Probability Density Functions of the time response of a PMT. More...

#include <JLED.hh>

Inheritance diagram for JPHYSICS::JLED:

Public Member Functions
	JLED (const double lambda, const double Tmin_ns, const double Tmax_ns, const JQuadrature &engine=JCotangent(20), const int numberOfPoints=20, const double epsilon=1e-12)
	Constructor.

double	getDirectLightFromLED (const double D_m, const double cd, const double theta, const double phi, const double t_ns) const
	Probability density function for direct light from LED.

double	getScatteredLightFromLED (const double D_m, const double cd, const double theta, const double phi, const double t_ns) const
	Probability density function for scattered light from LED.

virtual double	getIndexOfRefractionPhase (const double lambda) const =0
	Index of refraction for phase velocity.

virtual double	getDispersionPhase (const double lambda) const =0
	Dispersion of light for phase velocity.

virtual double	getIndexOfRefractionGroup (const double lambda) const
	Index of refraction for group velocity.

virtual double	getDispersionGroup (const double lambda) const =0
	Dispersion of light for group velocity.

double	getKappa (const double lambda) const
	Get effective index of refraction for muon light.

double	getKmin (const double lambda) const
	Get smallest index of refraction for Bremsstrahlung light (i.e. point at which dt/dz = 0).

virtual double	getPhotocathodeArea () const =0
	Photo-cathode area of PMT.

virtual double	getQE (const double lambda) const =0
	Quantum efficiency of PMT (incl.

virtual double	getAngularAcceptance (const double ct) const =0
	Angular acceptence of PMT.

virtual double	getLightFromLED (const double ct, const double phi, const double dt) const =0
	Light yield from LED (number of p.e.

virtual double	getAbsorptionLength (const double lambda) const =0
	Absorption length.

virtual double	getScatteringLength (const double lambda) const =0
	Scattering length.

virtual double	getScatteringProbability (const double ct) const =0
	Model specific function to describe light scattering in water (integral over full solid angle normalised to unity).

Protected Attributes
double	wavelength

double	tmin

double	tmax

JQuadrature	main_engine

JQuadrature	beta_engine

std::vector< JElement3D_t >	phi_engine

Detailed Description

Probability Density Functions of the time response of a PMT.

Definition at line 61 of file JLED.hh.

Constructor & Destructor Documentation

◆ JLED()

JPHYSICS::JLED::JLED	(	const double	lambda,
		const double	Tmin_ns,
		const double	Tmax_ns,
		const JQuadrature &	engine = JCotangent(20),
		const int	numberOfPoints = 20,
		const double	epsilon = 1e-12 )

inline

Constructor.

Parameters

lambda	wavelength photon [nm]
Tmin_ns	minimal time of emmision [ns]
Tmax_ns	minimal time of emmision [ns]
engine	scattering angle integrator
numberOfPoints	number of points for integration
epsilon	precision of points for integration

Definition at line 78 of file JLED.hh.

                                                    :
      wavelength(lambda),
      tmin(Tmin_ns),
      tmax(Tmax_ns),
      main_engine(JGaussLegendre(numberOfPoints,epsilon)),
      beta_engine(engine)
    {
      const double dp = PI / numberOfPoints;
 
      for (double x = 0.5*dp; x < PI; x += dp) {
        phi_engine.push_back(JElement3D_t(cos(x),sin(x), dp));
      }
    }

Member Function Documentation

◆ getDirectLightFromLED()

double JPHYSICS::JLED::getDirectLightFromLED	(	const double	D_m,
		const double	cd,
		const double	theta,
		const double	phi,
		const double	t_ns ) const

inline

Probability density function for direct light from LED.

Parameters

D_m	distance between LED and PMT [m]
cd	cosine angle LED orientation and LED - PMT position
theta	zenith angle orientation PMT
phi	azimuth angle orientation PMT
t_ns	time difference relative to direct light [ns]

Returns: dP/dt [npe/ns]

Definition at line 108 of file JLED.hh.

    {
      const double sd =  sqrt((1.0 + cd)*(1.0 - cd));
      const double d  =  D_m;                                  // photon path [m]
 
      const double A  =  getPhotocathodeArea();
 
      const double px =  sin(theta)*cos(phi);
      //const double py =  sin(theta)*sin(phi);
      const double pz =  cos(theta);
 
      const double ct = sd*px + cd*pz;                         // cosine angle of incidence on PMT
 
      const double qe    = getQE(wavelength);
      const double l_abs = getAbsorptionLength(wavelength);
      const double ls    = getScatteringLength(wavelength);
 
      const double U  = getAngularAcceptance(ct);
      const double V  = exp(-d/l_abs) * exp(-d/ls);            // absorption & scattering
      const double W  = A/(d*d);                               // solid angle
  
      return qe * getLightFromLED(cd, 0.0, t_ns) * U * V * W;
    }

◆ getScatteredLightFromLED()

double JPHYSICS::JLED::getScatteredLightFromLED	(	const double	D_m,
		const double	cd,
		const double	theta,
		const double	phi,
		const double	t_ns ) const

inline

Probability density function for scattered light from LED.

Parameters

D_m	distance between LED and PMT [m]
cd	cosine angle LED orientation and LED - PMT position
theta	zenith angle orientation PMT
phi	azimuth angle orientation PMT
t_ns	time difference relative to direct light [ns]

Returns: dP/dt [npe/ns]

Definition at line 147 of file JLED.hh.

    {
      using namespace std;
 
      double value = 0;
 
      if (t_ns >= tmin) {
 
        const double ng =  getIndexOfRefractionGroup(wavelength);
 
        const double sd =  sqrt((1.0 + cd)*(1.0 - cd));
        const double l  =  D_m;                                    // distance [m]
 
        const double A  =  getPhotocathodeArea();
        //const double sr =  sqrt(A/PI) / D_m;
        //const double cr =  sqrt((1.0 + sr)*(1.0 - sr));
 
        const double px =  sin(theta)*cos(phi);
        const double py =  sin(theta)*sin(phi);
        const double pz =  cos(theta);
 
        const double qx = cd*px +  0  - sd*pz;
        const double qy =         1*py;
        const double qz = sd*px +  0  + cd*pz;
 
        const double qe    = getQE(wavelength);
        const double l_abs = getAbsorptionLength(wavelength);
        const double ls    = getScatteringLength(wavelength);
 
        const double Jc = 1.0 / ls;                                // dN/dx
 
        const double xmin = tmin;
        const double xmax = std::min(tmax, t_ns);
 
        JQuadrature buffer;
        
        if (xmax > xmin) {
 
          for (JQuadrature::const_iterator i = main_engine.begin(); i != main_engine.end(); ++i) {
 
            const double t  = 0.5 * (xmax + xmin)  +  i->getX() * 0.5 * (xmax - xmin);
            const double dt = i->getY() * 0.5 * (xmax - xmin);
 
            buffer[t] = dt;
          }
 
        } else {
 
          buffer[tmin] = 1.0;
        }
 
        for (JQuadrature::const_iterator i = buffer.begin(); i != buffer.end(); ++i) {
 
          const double t  = i->getX();
          const double dt = i->getY();
 
          const double d  = l + C*(t_ns - t)/ng;                   // photon path
          const double V  = exp(-d/l_abs);                         // absorption
 
          for (JQuadrature::const_iterator j = beta_engine.begin(); j != beta_engine.end(); ++j) {
 
            const double cb = j->getX();
            const double dc = j->getY();
            
            const double sb = sqrt((1.0 + cb)*(1.0 - cb));
            
            const double v  = 0.5 * (d + l) * (d - l) / (d - l*cb);
            const double u  = d - v;
            
            if (u <= 0) continue;
            if (v <= 0) continue;
            
            const double cts = (l*cb - v) / u;                   // cosine scattering angle
            
            const double W  = min(A/(v*v), 2.0*PI);              // solid angle
            const double Ja = getScatteringProbability(cts);     // P(cos(),phi)
            const double Jd = ng * (1.0 - cts) / C;              // dt/du
            
            const double ca = (l - v*cb) / u;
            const double sa =      v*sb  / u;
            
            for (std::vector<JElement3D_t>::const_iterator k = phi_engine.begin(); k != phi_engine.end(); ++k) {
              
              const double cp = k->getX();
              const double sp = k->getY();
              const double dp = k->getZ();
 
              const double dom = dc * dp * v*v / (u*u);
              
              const double ct0 = cd*ca - sd*sa*cp;
              const double ph0 = atan2(sa*sp, cd*sa*cp + sd*ca);
              
              const double vx  = -sb*cp * qx;
              const double vy  = -sb*sp * qy;
              const double vz  =  cb    * qz;
              
              const double U  =
                getAngularAcceptance(vx + vy + vz) * getLightFromLED(ct0, +ph0, t) +
                getAngularAcceptance(vx - vy + vz) * getLightFromLED(ct0, -ph0, t);
              
              value += qe * dt * dom * Ja * Jc * U * V * W / Jd;
            }
          }
        }
      }
 
      return value; 
    }                            

◆ getIndexOfRefractionPhase()

virtual double JPHYSICS::JDispersionInterface::getIndexOfRefractionPhase ( const double lambda ) const

pure virtualinherited

Index of refraction for phase velocity.

Parameters

lambda wavelenth [nm]

Returns: index of refraction

Implemented in JPHYSICS::JDispersion.

◆ getDispersionPhase()

virtual double JPHYSICS::JDispersionInterface::getDispersionPhase ( const double lambda ) const

pure virtualinherited

Dispersion of light for phase velocity.

Parameters

lambda wavelength of light [nm]

Returns: dn/dlambda

Implemented in JPHYSICS::JDispersion.

◆ getIndexOfRefractionGroup()

virtual double JPHYSICS::JDispersionInterface::getIndexOfRefractionGroup ( const double lambda ) const

inlinevirtualinherited

Index of refraction for group velocity.

Parameters

lambda wavelenth [nm]

Returns: index of refraction

Definition at line 52 of file JDispersionInterface.hh.

    {
      const double n = getIndexOfRefractionPhase(lambda);
      const double y = getDispersionPhase(lambda);
      
      return n / (1.0 + y*lambda/n);
    }

◆ getDispersionGroup()

virtual double JPHYSICS::JDispersionInterface::getDispersionGroup ( const double lambda ) const

pure virtualinherited

Dispersion of light for group velocity.

Parameters

lambda wavelength of light [nm]

Returns: dn/dlambda

Implemented in JPHYSICS::JDispersion.

◆ getKappa()

double JPHYSICS::JDispersionInterface::getKappa ( const double lambda ) const

inlineinherited

Get effective index of refraction for muon light.

Parameters

lambda wavelength of light [nm]

Returns: index of refraction

Definition at line 76 of file JDispersionInterface.hh.

    {
      const double n  = getIndexOfRefractionPhase(lambda);
      const double ng = getIndexOfRefractionGroup(lambda);
 
      return (ng * n - 1.0) / sqrt(n*n - 1.0);
    }

◆ getKmin()

double JPHYSICS::JDispersionInterface::getKmin ( const double lambda ) const

inlineinherited

Get smallest index of refraction for Bremsstrahlung light (i.e. point at which dt/dz = 0).

Parameters

lambda wavelength of light [nm]

Returns: index of refraction

Definition at line 91 of file JDispersionInterface.hh.

    {
      const double ng = getIndexOfRefractionGroup(lambda);
 
      return sqrt(ng*ng - 1.0);
    }

◆ getPhotocathodeArea()

virtual double JPHYSICS::JAbstractPMT::getPhotocathodeArea ( ) const

pure virtualinherited

Photo-cathode area of PMT.

Returns: photo-cathode area [m^2]

Implemented in JPHYSICS::JLED_C, and JPHYSICS::JPDF_C.

◆ getQE()

virtual double JPHYSICS::JAbstractPMT::getQE ( const double lambda ) const

pure virtualinherited

Quantum efficiency of PMT (incl.

absorption in glass, gel, etc.).

Parameters

lambda wavelenth [nm]

Returns: QE

Implemented in JPHYSICS::JLED_C, and JPHYSICS::JPDF_C.

◆ getAngularAcceptance()

virtual double JPHYSICS::JAbstractPMT::getAngularAcceptance ( const double ct ) const

pure virtualinherited

Angular acceptence of PMT.

Parameters

ct	cosine angle of incidence

Returns: acceptance

Implemented in JPHYSICS::JLED_C, and JPHYSICS::JPDF_C.

◆ getLightFromLED()

virtual double JPHYSICS::JAbstractLED::getLightFromLED	(	const double	ct,
		const double	phi,
		const double	dt ) const

pure virtualinherited

Light yield from LED (number of p.e.

per unit solid angle per unit time).

Parameters

ct	zenith angle of emission
phi	azimuth angle of emission
dt	time of emission [ns]

Returns: d^2P / dOmega dt [npe/ns/sr]

Implemented in JPHYSICS::JLED_C, and LED.

◆ getAbsorptionLength()

virtual double JPHYSICS::JAbstractMedium::getAbsorptionLength ( const double lambda ) const

pure virtualinherited

Absorption length.

Parameters

lambda wavelenth [nm]

Returns: absorption length [m]

Implemented in JPHYSICS::JLED_C, and JPHYSICS::JPDF_C.

◆ getScatteringLength()

virtual double JPHYSICS::JAbstractMedium::getScatteringLength ( const double lambda ) const

pure virtualinherited

Scattering length.

Parameters

lambda wavelenth [nm]

Returns: scattering length [m]

Implemented in JPHYSICS::JLED_C, and JPHYSICS::JPDF_C.

◆ getScatteringProbability()

virtual double JPHYSICS::JAbstractMedium::getScatteringProbability ( const double ct ) const

pure virtualinherited

Model specific function to describe light scattering in water (integral over full solid angle normalised to unity).

Parameters

ct	cosine scattering angle

Returns: probability

Implemented in JPHYSICS::JLED_C, and JPHYSICS::JPDF_C.

Member Data Documentation

◆ wavelength

double JPHYSICS::JLED::wavelength

protected

Definition at line 261 of file JLED.hh.

◆ tmin

double JPHYSICS::JLED::tmin

protected

Definition at line 263 of file JLED.hh.

◆ tmax

double JPHYSICS::JLED::tmax

protected

Definition at line 264 of file JLED.hh.

◆ main_engine

JQuadrature JPHYSICS::JLED::main_engine

protected

Definition at line 266 of file JLED.hh.

◆ beta_engine

JQuadrature JPHYSICS::JLED::beta_engine

protected

Definition at line 267 of file JLED.hh.

◆ phi_engine

std::vector<JElement3D_t> JPHYSICS::JLED::phi_engine

protected

Definition at line 268 of file JLED.hh.

The documentation for this class was generated from the following file:

JLED.hh

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ JLED()

Member Function Documentation

◆ getDirectLightFromLED()

◆ getScatteredLightFromLED()

◆ getIndexOfRefractionPhase()

◆ getDispersionPhase()

◆ getIndexOfRefractionGroup()

◆ getDispersionGroup()

◆ getKappa()

◆ getKmin()

◆ getPhotocathodeArea()

◆ getQE()

◆ getAngularAcceptance()

◆ getLightFromLED()

◆ getAbsorptionLength()

◆ getScatteringLength()

◆ getScatteringProbability()

Member Data Documentation

◆ wavelength

◆ tmin

◆ tmax

◆ main_engine

◆ beta_engine

◆ phi_engine