# Estimation of Uncertainties in the DCOPS Primary Reference to CSC Average Active Area Reference Point

# 

# Digital CCD Optical Position Sensor (DCOPS) Sensors

DCOPS sensors are viewed as a collection of four independent vectors,
corresponding to the four CCD pixel arrays, referenced to a common
calibration slot on the DCOPS hardware assembly (where the CSC
calibration pin is to be inserted). Systematic uncertainties in the
location of the origin of these vectors, i.e. the first active pixel
position, is generally independent of the uncertainties associated with
the pixel array orientation. Uncertainties in the location of any given
pixel in a CCD to the calibration slot can be separated into
uncertainties directly associated with the calibration of the first
pixel position and those associated with the pixel array orientation and
length.

1\. Uncertainties in Direct Calibration of First Pixel Position.

Calibration of first active pixel positions to the reference pins for
large numbers of sensors is done on a specially designed test bench at
Northeastern University (NEU). The calibration bench is constructed of a
laser diode assembly, a single directional DCOPS sensor which has been
previously calibrated under a microscope, and a mount for the DCOPS
sensor which is to be calibrated. In this arrangement, the calibrated
DCOPS sensor acts as a mask to calibrate the uncalibrated DCOPS sensor.
NEU indicates typical uncertainties in the first pixel location using
this calibration technique will not exceed 40 μm (COPS Sensor Board
Calibration, J. Moromisato et al, Oct 2000, unpublished).

2\. Uncertainties in Pixel Array Orientation and Length

For simulation and reconstruction purposes, it is assumed that the four
CCD vectors lie in the local DCOPS XY reference plane and run parallel
to the X or Y axis. The error introduced by this assumption manifests
itself as a correction to the Sony specified pixel-to-displacement
conversion of 14μm per pixel along the array. The uncertainty in the
determination of the position of the charge distribution will scale
across the pixel array as the cosine of the angle by which the CCD array
deviates from its optimal orientation.

The uncertainty introduced by the error in pixel array length and the
misorientation of the pixel arrays can be estimated as the quadrature of
the maximal error due to the misalignment of the pixel arrays within the
CCD packages, the uncertainty in the length of the pixel array, and the
maximal error due to misalignment of the CCD package within the DCOPS
window frame.

2.1 Error Inherent in Manufacture of CCD Arrays and Packaging

Direct measurement of the pixel array length was performed on a
representative sample of ILX-551 CCDs. In addition to the 2048 active
pixels in each pixel array, one end of the array contains an additional
33 dummy pixels while the other end contains an additional 6 dummy
pixels. The total length of the pixel strip is calculated to be 29.218
mm based on the Sony pixel specification of 14 x 14 µm^2^ with no
manufacturer quote on the uncertainty in pixel size.

Sony has provided estimates of uncertainties for the placement of the
first pixel in the array in the CCD package, but does not offer any
estimate as to the uncertainty in the pixel array length or orientation.
These uncertainties where estimated as the maximal deviation from Sony
specifications found in the small set of CCDs studied. Systematic errors
embedded in the ILX551A CCD packages have been studied on a small sample
of unmounted CCDs. Direct measurements of the pixel array lengths on
these samples revealed a maximum discrepancy of (50 ± 10) µm with the
Sony specification (COPS Sensor Board Calibration, J. Moromisato et al,
Oct 2000). All measurements of the array lengths yielded a result which
was always greater than the Sony specified value.

Uncertainty occurring in the final active pixel position as the result
of a misalignment of the pixel array within the CCD package has been
determined to be less than 4 μm based on a measured 15 mrad deviation of
the array with the package edge (maximum misorientation found in the
small sample of measured CCDs) (COPS Sensor Board Calibration, J.
Moromisato et al, Oct 2000).

![](media/image1.jpeg){width="3.7291666666666665in"
height="3.6041666666666665in"}

**Figure E1 : SONY ILX-551 CCD Specification and Direct Measurement
(mm).** Diagram A shows the dimensional specifications and tolerances
for the ILX-551. Diagram B shows the dimensions of the CCD taken from
the small sample of studied ILX-551s which exhibits the greatest
deviation of the pixel array (in red) placement from the optimal
location.

2.2 Uncertainty of CCD Package Orientation Inside DCOPS Window Frame

Uncertainty occurring in the final active pixel position as the result
of the misalignment of the CCD package, and thus the encased pixel
array, scales as the cosine of misalignment. The present DCOPS window
frame design incorporates a specially designed polycarbonate mount for
the CCDs. Tolerances for the positioning of each end of the 53.71 mm
long CCD mounts in the window frame is ±100 µm, contributing an error of
less than 1 µm in the determination of the distance along the pixel
array. Tolerances for the placement (orientation) of the CCDs within the
polycarbonate mounts are estimated at \>?? mrad \[waiting for Rich's
Estimate\], contributing a maximal uncertainty of less than 10 µm
\[waiting for Rich's Estimate\] in the determination of the last active
pixel in the array.

3\. Final Estimation of Uncertainty in CCD Pixel - DCOPS Reference Pin
Calibration

The final estimation of the uncertainty associated with the
determination of the location of any given pixel in the DCOPS sensor
relative to the CSC reference slot is taken to be the quadrature of all
known errors in the determination of the first and last active pixel
positions in the pixel array. In addition to the systematic errors
associated with the placement of CCD arrays relative to the primary
reference pin, the manner and stability in which the centroid of charge
distributions is determined must be considered. It has been determined
that centroids from successive measurements on the CCD are repeatable to
±14 µm. This uncertainty is characterized as the uncertainty associated
with a particular measurement and considered separately in the COCOA
simulation. The contributions and final estimate of the systematic
uncertainty associated with the placement of pixels is given in Table
E1.

  --------------------------------------------------- -------------------
  **Uncertainty Origin**                              **Magnitude (µm)**

                                                      

  Direct Calibration of First Pixel (NEU Estimate)    40

  Array Misalignment (inside package)                 4

  Array Length                                        50

  Package Misalignment                                10

                                                      
  --------------------------------------------------- -------------------

Final Estimation of Uncertainty : 65µm

**Table E1 : Contributions to Final Error in Determination of
Pixel-to-CSC Reference Pin Calibration.** Uncertainties due to
misalignment and pixel array length are estimated as the worst case
errors in the determination of the final active pixel position.

# CSC Active Center - DCOPS Reference Pin Calibration

As previously discussed, Cathode Strip Chambers are described in terms
of their 'active center', which corresponds to the average of the
individual panel active areas projected onto the plane of the first
panel (See Section XX for more detail on chamber definition).
Determining the certainty with which this active center can be
externally referenced is crucial to the successful simulation and
reconstruction of the endcap muon system. Uncertainties in the
determination of the relationship between CSC active cathode strips and
DCOPS reference pins can be separated into uncertainties associated with
individual panel definitions and manufacture, assembly of multiple
panels to form the complete CSC chamber, the mounting assemblies which
affix the DCOPS sensors to the surface of the assembled chamber, and
deformations in the chamber after installation in CMS.

All estimations of uncertainties addressed here regarding CSC chamber
and DCOPS mounting hardware tolerances are typically gathered from the
specified tolerances placed on the fabrication of components. In most
cases, particularly CSC panel definitions, adherence to these tolerances
has been confirmed by direct measurement on an appropriate number of
preproduction samples. However, there are many components which have not
yet been produced on a large scale. Uncertainties for these components
have been estimated from production drawings. A far more meaningful
estimation of uncertainties for such components should be taken from the
rms value of deviations found from a sufficient sample of the finished
products.

In keeping with the convention established earlier (Section XX), the
local chamber coordinate system is taken as right handed with the local
Z axis running across the chamber centerline from the narrow end of the
chamber to the wider end and the local Y axis running from the bottom
layer to the top layer of cathode strips.

1\. CSC Panel Definition

All cathode strip chambers are constructed of a polycarbonate honeycomb
panels with 1.5 mm G-10 epoxy fiberglass skins coated with a 34 μm layer
of copper. Individual panels are first drilled with two CSC Alignment
Holes (where the CSC Alignment Pin will ultimately be inserted) along
the centerline (See Figure E2). These two holes (±25 μm tolerance on the
diameters) establish the reference system from which all other machining
on the panel is established. A high precision router is then used to
mill the cathode strips and associated artwork directly into the copper
surface of the panel. Accuracy of the router has been confirmed by
direct measurement. Errors in absolute strip position exhibit
accumulative systematics of \<15 μm over chamber width and have σ(local
rms spread) of 30 μm. The straightness strips have been measured as
having a σ(rms) of 22 μm

![](media/image2.jpeg){width="5.998611111111111in"
height="2.859722222222222in"}

**Figure E2 : Placement of Pins, Holes, and Etchings Required on CSC
Chamber.** Diagram A shows the dimensional specifications and tolerances
for the ILX-551. Diagram B shows the dimensions of the C

Additionally, a series of ten slot cuts are placed on each panel for
future calibration and quality control as well. The slot cuts are
referenced directly to the center line defined by the two CSC Alignment
Holes as well as a particular cathode strip number \-- but not
necessarily the first strip nor the same strip in all chambers. Each
mark is referenced within ±25 μm to the center point of the CSC
Alignment Holes and within ±25 μm to the particular strip being
referenced (the "Reference Strip").

A series of secondary dowel pins and slots used to mount the DCOPS
sensors to the chamber surface are also drilled at this time. On the
wider end of the chamber, these holes position the precision pins and
bolts used by the DCOPS mounting brackets to reference the CCDs directly
to the cathode strips. On the narrow end, a series of holes for
alignment pins are established which locate the plates for DCOPS
mounting hardware to be glued to the panel surface. The location of all
holes are placed with a certainty of ±25 μm on the surface of each panel
and have their diameters drilled to a certainty of ±25 μm.

2\. Assembly of Final Chamber from Multiple Panels

Once all six panels are milled and prepared, they are layered to form
the composite six layer CSC chamber. The precision with which each panel
in the chamber is positioned with respect to neighboring panels can be
estimated from the uncertainty with which the central CSC Alignment
Holes are placed (±25 μm) and the tolerance placed on the diameter of
the hole itself. Since the placement of all six layers are independent
of each other, the maximal misalignment of any two given planes (two
sets of holes, each with 25μm uncertainty in the diameter and relative
location of their center points) is estimated to be ±50 μm. The
uncertainty in the average center point across all six chamber planes is
±87 μm.

After the panels are stacked together, a frame is mounted to the edges
of the chamber to add rigidity to the structure, protect connections,
and form a Faraday shield around the electronics. Though the DCOPS
mounting tower assemblies will mount on top of the frame structure,
placement of the tower mounting hardware is completely determined by an
alignment pin that sits in the previously drilled alignment holes. Since
the CMS triggering requirements will accommodate relatively large
uncertainties in the final determination of the chambers along the CMS Z
coordinate, the placement of elements along the local Y axis of the
chamber (CMS Z), including the frame, is not tightly controlled during
manufacturing. The certainty with which the placement of the frame above
the first strip plane will be known is estimated to be ±127 μm. The
frame itself is estimated as being flat to ±25 μm whereas chamber
flatness is estimated as no worse than ±200 μm across any 60 cm span.
Tolerances on the panel thickness are asymmetric, +508 μm to -254 μm,
and determined by the manner in which the panels are manufactured and
cut.

3\. Alignment Mounting Hardware

Mounting hardware to attach the DCOPS sensors to the chamber frames is
similar across all chamber varieties. The mounting hardware consists of
a series of spacers, shims, and mounting plates which secure the primary
DCOPS mounting bar (where CCD-dowel calibration is done). CSC chambers
in both inner and outer rings of ME ±2, ±3, and ±4 disks are placed into
two layers. The chamber configuration for Trigger towers makes it
necessary to mount hardware on the back layer for one outer CSC.
Chambers on back layers will have mounting hardware called towers to
give the attached DCOPS sensor an elevation in the SLM line which
matches the front layer.

As previously noted, sensors affixed to the larger end of the chambers
(+Z local end) are mounted directly to the chamber frame while sensors
on the smaller end of the chamber (-Z local end) are attached to a
special plate which is glued into position with the aid of a special pin
and slot set during the fabrication of the chamber. The precision with
which the inner plate can be glued to the surface of the chamber is
determined from the tolerance with which the pin and slot are placed on
the chamber surface (± 25 μm each) as well as the precision with which
the receiving pin and slot are placed on the plate to be glued (± 25 μm
each). Therefore, it is estimated that the DCOPS plates on the narrow
end of the chamber can be glued in position within ±50 μm of the
specified location - approximately the same tolerance with which they
can be attached on the +Z local end to the chamber frame.

Although the heights of the towers on the back layers differ by 290mm
from the standard brackets, the plates and assemblies used are
essentially the same. The mounting brackets are attached across two
standoffs, each with an asymmetric tolerance of +.100 -0.000 . The
standoffs locate a set of dowel pins on a stock Aluminum jig plate (±
125 μm thickness). The DCOPS mounting bar connects directly to this
plate. Holes and pins used to secure the DCOPS are positioned and
drilled to ± 25 μm, contributing an additional ±50μm uncertainty in the
referencing of the sensors to the strip positions.

The potential uncertainty in the orientation of the DCOPS sensors about
the primary DCOPS dowel pin due to the uncertainty of the standoffs
(separation of 88mm) is less than ±1μrad. Likewise, the uncertainties of
the chamber frame positioning above the first panel on the chamber
contribute an angular uncertainty about the same axis of less than
±1μrad as well. Rotational uncertainties about other axes are found to
be only slightly larger, but can be safely neglected by COCOA as each
CCD is one dimensional.

4\. Deformation

One final consideration in defining the precision with which individual
layers can be externally referenced is the deformation of the chambers
when mounted in the detector. Since the CSC chambers are mounted
vertically, the weight of the chambers creates a shearing effect across
the six layers of the chamber. This effect is will be most prevalent
when the shearing occurs perpendicular to the direction of the cathode
strips. Thus, the effect is largest for chambers lying along the CMS X
axis. The displacement of the individual layers due to the shearing
force increases from the bottom layer (closest to the RF iron mounts) to
the top layer. The maximal displacement of the uppermost layer has been
directly measured as less than 25 μm.

5\. Angular/Rotational Uncertiainties

Components in COCOA are specified by their location and orientation
making it necessary to estimate the rotational uncertaities with which
the DCOPS sensors are placed on the chamber. Since the CCDs used in the
DCOPS sensors are one demensional pixel arrays, rotational uncertainties
about the axis normal to the plane of the CCDs (DCOPS local Z axis) are
the most important. Estimations of uncertainties about this axis, where
it might be expected the slope and flatness of surfaces will contribute
most, can also be estimated from the tolerance and separation on the
mounting bracket standoffs, CSC panel/frame uncertainty (127μm), length
(\>\>100cm), and flatness (±200 μm across 60 cm), and other tolerances
placed on the components in the mounting bracket (Al plate, DCOPS window
mounting bar - both ∼25-50μm across ∼90mm). The uncertainties about the
DCOPS Z axis are summarized in Table E4.

Uncertainties about the DCOPS X and Y axis are determined from the
uncertainties of the two precision pins or holes used to position
components on the chamber and mounting brackets and the separation
between them. In all cases, the uncertainties associated with the
placement of pins and holes (∼25-50μm) and the relatively large span of
between them (∼90mm) mean individual contributions to the rotational
uncertainty in the orientation of the DCOPS sensors is on the order of 1
μrad. The uncertainties about the DCOPS X and Y axes are summarized in
Table E5.

6\. Final Estimation of DCOPS - CSC Active Center Uncertainties

The final uncertainty associated with the DCOPS reference pin - CSC
active centers are determined from the quadrature of all estimated
uncertainties in the plane of the strips (Table E2) and perpendicular to
the plane of the strips (Table E3). The estimated rotational
uncertainties about the DCOPS X, Y, and Z axes are summarized in Tables
E4 (DCOPS Z axis) and E5 (DCOPS X and Y axes). The rotational
uncertainties have been estimated from the uncertainty and separation of
the pins and/or holes which join components.

  ------------------------------------------------------ ----------------
  **Uncertainty Origin**                                 **Magnitude
                                                         (µm)**

                                                         

  Central Alignment Pin - Notched Alignment Marks        25

  Notched Alignment Mark - Numbered Reference Strip      25

  Intrinsic Strip Positioning (from milling)             30

  Averaged Centerline Across 6 Assembled Planes          87

  Positioning of Primary DCOPS Alignment Pins/Holes      25

  Diameter of Primary DCOPS Alignment Pins/Holes         25

  Placement of Mounting Plate On Chamber                 50

  Placement of DCOPS Mounting Plate                      50

  DCOPS Calibration, Construction (Table E1 Result)      65

  Maximal Shearing Effect                                25

                                                         
  ------------------------------------------------------ ----------------

Final Estimation of Uncertainty Along X Axis of Chamber: 144 µm

**Table E2 : Estimation of Error Transverse to CSC Chamber Centerline.**
This table shows the uncertainties associated with the determination of
the displacement between the DCOPS alignment pin and the cathode strips
transverse to the chamber centerline (local chamber X axis).

  ------------------------------------------------------ ----------------
  **Uncertainty Origin**                                 **Magnitude
                                                         (µm)**

                                                         

  Panel Thickness (Maximal deviation)                    508

  Frame to Panel Placement                               127

  Mounting Bracket Chamber-Shim Standoff                 100

  Mounting Bracket Al. Plate                             125

                                                         
  ------------------------------------------------------ ----------------

Final Estimation of Uncertainty in Y Plane of Chamber: 538 µm

**Table E3 : Estimation of Error of DCOPS Positioning Above First Strip
Layer (local Y axis).** This table shows the uncertainties associated
with the determination of the displacement between the DCOPS mounting
plate and the first plane of cathode strips. Tolerances for CSC
construction are not as tight along this direction since the
uncertainties will lie along the CMS Z axis.

+----------------------------------------------------+-----------------+
| # Uncertainty Origin                               | **Magnitude     |
|                                                    | (µrad)**        |
+----------------------------------------------------+-----------------+
|                                                    |                 |
+----------------------------------------------------+-----------------+
| Upper Cathode Panel - Frame Relationship           | 1               |
+----------------------------------------------------+-----------------+
| Frame (or Fwd Glue Plate) - DCOPS Mounting Bracket | 1               |
| Base                                               |                 |
+----------------------------------------------------+-----------------+
| DCOPS Mounting Bracket Base - Mounting Bracket     | 1               |
| Shim Plate                                         |                 |
+----------------------------------------------------+-----------------+
| Mounting Bracket Shim Plate - DCOPS Mount Bar      | 1               |
+----------------------------------------------------+-----------------+
| Straightness of DCOPS Mount Bar - DCOPS Window     | 1               |
| Frame                                              |                 |
+----------------------------------------------------+-----------------+
|                                                    |                 |
+----------------------------------------------------+-----------------+

Final Estimation of Uncertainty in DCOPS Orientation on Chamber: 2.2
µrad

**Table E4 : Estimation of Error of DCOPS Orientation About DCOPS CCD
Plane Normal (local DCOPS Z axis).** This table shows the uncertainties
associated with the determination of the orientation between the DCOPS
ccds and the first plane of cathode strips. Most uncertainties were less
than 1 µrad and have been rounded up.

+----------------------------------------------------+-----------------+
| # Uncertainty Origin                               | **Magnitude     |
|                                                    | (µrad)**        |
+----------------------------------------------------+-----------------+
|                                                    |                 |
+----------------------------------------------------+-----------------+
| Upper Cathode Panel Pins/Holes                     | 1               |
+----------------------------------------------------+-----------------+
| DCOPS Mounting Bracket Base                        | 1               |
+----------------------------------------------------+-----------------+
| Mounting Bracket Shim Plate                        | 1               |
+----------------------------------------------------+-----------------+
| DCOPS Mount Bar                                    | 1               |
+----------------------------------------------------+-----------------+
|                                                    |                 |
+----------------------------------------------------+-----------------+

Final Estimation of Uncertainty in DCOPS Orientation on Chamber: 2 µrad

**Table E5 : Estimation of Error of DCOPS Orientation of DCOPS CCD Plane
(local DCOPS X/Y axis).** This table shows the uncertainties associated
with the determination of the orientation between the DCOPS ccds and the
first plane of cathode strips. Most uncertainties were less than 1 µrad
and have been rounded up. Rotation uncertainties and misorientation are
not as important about these axes, as the CCDs are one dimensional.

References :

CMS Technical Proposal, CERN / LHCC 94-38, LHCC/P1, 15 December 1994

CMS Muon System Proposal, CERN / LHCC 97-32, CMS TDR 3, 15 December 1997

SONY ILX551A 2048-pixel CCD Linear Sensor (B/W) Product Specification,
Sony Electronics Inc., Document E00439-PS

(<http://www.sel.sony.com/semi/PDF/ILX551A.pdf>)

COPS Sensor Board Calibration, J. Moromisato et al, unpublished, Oct
2000

(<http://www.dac.neu.edu/physics/j.moromisato/emu/alignment/cops_calib.pdf>)

Conversation with Oleg Prokofiev, 7 July 2001

Conversation with Nelson Chester (lead engineer), 5 July 2001