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New data members: distance to bad channels from the center of a reconstructed cluster...
[u/mrichter/AliRoot.git] / HMPID / AliHMPIDRecon.cxx
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d3da6dc4 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16//////////////////////////////////////////////////////////////////////////
17// //
18// AliHMPIDRecon //
19// //
20// HMPID class to perfom pattern recognition based on Hough transfrom //
21// for single chamber //
22//////////////////////////////////////////////////////////////////////////
23
a591e55f 24#include "AliHMPIDRecon.h" //class header
25#include "AliHMPIDParam.h" //CkovAngle()
d3da6dc4 26#include "AliHMPIDCluster.h" //CkovAngle()
a591e55f 27#include <TRotation.h> //TracePhot()
28#include <TH1D.h> //HoughResponse()
29#include <TClonesArray.h> //CkovAngle()
30#include <AliESDtrack.h> //CkovAngle()
d3da6dc4 31
32const Double_t AliHMPIDRecon::fgkRadThick=1.5;
33const Double_t AliHMPIDRecon::fgkWinThick=0.5;
34const Double_t AliHMPIDRecon::fgkGapThick=8.0;
d3da6dc4 35const Double_t AliHMPIDRecon::fgkWinIdx =1.5787;
36const Double_t AliHMPIDRecon::fgkGapIdx =1.0005;
37
d3da6dc4 38//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
39AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
abb5f786 40 fRadNmean(1.292),
d3da6dc4 41 fPhotCnt(-1),
42 fCkovSigma2(0),
43 fIsWEIGHT(kFALSE),
44 fDTheta(0.001),
45 fWindowWidth(0.045),
46 fTrkDir(TVector3(0,0,1)),fTrkPos(TVector2(30,40))
47{
48// main ctor
49 for (Int_t i=0; i<3000; i++) {
50 fPhotFlag[i] = 0;
51 fPhotCkov[i] = -1;
52 fPhotPhi [i] = -1;
53 fPhotWei [i] = 0;
54 }
55}
56//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 57void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
d3da6dc4 58{
59// Pattern recognition method based on Hough transform
59280a5a 60// Arguments: pTrk - track for which Ckov angle is to be found
61// pCluLst - list of clusters for this chamber
62// Returns: - track ckov angle, [rad],
a591e55f 63
64 AliHMPIDParam *pParam=AliHMPIDParam::Instance();
d3da6dc4 65
a591e55f 66 if(pCluLst->GetEntries()>pParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
67 else fIsWEIGHT = kFALSE;
d3da6dc4 68
a591e55f 69 Float_t xRa,yRa,th,ph;
70 pTrk->GetHMPIDtrk(xRa,yRa,th,ph); //initialize this track: th and ph angles at middle of RAD
a591e55f 71 SetTrack(xRa,yRa,th,ph);
72
abb5f786 73 fRadNmean=nmean;
d3da6dc4 74
59280a5a 75 Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
d3da6dc4 76 fPhotCnt=0;
77 for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
78 AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu); //get pointer to current cluster
59280a5a 79 chId=pClu->Ch();
a591e55f 80 if(pClu->Q()>pParam->QCut()){ //charge compartible with MIP clusters
81 Float_t dX=fPc.X()-pClu->X(),dY=fPc.Y()-pClu->Y(),d =TMath::Sqrt(dX*dX+dY*dY); //distance between current cluster and intersection point
82 if( d < dMin) {mipId=iClu; dMin=d;mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();} //current cluster is closer, overwrite data for min cluster
83 }else{ //charge compatible with photon cluster
84 Double_t thetaCer,phiCer;
85 if(FindPhotCkov(pClu->X(),pClu->Y(),thetaCer,phiCer)){ //find ckov angle for this photon candidate
86 fPhotCkov[fPhotCnt]=thetaCer; //actual theta Cerenkov (in TRS)
b4ad85e9 87 fPhotPhi [fPhotCnt]=phiCer; //actual phi Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
a591e55f 88 fPhotCnt++; //increment counter of photon candidates
89 }
59280a5a 90 }
d3da6dc4 91 }//clusters loop
a591e55f 92 Int_t iNacc=FlagPhot(HoughResponse()); //flag photons according to individual theta ckov with respect to most probable
93 pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc); //store mip info
59280a5a 94
a591e55f 95 if(mipId==-1) {pTrk->SetHMPIDsignal(kMipQdcCut); return;} //no clusters with QDC more the threshold at all
96 if(dMin>pParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;} //closest cluster with enough charge is still too far from intersection
97 pTrk->SetHMPIDcluIdx(chId,mipId); //set index of cluster
98 if(iNacc<1) pTrk->SetHMPIDsignal(kNoPhotAccept); //no photon candidates is accepted
99 else pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries())); //find best Theta ckov for ring i.e. track
59280a5a 100
a591e55f 101 pTrk->SetHMPIDchi2(fCkovSigma2); //errors squared
d3da6dc4 102
d3da6dc4 103}//ThetaCerenkov()
104//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 105Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
d3da6dc4 106{
107// Finds Cerenkov angle for this photon candidate
108// Arguments: cluX,cluY - position of cadidate's cluster
a591e55f 109// Returns: Cerenkov angle
d3da6dc4 110
a591e55f 111 TVector3 dirCkov;
112
67a1c24c 113 Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick; //z position of middle of RAD
114 TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad); //impact point at middle of RAD
115 TVector3 pc(cluX,cluY,0.5*fgkWinThick+fgkGapIdx); //mip at PC
a591e55f 116 Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
117 (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
67a1c24c 118 Double_t phi=(pc-rad).Phi(); //phi of photon
a591e55f 119
b4ad85e9 120 Double_t ckov1=0;
67a1c24c 121 Double_t ckov2=0.75+fTrkDir.Theta(); //start to find theta cerenkov in DRS
b4ad85e9 122 const Double_t kTol=0.01;
d3da6dc4 123 Int_t iIterCnt = 0;
124 while(1){
a591e55f 125 if(iIterCnt>=50) return kFALSE;
d3da6dc4 126 Double_t ckov=0.5*(ckov1+ckov2);
67a1c24c 127 dirCkov.SetMagThetaPhi(1,ckov,phi);
a591e55f 128 TVector2 posC=TraceForward(dirCkov); //trace photon with actual angles
129 Double_t dist=cluR-(posC-fTrkPos).Mod(); //get distance between trial point and cluster position
130 if(posC.X()==-999) dist = - 999; //total reflection problem
131 iIterCnt++; //counter step
b4ad85e9 132 if (dist> kTol) ckov1=ckov; //cluster @ larger ckov
d3da6dc4 133 else if(dist<-kTol) ckov2=ckov; //cluster @ smaller ckov
a591e55f 134 else{ //precision achived: ckov in DRS found
135 dirCkov.SetMagThetaPhi(1,ckov,phi); //
136 RecPhot(dirCkov,thetaCer,phiCer); //find ckov (in TRS:the effective Cherenkov angle!)
137 return kTRUE;
138 }
d3da6dc4 139 }
140}//FindPhotTheta()
141//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 142TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
d3da6dc4 143{
a591e55f 144 //Trace forward a photon from (x,y) up to PC
145 // Arguments: dirCkov photon vector in LORS
146 // Returns: pos of traced photon at PC
147 TVector2 pos(-999,-999);
67a1c24c 148 Double_t thetaCer = dirCkov.Theta();
149 if(thetaCer > TMath::ASin(1./fRadNmean)) return pos; //total refraction on WIN-GAP boundary
150 Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick; //z position of middle of RAD
151 TVector3 posCkov(fTrkPos.X(),fTrkPos.Y(),zRad); //RAD: photon position is track position @ middle of RAD
152 Propagate(dirCkov,posCkov, -0.5*fgkWinThick); //go to RAD-WIN boundary
153 Refract (dirCkov, fRadNmean,fgkWinIdx); //RAD-WIN refraction
154 Propagate(dirCkov,posCkov, 0.5*fgkWinThick); //go to WIN-GAP boundary
155 Refract (dirCkov, fgkWinIdx,fgkGapIdx); //WIN-GAP refraction
156 Propagate(dirCkov,posCkov,0.5*fgkWinThick+fgkGapThick); //go to PC
a591e55f 157 pos.Set(posCkov.X(),posCkov.Y());
158 return pos;
159}//TraceForward()
160//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
161void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
162{
163 //Theta Cerenkov reconstruction
164 // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
165 // Returns: thetaCer theta cerenkov reconstructed
166// TVector3 dirTrk;
167// dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
168// Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
169 TRotation mtheta; mtheta.RotateY(- fTrkDir.Theta());
170 TRotation mphi; mphi.RotateZ(- fTrkDir.Phi());
171 TRotation mrot=mtheta*mphi;
172 TVector3 dirCkovTRS;
173 dirCkovTRS=mrot*dirCkov;
174 phiCer = dirCkovTRS.Phi(); //actual value of the phi of the photon
175 thetaCer= dirCkovTRS.Theta(); //actual value of thetaCerenkov of the photon
d3da6dc4 176}
177//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
178Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
179{
180// Find area inside the cerenkov ring which lays inside PCs
a591e55f 181// Arguments: ckovAng - cerenkov angle
d3da6dc4 182// Returns: area of the ring in cm^2 for given theta ckov
183
d3da6dc4 184 const Int_t kN=100;
185 Double_t area=0;
186 for(Int_t i=0;i<kN;i++){
a591e55f 187 TVector2 pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*i /kN));//trace this photon
188 TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));//trace the next photon
189 area+=(pos1-fTrkPos)*(pos2-fTrkPos); //add area of the triangle...
d3da6dc4 190 }
191 return area;
192}//FindRingArea()
193//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
194Double_t AliHMPIDRecon::FindRingCkov(Int_t)
195{
196// Loops on all Ckov candidates and estimates the best Theta Ckov for a ring formed by those candidates. Also estimates an error for that Theat Ckov
197// collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
198// Arguments: iNclus- total number of clusters in chamber for background estimation
199// Return: best estimation of track Theta ckov
200
201 Double_t wei = 0.;
202 Double_t weightThetaCerenkov = 0.;
203
204 Double_t ckovMin=9999.,ckovMax=0.;
205 Double_t sigma2 = 0; //to collect error squared for this ring
206
207 for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
208 if(fPhotFlag[i] == 2){
a591e55f 209 if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i]; //find max and min Theta ckov from all candidates within probable window
d3da6dc4 210 if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
a591e55f 211 weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
212 wei += fPhotWei[i]; //collect weight as sum of all candidate weghts
d3da6dc4 213
d3da6dc4 214 sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
215 }
216 }//candidates loop
217
218 if(sigma2>0) fCkovSigma2=1./sigma2;
219 else fCkovSigma2=1e10;
220
b4ad85e9 221 if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
d3da6dc4 222 return weightThetaCerenkov;
223}//FindCkovRing()
224//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
225Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
226{
227// Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by HoughResponse()
228// Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
229// Returns: number of photon candidates happened to be inside the window
230
a591e55f 231// Photon Flag: Flag = 0 initial set;
232// Flag = 1 good candidate (charge compatible with photon);
233// Flag = 2 photon used for the ring;
d3da6dc4 234
235 Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0 and thetaCkovHough
236
237 Double_t tmin = (Double_t)(steps - 1)*fDTheta;
238 Double_t tmax = (Double_t)(steps)*fDTheta;
239 Double_t tavg = 0.5*(tmin+tmax);
240
241 tmin = tavg - 0.5*fWindowWidth; tmax = tavg + 0.5*fWindowWidth;
242
243 Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
244 for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
245 if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax) {
246 fPhotFlag[i]=2;
247 iInsideCnt++;
248 }
249 }
250 return iInsideCnt;
251}//FlagPhot()
252//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 253TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
d3da6dc4 254{
255// Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
a591e55f 256// Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]
d3da6dc4 257// Returns: distance between photon point on PC and track projection
258 TRotation mtheta; mtheta.RotateY(fTrkDir.Theta());
259 TRotation mphi; mphi.RotateZ(fTrkDir.Phi());
260 TRotation mrot=mphi*mtheta;
a591e55f 261 TVector3 dirCkov,dirCkovTors;
262
263 dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi); //initially photon is directed according to requested ckov angle
264 dirCkov=mrot*dirCkovTors; //now we know photon direction in LORS
265 return TraceForward(dirCkov);
266}//TracePhot()
d3da6dc4 267//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 268void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
d3da6dc4 269{
270// Finds an intersection point between a line and XY plane shifted along Z.
271// Arguments: dir,pos - vector along the line and any point of the line
272// z - z coordinate of plain
273// Returns: none
274// On exit: pos is the position if this intesection if any
275 static TVector3 nrm(0,0,1);
276 TVector3 pnt(0,0,z);
277
278 TVector3 diff=pnt-pos;
279 Double_t sint=(nrm*diff)/(nrm*dir);
280 pos+=sint*dir;
281}//Propagate()
282//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
283void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
284{
285// Refract direction vector according to Snell law
286// Arguments:
287// n1 - ref idx of first substance
288// n2 - ref idx of second substance
289// Returns: none
290// On exit: dir is new direction
67a1c24c 291 Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
d3da6dc4 292 if(sinref>1.) dir.SetXYZ(-999,-999,-999);
67a1c24c 293 else dir.SetTheta(TMath::ASin(sinref));
d3da6dc4 294}//Refract()
295//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
296Double_t AliHMPIDRecon::HoughResponse()
297{
298//
299//
300//
301 Double_t kThetaMax=0.75;
302 Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
303 TH1D *phots = new TH1D("Rphot" ,"phots" ,nChannels,0,kThetaMax);
304 TH1D *photsw = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
305 TH1D *resultw = new TH1D("resultw","resultw" ,nChannels,0,kThetaMax);
306 Int_t nBin = (Int_t)(kThetaMax/fDTheta);
307 Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
308
309 for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
310 Double_t angle = fPhotCkov[i]; if(angle<0||angle>kThetaMax) continue;
311 phots->Fill(angle);
312 Int_t bin = (Int_t)(0.5+angle/(fDTheta));
313 Double_t weight=1.;
314 if(fIsWEIGHT){
315 Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta; Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
316 Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
317 if(diffArea>0) weight = 1./diffArea;
318 }
319 photsw->Fill(angle,weight);
320 fPhotWei[i]=weight;
321 }//photon candidates loop
322
323 for (Int_t i=1; i<=nBin;i++){
324 Int_t bin1= i-nCorrBand;
325 Int_t bin2= i+nCorrBand;
326 if(bin1<1) bin1=1;
327 if(bin2>nBin)bin2=nBin;
328 Double_t sumPhots=phots->Integral(bin1,bin2);
329 if(sumPhots<3) continue; // if less then 3 photons don't trust to this ring
330 Double_t sumPhotsw=photsw->Integral(bin1,bin2);
331 resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
332 }
333// evaluate the "BEST" theta ckov as the maximum value of histogramm
334 Double_t *pVec = resultw->GetArray();
335 Int_t locMax = TMath::LocMax(nBin,pVec);
336 phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
337
338 return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
339}//HoughResponse()
340//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
341Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
342{
343// Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
344// created by a given MIP. Fromulae according to CERN-EP-2000-058
345// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
346// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
347// MIP beta
348// Returns: absolute error on Cerenkov angle, [radians]
349
350 TVector3 v(-999,-999,-999);
abb5f786 351 Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
d3da6dc4 352
353 v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
354 v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
355 v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
356
357 return v.Mag2();
358}
359//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
360Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
361{
362// Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
363// created by a given MIP. Fromulae according to CERN-EP-2000-058
364// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
365// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
366// MIP beta
367// Returns: absolute error on Cerenkov angle, [radians]
368 Double_t phiDelta = phiC - fTrkDir.Phi();
369
370 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
abb5f786 371 Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
d3da6dc4 372 if (k<0) return 1e10;
373
374 Double_t mu =TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()));
375 Double_t e =TMath::Sin(fTrkDir.Theta())*TMath::Cos(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()));
376
377 Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
378 Double_t dtdxc = kk*(k*(TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()))-(alpha*mu/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
379 Double_t dtdyc = kk*(k*(TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()))+(alpha* e/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
380
381 return TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
382}
383//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
384Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
385{
386// Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
387// created by a given MIP. Fromulae according to CERN-EP-2000-058
388// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
389// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
390// MIP beta
391// Returns: absolute error on Cerenkov angle, [radians]
392 Double_t phiDelta = phiC - fTrkDir.Phi();
393 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
394
abb5f786 395 Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fRadNmean*betaM*betaM/(alpha*TMath::Tan(thetaC));
d3da6dc4 396
397 Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
398
399 return f*dtdn;
400}//SigCrom()
401//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
402Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
403{
404// Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
405// created by a given MIP. Formulae according to CERN-EP-2000-058
406// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
407// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
408// MIP beta
409// Returns: absolute error on Cerenkov angle, [radians]
410
411 Double_t phiDelta = phiC - fTrkDir.Phi();
412 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
413
abb5f786 414 Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
d3da6dc4 415 if (k<0) return 1e10;
416
417 Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
418 Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
419
420 Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
421 Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
422 Double_t ii = 1.+eTr*betaM*i;
423
424 Double_t err = c * (i/(alpha*alpha*8) + ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
425 Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
426
427 return trErr*err;
428}//SigGeom()
429//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++