Download - Global Chi2 alignment OF TGC chambers
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Yair Mahalalel, Feb. 17th MMX
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Complementary to optical/mechanical alignment.
Advantages – 6D alignment Generated from experimental dataDisadvantages – Module alignment is only relative to other
modules (only option for most modules) Requires available tracks, ideally a working
collider
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Relies on /Tracking/TrkAlignment , a generic reimplementation of the inner detector toolset which has been developed for many years
Provides all the necessary services, database interfaces etc. out of the box
Uses ATHENA reconstruction and tracking for state of the art handling of data
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Minimization of Where V is the covariance matrix and are the residuals Requires calculating
either analytically or numerically.
tracks
T rVr 12
kaemr iiiˆ)),((
0000 da
dr
a
r
da
dr
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Is implicit in the analytical derivative calculation. Incorrect when large non-uniformity exists along
a chamber, e.g. in the MDTs. Can neither be used when aligning compound
modules (e.g. wheels). In these cases the derivatives are calculated
numerically by shifting and rotating the module and refitting the track. Adds computation complexity and non-trivial parameter dependence.
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Currently a software design flaw prevents chamber shifting because TGC hits are combined to form a CompetingRIOsOnTrack measurement, generating a new surface which is the average of individual hit surfaces.
The new surface is not connected to the module so the shifting the module doesn’t move the hit.
A new approach is currently being tested.
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Implementation complete – Level 3 (single chamber) align modules Using analytical derivatives Geometry transformations Debug ntuples Alignment DB I/O
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AMDB geometry description difference between TGC and MDTs
Various enhancements to generic tools to support 2D chambers and second coordinate measurements
Off by 2 chamber phi indexing
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Found in AnalyticalDerivCalcTool by CSC aligners
Triggers when a single chamber has one 1D measurement (wires) and one 2D (strips)
Might explain strange behavior when running 6D alignment
Patch received a few days ago. Will be validated by us.
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GeoModel support for aligning individual endcap TGC modules doesn’t exist yet – no code to read chamber eta index.
A fix should be comitted in a couple of weeks by Stefania Spagnolo.
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Typical A-line in ASZT file –W Stat jff jzz job Translations RotationsA T1E 1 2 0 1.234 1.234 1.234 0.00123 0.00123 0.00123
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Convergence slow and erratic, and to the wrong point.
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Implementation complete but validation is proving more confusing and slow than expected
Currently known problems are in external services (but are being fixed)
Hopefully once we finish validating these fixes we’ll start seeing more reasonable results
Then – more serious validation of our code using MC and real data
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Backup slides
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Corrections to nominal chamber locations are collected from various sources –
Optical sensors Resistive sensors Track based alignmentThe corrections specific for every run are
applied by GeoModel at ATHENA initialization.
Huge problem – thousands of modules to align
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Many approaches – Robust method – fits distributions to
tracks Local fit – needs many iterations Global fit – few iterations, but
potentially huge memory requirement.Algorithms also vary by their ability to
handle magnetic fields (curved tracks), multiple Coulomb scattering, etc.
22
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Main methodology – minimization of global error
Where V is the covariance matrix and the
Are the measurement residuals, defined as the distance between measurements and intersection of track with the sensor plane.
tracks
T rVr 12
kaemr iiiˆ)),((
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The intersection of the extrapolated track with the sensor plane depends on two parameter sets –
The track parameters
The align parameters
}/),(cot,,,{ 000 Tpqanza
},,,,,{ ZYXZYX RRRTTTa
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Should be diagonal, or at least block diagonal within the module but rarely is because of –
Multiple Coulomb scattering Additional constraints (event main
vertex)
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The equation which needs to be solved is
In order to solve it we need to calculate the full derivative
Under the linearity assumption that for small enough changes.
02
a
0000 da
dr
a
r
da
dr
02
ji
r
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The linear expansion around the original yields the equation
With the solution
0
0)),((0
01
0
r
arVrT
),( 01
0
1
0
1
000 arV
rrV
r TT
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We can look at this expression for as function of and use its derivative to rewrite the full derivative as
Where
a
0
111
0
))(1(a
rVEEVEE
da
dr TT
0
r
E
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Similarly to our track parameter treatment, we can write the equation for the align parameter derivative –
Where
tracks
T
tracks a
T
arVda
dra
da
drV
da
dr0),( 00
1
0
1
0
tracks
T
tracks
T
aWra
r
a
rW
a
ra ),( 00
0
1
00
111111 )(ˆ VEEVEEVVWVW TT
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We define the unit vectors crossing the strips,
along the strips and perpendicular to the sensor plane. The two residuals are then
And their derivatives with respect to a
general parameter are
X
Y Z
Yemres
Xemres
Y
X
ˆ)(
ˆ)(
Ydp
ed
p
res
Xdp
ed
p
res
Y
X
ˆ
ˆ
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The intersection of the path length with the detector plane, , is given by the equation
Which is solved iteratively. Can now be written as .
Since is an implicit function of ,
intl0ˆ)( Zme
dp
ed
dp
dl
l
e
p
e
dp
ed int
int
intl p
int
int
)ˆ(
)ˆ(
lZe
pZe
dp
dl
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The residual derivatives can now be written as
where
Or using local track direction of ,
Zlele
p
e
p
res
ˆ
ˆ
ˆ
int
int
YX ,
),(
ZYp
e
p
res
ZXp
e
p
res
Y
X
ˆ)tan()sin(ˆ
ˆ)tan()cos(ˆ