully refitting several of the raw CCD
charge distributions 'by hand'. The reconstructed position of the
sensors was found to remain in essentially the same location as when
reconstructed with the original FLAP automated fits. We have concluded
that the fitting of the centroids performed by FLAP is more than
adequate for reconstruction of alignment positions within the required
performance specifications.

###### Acknowledgements for ISR Testing and DCOPS Prototype Development

We especially thank our collaborators of Northeastern University (J.
Moromisato, Eb vonGoeler, R. Terry) who built the mechanical parts,
calibrated and filtered the DCOPS sensors, and worked with us in the
development, setup, and some execution of the tests.

We also thank S. Hanson, E. Cowden, J. Lofgrin, R. Martin (Fermilab PPD
Electronics group) and V. Sknar, E. Orischin (Petersburg Nuclear Physics
Institute) for their development, construction, testing, DSP
programming, etc. of the DCOPS sensor and electronics for the ISR I4
tests. P. Arce's help and effort adapting COCOA for use with DCOPS
sensors is also appreciated.

We thank the CERN Laboratory EP/CMS (A. Ball, D. Arevalo, R. Riberio)
for establishing the ISR I4 test area, utilities, supports; for survey
services and Photogrammetry (C.Lasseur, C. Humbertclaude, D. Mergelkuhl,
R. Goudard, J.Noel. Joux and crew- CERN Geodesy). We also thank the
Fermilab Geodesy (J. Greenwood and crew) for Photogrammetry measurements
of our sensor assemblies; and the Fermilab Technical Division for CMM
measurements of brackets and the transfer plate.