Right LRS for photon cerenkov angle reconstruction
[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 "AliHMPIDParam.h"   //CkovAngle()
26 #include "AliHMPIDCluster.h" //CkovAngle()
27 #include <TRotation.h>       //TracePhot()
28 #include <TH1D.h>            //HoughResponse()
29 #include <TClonesArray.h>    //CkovAngle()
30 #include <AliESDtrack.h>     //CkovAngle()
31
32 const Double_t AliHMPIDRecon::fgkRadThick=1.5;
33 const Double_t AliHMPIDRecon::fgkWinThick=0.5;
34 const Double_t AliHMPIDRecon::fgkGapThick=8.0;
35 const Double_t AliHMPIDRecon::fgkWinIdx  =1.5787;
36 const Double_t AliHMPIDRecon::fgkGapIdx  =1.0005;
37
38 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
39 AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
40   fRadNmean(1.292),  
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,Double_t nmean)
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   AliHMPIDParam *pParam=AliHMPIDParam::Instance();
65   
66   if(pCluLst->GetEntries()>pParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
67   else                                        fIsWEIGHT = kFALSE;
68
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 
71 //  ph-=TMath::Pi();                                                                            // right XYZ local orientation
72   SetTrack(xRa,yRa,th,ph);
73   
74   fRadNmean=nmean;
75
76   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;                                                                           
77   fPhotCnt=0;                                                      
78   for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
79     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster    
80     chId=pClu->Ch();
81     if(pClu->Q()>pParam->QCut()){                                                             //charge compartible with MIP clusters      
82       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
83       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
84     }else{                                                                                    //charge compatible with photon cluster
85       Double_t thetaCer,phiCer;
86       if(FindPhotCkov(pClu->X(),pClu->Y(),thetaCer,phiCer)){                                  //find ckov angle for this  photon candidate
87         fPhotCkov[fPhotCnt]=thetaCer;                                                         //actual theta Cerenkov (in TRS)
88         fPhotPhi [fPhotCnt]=phiCer;                                                           //actual phi   Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
89         fPhotCnt++;                                                                           //increment counter of photon candidates
90       }
91     }
92   }//clusters loop
93   Int_t iNacc=FlagPhot(HoughResponse());                                                      //flag photons according to individual theta ckov with respect to most probable
94   pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc);                                                    //store mip info 
95
96   if(mipId==-1)              {pTrk->SetHMPIDsignal(kMipQdcCut);  return;}                     //no clusters with QDC more the threshold at all
97   if(dMin>pParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;}                     //closest cluster with enough charge is still too far from intersection
98   pTrk->SetHMPIDcluIdx(chId,mipId);                                                           //set index of cluster
99   if(iNacc<1)    pTrk->SetHMPIDsignal(kNoPhotAccept);                                         //no photon candidates is accepted
100   else           pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries()));                   //find best Theta ckov for ring i.e. track
101   
102   pTrk->SetHMPIDchi2(fCkovSigma2);                                                            //errors squared 
103
104 }//ThetaCerenkov()
105 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
106 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
107 {
108 // Finds Cerenkov angle  for this photon candidate
109 // Arguments: cluX,cluY - position of cadidate's cluster  
110 // Returns: Cerenkov angle 
111
112   TVector3 dirCkov;
113   
114   Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick;                   //z position of middle of RAD
115   TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad);                        //impact point at middle of RAD
116   TVector3  pc(cluX,cluY,0.5*fgkWinThick+fgkGapIdx);                 //mip at PC
117   Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
118                               (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER   
119   Double_t phi=(pc-rad).Phi();                                       //phi of photon
120     
121   Double_t ckov1=0;
122   Double_t ckov2=0.75+fTrkDir.Theta();                        //start to find theta cerenkov in DRS
123   const Double_t kTol=0.01;
124   Int_t iIterCnt = 0;
125   while(1){
126     if(iIterCnt>=50) return kFALSE;
127     Double_t ckov=0.5*(ckov1+ckov2);
128     dirCkov.SetMagThetaPhi(1,ckov,phi);
129     TVector2 posC=TraceForward(dirCkov);                      //trace photon with actual angles
130     Double_t dist=cluR-(posC-fTrkPos).Mod();                  //get distance between trial point and cluster position
131     if(posC.X()==-999) dist = - 999;                          //total reflection problem
132     iIterCnt++;                                               //counter step
133     if     (dist> kTol) ckov1=ckov;                           //cluster @ larger ckov
134     else if(dist<-kTol) ckov2=ckov;                           //cluster @ smaller ckov
135     else{                                                     //precision achived: ckov in DRS found
136       dirCkov.SetMagThetaPhi(1,ckov,phi);                     //
137       RecPhot(dirCkov,thetaCer,phiCer);                       //find ckov (in TRS:the effective Cherenkov angle!)
138       return kTRUE;
139     }
140   }
141 }//FindPhotTheta()
142 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
143 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
144 {
145   //Trace forward a photon from (x,y) up to PC
146   // Arguments: dirCkov photon vector in LORS
147   //   Returns: pos of traced photon at PC
148   TVector2 pos(-999,-999);
149   Double_t thetaCer = dirCkov.Theta();
150   if(thetaCer > TMath::ASin(1./fRadNmean))  return pos;         //total refraction on WIN-GAP boundary
151   Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick;              //z position of middle of RAD
152   TVector3  posCkov(fTrkPos.X(),fTrkPos.Y(),zRad);              //RAD: photon position is track position @ middle of RAD 
153   Propagate(dirCkov,posCkov,           -0.5*fgkWinThick);       //go to RAD-WIN boundary  
154   Refract  (dirCkov,         fRadNmean,fgkWinIdx);              //RAD-WIN refraction
155   Propagate(dirCkov,posCkov,            0.5*fgkWinThick);       //go to WIN-GAP boundary
156   Refract  (dirCkov,         fgkWinIdx,fgkGapIdx);              //WIN-GAP refraction
157   Propagate(dirCkov,posCkov,0.5*fgkWinThick+fgkGapThick);       //go to PC
158   pos.Set(posCkov.X(),posCkov.Y());
159   return pos;
160 }//TraceForward()
161 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
162 void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
163 {
164   //Theta Cerenkov reconstruction 
165   // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
166   //   Returns: thetaCer theta cerenkov reconstructed
167 //  TVector3 dirTrk;
168 //  dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
169 //  Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
170   TRotation mtheta;   mtheta.RotateY(- fTrkDir.Theta());
171   TRotation mphi;       mphi.RotateZ(- fTrkDir.Phi());
172   TRotation mrot=mtheta*mphi;
173   TVector3 dirCkovTRS;
174   dirCkovTRS=mrot*dirCkov;
175   phiCer  = dirCkovTRS.Phi();                                          //actual value of the phi of the photon
176   thetaCer= dirCkovTRS.Theta();                                        //actual value of thetaCerenkov of the photon
177 }
178 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
179 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
180 {
181 // Find area inside the cerenkov ring which lays inside PCs
182 // Arguments: ckovAng - cerenkov angle    
183 //   Returns: area of the ring in cm^2 for given theta ckov
184    
185   const Int_t kN=100;
186   Double_t area=0;
187   for(Int_t i=0;i<kN;i++){
188     TVector2 pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*i    /kN));//trace this photon 
189     TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));//trace the next photon 
190     area+=(pos1-fTrkPos)*(pos2-fTrkPos);                               //add area of the triangle... 
191   }
192   return area;
193 }//FindRingArea()
194 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
195 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
196 {
197 // 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
198 // collecting errors for all single Ckov candidates thetas. (Assuming they are independent)  
199 // Arguments: iNclus- total number of clusters in chamber for background estimation
200 //    Return: best estimation of track Theta ckov
201
202   Double_t wei = 0.;
203   Double_t weightThetaCerenkov = 0.;
204
205   Double_t ckovMin=9999.,ckovMax=0.;
206   Double_t sigma2 = 0;   //to collect error squared for this ring
207   
208   for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
209     if(fPhotFlag[i] == 2){
210       if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i];                         //find max and min Theta ckov from all candidates within probable window
211       if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i]; 
212       weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
213       wei += fPhotWei[i];                                                    //collect weight as sum of all candidate weghts   
214       
215       sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
216     }
217   }//candidates loop
218   
219   if(sigma2>0) fCkovSigma2=1./sigma2;
220   else         fCkovSigma2=1e10;  
221   
222   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
223   return weightThetaCerenkov;
224 }//FindCkovRing()
225 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
226 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
227 {
228 // Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by  HoughResponse()
229 // Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
230 //   Returns: number of photon candidates happened to be inside the window
231
232 // Photon Flag:  Flag = 0 initial set; 
233 //               Flag = 1 good candidate (charge compatible with photon); 
234 //               Flag = 2 photon used for the ring;
235   
236   Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0  and thetaCkovHough
237
238   Double_t tmin = (Double_t)(steps - 1)*fDTheta;
239   Double_t tmax = (Double_t)(steps)*fDTheta;
240   Double_t tavg = 0.5*(tmin+tmax);
241
242   tmin = tavg - 0.5*fWindowWidth;  tmax = tavg + 0.5*fWindowWidth;
243
244   Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
245   for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
246     if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax)    { 
247       fPhotFlag[i]=2;     
248       iInsideCnt++;
249     }
250   }
251   return iInsideCnt;
252 }//FlagPhot()
253 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
254 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
255 {
256 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
257 // Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]    
258 //   Returns: distance between photon point on PC and track projection  
259   TRotation mtheta;   mtheta.RotateY(fTrkDir.Theta());
260   TRotation mphi;       mphi.RotateZ(fTrkDir.Phi());  
261   TRotation mrot=mphi*mtheta;
262   TVector3  dirCkov,dirCkovTors;   
263
264   dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi);                    //initially photon is directed according to requested ckov angle
265   dirCkov=mrot*dirCkovTors;                                         //now we know photon direction in LORS
266   return TraceForward(dirCkov);
267 }//TracePhot()
268 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
269 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
270 {
271 // Finds an intersection point between a line and XY plane shifted along Z.
272 // Arguments:  dir,pos   - vector along the line and any point of the line
273 //             z         - z coordinate of plain 
274 //   Returns:  none
275 //   On exit:  pos is the position if this intesection if any
276   static TVector3 nrm(0,0,1); 
277          TVector3 pnt(0,0,z);
278   
279   TVector3 diff=pnt-pos;
280   Double_t sint=(nrm*diff)/(nrm*dir);
281   pos+=sint*dir;
282 }//Propagate()
283 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
284 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
285 {
286 // Refract direction vector according to Snell law
287 // Arguments: 
288 //            n1 - ref idx of first substance
289 //            n2 - ref idx of second substance
290 //   Returns: none
291 //   On exit: dir is new direction
292   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
293   if(sinref>1.)    dir.SetXYZ(-999,-999,-999);
294   else             dir.SetTheta(TMath::ASin(sinref));
295 }//Refract()
296 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
297 Double_t AliHMPIDRecon::HoughResponse()
298 {
299 //
300 //
301 //       
302   Double_t kThetaMax=0.75;
303   Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
304   TH1D *phots   = new TH1D("Rphot"  ,"phots"         ,nChannels,0,kThetaMax);
305   TH1D *photsw  = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
306   TH1D *resultw = new TH1D("resultw","resultw"       ,nChannels,0,kThetaMax);
307   Int_t nBin = (Int_t)(kThetaMax/fDTheta);
308   Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
309   
310   for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
311     Double_t angle = fPhotCkov[i];  if(angle<0||angle>kThetaMax) continue;
312     phots->Fill(angle);
313     Int_t bin = (Int_t)(0.5+angle/(fDTheta));
314     Double_t weight=1.;
315     if(fIsWEIGHT){
316       Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta;  Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;   
317       Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
318       if(diffArea>0) weight = 1./diffArea;
319     }
320     photsw->Fill(angle,weight);
321     fPhotWei[i]=weight;
322   }//photon candidates loop 
323    
324   for (Int_t i=1; i<=nBin;i++){
325     Int_t bin1= i-nCorrBand;
326     Int_t bin2= i+nCorrBand;
327     if(bin1<1) bin1=1;
328     if(bin2>nBin)bin2=nBin;
329     Double_t sumPhots=phots->Integral(bin1,bin2);
330     if(sumPhots<3) continue;                            // if less then 3 photons don't trust to this ring
331     Double_t sumPhotsw=photsw->Integral(bin1,bin2);
332     resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
333   } 
334 // evaluate the "BEST" theta ckov as the maximum value of histogramm
335   Double_t *pVec = resultw->GetArray();
336   Int_t locMax = TMath::LocMax(nBin,pVec);
337   phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
338   
339   return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov   
340 }//HoughResponse()
341 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
342 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
343 {
344 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon 
345 // created by a given MIP. Fromulae according to CERN-EP-2000-058 
346 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
347 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]        
348 //            MIP beta
349 //   Returns: absolute error on Cerenkov angle, [radians]    
350   
351   TVector3 v(-999,-999,-999);
352   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
353
354   v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
355   v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
356   v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
357
358   return v.Mag2();
359 }
360 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
361 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
362 {
363 // Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon 
364 // created by a given MIP. Fromulae according to CERN-EP-2000-058 
365 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
366 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]        
367 //            MIP beta
368 //   Returns: absolute error on Cerenkov angle, [radians]    
369   Double_t phiDelta = phiC - fTrkDir.Phi();
370
371   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
372   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
373   if (k<0) return 1e10;
374
375   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()));
376   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()));
377
378   Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
379   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));
380   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));
381
382   return  TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
383 }
384 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
385 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
386 {
387 // Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon 
388 // created by a given MIP. Fromulae according to CERN-EP-2000-058 
389 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
390 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]        
391 //            MIP beta
392 //   Returns: absolute error on Cerenkov angle, [radians]    
393   Double_t phiDelta = phiC - fTrkDir.Phi();
394   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
395
396   Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fRadNmean*betaM*betaM/(alpha*TMath::Tan(thetaC));
397             
398   Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
399
400   return f*dtdn;
401 }//SigCrom()
402 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
403 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
404 {
405 // Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon 
406 // created by a given MIP. Formulae according to CERN-EP-2000-058 
407 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
408 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]        
409 //            MIP beta
410 //   Returns: absolute error on Cerenkov angle, [radians]    
411
412   Double_t phiDelta = phiC - fTrkDir.Phi();
413   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
414
415   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
416   if (k<0) return 1e10;
417
418   Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
419   Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
420
421   Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
422   Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
423   Double_t ii = 1.+eTr*betaM*i;
424
425   Double_t err = c * (i/(alpha*alpha*8) +  ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
426   Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
427
428   return trErr*err;
429 }//SigGeom()
430 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++