HMPID/AliHMPIDRecon.cxx

   1 /**************************************************************************
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   3  *                                                                        *
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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>       //TracePhot()
  27 #include <TH1D.h>            //HoughResponse()
  28 #include <TClonesArray.h>    //CkovAngle()
  29 #include <AliESDtrack.h>     //CkovAngle()
  30
  31 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  32 AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat")
  33 {
  34 //..
  35 //init of data members
  36 //..
  37
  38   fPhotCnt  = -1;
  39   fPhotFlag = 0x0;
  40   fPhotCkov = 0x0;
  41   fPhotPhi  = 0x0;
  42   fPhotWei  = 0x0;
  43   fCkovSigma2 = 0;
  44   fIsWEIGHT = kFALSE;
  45   fDTheta   = 0.001;
  46   fWindowWidth = 0.045;
  47   fTrkDir = TVector3(0,0,1); // init just for test
  48   fTrkPos = TVector2(30,40); // init just for test
  49
  50   AliHMPIDParam *pParam=AliHMPIDParam::Instance();
  51   fParam = pParam;
  52
  53   fParam->SetRefIdx(fParam->MeanIdxRad()); // initialization of ref index to a default one
  54 }
  55 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  56 void AliHMPIDRecon::InitVars(Int_t n)
  57 {
  58 //..
  59 //Init some variables
  60 //..
  61   if(n<0) return;
  62   fPhotFlag = new Int_t[n];
  63   fPhotCkov = new Double_t[n];
  64   fPhotPhi  = new Double_t[n];
  65   fPhotWei  = new Double_t[n];
  66 //
  67 }
  68 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  69 void AliHMPIDRecon::DeleteVars()
  70 {
  71 //..
  72 //Delete variables
  73 //..
  74   delete fPhotFlag;
  75   delete fPhotCkov;
  76   delete fPhotPhi;
  77   delete fPhotWei;
  78 }
  79 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  80 void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean,Double_t qthre)
  81 {
  82 // Pattern recognition method based on Hough transform
  83 // Arguments:   pTrk     - track for which Ckov angle is to be found
  84 //              pCluLst  - list of clusters for this chamber
  85 //   Returns:            - track ckov angle, [rad],
  86
  87   Int_t nClusTot = pCluLst->GetEntries();
  88   if(nClusTot>fParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
  89   else                           fIsWEIGHT = kFALSE;
  90
  91   InitVars(nClusTot);
  92
  93   Float_t xRa,yRa,th,ph;
  94   pTrk->GetHMPIDtrk(xRa,yRa,th,ph);        //initialize this track: th and ph angles at middle of RAD
  95   SetTrack(xRa,yRa,th,ph);
  96
  97   fParam->SetRefIdx(nmean);
  98
  99   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
 100   fPhotCnt=0;
 101   for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
 102     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster
 103     chId=pClu->Ch();
 104     if(pClu->Q()>qthre){                                                                      //charge compartible with MIP clusters
 105       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
 106       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
 107     }else{                                                                                    //charge compatible with photon cluster
 108       Double_t thetaCer,phiCer;
 109       if(FindPhotCkov(pClu->X(),pClu->Y(),thetaCer,phiCer)){                                  //find ckov angle for this  photon candidate
 110         fPhotCkov[fPhotCnt]=thetaCer;                                                         //actual theta Cerenkov (in TRS)
 111         fPhotPhi [fPhotCnt]=phiCer;                                                           //actual phi   Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
 112         //PH        Printf("photon n. %i reconstructed theta = %f",fPhotCnt,fPhotCkov[fPhotCnt]);
 113         fPhotCnt++;                                                                           //increment counter of photon candidates
 114       }
 115     }
 116   }//clusters loop
 117   fMipPos.Set(mipX,mipY);
 118   if(fPhotCnt<=3) pTrk->SetHMPIDsignal(kNoPhotAccept);                                        //no reconstruction with <=3 photon candidates
 119   Int_t iNacc=FlagPhot(HoughResponse());                                                      //flag photons according to individual theta ckov with respect to most probable
 120   pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc);                                                    //store mip info
 121
 122   if(mipId==-1)              {pTrk->SetHMPIDsignal(kMipQdcCut);  return;}                     //no clusters with QDC more the threshold at all
 123   if(dMin>fParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;}                     //closest cluster with enough charge is still too far from intersection
 124   pTrk->SetHMPIDcluIdx(chId,mipId);                                                           //set index of cluster
 125   if(iNacc<1){
 126     pTrk->SetHMPIDsignal(kNoPhotAccept);                                                      //no photon candidates is accepted
 127   }
 128   else {
 129     pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries()));                                //find best Theta ckov for ring i.e. track
 130     pTrk->SetHMPIDchi2(fCkovSigma2);                                                          //errors squared
 131   }
 132
 133   DeleteVars();
 134 }//CkovAngle()
 135 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 136 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
 137 {
 138 // Finds Cerenkov angle  for this photon candidate
 139 // Arguments: cluX,cluY - position of cadidate's cluster
 140 // Returns: Cerenkov angle
 141
 142   TVector3 dirCkov;
 143
 144   Double_t zRad= -0.5*fParam->RadThick()-0.5*fParam->WinThick();     //z position of middle of RAD
 145   TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad);                        //impact point at middle of RAD
 146   TVector3  pc(cluX,cluY,0.5*fParam->WinThick()+fParam->GapIdx());   //mip at PC
 147   Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
 148                               (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
 149   Double_t phi=(pc-rad).Phi();                                       //phi of photon
 150
 151   Double_t ckov1=0;
 152   Double_t ckov2=0.75+fTrkDir.Theta();                        //start to find theta cerenkov in DRS
 153   const Double_t kTol=0.01;
 154   Int_t iIterCnt = 0;
 155   while(1){
 156     if(iIterCnt>=50) return kFALSE;
 157     Double_t ckov=0.5*(ckov1+ckov2);
 158     dirCkov.SetMagThetaPhi(1,ckov,phi);
 159     TVector2 posC=TraceForward(dirCkov);                      //trace photon with actual angles
 160     Double_t dist=cluR-(posC-fTrkPos).Mod();                  //get distance between trial point and cluster position
 161     if(posC.X()==-999) dist = - 999;                          //total reflection problem
 162     iIterCnt++;                                               //counter step
 163     if     (dist> kTol) ckov1=ckov;                           //cluster @ larger ckov
 164     else if(dist<-kTol) ckov2=ckov;                           //cluster @ smaller ckov
 165     else{                                                     //precision achived: ckov in DRS found
 166       dirCkov.SetMagThetaPhi(1,ckov,phi);                     //
 167       RecPhot(dirCkov,thetaCer,phiCer);                       //find ckov (in TRS:the effective Cherenkov angle!)
 168       return kTRUE;
 169     }
 170   }
 171 }//FindPhotTheta()
 172 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 173 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
 174 {
 175   //Trace forward a photon from (x,y) up to PC
 176   // Arguments: dirCkov photon vector in LORS
 177   //   Returns: pos of traced photon at PC
 178
 179   TVector2 pos(-999,-999);
 180   Double_t thetaCer = dirCkov.Theta();
 181   if(thetaCer > TMath::ASin(1./fParam->GetRefIdx())) return pos;          //total refraction on WIN-GAP boundary
 182   Double_t zRad= -0.5*fParam->RadThick()-0.5*fParam->WinThick();          //z position of middle of RAD
 183   TVector3  posCkov(fTrkPos.X(),fTrkPos.Y(),zRad);                        //RAD: photon position is track position @ middle of RAD
 184   Propagate(dirCkov,posCkov,           -0.5*fParam->WinThick());          //go to RAD-WIN boundary
 185   Refract  (dirCkov,         fParam->GetRefIdx(),fParam->WinIdx());       //RAD-WIN refraction
 186   Propagate(dirCkov,posCkov,            0.5*fParam->WinThick());          //go to WIN-GAP boundary
 187   Refract  (dirCkov,         fParam->WinIdx(),fParam->GapIdx());          //WIN-GAP refraction
 188   Propagate(dirCkov,posCkov,0.5*fParam->WinThick()+fParam->GapThick());   //go to PC
 189   pos.Set(posCkov.X(),posCkov.Y());
 190   return pos;
 191 }//TraceForward()
 192 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 193 void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
 194 {
 195   //Theta Cerenkov reconstruction
 196   // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
 197   //   Returns: thetaCer theta cerenkov reconstructed
 198 //  TVector3 dirTrk;
 199 //  dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
 200 //  Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
 201   TRotation mtheta;   mtheta.RotateY(- fTrkDir.Theta());
 202   TRotation mphi;       mphi.RotateZ(- fTrkDir.Phi());
 203   TRotation mrot=mtheta*mphi;
 204   TVector3 dirCkovTRS;
 205   dirCkovTRS=mrot*dirCkov;
 206   phiCer  = dirCkovTRS.Phi();                                          //actual value of the phi of the photon
 207   thetaCer= dirCkovTRS.Theta();                                        //actual value of thetaCerenkov of the photon
 208 }
 209 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 210 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
 211 {
 212 // Find area covered in the PC acceptance
 213 // Arguments: ckovAng - cerenkov angle
 214 //   Returns: area of the ring in cm^2 for given theta ckov
 215
 216   const Int_t kN=50;
 217   TVector2 pos1;
 218   Double_t area=0;
 219   Bool_t first=kFALSE;
 220   for(Int_t i=0;i<kN;i++){
 221    if(!first) {
 222      pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));                                     //find a good trace for the first photon
 223      if(pos1.X()==-999) continue;                                                                   //no area: open ring
 224      if(!fParam->IsInside(pos1.X(),pos1.Y(),0)) pos1 = IntWithEdge(fMipPos,pos1);                   // ffind the very first intersection...
 225      first=kTRUE;
 226      continue;
 227    }
 228    TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));                              //trace the next photon
 229    if(pos2.X()==-999) continue;                                                                     //no area: open ring
 230    if(!fParam->IsInside(pos2.X(),pos2.Y(),0)) {
 231      pos2 = IntWithEdge(fMipPos,pos2);
 232    }
 233    area+=TMath::Abs((pos1-fMipPos).X()*(pos2-fMipPos).Y()-(pos1-fMipPos).Y()*(pos2-fMipPos).X());   //add area of the triangle...
 234    pos1 = pos2;
 235   }
 236 //---  find points from ring
 237   area*=0.5;
 238   return area;
 239 }//FindRingArea()
 240 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 241 TVector2 AliHMPIDRecon::IntWithEdge(TVector2 p1,TVector2 p2)const
 242 {
 243 // It finds the intersection of the line for 2 points traced as photons
 244 // and the edge of a given PC
 245 // Arguments: 2 points obtained tracing the photons
 246 //   Returns: intersection point with detector (PC) edges
 247
 248   Double_t xmin = (p1.X()<p2.X())? p1.X():p2.X();
 249   Double_t xmax = (p1.X()<p2.X())? p2.X():p1.X();
 250   Double_t ymin = (p1.Y()<p2.Y())? p1.Y():p2.Y();
 251   Double_t ymax = (p1.Y()<p2.Y())? p2.Y():p1.Y();
 252
 253   Double_t m = TMath::Tan((p2-p1).Phi());
 254   TVector2 pint;
 255   //intersection with low  X
 256   pint.Set((Double_t)(p1.X() + (0-p1.Y())/m),0.);
 257   if(pint.X()>=0 && pint.X()<=fParam->SizeAllX() &&
 258      pint.X()>=xmin && pint.X()<=xmax            &&
 259      pint.Y()>=ymin && pint.Y()<=ymax) return pint;
 260   //intersection with high X
 261   pint.Set((Double_t)(p1.X() + (fParam->SizeAllY()-p1.Y())/m),(Double_t)(fParam->SizeAllY()));
 262   if(pint.X()>=0 && pint.X()<=fParam->SizeAllX() &&
 263      pint.X()>=xmin && pint.X()<=xmax            &&
 264      pint.Y()>=ymin && pint.Y()<=ymax) return pint;
 265   //intersection with left Y
 266   pint.Set(0.,(Double_t)(p1.Y() + m*(0-p1.X())));
 267   if(pint.Y()>=0 && pint.Y()<=fParam->SizeAllY() &&
 268      pint.Y()>=ymin && pint.Y()<=ymax            &&
 269      pint.X()>=xmin && pint.X()<=xmax) return pint;
 270   //intersection with righ Y
 271   pint.Set((Double_t)(fParam->SizeAllX()),(Double_t)(p1.Y() + m*(fParam->SizeAllX()-p1.X())));
 272   if(pint.Y()>=0 && pint.Y()<=fParam->SizeAllY() &&
 273      pint.Y()>=ymin && pint.Y()<=ymax            &&
 274      pint.X()>=xmin && pint.X()<=xmax) return pint;
 275   return p1;
 276 }//IntWithEdge()
 277 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 278 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
 279 {
 280 // 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
 281 // collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
 282 // Arguments: iNclus- total number of clusters in chamber for background estimation
 283 //    Return: best estimation of track Theta ckov
 284
 285   Double_t wei = 0.;
 286   Double_t weightThetaCerenkov = 0.;
 287
 288   Double_t ckovMin=9999.,ckovMax=0.;
 289   Double_t sigma2 = 0;   //to collect error squared for this ring
 290
 291   for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
 292     if(fPhotFlag[i] == 2){
 293       if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i];                         //find max and min Theta ckov from all candidates within probable window
 294       if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
 295       weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
 296       wei += fPhotWei[i];                                                    //collect weight as sum of all candidate weghts
 297
 298       sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
 299     }
 300   }//candidates loop
 301
 302   if(sigma2>0) fCkovSigma2=1./sigma2;
 303   else         fCkovSigma2=1e10;
 304
 305   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
 306   return weightThetaCerenkov;
 307 }//FindCkovRing()
 308 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 309 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
 310 {
 311 // Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by  HoughResponse()
 312 // Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
 313 //   Returns: number of photon candidates happened to be inside the window
 314
 315 // Photon Flag:  Flag = 0 initial set;
 316 //               Flag = 1 good candidate (charge compatible with photon);
 317 //               Flag = 2 photon used for the ring;
 318
 319   Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0  and thetaCkovHough
 320
 321   Double_t tmin = (Double_t)(steps - 1)*fDTheta;
 322   Double_t tmax = (Double_t)(steps)*fDTheta;
 323   Double_t tavg = 0.5*(tmin+tmax);
 324
 325   tmin = tavg - 0.5*fWindowWidth;  tmax = tavg + 0.5*fWindowWidth;
 326
 327   Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
 328   for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
 329     fPhotFlag[i] = 0;
 330     if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax)    {
 331       fPhotFlag[i]=2;
 332       iInsideCnt++;
 333     }
 334   }
 335   return iInsideCnt;
 336 }//FlagPhot()
 337 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 338 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
 339 {
 340 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
 341 // Arguments: ckovThe,ckovPhi- photon ckov angles in TRS, [rad]
 342 //   Returns: distance between photon point on PC and track projection
 343   TRotation mtheta;   mtheta.RotateY(fTrkDir.Theta());
 344   TRotation mphi;       mphi.RotateZ(fTrkDir.Phi());
 345   TRotation mrot=mphi*mtheta;
 346   TVector3  dirCkov,dirCkovTors;
 347
 348   dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi);                    //initially photon is directed according to requested ckov angle
 349   dirCkov=mrot*dirCkovTors;                                         //now we know photon direction in LORS
 350   return TraceForward(dirCkov);
 351 }//TracePhot()
 352 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 353 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
 354 {
 355 // Finds an intersection point between a line and XY plane shifted along Z.
 356 // Arguments:  dir,pos   - vector along the line and any point of the line
 357 //             z         - z coordinate of plain
 358 //   Returns:  none
 359 //   On exit:  pos is the position if this intesection if any
 360   static TVector3 nrm(0,0,1);
 361          TVector3 pnt(0,0,z);
 362
 363   TVector3 diff=pnt-pos;
 364   Double_t sint=(nrm*diff)/(nrm*dir);
 365   pos+=sint*dir;
 366 }//Propagate()
 367 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 368 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
 369 {
 370 // Refract direction vector according to Snell law
 371 // Arguments:
 372 //            n1 - ref idx of first substance
 373 //            n2 - ref idx of second substance
 374 //   Returns: none
 375 //   On exit: dir is new direction
 376   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
 377   if(TMath::Abs(sinref)>1.) dir.SetXYZ(-999,-999,-999);
 378   else             dir.SetTheta(TMath::ASin(sinref));
 379 }//Refract()
 380 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 381 Double_t AliHMPIDRecon::HoughResponse()
 382 {
 383 //
 384 //    fIdxMip = mipId;
 385
 386 //
 387   Double_t kThetaMax=0.75;
 388   Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
 389   TH1D *phots   = new TH1D("Rphot"  ,"phots"         ,nChannels,0,kThetaMax);
 390   TH1D *photsw  = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
 391   TH1D *resultw = new TH1D("resultw","resultw"       ,nChannels,0,kThetaMax);
 392   Int_t nBin = (Int_t)(kThetaMax/fDTheta);
 393   Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
 394
 395   for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
 396     Double_t angle = fPhotCkov[i];  if(angle<0||angle>kThetaMax) continue;
 397     phots->Fill(angle);
 398     Int_t bin = (Int_t)(0.5+angle/(fDTheta));
 399     Double_t weight=1.;
 400     if(fIsWEIGHT){
 401       Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta;  Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
 402       Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
 403       if(diffArea>0) weight = 1./diffArea;
 404     }
 405     photsw->Fill(angle,weight);
 406     fPhotWei[i]=weight;
 407   }//photon candidates loop
 408
 409   for (Int_t i=1; i<=nBin;i++){
 410     Int_t bin1= i-nCorrBand;
 411     Int_t bin2= i+nCorrBand;
 412     if(bin1<1) bin1=1;
 413     if(bin2>nBin)bin2=nBin;
 414     Double_t sumPhots=phots->Integral(bin1,bin2);
 415     if(sumPhots<3) continue;                            // if less then 3 photons don't trust to this ring
 416     Double_t sumPhotsw=photsw->Integral(bin1,bin2);
 417     resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
 418   }
 419 // evaluate the "BEST" theta ckov as the maximum value of histogramm
 420   Double_t *pVec = resultw->GetArray();
 421   Int_t locMax = TMath::LocMax(nBin,pVec);
 422   delete phots;delete photsw;delete resultw; // Reset and delete objects
 423
 424   return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
 425 }//HoughResponse()
 426 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 427 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
 428 {
 429 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
 430 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 431 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 432 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 433 //            MIP beta
 434 //   Returns: absolute error on Cerenkov angle, [radians]
 435
 436   TVector3 v(-999,-999,-999);
 437   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fParam->GetRefIdx());
 438
 439   if(trkBeta > 1) trkBeta = 1;                 //protection against bad measured thetaCer
 440   if(trkBeta < 0) trkBeta = 0.0001;            //
 441
 442   v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
 443   v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
 444   v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
 445
 446   return v.Mag2();
 447 }
 448 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 449 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
 450 {
 451 // Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
 452 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 453 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 454 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 455 //            MIP beta
 456 //   Returns: absolute error on Cerenkov angle, [radians]
 457
 458   Double_t phiDelta = phiC - fTrkDir.Phi();
 459
 460   Double_t sint     = TMath::Sin(fTrkDir.Theta());
 461   Double_t cost     = TMath::Cos(fTrkDir.Theta());
 462   Double_t sinf     = TMath::Sin(fTrkDir.Phi());
 463   Double_t cosf     = TMath::Cos(fTrkDir.Phi());
 464   Double_t sinfd    = TMath::Sin(phiDelta);
 465   Double_t cosfd    = TMath::Cos(phiDelta);
 466   Double_t tantheta = TMath::Tan(thetaC);
 467
 468   Double_t alpha =cost-tantheta*cosfd*sint;                                                 // formula (11)
 469   Double_t k = 1.-fParam->GetRefIdx()*fParam->GetRefIdx()+alpha*alpha/(betaM*betaM);        // formula (after 8 in the text)
 470   if (k<0) return 1e10;
 471   Double_t mu =sint*sinf+tantheta*(cost*cosfd*sinf+sinfd*cosf);                             // formula (10)
 472   Double_t e  =sint*cosf+tantheta*(cost*cosfd*cosf-sinfd*sinf);                             // formula (9)
 473
 474   Double_t kk = betaM*TMath::Sqrt(k)/(fParam->GapThick()*alpha);                            // formula (6) and (7)
 475   Double_t dtdxc = kk*(k*(cosfd*cosf-cost*sinfd*sinf)-(alpha*mu/(betaM*betaM))*sint*sinfd); // formula (6)
 476   Double_t dtdyc = kk*(k*(cosfd*sinf+cost*sinfd*cosf)+(alpha* e/(betaM*betaM))*sint*sinfd); // formula (7)            pag.4
 477
 478   Double_t errX = 0.2,errY=0.25;                                                            //end of page 7
 479   return  TMath::Sqrt(errX*errX*dtdxc*dtdxc + errY*errY*dtdyc*dtdyc);
 480 }
 481 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 482 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 483 {
 484 // Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
 485 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 486 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 487 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 488 //            MIP beta
 489 //   Returns: absolute error on Cerenkov angle, [radians]
 490
 491   Double_t phiDelta = phiC - fTrkDir.Phi();
 492
 493   Double_t sint     = TMath::Sin(fTrkDir.Theta());
 494   Double_t cost     = TMath::Cos(fTrkDir.Theta());
 495   Double_t cosfd    = TMath::Cos(phiDelta);
 496   Double_t tantheta = TMath::Tan(thetaC);
 497
 498   Double_t alpha =cost-tantheta*cosfd*sint;                                                 // formula (11)
 499   Double_t dtdn = cost*fParam->GetRefIdx()*betaM*betaM/(alpha*tantheta);                    // formula (12)
 500
 501 //  Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
 502   Double_t f = 0.0172*(7.75-5.635)/TMath::Sqrt(24.);
 503
 504   return f*dtdn;
 505 }//SigCrom()
 506 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 507 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 508 {
 509 // Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
 510 // created by a given MIP. Formulae according to CERN-EP-2000-058
 511 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 512 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 513 //            MIP beta
 514 //   Returns: absolute error on Cerenkov angle, [radians]
 515
 516   Double_t phiDelta = phiC - fTrkDir.Phi();
 517
 518   Double_t sint     = TMath::Sin(fTrkDir.Theta());
 519   Double_t cost     = TMath::Cos(fTrkDir.Theta());
 520   Double_t sinf     = TMath::Sin(fTrkDir.Phi());
 521   Double_t cosfd    = TMath::Cos(phiDelta);
 522   Double_t costheta = TMath::Cos(thetaC);
 523   Double_t tantheta = TMath::Tan(thetaC);
 524
 525   Double_t alpha =cost-tantheta*cosfd*sint;                                                  // formula (11)
 526
 527   Double_t k = 1.-fParam->GetRefIdx()*fParam->GetRefIdx()+alpha*alpha/(betaM*betaM);         // formula (after 8 in the text)
 528   if (k<0) return 1e10;
 529
 530   Double_t eTr = 0.5*fParam->RadThick()*betaM*TMath::Sqrt(k)/(fParam->GapThick()*alpha);     // formula (14)
 531   Double_t lambda = 1.-sint*sint*sinf*sinf;                                                  // formula (15)
 532
 533   Double_t c1 = 1./(1.+ eTr*k/(alpha*alpha*costheta*costheta));                              // formula (13.a)
 534   Double_t c2 = betaM*TMath::Power(k,1.5)*tantheta*lambda/(fParam->GapThick()*alpha*alpha);  // formula (13.b)
 535   Double_t c3 = (1.+eTr*k*betaM*betaM)/((1+eTr)*alpha*alpha);                                // formula (13.c)
 536   Double_t c4 = TMath::Sqrt(k)*tantheta*(1-lambda)/(fParam->GapThick()*betaM);               // formula (13.d)
 537   Double_t dtdT = c1 * (c2+c3*c4);
 538   Double_t trErr = fParam->RadThick()/(TMath::Sqrt(12.)*cost);
 539
 540   return trErr*dtdT;
 541 }//SigGeom()