**************************************************************************/
/* $Id$ */
-
///////////////////////////////////////////////////////////////////////////////
// //
#include "AliTRDcluster.h"
#include "AliTRDgeometry.h"
#include "AliTRDCommonParam.h"
+#include "AliTRDtrackletWord.h"
ClassImp(AliTRDcluster)
for (Int_t i = 0; i < 7; i++) {
fSignals[i] = 0;
}
-
+ SetBit(kLUT);
}
//___________________________________________________________________________
memcpy(&fSignals, sig, 7*sizeof(Short_t));
fQ = fSignals[2]+fSignals[3]+fSignals[4];
SetVolumeId(vid);
+ SetBit(kLUT);
}
//___________________________________________________________________________
if (tracks) {
AddTrackIndex(tracks);
}
+ SetBit(kLUT);
+}
+//_____________________________________________________________________________
+AliTRDcluster::AliTRDcluster(const AliTRDtrackletWord *const tracklet, Int_t det, UShort_t volid)
+ :AliCluster(volid,tracklet->GetX(),tracklet->GetY(),tracklet->GetZ(),0,0,0)
+ ,fPadCol(0)
+ ,fPadRow(0)
+ ,fPadTime(0)
+ ,fLocalTimeBin(0)
+ ,fNPads(0)
+ ,fClusterMasking(0)
+ ,fDetector(det)
+ ,fQ(0.)
+ ,fCenter(0.)
+{
+ //
+ // Constructor from online tracklet
+ //
}
//_____________________________________________________________________________
// Copy constructor
//
- SetBit(kInChamber, c.IsInChamber());
SetLabel(c.GetLabel(0),0);
SetLabel(c.GetLabel(1),1);
SetLabel(c.GetLabel(2),2);
SetY(c.GetY());
SetZ(c.GetZ());
- SetSigmaY2(c.GetSigmaY2());
+ AliCluster::SetSigmaY2(c.GetSigmaY2());
SetSigmaZ2(c.GetSigmaZ2());
for (Int_t i = 0; i < 7; i++) {
fQ = 0;
fCenter = 0;
for (Int_t i = 0; i < 3; i++) SetLabel(0,i);
- SetX(0);
- SetY(0);
- SetZ(0);
- SetSigmaY2(0);
- SetSigmaZ2(0);
+ SetX(0.);
+ SetY(0.);
+ SetZ(0.);
+ AliCluster::SetSigmaY2(0.);
+ SetSigmaZ2(0.);
SetVolumeId(0);
}
//___________________________________________________________________________
Double_t AliTRDcluster::GetSX(Int_t tb, Double_t z)
{
+// Returns the error parameterization in the radial direction for TRD clusters as function of
+// the calibrated time bin (tb) and optionally distance to anode wire (z). By default (no z information)
+// the mean value over all cluster to wire distance is chosen.
+//
+// There are several contributions which are entering in the definition of the radial errors of the clusters.
+// Although an analytic defition should be possible for the moment this is not yet available but instead a
+// numerical parameterization is provided (see AliTRDclusterResolution::ProcessSigma() for the calibration
+// method). The result is displayed in the figure below as a 2D plot and also as the projection on the drift axis.
+//
+//Begin_Html
+//<img src="TRD/clusterXerrorDiff2D.gif">
+//End_Html
+//
+// Here is a list of uncertainty components:
+// - Time Response Function (TRF) - the major contribution. since TRF is also not symmetric (even if tail is
+// cancelled) it also creates a systematic shift dependent on the charge distribution before and after the cluster.
+// - longitudinal diffusion - increase the width of TRF and scales with square root of drift length
+// - variation in the drift velocity within the drift cell
+//
+// Author
+// A.Bercuci <A.Bercuci@gsi.de>
+
if(tb<1 || tb>=24) return 10.; // return huge [10cm]
const Double_t sx[24][10]={
{0.000e+00, 9.352e-01, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 2.309e+00},
};
if(z>=0. && z<.25) return sx[tb][Int_t(z/.025)];
- Double_t m = 1.e-8; for(Int_t id=10; id--;) if(sx[tb][id]>m) m=sx[tb][id];
- return m;
+ Double_t m = 0.; for(Int_t id=10; id--;) m+=sx[tb][id];
+ return m*.1;
}
//___________________________________________________________________________
-Double_t AliTRDcluster::GetSY(Int_t tb, Double_t z)
+Double_t AliTRDcluster::GetSYdrift(Int_t tb, Int_t ly, Double_t/* z*/)
{
+// Returns the error parameterization for TRD clusters as function of the drift length (here calibrated time bin tb)
+// and optionally distance to anode wire (z) for the LUT r-phi cluster shape. By default (no z information) the largest
+// value over all cluster to wire values is chosen.
+//
+// For the LUT method the dependence of s_y with x and d is obtained via a fit to the cluster to MC
+// resolution. (see class AliTRDclusterResolution for more details). A normalization to the reference radial position
+// x0 = 0.675 (tb=5 for ideal vd) is also applied (see GetSYprf()). The function is *NOT* calibration aware !
+// The result is displayed in the figure below as a 2D plot and also as the projection on the drift axis. A comparison
+// with the GAUS parameterization is also given
+//
+// For the GAUS method the dependence of s_y with x is *analytic* and it is expressed by the relation.
+// BEGIN_LATEX
+// #sigma^{2}_{y} = #sigma^{2}_{PRF} + #frac{x#delta_{t}^{2}}{(1+tg(#alpha_{L}))^{2}}
+// END_LATEX
+// The result is displayed in the figure below as function of the drift time and compared with the LUT parameterization.
+//Begin_Html
+//<img src="TRD/clusterYerrorDiff2D.gif">
+//<img src="TRD/clusterYerrorDiff1D.gif">
+//End_Html
+//
+// Author
+// A.Bercuci <A.Bercuci@gsi.de>
+
+
if(tb<1 || tb>=24) return 10.; // return huge [10cm]
- const Double_t sy[24][10]={
+ const Float_t lSy[6][24] = {
+ {75.7561, 0.0325, 0.0175, 0.0174, 0.0206, 0.0232,
+ 0.0253, 0.0262, 0.0265, 0.0264, 0.0266, 0.0257,
+ 0.0258, 0.0261, 0.0259, 0.0253, 0.0257, 0.0261,
+ 0.0255, 0.0250, 0.0259, 0.0266, 0.0278, 0.0319
+ },
+ {49.2252, 0.0371, 0.0204, 0.0189, 0.0230, 0.0261,
+ 0.0281, 0.0290, 0.0292, 0.0286, 0.0277, 0.0279,
+ 0.0285, 0.0281, 0.0291, 0.0281, 0.0281, 0.0282,
+ 0.0272, 0.0282, 0.0282, 0.0284, 0.0310, 0.0334
+ },
+ {55.1674, 0.0388, 0.0212, 0.0200, 0.0239, 0.0271,
+ 0.0288, 0.0299, 0.0306, 0.0300, 0.0296, 0.0303,
+ 0.0293, 0.0290, 0.0291, 0.0294, 0.0295, 0.0290,
+ 0.0293, 0.0292, 0.0292, 0.0293, 0.0316, 0.0358
+ },
+ {45.1004, 0.0411, 0.0225, 0.0215, 0.0249, 0.0281,
+ 0.0301, 0.0315, 0.0320, 0.0308, 0.0318, 0.0321,
+ 0.0312, 0.0311, 0.0316, 0.0315, 0.0310, 0.0308,
+ 0.0313, 0.0303, 0.0314, 0.0314, 0.0324, 0.0369
+ },
+ {43.8614, 0.0420, 0.0239, 0.0224, 0.0268, 0.0296,
+ 0.0322, 0.0336, 0.0333, 0.0326, 0.0321, 0.0325,
+ 0.0329, 0.0326, 0.0323, 0.0322, 0.0326, 0.0320,
+ 0.0329, 0.0319, 0.0314, 0.0329, 0.0341, 0.0373
+ },
+ {40.5440, 0.0434, 0.0246, 0.0236, 0.0275, 0.0311,
+ 0.0332, 0.0345, 0.0347, 0.0347, 0.0340, 0.0336,
+ 0.0339, 0.0344, 0.0339, 0.0341, 0.0341, 0.0342,
+ 0.0345, 0.0328, 0.0341, 0.0332, 0.0356, 0.0398
+ },
+ };
+ // adjusted ...
+ return TMath::Max(lSy[ly][tb]-0.0150, 0.0010);
+
+/* const Double_t sy[24][10]={
{0.000e+00, 2.610e-01, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 0.000e+00, 4.680e-01},
{3.019e-02, 3.036e-02, 3.131e-02, 3.203e-02, 3.294e-02, 3.407e-02, 3.555e-02, 3.682e-02, 3.766e-02, 3.824e-02},
{1.773e-02, 1.778e-02, 1.772e-02, 1.790e-02, 1.807e-02, 1.833e-02, 1.873e-02, 1.905e-02, 1.958e-02, 2.029e-02},
{2.812e-02, 2.786e-02, 2.776e-02, 2.723e-02, 2.695e-02, 2.650e-02, 2.642e-02, 2.617e-02, 2.612e-02, 2.610e-02},
{3.251e-02, 3.267e-02, 3.223e-02, 3.183e-02, 3.125e-02, 3.106e-02, 3.067e-02, 3.010e-02, 2.936e-02, 2.927e-02}
};
- if(z>=0. && z<.25) return sy[tb][Int_t(z/.025)];
+ if(z>=0. && z<.25) return sy[tb][Int_t(z/.025)] - sy[5][Int_t(z/.025)];
+
+ Double_t m = -1.e8; for(Int_t id=10; id--;) if((sy[tb][id] - sy[5][id])>m) m=sy[tb][id]-sy[5][id];
+
+ return m;*/
+}
- Double_t m = 1.e-8; for(Int_t id=10; id--;) if(sy[tb][id]>m) m=sy[tb][id];
+//___________________________________________________________________________
+Double_t AliTRDcluster::GetSYcharge(Float_t q)
+{
+// Parameterization of the r-phi resolution component due to cluster charge.
+// The value is the offset from the nominal cluster resolution defined as the
+// cluster resolution at average cluster charge (q0).
+//
+// BEGIN_LATEX
+// #Delta #sigma_{y}(q) = a*(#frac{1}{q} - #frac{1}{q_{0}})
+// q_{0} #approx 50
+// END_LATEX
+// The definition is *NOT* robust against gain fluctuations and thus two approaches are possible
+// when residual miscalibration are available:
+// - determine parameterization with a resolution matching those of the gain
+// - define an analytic model which scales with the gain.
+//
+// For more details please see AliTRDclusterResolution::ProcessCharge()
+//
+//Begin_Html
+//<img src="TRD/clusterQerror.gif">
+//End_Html
+//
+// Author
+// A.Bercuci <A.Bercuci@gsi.de>
+
+ const Float_t sq0inv = 0.019962; // [1/q0]
+ const Float_t sqb = 0.037328; // [cm]
+
+ return sqb*(1./q - sq0inv);
+}
- return m;
+//___________________________________________________________________________
+Double_t AliTRDcluster::GetSYprf(Int_t ly, Double_t center, Double_t s2)
+{
+// Parameterization of the cluster error in the r-phi direction due to charge sharing between
+// adiacent pads. Should be identical to what is provided in the OCDB as PRF [TODO]
+//
+// The parameterization is obtained from fitting cluster resolution at phi=exb and |x-0.675|<0.225.
+// For more details see AliTRDclusterResolution::ProcessCenter().
+//
+//Begin_Html
+//<img src="TRD/clusterPRFerror.gif">
+//End_Html
+//
+// Author
+// A.Bercuci <A.Bercuci@gsi.de>
+
+/* const Float_t scy[AliTRDgeometry::kNlayer][4] = {
+ {2.827e-02, 9.600e-04, 4.296e-01, 2.271e-02},
+ {2.952e-02,-2.198e-04, 4.146e-01, 2.339e-02},
+ {3.090e-02, 1.514e-03, 4.020e-01, 2.402e-02},
+ {3.260e-02,-2.037e-03, 3.946e-01, 2.509e-02},
+ {3.439e-02,-3.601e-04, 3.883e-01, 2.623e-02},
+ {3.510e-02, 2.066e-03, 3.651e-01, 2.588e-02},
+ };*/
+ const Float_t lPRF[] = {0.438, 0.403, 0.393, 0.382, 0.376, 0.345};
+
+ return s2*TMath::Gaus(center, 0., lPRF[ly]);
}
+
//___________________________________________________________________________
Double_t AliTRDcluster::GetXcorr(Int_t tb, Double_t z)
{
- // drift length correction [cm]
- // TODO to be parametrized in term of drift velocity
- // A.Bercuci (Mar 28 2009)
+// Drift length correction [cm]. Due to variation of mean drift velocity along the drift region
+// from nominal vd at xd->infinity. For drift velocity determination based on tracking information
+// the correction should be negligible.
+//Begin_Html
+//<img src="TRD/clusterXcorr.gif">
+//End_Html
+// TODO to be parametrized in term of drift velocity at infinite drift length
+// A.Bercuci (Mar 28 2009)
if(tb<0 || tb>=24) return 0.;
const Int_t nd = 5;
//___________________________________________________________________________
Double_t AliTRDcluster::GetYcorr(Int_t ly, Float_t y)
{
-// PRF correction TODO to be replaced by the gaussian
-// approximation with full error parametrization
+// PRF correction for the LUT r-phi cluster shape.
+//Begin_Html
+//<img src="TRD/clusterYcorr.gif">
+//End_Html
+
const Float_t cy[AliTRDgeometry::kNlayer][3] = {
{ 4.014e-04, 8.605e-03, -6.880e+00},
{-3.061e-04, 9.663e-03, -6.789e+00},
// Input parameters:
// t0 - calibration aware trigger delay [us]
// vd - drift velocity in the region of the cluster [cm/us]
-// z - distance to the anode wire [cm]. By default 0.2 !!
+// z - distance to the anode wire [cm]. By default average over the drift cell width.
// q & xq - array of charges and cluster positions from previous clusters in the tracklet [a.u.]
// Output values :
// return x position of the cluster with respect to the
// END_LATEX
// where t_0 is the delay of the trigger signal. t_cause is the causality delay between ionisation electrons hitting
// the anode and the registration of maximum signal by the electronics - it is due to the rising time of the TRF
-// convoluted with the diffusion width. t_TC is the residual charge from previous bins due to residual tails after tail
-// cancellation.
+// A second order correction here comes from the fact that the time spreading of charge at anode is the convolution of
+// TRF with the diffusion and thus cross-talk between clusters before and after local clusters changes with drift length.
+// t_TC is the residual charge from previous (in time) clusters due to residual tails after tail cancellation.
+// This tends to push cluster forward and depends on the magnitude of their charge.
//
-// The drift velocity is considered to vary linearly with the drift length (independent of the distance to the anode wire
-// in the z direction). Thus one can write the calculate iteratively the drift length from the expression:
+// The drift velocity varies with the drift length (and distance to anode wire) as described by cell structure simulation.
+// Thus one, in principle, can calculate iteratively the drift length from the expression:
// BEGIN_LATEX
-// x = t_{drift}(x)*v_{drfit}(x)
+// x = t_{drift}(x)*v_{drift}(x)
// END_LATEX
+// In practice we use a numerical approach (AliTRDcluster::GetXcorr()) to correct for anisochronity obtained from MC
+// comparison (see AliTRDclusterResolution::ProcessSigma()). Also the calibration of 0 approximation (no x dependence)
+// for t_cause is obtained from MC comparisons and impossible to disentangle in real life from trigger delay.
//
-// Authors
+// Author
// Alex Bercuci <A.Bercuci@gsi.de>
//
// correction for t0
td -= t0;
// time bin corrected for t0
- // BUG in TMath::Nint().root-5.23.02
+ // Bug in TMath::Nint().root-5.23.02
// TMath::Nint(3.5) = 4 and TMath::Nint(4.5) = 4
Double_t tmp = td*fFreq;
fLocalTimeBin = Char_t(TMath::Floor(tmp));
return x;
/*
+ // calculate radial posion of clusters in the drift region
+
// invert drift time function
Double_t xM= AliTRDgeometry::CamHght()+AliTRDgeometry::CdrHght(),
x = vd*td + .5*AliTRDgeometry::CamHght(),
//_____________________________________________________________________________
Float_t AliTRDcluster::GetYloc(Double_t y0, Double_t s2, Double_t W, Double_t *const y1, Double_t *const y2)
{
+// Calculate, in tracking cooordinate system, the r-phi offset the cluster from the middle of the center pad. Three possible methods are implemented:
+// - Center of Gravity (COG) see AliTRDcluster::GetDYcog()
+// - Look-up Table (LUT) see AliTRDcluster::GetDYlut()
+// - Gauss shape (GAUS) see AliTRDcluster::GetDYgauss()
+// In addition for the case of LUT method position corrections are also applied (see AliTRDcluster::GetYcorr())
- //printf(" s[%3d %3d %3d] w[%f %f] yr[%f %f]\n", fSignals[2], fSignals[3], fSignals[4], w1/(w1+w2), w2/(w1+w2), y1r*W, y2r*W);
if(IsRPhiMethod(kCOG)) GetDYcog();
else if(IsRPhiMethod(kLUT)) GetDYlut();
- if(IsRPhiMethod(kGAUS)) GetDYgauss(s2/W/W, y1, y2);
+ else if(IsRPhiMethod(kGAUS)) GetDYgauss(s2/W/W, y1, y2);
+ else return 0.;
if(y1) (*y1)*=W;
if(y2) (*y2)*=W;
return y0+fCenter*W+(IsRPhiMethod(kLUT)?GetYcorr(AliTRDgeometry::GetLayer(fDetector), fCenter):0.);
}
+//___________________________________________________________________________
+void AliTRDcluster::SetSigmaY2(Float_t s2, Float_t dt, Float_t exb, Float_t x, Float_t z, Float_t tgp)
+{
+// Set variance of TRD cluster in the r-phi direction for each method.
+// Parameters :
+// - s2 - variance due to PRF width for the case of Gauss model. Replaced by parameterization in case of LUT.
+// - dt - transversal diffusion coeficient
+// - exb - tg of lorentz angle
+// - x - drift length - with respect to the anode wire
+// - z - offset from the anode wire
+// - tgp - local tangent of the track momentum azimuthal angle
+//
+// The ingredients from which the error is computed are:
+// - PRF (charge sharing on adjacent pads) - see AliTRDcluster::GetSYprf()
+// - diffusion (dependence with drift length and [2nd order] distance to anode wire) - see AliTRDcluster::GetSYdrift()
+// - charge of the cluster (complex dependence on gain and tail cancellation) - see AliTRDcluster::GetSYcharge()
+// - lorentz angle (dependence on the drift length and [2nd order] distance to anode wire) - see AliTRDcluster::GetSX()
+// - track angle (superposition of charges on the anode wire) - see AliTRDseedV1::Fit()
+// - projection of radial(x) error on r-phi due to fixed value assumed in tracking for x - see AliTRDseedV1::Fit()
+//
+// The last 2 contributions to cluster error can be estimated only during tracking when the track angle
+// is known (tgp). For this reason the errors (and optional position) of TRD clusters are recalculated during
+// tracking and thus clusters attached to tracks might differ from bare clusters.
+//
+// Taking into account all contributions one can write the the TRD cluster error parameterization as:
+// BEGIN_LATEX
+// #sigma_{y}^{2} = (#sigma_{diff}*Gauss(0, s_{ly}) + #delta_{#sigma}(q))^{2} + tg^{2}(#alpha_{L})*#sigma_{x}^{2} + tg^{2}(#phi-#alpha_{L})*#sigma_{x}^{2}+[tg(#phi-#alpha_{L})*tg(#alpha_{L})*x]^{2}/12
+// END_LATEX
+// From this formula one can deduce a that the simplest calibration method for PRF and diffusion contributions is
+// by measuring resolution at B=0T and phi=0. To disentangle further the two remaining contributions one has
+// to represent s2 as a function of drift length.
+//
+// In the gaussian model the diffusion contribution can be expressed as:
+// BEGIN_LATEX
+// #sigma^{2}_{y} = #sigma^{2}_{PRF} + #frac{x#delta_{t}^{2}}{(1+tg(#alpha_{L}))^{2}}
+// END_LATEX
+// thus resulting the PRF contribution. For the case of the LUT model both contributions have to be determined from
+// the fit (see AliTRDclusterResolution::ProcessCenter() for details).
+//
+// Author:
+// A.Bercuci <A.Bercuci@gsi.de>
+
+ Float_t sigmaY2 = 0.;
+ Int_t ly = AliTRDgeometry::GetLayer(fDetector);
+ if(IsRPhiMethod(kCOG)) sigmaY2 = 4.e-4;
+ else if(IsRPhiMethod(kLUT)){
+ Float_t sd = GetSYdrift(fLocalTimeBin, ly, z); //printf("drift[%6.2f] ", 1.e4*sd);
+ sigmaY2 = GetSYprf(ly, fCenter, sd); //printf("PRF[%6.2f] ", 1.e4*sigmaY2);
+ // add charge contribution TODO scale with respect to s2
+ sigmaY2+= GetSYcharge(TMath::Abs(fQ)); //printf("Q[%6.2f] ", 1.e4*sigmaY2);
+ sigmaY2 = TMath::Max(sigmaY2, Float_t(0.0010)); //!! protection
+ sigmaY2*= sigmaY2;
+ } else if(IsRPhiMethod(kGAUS)){
+ // PRF contribution
+ sigmaY2 = s2;
+ // Diffusion contribution
+ Double_t sD2 = dt/(1.+exb); sD2 *= sD2; sD2 *= x;
+ sigmaY2+= sD2;
+ // add charge contribution TODO scale with respect to s2
+ //sigmaY2+= GetSYcharge(TMath::Abs(fQ));
+ }
+
+ // store tg^2(phi-a_L) and tg^2(a_L)
+ Double_t tgg = (tgp-exb)/(1.+tgp*exb); tgg *= tgg;
+ Double_t exb2= exb*exb;
+
+ // Lorentz angle shift contribution
+ Float_t sx = GetSX(fLocalTimeBin, z); sx*=sx;
+ sigmaY2+= exb2*sx; //printf("Al[%6.2f] ", 1.e4*TMath::Sqrt(sigmaY2));
+
+ // Radial contribution due to not measuring x in Kalman model
+ sigmaY2+= tgg*sx; //printf("x[%6.2f] ", 1.e4*TMath::Sqrt(sigmaY2));
+
+ // Track angle contribution
+ sigmaY2+= tgg*x*x*exb2/12.; //printf("angle[%6.2f]\n", 1.e4*TMath::Sqrt(sigmaY2));
+
+ AliCluster::SetSigmaY2(sigmaY2);
+}
+
//_____________________________________________________________________________
Bool_t AliTRDcluster::IsEqual(const TObject *o) const
{