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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
24#include "AliHMPIDRecon.h" //class header
25#include "AliHMPIDCluster.h" //CkovAngle()
26#include <TRotation.h> //TracePhoton()
27#include <TH1D.h> //HoughResponse()
28#include <TClonesArray.h> //CkovAngle()
59280a5a 29#include <AliESDtrack.h> //CkovAngle()
d3da6dc4 30
31const Double_t AliHMPIDRecon::fgkRadThick=1.5;
32const Double_t AliHMPIDRecon::fgkWinThick=0.5;
33const Double_t AliHMPIDRecon::fgkGapThick=8.0;
34const Double_t AliHMPIDRecon::fgkRadIdx =1.292;
35const Double_t AliHMPIDRecon::fgkWinIdx =1.5787;
36const Double_t AliHMPIDRecon::fgkGapIdx =1.0005;
37
38
39//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
40AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
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//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
59280a5a 57void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst)
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],
d3da6dc4 63
64 if(pCluLst->GetEntries()>200) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
65 else fIsWEIGHT = kFALSE;
66
67 // Photon Flag: Flag = 0 initial set; Flag = 1 good candidate (charge compatible with photon); Flag = 2 photon used for the ring;
59280a5a 68 Float_t xPc,yPc,th,ph; pTrk->GetHMPIDtrk(xPc,yPc,th,ph); SetTrack(xPc,yPc,th,ph); //initialize this track
d3da6dc4 69
59280a5a 70
71
72 Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
d3da6dc4 73 fPhotCnt=0;
74 for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
75 AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu); //get pointer to current cluster
59280a5a 76 chId=pClu->Ch();
77 if(pClu->Q()>100){ //charge compartible with MIP clusters
78 Float_t dX=xPc-pClu->X(),dY=yPc-pClu->Y(),d =TMath::Sqrt(dX*dX+dY*dY); //distance between current cluster and intersection point
79 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
80 }else{ //charge compartible with photon cluster
81 fPhotCkov[fPhotCnt]=FindPhotCkov(pClu->X(),pClu->Y()); //find ckov angle for this photon candidate
82 fPhotCnt++; //increment counter of photon candidates
83 }
d3da6dc4 84 }//clusters loop
59280a5a 85 Int_t iNacc=FlagPhot(HoughResponse()); //flag photons according to individual theta ckov with respect to most probable
86
87 pTrk->SetHMPIDmip (mipX,mipY,mipQ,iNacc); //store mip info
88
89 if(mipId==-1) {pTrk->SetHMPIDsignal (kMipQdcCut); return;} //no clusters with QDC more the threshold at all
90 if(dMin>1) {pTrk->SetHMPIDsignal (kMipDistCut); return;} //closest cluster with enough charge is still too far from intersection
91 pTrk->SetHMPIDcluIdx(chId,mipId);
92 if(iNacc<1) pTrk->SetHMPIDsignal(kNoPhotAccept); //no photon candidates is accepted
93 else pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries())); //find best Theta ckov for ring i.e. track
94
95 pTrk->SetHMPIDchi2(fCkovSigma2); //error squared
d3da6dc4 96
d3da6dc4 97}//ThetaCerenkov()
98//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
99Double_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY)
100{
101// Finds Cerenkov angle for this photon candidate
102// Arguments: cluX,cluY - position of cadidate's cluster
103// Returns: Cerenkov angle
104
105 TVector2 pos(cluX,cluY); Double_t cluR=(pos-fTrkPos).Mod(); Double_t phi=FindPhotPhi(cluX,cluY);
d3da6dc4 106 Double_t ckov1=0,ckov2=0.75;
107 const Double_t kTol=0.05;
108 Int_t iIterCnt = 0;
109 while(1){
110 if(iIterCnt>=50) return -1;
111 Double_t ckov=0.5*(ckov1+ckov2);
112 Double_t dist=cluR-TracePhot(ckov,phi,pos); iIterCnt++; //get distance between trial point and cluster position
d3da6dc4 113 if (dist> kTol) ckov1=ckov; //cluster @ larger ckov
114 else if(dist<-kTol) ckov2=ckov; //cluster @ smaller ckov
115 else return ckov; //precision achived
116 }
117}//FindPhotTheta()
118//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
119Double_t AliHMPIDRecon::FindPhotPhi(Double_t cluX,Double_t cluY)
120{
121// Finds phi angle og photon candidate by considering the cluster's position of this candudate w.r.t track position
122
123 Double_t emiss=0;
124 return fPhotPhi[fPhotCnt]=TMath::ATan2(cluY-fTrkPos.Y()-emiss*TMath::Tan(fTrkDir.Theta())*TMath::Sin(fTrkDir.Phi()),
125 cluX-fTrkPos.X()-emiss*TMath::Tan(fTrkDir.Theta())*TMath::Cos(fTrkDir.Phi()));
126}
127//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
128Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
129{
130// Find area inside the cerenkov ring which lays inside PCs
131// Arguments: ckovThe - cernkov
132// Returns: area of the ring in cm^2 for given theta ckov
133
134
135 TVector2 pos1,pos2;
136
137 const Int_t kN=100;
138 Double_t area=0;
139 for(Int_t i=0;i<kN;i++){
140 TracePhot(ckovAng,Double_t(TMath::TwoPi()*i /kN),pos1);//trace this photon
141 TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN),pos2);//trace this photon
142 area+=(pos1-fTrkPos)*(pos2-fTrkPos);
143
144 }
145 return area;
146}//FindRingArea()
147//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
148Double_t AliHMPIDRecon::FindRingCkov(Int_t)
149{
150// 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
151// collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
152// Arguments: iNclus- total number of clusters in chamber for background estimation
153// Return: best estimation of track Theta ckov
154
155 Double_t wei = 0.;
156 Double_t weightThetaCerenkov = 0.;
157
158 Double_t ckovMin=9999.,ckovMax=0.;
159 Double_t sigma2 = 0; //to collect error squared for this ring
160
161 for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
162 if(fPhotFlag[i] == 2){
3c6274c1 163 if(fPhotCkov[i]<=0) continue;//?????????????????Flag photos = 2 may imply CkovEta = 0??????????????
d3da6dc4 164 if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i]; //find max and min Theta ckov from all candidates within probable window
165 if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
166 weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i]; wei += fPhotWei[i]; //collect weight as sum of all candidate weghts
167
d3da6dc4 168 sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
169 }
170 }//candidates loop
171
172 if(sigma2>0) fCkovSigma2=1./sigma2;
173 else fCkovSigma2=1e10;
174
d3da6dc4 175 if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
176 return weightThetaCerenkov;
177}//FindCkovRing()
178//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
179Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
180{
181// Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by HoughResponse()
182// Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
183// Returns: number of photon candidates happened to be inside the window
184
185
186 Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0 and thetaCkovHough
187
188 Double_t tmin = (Double_t)(steps - 1)*fDTheta;
189 Double_t tmax = (Double_t)(steps)*fDTheta;
190 Double_t tavg = 0.5*(tmin+tmax);
191
192 tmin = tavg - 0.5*fWindowWidth; tmax = tavg + 0.5*fWindowWidth;
193
194 Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
195 for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
196 if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax) {
197 fPhotFlag[i]=2;
198 iInsideCnt++;
199 }
200 }
201 return iInsideCnt;
202}//FlagPhot()
203//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
204Double_t AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi,TVector2 &pos)const
205{
206// Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
207// Arguments: ckovThe,ckovPhi- photon ckov angles, [rad] (warning: not photon theta and phi)
208// Returns: distance between photon point on PC and track projection
209 TRotation mtheta; mtheta.RotateY(fTrkDir.Theta());
210 TRotation mphi; mphi.RotateZ(fTrkDir.Phi());
211 TRotation mrot=mphi*mtheta;
212
213 TVector3 posCkov(fTrkPos.X(),fTrkPos.Y(),-0.5*fgkRadThick-fgkWinThick-fgkGapThick); //RAD: photon position is track position @ middle of RAD
214 TVector3 dirCkov; dirCkov.SetMagThetaPhi(1,ckovThe,ckovPhi); //initially photon is directed according to requested ckov angle
215 dirCkov=mrot*dirCkov; //now we know photon direction in LORS
216 dirCkov.SetPhi(ckovPhi);
217 if(dirCkov.Theta() > TMath::ASin(1./fgkRadIdx)) return -999;//total refraction on WIN-GAP boundary
218
219 Propagate(dirCkov,posCkov,-fgkWinThick-fgkGapThick); //go to RAD-WIN boundary remeber that z=0 is PC plane
220 Refract (dirCkov, fgkRadIdx,fgkWinIdx ); //RAD-WIN refraction
221 Propagate(dirCkov,posCkov,-fgkGapThick ); //go to WIN-GAP boundary
222 Refract (dirCkov, fgkWinIdx,fgkGapIdx ); //WIN-GAP refraction
223 Propagate(dirCkov,posCkov,0 ); //go to PC
224
225 pos.Set(posCkov.X(),posCkov.Y());
226 return (pos-fTrkPos).Mod();
227}//TracePhoton()
228//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
229void AliHMPIDRecon::Propagate(const TVector3 &dir,TVector3 &pos,Double_t z)const
230{
231// Finds an intersection point between a line and XY plane shifted along Z.
232// Arguments: dir,pos - vector along the line and any point of the line
233// z - z coordinate of plain
234// Returns: none
235// On exit: pos is the position if this intesection if any
236 static TVector3 nrm(0,0,1);
237 TVector3 pnt(0,0,z);
238
239 TVector3 diff=pnt-pos;
240 Double_t sint=(nrm*diff)/(nrm*dir);
241 pos+=sint*dir;
242}//Propagate()
243//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
244void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
245{
246// Refract direction vector according to Snell law
247// Arguments:
248// n1 - ref idx of first substance
249// n2 - ref idx of second substance
250// Returns: none
251// On exit: dir is new direction
252 Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
253 if(sinref>1.) dir.SetXYZ(-999,-999,-999);
254 else dir.SetTheta(TMath::ASin(sinref));
255}//Refract()
256//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
257Double_t AliHMPIDRecon::HoughResponse()
258{
259//
260//
261//
262 Double_t kThetaMax=0.75;
263 Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
264 TH1D *phots = new TH1D("Rphot" ,"phots" ,nChannels,0,kThetaMax);
265 TH1D *photsw = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
266 TH1D *resultw = new TH1D("resultw","resultw" ,nChannels,0,kThetaMax);
267 Int_t nBin = (Int_t)(kThetaMax/fDTheta);
268 Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
269
270 for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
271 Double_t angle = fPhotCkov[i]; if(angle<0||angle>kThetaMax) continue;
272 phots->Fill(angle);
273 Int_t bin = (Int_t)(0.5+angle/(fDTheta));
274 Double_t weight=1.;
275 if(fIsWEIGHT){
276 Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta; Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
277 Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
278 if(diffArea>0) weight = 1./diffArea;
279 }
280 photsw->Fill(angle,weight);
281 fPhotWei[i]=weight;
282 }//photon candidates loop
283
284 for (Int_t i=1; i<=nBin;i++){
285 Int_t bin1= i-nCorrBand;
286 Int_t bin2= i+nCorrBand;
287 if(bin1<1) bin1=1;
288 if(bin2>nBin)bin2=nBin;
289 Double_t sumPhots=phots->Integral(bin1,bin2);
290 if(sumPhots<3) continue; // if less then 3 photons don't trust to this ring
291 Double_t sumPhotsw=photsw->Integral(bin1,bin2);
292 resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
293 }
294// evaluate the "BEST" theta ckov as the maximum value of histogramm
295 Double_t *pVec = resultw->GetArray();
296 Int_t locMax = TMath::LocMax(nBin,pVec);
297 phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
298
299 return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
300}//HoughResponse()
301//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
302Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
303{
304// Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
305// created by a given MIP. Fromulae according to CERN-EP-2000-058
306// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
307// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
308// MIP beta
309// Returns: absolute error on Cerenkov angle, [radians]
310
311 TVector3 v(-999,-999,-999);
312 Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fgkRadIdx);
313
314 v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
315 v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
316 v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
317
318 return v.Mag2();
319}
320//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
321Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
322{
323// Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
324// created by a given MIP. Fromulae according to CERN-EP-2000-058
325// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
326// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
327// MIP beta
328// Returns: absolute error on Cerenkov angle, [radians]
329 Double_t phiDelta = phiC - fTrkDir.Phi();
330
331 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
332 Double_t k = 1.-fgkRadIdx*fgkRadIdx+alpha*alpha/(betaM*betaM);
333 if (k<0) return 1e10;
334
335 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()));
336 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()));
337
338 Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
339 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));
340 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));
341
342 return TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
343}
344//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
345Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
346{
347// Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
348// created by a given MIP. Fromulae according to CERN-EP-2000-058
349// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
350// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
351// MIP beta
352// Returns: absolute error on Cerenkov angle, [radians]
353 Double_t phiDelta = phiC - fTrkDir.Phi();
354 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
355
356 Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fgkRadIdx*betaM*betaM/(alpha*TMath::Tan(thetaC));
357
358 Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
359
360 return f*dtdn;
361}//SigCrom()
362//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
363Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
364{
365// Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
366// created by a given MIP. Formulae according to CERN-EP-2000-058
367// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
368// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
369// MIP beta
370// Returns: absolute error on Cerenkov angle, [radians]
371
372 Double_t phiDelta = phiC - fTrkDir.Phi();
373 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
374
375 Double_t k = 1.-fgkRadIdx*fgkRadIdx+alpha*alpha/(betaM*betaM);
376 if (k<0) return 1e10;
377
378 Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
379 Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
380
381 Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
382 Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
383 Double_t ii = 1.+eTr*betaM*i;
384
385 Double_t err = c * (i/(alpha*alpha*8) + ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
386 Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
387
388 return trErr*err;
389}//SigGeom()
390//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++