LAT Performance - Overview of the Instrument Response ... · 36.9 53.1 66.4 78.5 ° 0.0 ° 180.0 °...

LAT Performance

Overview of theInstrument Response

Functions

Luca BaldiniINFN–Pisa and University of Pisa

[email protected]

Fermi Summer School 2012Lewes, June 2, 2012

Outline

I Introduction and context.

I The Instrument Response Functions (IRFs):I effective area;I point-spread function;I energy dispersion.

I Systematic uncertainties on the IRFs (time permitting).

I Propagating the systematic uncertainties to high-level scienceanalysis.

I And, of course, more exercises !

Luca Baldini (INFN and UniPi) Fermi Summer School 2012 2 / 33

Parametrization of the IRFs


Definition of the coordinate system

+x+y

+zv

φ

θ

I IRFs parametrized as a function of the energy E and the direction(θ, φ) in instrument coordinates.

I Strong dependence on E and θ, much weaker dependence on φ.I Also: front- and back-converting events treated separately:

I remember: front and back sections of the TKR have very differentperformance.


Monte Carlo Aeff

Energy [MeV]210 310 410 510

)θco

s(

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 ]2 [m

eff

A

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

(a) Front

Energy [MeV]210 310 410 510

)θco

s(

0.2

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0.7

0.8

0.9

1 ]2 [m

eff

A

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0.5

(b) Back

I Aeff(E , v , s): the product of the geometrical collection area, γ-rayconversion probability, and selection efficiency for a γ ray withenergy E and direction v in the LAT frame.

I Generating the effective area tables (i.e., 2-dimensional histograms):I generate known isotropic incoming flux (with E−1 spectrum, i.e.,

with the same number of events for each logarithmic bin);I count how many events pass the selection cuts in each (Ei , θj) bin;I normalize to input flux.

I Note: we bin events in log E and cos θ:I φ dependence treated as a correction (more on this later);I the ScienceTools take care of the interpolations for you.


Aeff tables derivatives1 (1/2)

Energy [MeV]210 310 410 510

]2 [m

eff

On-

axis

A

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P7SOURCE_V6 TotalP7SOURCE_V6 FrontP7SOURCE_V6 Back

(a)

]° [θ0 10 20 30 40 50 60 70

]2 a

t 10

GeV

[mef

fA

0

0.1

0.2

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0.5

0.6

0.7

0.8

0.9

1

P7SOURCE_V6 TotalP7SOURCE_V6 FrontP7SOURCE_V6 Back

(b)

—Aeff vs. E (at fixed θ).

I On-axis Aeff increases up∼ 100 GeV.

I > 100 GeV: events are harder toreconstruct (backsplash).

—Aeff vs. θ (at fixed E ).

I Less cross section as you gooff-axis.

I Off-axis events: easier forback-converting events tointercept the CAL.

I Exercise: Why is the effective area decreasing below ∼ 1 GeV?

1Here and in the following the IRFs are tabulated in correspondence of the markersand the points are smoothly connected


Aeff tables derivatives (2/2)

Energy [MeV]210 310 410 510

sr]

2A

ccep

tanc

e [m

0

0.5

1

1.5

2

2.5 P7SOURCE_V6 TotalP7SOURCE_V6 FrontP7SOURCE_V6 Back

(a)

Energy [MeV]210 310 410 510

FO

V [s

r]

0

0.5

1

1.5

2

2.5

3

3.5

P7SOURCE_V6 FrontP7SOURCE_V6 BackP7SOURCE_V6 Combined

—Acceptance A(E ):

A(E ) =

∫Aeff(E , θ, φ) dΩ

— Field of view FoV:

FoV(E ) =A(E )

Aeff(E , θ = 0)

I Exercise: Estimate the high-energy on-axis Aeff , the high-energyacceptance and the corresponding FoV with paper and pencil.


Aeff corrections

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

0

0.1

0.2

0.3

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0.5

0.6

0.7

°90.0

°78.5

°66.4

°53.1

°36.9

° 0.0°180.0

°22.5

°202.5

°45.0

°225.0

°67.5

°247.5

°90.0

°270.0

°112.5

°292.5

°135.0

°315.0

°157.5

°337.5

]2 [m

eff

A

I Correction for livetime dependence:I the ghost effect is taken into account on average in the MC

simulations by overlaying a library of out-of-time triggers.I but the background rate is dependent on the geomagnetic location

of the spacecraft, and tracked by the livetime fraction.

I Correction for the φ dependence:I treated as a correction on top of the average Aeff and included in the

FITS files of the IRFs;I by default the phi dependence is not used in the ScienceTools;I generally negligible for long-time observations (see next slide).


Aeff and solar flares

UTC

]-2

X-r

ay fl

ux [W

m

-810

-710

-610

-510

-410 ÅGOES15 0.5-4.0 ÅGOES15 1.0-8.0

(a)

A

B

C

M

X

UTC

Tile

63

occu

panc

y

0

0.2

0.4

0.6

0.8

1

Threshold: 0.22

Candidate BTI(b)

UTC22:30 23:00 23:30

Nor

m. A

CD

mul

tiplic

ity

012345678

Threshold: 1.60

Candidate BTI(c)

UTC

rat

e [a

. u.]

γN

orm

.

00.20.40.60.8

11.21.41.6 (a)

UTC22:30 23:00 23:30

Int.

loss

[s]

0100200300400500

(b)

I During the brightest solar flares hard X-rays cause spurious activityin the ACD;

I this causes otherwise reconstructable photons to be tagged ascharged particles;

I the IRFs do not adequately describe the instrument during theseintervals.


Can you guess what these are?

1

10

210

310

°90.0

°78.5

°66.4

°53.1

°36.9

° 0.0°180.0

°22.5

°202.5

°45.0

°225.0

°67.5

°247.5

°90.0

°270.0

°112.5

°292.5

°135.0

°315.0

°157.5

°337.5

Live

time

[s]

(a)

1

10

210

310

°90.0

°78.5

°66.4

°53.1

°36.9

° 0.0°180.0

°22.5

°202.5

°45.0

°225.0

°67.5

°247.5

°90.0

°270.0

°112.5

°292.5

°135.0

°315.0

°157.5

°337.5

Live

time

[s]

(b)


Can you guess what these are?

1

10

210

310

°90.0

°78.5

°66.4

°53.1

°36.9

° 0.0°180.0

°22.5

°202.5

°45.0

°225.0

°67.5

°247.5

°90.0

°270.0

°112.5

°292.5

°135.0

°315.0

°157.5

°337.5

Live

time

[s]

(a)

1

10

210

310

°90.0

°78.5

°66.4

°53.1

°36.9

° 0.0°180.0

°22.5

°202.5

°45.0

°225.0

°67.5

°247.5

°90.0

°270.0

°112.5

°292.5

°135.0

°315.0

°157.5

°337.5

Live

time

[s]

(b)

I Livetime maps in instrument coordinates.

I Credits: Eric Charles2

I check them out at http://apod.nasa.gov/apod/ap120504.html.

I Take-away message: things that average out in long-termobservations do not necessarily do so on short timescales.

2If you were here last year you would have met him in person.Luca Baldini (INFN and UniPi) Fermi Summer School 2012 10 / 33

http://apod.nasa.gov/apod/ap120504.html

Point-Spread Function

I P(v ′;E , v , s): the probability density to reconstruct an incidentdirection v ′ for a gamma ray with (E , v) in a given event selection.

I For a given point (E , θ) in the LAT phase space the PSF is not asingle number (like Aeff) but rather a p.d.f.:

I need a functional form to parametrize it;I for the Monte Carlo PSF we use the sum of two King functions.

K(x , σ, γ) =1

2πσ2

(1− 1

γ

)·[

1 +1

2γ· x2

σ2

]−γ

I The PSF varies by orders of magnitude across the LAT energyrange:

I at low energy it is dominated by multiple Coulomb scattering in theW conversion foils (which scales like E−1);

I at high energy it is determined by the TKR strip pitch and lever arm.

I Exercise: Estimate the asymptotic high-energy PSF for front- andback-converting events. Why are they different?

I Exercise: Estimate the rollover energy of the transition between thetwo regimes.


PSF prescaling and fitting

Scaled angular deviation-110 1 10

Cou

nts

/ 0.0

33 d

ecad

e

210

310

410

(a) coreN 0.1989 tailN 0.08639 coreσ 0.5399

tailσ 1.063

coreγ 2.651

tail

γ 2.932

Scaled angular deviation-110 1 10

PS

F e

stim

ate

-610

-510

-410

-310

-210

-110

1 coreN 0.1989

tailN 0.08639 coreσ 0.5399

tailσ 1.063

coreγ 2.651

tail

γ 2.932

(b)

I PSF tables are generated with the same MC sample used for Aeff :I calculate δv = |v′ − v| event by event.

I First step: prescaling takes care of the PSF energy dependence:

I Scaling function: SP(E) =

√[c0 ·(

E100 MeV

)−β]2

+ c21 .

I Scaled angular deviation: x = δv/SP(E).

I x histogram is converted into a p.d.f. wrt solid angle and fitted witha double King function.

I In the FITS files of the IRFs we store the SP(E ) parameters and thefit parameters.


Scaled angular deviation behavior

Energy [MeV]210 310 410 510

)θco

s(

0.2

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Sca

led

68%

con

tain

men

t rad

ius

0

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(a) Front

Energy [MeV]210 310 410 510

)θco

s(

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1

Sca

led

68%

con

tain

men

t rad

ius

0

0.5

1

1.5

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5

(b) Back

Energy [MeV]210 310 410 510

)θco

s(

0.2

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1

95%

to 6

8% c

onta

inm

ent r

atio

2

2.5

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(c) Front

Energy [MeV]210 310 410 510

)θco

s(0.2

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95%

to 6

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onta

inm

ent r

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(d) Back

I A lot of richness in the (E , θ) plane.I remember: we prescale in energy, not in inclination angle.I (And we neglect the φ dependence of the PSF.)


In-flight PSF

Energy [MeV]210 310 410 510

]°C

onta

inm

ent a

ngle

[-110

1

10 P7SOURCE_V6 Back 68%P7SOURCE_V6 Combined 68%P7SOURCE_V6 Front 68%P6_V3_DIFFUSE Back 68%P6_V3_DIFFUSE Combined 68%P6_V3_DIFFUSE Front 68%

(a)

I Monte Carlo prediction for the width of the core of the PSF isunderpredicted above a few GeV;

I we think we understand the root cause and can mitigate it to a largeextent (massive data reprocessing undergoing to demonstrate that).

I For the time being we derive the PSF directly from flight data, bymeans of a stacking analysis of selected point sources:

I the statistics do not allow to determine the θ dependence;I the in-flight PSF is really a PSF averaged over the FoV;I (which is perfectly adequate for most long-time observations).I Also: in-flight PSF uses a single King function (does not match the

95% containmebt very well).


Fisheye effect

I Definition: bias in the reconstruction γ-ray directions toward theLAT boresight.

I Why does that happen?I Particles scattering toward the LAT boresight are more likely to

trigger the instrument and be reconstructed;I especially true at low energy and large angles.

I Is it an important effect?I Generally not;I this is only a systematic bias in instrument coordinates;I over long integration time any source is typically seen at all angles;I our PSF parametrization includes the broadening due to the fisheye

effect.I It is potentially important for short observations!

I How do you measure it?

φ =z × v

|z × v |θ =

φ× v

|φ× v |δθ = − sin−1

(θ · (v ′ − v )

)


Fisheye effect

Energy [MeV]210 310 410 510

θδ /

rms

θδm

ean

-210

-110

1 ° = 63.3θ° = 49.5θ° = 31.8θ

(a) Front

Energy [MeV]210 310 410 510

θδ /

rms

θδm

ean

-210

-110

1 ° = 75.5θ° = 63.3θ° = 49.5θ° = 31.8θ

(b) Back

Energy [MeV]210 310 410 510

θδ /

rms

θδm

ean

-210

-110

1 ° = 63.3θ° = 49.5θ° = 31.8θ

(a) Front

Energy [MeV]210 310 410 510

θδ /

rms

θδm

ean

-210

-110

1 ° = 75.5θ° = 63.3θ° = 49.5θ° = 31.8θ

(b) Back

P7SOURCE

class

P7TRANSIENT class

I Typically smaller than 1;I except for very low energies and very large angles;I and especially for the TRANSIENT class.


Energy Dispersion

I D(E ′;E , v , s): the probability density to measure an event energy E ′

for a gamma ray with (E , v) in the event selection s.

I Parametrization strategy similar to that of the PSF in many respects.

I Unlike the PSF, the energy dispersion is ignored by default in thestandard likelihood fitting:

I negligible effect in many situations—except for energies below100 MeV;

I ScienceTools can now be told to take it into account.I Is it important? This will be the subject of our hands-on session.

I Energy dispersion prescaling:I scaling function: SD(E , θ) =

c0(log10 E)2 + c1(cos θ)2 + c2 log10 E + c3 cos θ + c4 log10 E cos θ + c5;I scaled energy deviation: x = (E ′ − E)/(ESD(E , θ)).

I Fitting of the scaled variable:I 4 piecewise Rando functions: R(x , x0, σ, γ) = N exp

(− 1

2

∣∣ x−x0σ

∣∣γ);I fit parameters stored in the FITS files of the IRFs.


Energy dispersion scaling function

Energy [MeV]210 310 410 510

)θco

s(

0.2

0.3

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1

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(a) Front

Energy [MeV]210 310 410 510

)θco

s(

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0.7

0.8

0.9

1

0.05

0.1

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(b) Back

I Again, a lot of richness as a function of E and θ.

I Beware: the value of the scaling function at a particularenergy/angle is not the energy resolution at that energy/angle;

I (the two things are obviously related to each other, though, as bothrepresent the width of the energy dispersion.)

I We define the energy resolution as the half width of the energywindow containing 34% + 34% (i.e., 68%) of the energy dispersionon both sides of its MPV, divided by the MPV itself.


Scaled deviation and energy dispersion

N 0.07687 Lσ 0.7168 Rσ 0.5806 0x -0.1037 lσ 0.08331 rσ 0.05593

Scaled deviation-6 -4 -2 0 2 4 6

Ene

rgy

disp

ersi

on e

stim

ate

-610

-510

-410

-310

-210

-110

1N 0.07687

Lσ 0.7168 Rσ 0.5806 0x -0.1037 lσ 0.08331 rσ 0.05593

L l r R

0x

Energy [MeV]6000 8000 10000 12000 14000

Ene

rgy

disp

ersi

on P

. D. F

.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9-310×

Peak @ 9900 MeV

Full width 68% containment: 1360 MeV

= 6.9%E E∆

I Note that the low-energy tail is relatively more prominent than thehigh-energy one.

I Exercise: If you had to choose, would you prefer a pronouncedlow-energy or high-energy tail?


Energy resolution

Energy [MeV]210 310 410 510

On-

axis

ene

rgy

reso

lutio

n

0

0.05

0.1

0.15

0.2

0.25

0.3

P7SOURCE_V6 FrontP7SOURCE_V6 CombinedP7SOURCE_V6 Back

(a)

]° [θ0 10 20 30 40 50 60 70

Ene

rgy

reso

lutio

n at

10

GeV

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14 P7SOURCE_V6 FrontP7SOURCE_V6 CombinedP7SOURCE_V6 Back

(b)

—Energy resolution vs E :

I sweet spot between∼ 1–100 GeV;

I low energy: energy deposited inthe TKR not negligibleanymore;

I high-energy: shower leakagebecoming dominant.

— Energy resolution vs. θ:

I energy resolution improves atlarge angle (more path lengthin the CAL);

I more pronounced at very highenergy (above 100 GeV);

I behavior above 60 off axisirrelevant (no acceptancethere).


Validation of the IRFs


Validation data samples

Pulse phase0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cou

nts

/ 0.0

125

perio

d

0

20

40

60

80

100

120

140

160

180310×

SignalBackground

Velapulsa

r

]2°[2α0 2 4 6 8 10 12 14 16

2 °C

ount

s / 0

.2

0

5

10

15

20

25

30

35

40310×

SignalBackground

Stacked AGNs

]°[zθ107 108 109 110 111 112 113 114 115 116 117

°C

ount

s / 0

.1

210

310

SignalBackground

Earthlim

b

sin(b)-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

sr

πC

ount

s / 0

.05

0

5

10

15

20

25

30

35

40

45310×

CleanDirty

Galacticrid

ge

I We have plenty of flight data for validation purposes:I different sources and background subtraction methods allow to

extract clean photon samples across most of the LAT phase space.


Effective area validation

I There is no astrophysical source whose flux is perfectly known.

I But the effective area is essentially a measure of the selectionefficiency:

I can study the efficiency cut by cut;I (remember: this includes all the selection steps: from triggering and

filtering to the definition of the event classes).

I Compare the cut efficiency on Monte Carlo and flight data sets.

I Also: devise and perform consistency checks:I e.g., do events split themselves between front and back as predicted

by the Monte Carlo simulations?


An important consistency check

Energy [MeV]210 310 410 510

R

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

VelaAGN sampleEarth Limb

(d) Front-converting

I Fraction of events converting in the front section of the TKRrelative to the MC prediction:

I sensitive to possible inaccuracies in our description of the detectormaterials and geometry.

I This is one of the most significant discrepancies observed whencomparing flight data with Monte Carlo simulations;

I and the most important piece of information for estimating theuncertainties of our effective area.


Effective area validation

Energy [MeV]210 310 410 510

eff

Sys

tem

atic

unc

erta

inty

on

A

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

effUncertainty on A

< 100 MeV: caution for spectral analysis

I Summary of our understanding of the effective area.I Below 100 MeV the worsening of the energy resolution, coupled with

the steep falling of the effective are make the effect of the energydispersion potentially noticeable.

I Note that this is just an error envelope:I no information about what type of deviation we might expect within

the uncertainty band.

I Point-to-point correlations?I Yes: strong correlation on energy scales much lower than half a

decade (look at the previous slide).


PSF validation

I In many respects easier than Aeff : we have point sources at known(from other wavelengths) locations:

I most notably pulsars and AGNs;I which is what we use to derive the in-flight PSF;I caveat: in some cases a deviation from a point source (e.g., a halo)

is the physical effect we are searching for.

I Compare the measured 68% and 95% PSF containment radii forselected point sources with the PSF parametrization:

I do it for on-axis and off axis events: this tells you how much of thePSF richness we are really capturing in our representation.

I Remember: by default you are using a PSF parametrizationaveraged over the LAT field of view:

I for short-time observations this might be an issue!


Energy measurement validation

I Two very different aspects of the validation of the energymeasurement:

I energy dispersion (event by event fluctuations around true value);I absolute energy scale (common systematic error).

I Suppose you are studying a strong γ-ray line:I the uncertainty in the energy dispersion determines how the line

looks smeared in the detector;I the uncertainty in the absolute energy scale determines the offset in

the peak position.

I This is where things get really tricky in terms of in-flight validation:I there is no astrophysical γ-ray source with a sharp feature at a

perfectly known energy.

I We do have many pieces of information anyway: ground tests, beamtests, measurement of the CRE geomagnetic cutoff.

I We understand the energy resolution at the ∼ 10% level. . .I negligible in most practical situations.

I . . . and the absolute scale within +2/− 5%.


The geomagnetic rigidity cutoff

I The power-law spectrum of primary CRs is effectively shielded by themagnetic field of the Earth;

I the effect depends on the position of the LAT across the orbit.

I The cutoff energy can be predicted by means of a model of themagnetic field and a ray-tracing code:

I several calibration point between ∼ 5 and ∼ 15 GeV.


Propagating systematic uncertainties.


Aeff bracketing functions

I Scale Aeff by the product of the relative error ε(E ) = δAeff (E)Aeff (E) (see

slide 25) and an arbitrary bracketing function B(E ):I A′eff (E , θ) = Aeff (E , θ) · (1 + ε(E)B(E)) .I Creating modified Aeff curves is as easy as opening the Aeff FITS

files, doing some multiplications and saving new files.

I The most appropriate choice of the bracketing function depends onthe quantity we’re interested in:

I B(E) = ±1 maximizes/minimizes Aeff within its uncertainty bandleaving the spectral index ∼ unaffected.

I Note: the public Galactic and isotropic diffuse emission models arefit to the data using the standard effective area tables:

I need to rescale the diffuse models by the inverse of B(E) to ensurethe expected numbers of counts are unchanged.

I Basic idea: repeat the analysis with a family of modified Aeff curvesand see how the measured quantities change:

I use the maximal changes to estimate the systematic errors.

I On a separate note: modified IRFs can be used with gtobssim too.


Aeff bracketing function exampleMaximizing the effect on the spectral index in a power-law fit

Energy [MeV]210 310 410 510

eff

Rel

ativ

e A

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2Base LineIndex Biased SoftIndex Biased Hard

(a)

Energy [MeV]210 310 410 510

sr]

2A

ccep

tanc

e [m

0

0.5

1

1.5

2

2.5

Base LineIndex Biased SoftIndex Biased Hard

(b)

I Use a function that changes sign at the pivot (or decorrelation)energy (i.e., the energy at which the fitted index and normalizationare uncorrelated):

I for example B(E) = ± tanh(

1k

log(E/E0));

I k = 0.13 corresponds to smoothing over twice the LAT energyresolution.


PSF and edisp bracketing functions

I The PSF and energy dispersion being probability density functions,using bracketing IRFs is more tricky;

I you have to modify the appropriate parameters in a self-consistentway to generate families of reasonable IRFs;

I (e.g., wider or narrower PSF and energy dispersion, offset in theabsolute energy scale).

I the way the IRFs are parametrized and stored in the FITS files of theIRFs is not always optimal for that.

I But it can be done with a little bit of thought!

I Exercise: Evaluate (with paper and pencil) how an error ε in theabsolute energy scale affects the measured flux for a power-lawspectrum assuming Aeff is constant.


Conclusions

I The LAT is a complicated instrument:I performance figures vary a lot across the phase space;I there’s a lot going on behind the scenes as you run a typical science

analysis.

I The LAT team has put a huge effort into understanding theinstrument and is continuing to do so:

I the IRFs are being regularly updated and released to the public.

I Propagating the systematic uncertainties to high-level scienceanalysis can be tricky:

I Wouldn’t it be nice if it was possible to produce a table with all thenumbers that you need for your preferred analysis?

I Unfortunately that’s impossible: the answer can be given only on acase-by-case basis.


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