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June 12, 2002

# COCOA Simulation of the EMU Alignment System

(Draft v2)

D. Eartly, R. Lee, K. Maeshima

####### Fermi National Accelerator Laboratory

#### Abstract

A general simulation of the CMS Endcap Muon Position Monitoring System
(EMPMS) has been performed to evaluate the operational viability of the
system as a whole, estimate the precision with which the system can
reconstruct CSC chamber positions, and relate the contribution of
uncertainties in the construction of individual components to the
performance of the system as a whole. Simulations of an idealized EMU
system were performed with COCOA v2.0.0. The simulations included all
major system components and appropriate CSC chamber geometries. This
report is a summary of the work presented in Ref \[1\].

## COCOA Simulation of the Endcap Muon Alignment Scheme

A detailed description of the Endcap Muon Position Monitoring System
(EMPMS) may be found in Reference \[1\] and \[2\]. The EMPMS system is
charged with the determination and monitoring of Cathode Strip Chamber
(CSC) locations and orientations in the Muon Endcap System. The system
employs crosshair laser diodes and Digital CCD Optical Position Sensors
(DCOPS) to determine CSC positions along three Straight Line Monitoring
(SLM) laser lines and the positions of the iron Muon Endcap (ME) Layers
upon which the all CSC chambers are mounted.

An object oriented model of an idealized EMPMS has been constructed in
the framework of the CMS Object Oriented Code for Optical Alignment
(COCOA v2.0.0) \[3\]. COCOA allows the user to reconstruct the position
and angles of optical objects in a given system as well as propagate
associated (RMS) errors. The COCOA simulation includes all major system
components and appropriate CSC chamber geometries. Since the system is
idealized, it has been assumed that all measurement devices are able to
make a successful measurement and the full redundancy of the alignment
scheme (multiple measurements of opposing lasers) is exploited. The
effects of component failure (missing CCD measurements from DCOPS,
faulty laser modules, inadequate resolutions) should be examined
separately.

1.  **Definition of Simulation Components and Uncertainties**

All components of the EMPMS system have been included in the present
COCOA simulation including CSC chambers, DCOPS sensors, inclinometers,
and proximity sensors. The description and estimation of mechanical
uncertainties on each component in the simulation is based upon official
CMS production drawings. The operational performance of DCOPS and analog
sensors in the simulation is taken from the findings of the full scale
prototype of the partial system tested at the CERN ISR tunnel in the
summer of 2000 \[4\].

The most important object in the simulation is the basic Cathode Strip
Chamber (CSC) object. Of principle importance is the manner in which the
chamber 'center' is related to the reference pin on the DCOPS sensors.
Since tolerances between the separation of strip layers is not
controlled in CSC chamber production, it has been decided to define a
'Reference Center' (or 'Active Centerpoint') for the chambers as the
average strip position projected onto the upper strip plane. For a
perfectly constructed CSC chamber (no uncertainties in construction),
the geometrical centerline of the CSC chamber will fall along the Active
Reference Center of the simulated chambers. The uncertainty between the
Active Reference Center and primary DCOPS reference pin is estimated as
±129 µm in the CMS RΦ plane and includes estimations of uncertainties
arising from the distortion and shearing between CSC layers. Other
uncertainties considered by the simulation include the LINK
reconstruction of MAB positions (±135 µm, ±10 µrad) and Secondary Link
Lines on ME ±1 (±10 µm, ±2 µrad) \[5\] as well as uncertainties in the
calibration of DCOPS sensors \[6\].

The final COCOA simulation script contained approximately 6200 separate
objects to fit with at least 4700 non-zero correlations. A VRML model of
the system constructed by COCOA is shown in Figure 1.

![](media/image2.jpeg){width="5.992361111111111in"
height="4.956944444444445in"}

Figure 1: The Simulated EMU Alignment System. This is a COCOA generated
VRML representation of the simulated geometry used for the idealized
simulations of the EMU Alignment System.

2.  **Simulation Results**

Using the full COCOA simulation model, several attempts were made to
obtain a fit of the complete 8 ME disc system. These attempts failed
with the computers reporting abnormal utilization and allocation of
memory. Indeed, when the memory usage of the system was examined, it was
found that the memory required for the storage of the resulting matrices
exceeded the 1GB. The largest simulation successfully fit with the
available memory was a complete ME ±2, ±3, ±4 layer system (6 of 8 ME
Layers + Transfer Laser Lines).

Fifty-three smaller subsets of the ME ±2, ±3, ±4 Layers and Transfer
Line simulation were also completed and compared amongst themselves and
the larger 6 ME layer simulations. These subsets included all possible
permutations of systems composed of at least two ME layers with full
transfer line systems.

### Comparison of Large Simulations vs. Small Simulations

Comparisons made between systems within the 53 subsets of two ME disc
systems showed very little variation (\< 10%) between the certainties
with which identical chambers could be reconstructed. Comparisons made
between these two ME Layer systems and the larger six ME Layer system
also yielded very little variation (\< 5%) between the uncertainties
with which identical chambers could be reconstructed. This seems to
confirm that there is very little coupling of components across
different ME Layers.

1.  **Reconstruction of CSC Chambers Locations and Orientations**

The uncertainty in spatial definition for CSC chambers along a
particular SLM line may vary from the uncertainty of similar chambers in
other SLM lines. However, the discrepancies between chamber
uncertainties in ME Layers with the same SLM arrangement of components
is expected to be small (\<10µm). For chambers in a given Endcap layer,
these variations are primarily due to differences in the separation
(i.e. lever arm) between transfer line and reference sensors located at
the SLM endpoints. Likewise, variations in the size and type of CSC
chambers across different ME Layers create similar discrepancies in the
spatial definition of CSC chamber locations. Since SLM lines on ME ±1
discs are constructed in a very different manner from those on SLM ME
±2, ±3, and ±4 discs, more substantial variations are expected between
chamber uncertainties when comparisons are made to ME ±1 chambers. The
mean uncertainty with which chamber locations and orientations along the
SLM lines can be reconstructed in the EMU alignment scheme is summarized
in Tables 2 and 3. The average deviations presented alongside the
estimates represent the average deviation from the mean uncertainty for
the all chambers of similar type or placement in the CMS detector.

The original ME ±1 alignment scheme did not incorporate inclinometers on
ME ±1/2 chambers. It had been assumed that the ME ±1/3 SLM lines, having
been offset from the Secondary Link laser lines, would provide
sufficient angular definition about the local chamber Z axis for the ME
±1/2 chambers (sensors on these chambers cannot discern rotations about
the laser lines). Simulations of the ME ±1 layer without inclinometers
revealed poor spatial and rotational resolution on all ME ±1 chambers.
For this reason, inclinometers similar to those employed on the transfer
plates were incorporated into the ME ±1/2 chamber frames. Simulations of
the idealized system are performed with the resolution of these
inclinometers set to be equivalent to the long term resolution of the
inclinometers studied during the 2000 ISR tests.

+--------------------+------------+----------+------------+----------+
| CSC Chamber        | Mean       |          | Average    |          |
|                    | U          |          | Deviation  |          |
|                    | ncertainty |          | of         |          |
|                    | in Chamber |          | U          |          |
|                    | Locations  |          | ncertainty |          |
+--------------------+------------+----------+------------+----------+
|                    | **CMS RΦ   | **CMS Z  | **CMS RΦ   | **CMS Z  |
|                    | (µm)**     | (µm)**   | (µm)**     | (µm)**   |
+--------------------+------------+----------+------------+----------+
|                    |            |          |            |          |
+--------------------+------------+----------+------------+----------+
| ME±1/2             | 515        | 717      | 17         | 9        |
|                    |            |          |            |          |
| (no inclinometer)  |            |          |            |          |
+--------------------+------------+----------+------------+----------+
| ME±1/2             | 90         | 385      | 2          | 5        |
|                    |            |          |            |          |
| (σ inclinometer =  |            |          |            |          |
| short term ISR σ)  |            |          |            |          |
+--------------------+------------+----------+------------+----------+
| ME±1/2             | 187        | 415      | 2          | 1        |
|                    |            |          |            |          |
| (σ inclinometer =  |            |          |            |          |
| long term ISR σ)   |            |          |            |          |
+--------------------+------------+----------+------------+----------+
| ME±1/3             | 216        | 878      | 3          | 22       |
+--------------------+------------+----------+------------+----------+
| ME±2/1             | 205        | 467      | 10         | 12       |
+--------------------+------------+----------+------------+----------+
| ME±2/2             | 221        | 509      | 7          | 24       |
+--------------------+------------+----------+------------+----------+
| ME±3/1             | 230        | 491      | 14         | 15       |
+--------------------+------------+----------+------------+----------+
| ME±3/2             | 248        | 520      | 20         | 22       |
+--------------------+------------+----------+------------+----------+
| ME±4/1             | 241        | 525      | 14         | 17       |
+--------------------+------------+----------+------------+----------+
| ME±4/2             | 259        | 524      | 20         | 17       |
+--------------------+------------+----------+------------+----------+

Figure 2: Uncertainty in CSC locations along the SLM lines for the
Idealized EMU System. The uncertainty estimates for chambers in ME ±1/2
layer have been done using two sets of resolutions for the inclinometers
placed on the ME ±1/2 CSC chamber frames.

+--------------------+------------+----------+------------+----------+
| **CSC Chamber**    | **Mean     |          | **Average  |          |
|                    | U          |          | Deviation  |          |
|                    | ncertainty |          | of         |          |
|                    | in Chamber |          | Unc        |          |
|                    | Ori        |          | ertainty** |          |
|                    | entation** |          |            |          |
+--------------------+------------+----------+------------+----------+
|                    | **CMS RΦ   | **CMS Z  | **CMS RΦ   | **CMS Z  |
|                    | (µrad)**   | (µrad)** | (µrad)**   | (µrad)** |
+--------------------+------------+----------+------------+----------+
|                    |            |          |            |          |
+--------------------+------------+----------+------------+----------+
| ME±1/2             | 95         | 95       | N/A        | N/A      |
|                    |            |          |            |          |
| (inclinometer      |            |          |            |          |
| short term ISR σ)  |            |          |            |          |
+--------------------+------------+----------+------------+----------+
| ME±1/2             | 698        | 698      | N/A        | N/A      |
|                    |            |          |            |          |
| (inclinometer long |            |          |            |          |
| term ISR σ)        |            |          |            |          |
+--------------------+------------+----------+------------+----------+
| ME±1/3             | 138        | 1168     | 3          | 360      |
+--------------------+------------+----------+------------+----------+
| ME±2/1             | 113        | 812      | 0          | 252      |
+--------------------+------------+----------+------------+----------+
| ME±2/2             | 74         | 771      | 0          | 297      |
+--------------------+------------+----------+------------+----------+
| ME±3/1             | 834        | 888      | 244        | 261      |
+--------------------+------------+----------+------------+----------+
| ME±3/2             | 742        | 777      | 303        | 323      |
+--------------------+------------+----------+------------+----------+
| ME±4/1             | 725        | 909      | 383        | 241      |
+--------------------+------------+----------+------------+----------+
| ME±4/2             | 1105       | 839      | 126        | 315      |
+--------------------+------------+----------+------------+----------+

Figure 3: Uncertainty in CSC Orientations About Axes Parallel to CMS
Coordinate System and Through CSC Chamber Centers in the Idealized EMU
System. The uncertainty estimates for chambers in ME ±1/2 layer have
been done using two sets of resolutions for the inclinometers placed on
the ME ±1/2 CSC chamber frames.

2.  **Dependency of Reconstruction on DCOPS-Reference Center
    Uncertainties**

Figure 4 shows how the uncertainties in the CMS RPhi position of the CSC
chambers vary with the uncertainty in the chamber construction (along
the chamber's local X axis). For all chambers, this relationship is
linear. The slope indicates the correlation between uncertainties in
chamber construction and reconstructed chamber RPhi positions is roughly
1:3, except on the ME ±1/2 chambers where it is closer to 1:4. The
significantly higher correlation on the ME ±1/2 chambers is due the much
lower uncertainties associated with the definition of the Secondary Link
lines and resolution of the ME ±1/2 LINK CMOS sensors. Correlations
decrease slightly for chambers located in ME layers further away from
the MABs as the net uncertainty is generally larger.

![](media/image3.wmf)

Figure 4: Reconstructed CSC RPhi Chamber Uncertainty vs. DCOPS-CSC
Reference Center Tolerance. The plot shows the average uncertainty in
reconstructed chamber locations as a function of the uncertainty
estimate on the relative placement of the primary DCOPS calibration pin
with the chamber reference centerpoint.

3.  **References**

\[1\] R. Lee. Simulation and Study of the CMS Endcap Alignment Scheme.
PhD Thesis, Purdue University, 2002.

\[2\] <http://home.fnal.gov/~maeshima/alignment/outline/outline.html>

\[3\] Brunel, L., Simulation and Reconstruction Software for
Opto-Geometrical Systems. CMS Note 1998/079, Nov 10, 1998.

P. Arce. CMS Object Oriented Code for Optical Alignment (COCOA). CMS
NOTE-2002/001.

\[4\] D. Eartly, R. Lee, K. Maeshima. ISR 2000 EMU Alignment Test
Results Summary. CMS IN-2002/004.

\[5\] Link Alignment Group, "Simulation and Performance", Muon Alignment
EDR / Muon EDR-3 Documentation, Nov 2000.

> Private communication with Pedro Arce, CERN, Nov 2000.

\[6\] COPS Sensor Board Calibration, J. Moromisato et al, Oct 2000,
unpublished.