Lecture 9.1: Textbook Revisited, and Calibration Examples ...odessa.phy.sdsmt.edu/~bai/zzteaching_2013Fall/PHYS-733/PHYS733_Fall... · Lecture 9.1: Textbook Revisited, and Calibration

Lecture 9.1: Textbook Revisited, and

Calibration Examples from Several Experiments

Prof. Luke A. CorwinPHYS 733

South Dakota School of Mines & Technology

Oct. 25, 2013

L. Corwin, PHYS 733 (SDSM&T) Lec. 9: Calibration Examples Oct. 25, 2013 1 / 27

Outline

1 Textbook Example Redux

2 Calibration Example from NOvANOvA Experiment OverviewCosmic Rays for Attenuation Calibration

3 Papers for Remaining Experiments

4 References


Textbook Example Redux

Plot from Lecture 7.2



Lingering Questions

x E/keV141 725222 1131366 1845

We were all able to agree that the slope of the line, which is theMCA channel width, was about 5 keV. We disagreed on theintercept, getting values scattered around 22 keV; we alsodisagreed with the book [2], which claims

m = 5.00 keV b = 18 keV, (1)

where E(x) = mx+ b. This has bothered me ever since.



Attempting to Resolve the Discrepancy

Lesson 1: Every physicist needs a little Captain (Ahab)

I neglected to give you one of the data points in the book(carbon).

I realized that the proper way to perform the calibration is tofit a line to the data.

Two fitting options: Exact analytical solution or ROOTfitting

Lesson 2: Always use all good data.

x E/keV98 505141 725222 1131366 1845



Exact Analytical Solution

For the exact analytical solution, I use the method of leastsquares from Bevington and Robinson [1], a book I highlyrecommend.

We are not given the uncertainty on E, so I assumed theuncertainties were equal and used the solution given in thatcase.

∆′ = N∑x2i − (

∑xi)

2 (2)

b = 1∆′

(∑x2i

∑yi −

∑xi∑xiyi) (3)

m = 1∆′

(N∑xiyi −

∑xi∑yi) (4)



Results of Least Squares Method

Some analytical method was probably used in the bookbecause it was published in 1978, before I was born.

The results from my spreadsheet calculations of the leastsquares method:

m = 4.99431637829324 b = 18.9250887878733 (5)

The slope agrees to two significant figures with the book, butnot the three claimed in the book.

The intercept still disagrees at two significant figures.

What will ROOT say?



#include "TMath.h"

#include "TH1F.h"

#include "TF1.h"

#include "TStyle.h"

void CMN_CalibDemo(){

TH1F* h1 = new TH1F("h1","Calibration Points",400,-0.5,399.5);

Float_t common_error = 0.1; //keV

h1->Fill(98,505);

h1->SetBinError(h1->FindBin(98),common_error);

h1->Fill(141,725);


h1->Fill(222,1131);


h1->Fill(366,1845);


h1->SetMarkerStyle(20);

TF1* myline = new TF1("myline","[0]*x + [1]",0,400);

myline->SetParNames("slope","intercept");

gStyle->SetOptStat(0);

gStyle->SetOptFit(1);

h1->Fit("myline","R");

h1->Draw("PE1");

}L. Corwin, PHYS 733 (SDSM&T) Lec. 9: Calibration Examples Oct. 25, 2013 8 / 27




Comparing Our Results

Full Results from ROOT using TF1

EXT PARAMETER

NO. NAME VALUE ERROR

1 slope 4.99432e+00 4.89452e-04

2 intercept 1.89251e+01 1.12873e-01

Source Slope, Channel Width m Intercept bBook [2] 5.00 keV 18 keV

Least Squares 4.994316 keV 18.92508879 keVROOT with TF1 4.99432 keV 18.9251 keV

Table : ROOT and the analytical method agree with each other butdisagree with the book. So, what do we do now?


TF1

TF1


Our Options

1 Ideally, we would ask the authors of the book how they madetheir calculations; however, since the book is 35 years old,that may not be possible.

2 We could explore and test other fitting methods to see if wecan reproduce their results.

3 Assign the discrepancies as a systematic uncertainty

σ2E = σ2

mx2 + σ2

b [1] σm = 0.006 keV σb = 0.93 keV (6)

σE(x = 1100) =√

(0.006 keV)2 · 11002 + (0.93 keV)2 (7)

= 6.32 keV (8)

We then need to decide whether this is an acceptable systematicor use option 2. Which uncertainty (σm or σb) do we need tofocus on reducing?


Calibration Example from NOvA

Calibration of NOvA Relative Energy Scale

Basic Information

Experiment: NOvA (a.k.a. NOνA) = NuMI Off-axis νeAppearance

NuMI = Neutrinos at the Main Injector

Instrument Calibrated: Avalanche Photo Diodes (APDs)

Standard: Cosmic Ray Energy Deposits.

Sources

NOvA Document Database http:

//nova-docdb.fnal.gov/cgi-bin/DocumentDatabase/

Public Documents 6554, 7534, 7546, 7556, 9245


http://nova-docdb.fnal.gov/cgi-bin/DocumentDatabase/

http://nova-docdb.fnal.gov/cgi-bin/DocumentDatabase/

Calibration Example from NOvA NOvA Experiment Overview

NOvA Experiment Overview












Calibration Example from NOvA Cosmic Rays for Attenuation Calibration

Motivation

Especially in the Far Detector, the fibers are very long

They attenuate light on the way from the interaction point tothe APD

We want to know how many photoelectrons (PEs) wereproduced based on track location and how many PEs weredetected by the APD (relative calibration)

The APDs output a quantity called Access Deficit Charge(ADC), which we want to convert into the number of PEsgenerated (PECorr)

The conversion from PECorr to actual energy deposited iscalled absolute calibration, and we are not covering thattoday.



Selecting Cells

Figure : Use only cells where both neighbors are also illuminated

From the track through the detector, we know the cells thatare lit and the angle of the track through the detector.Since the tracks can traverse different lengths (L) in the cell,we actually measure ADC/cm.cy ≡ cos(θ) = Ly/L⇒ L = Ly/cy



Attenuation Length Review

I = I0e−xλ (9)

I is the intensity after light has traveled a distance x

I0 is the initial intensity

λ is the attenuation length.



Functional Form

To assess the affect of attenuation on our scintillationphotons, we want to fit the response A as a function ofdistance from the center of the cell W .

NOvA calls the attenuation length Xs

In Class Exercise (may work in teams)

Given that the light has two paths to reach the APD, W = 0 atthe center of the cell, and the attenuation length above, what isthe functional form of the response of the APD A(W )?



A(W ) = A0

(eW−L/2Xs + e−

3L/2+WXs

)+ C



Figure : Example fit result from NDOS.



Figure : ADC distributions for different bins of W before (left) andafter(right) calibration.


Papers for Remaining Experiments

Papers for Remainder of Class

ICARUS: http://arxiv.org/abs/hep-ex/0311040

Super-Kamiokande:http://arxiv.org/abs/hep-ex/0005014

BaBar: http://arxiv.org/abs/physics/0601138

IceCube: Guest Appearance from Prof. Bai


http://arxiv.org/abs/hep-ex/0311040

http://arxiv.org/abs/hep-ex/0005014

http://arxiv.org/abs/physics/0601138

References

References I

[1] P. R. Bevington and D. K. Robinson.Data Reduction and Error Analysis for the Physical Sciences.WCB/McGraw-Hill, Madison, WI, 2nd. edition, 1992.

[2] W.-K. Chu, J. W. Mayer, and M.-A. Nicolet.Backscattering Spectrometry.Academic Press, New York, NY, USA, 1978.
