new 2d event display + optical properties restored in v1
[u/mrichter/AliRoot.git] / HMPID / AliHMPIDRecon.cxx
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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()
29 #include <AliESDtrack.h>   //CkovAngle()
30
31 const Double_t AliHMPIDRecon::fgkRadThick=1.5;
32 const Double_t AliHMPIDRecon::fgkWinThick=0.5;
33 const Double_t AliHMPIDRecon::fgkGapThick=8.0;
34 const Double_t AliHMPIDRecon::fgkRadIdx  =1.292;
35 const Double_t AliHMPIDRecon::fgkWinIdx  =1.5787;
36 const Double_t AliHMPIDRecon::fgkGapIdx  =1.0005;
37
38
39 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
40 AliHMPIDRecon::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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
57 void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst)
58 {
59 // Pattern recognition method based on Hough transform
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], 
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;
68   Float_t xPc,yPc,th,ph;      pTrk->GetHMPIDtrk(xPc,yPc,th,ph);  SetTrack(xPc,yPc,th,ph); //initialize this track            
69
70   
71   
72   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;                                                                           
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    
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     }
84   }//clusters loop
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 
96
97 }//ThetaCerenkov()
98 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
99 Double_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);      
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
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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
119 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
128 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
148 Double_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){
163       if(fPhotCkov[i]<=0) continue;//?????????????????Flag photos = 2 may imply CkovEta = 0?????????????? 
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       
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   
175   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;  
176   return weightThetaCerenkov;
177 }//FindCkovRing()
178 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
179 Int_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
204 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
229 void 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
244 void 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
257 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
302 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
321 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
345 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
363 Double_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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++