Probability Density Functions of the time response of a PMT (C-like interface) More...

#include <JLED.hh>

Inheritance diagram for JPHYSICS::JLED_C:

Public Member Functions
	JLED_C (const double Area, const JAbstractLED LED, double(QE)(const double), double(Pmt)(const double), const double L_abs, const double L_s, double(Km3)(const double), const double P_atm, const double wavelength, const double Tmin_ns, const double Tmax_ns, const JQuadrature &engine=JCotangent(20), const int numberOfPoints=20, const double epsilon=1e-12)
	Constructor.

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

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

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

virtual double	getAngularAcceptance (const double ct) const override
	Angular acceptance of PMT.

virtual double	getAbsorptionLength (const double lambda) const override
	Absorption length.

virtual double	getScatteringLength (const double lambda) const override
	Scattering length.

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

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
	Index of refraction (phase velocity).

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

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

virtual double	getIndexOfRefractionGroup (const double lambda) const
	Index of refraction 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).

Public Attributes
const double	P
	Dispersion parameters (x = 1/lambda)

const double	a0
	offset

const double	a1
	dn/dP

const double	a2
	d^1n/(dx)^1

const double	a3
	d^2n/(dx)^2

const double	a4
	d^3n/(dx)^3

Protected Attributes
const double	A
	photo-cathode area [m2]

const JAbstractLED *	led
	Pointer to interface for emission profile from LED.

double(*	qe )(const double lambda)
	Quantum efficiency of PMT (incl.

double	l_abs
	Absorption length.

double	ls
	Scattering length.

double(*	pmt )(const double ct)
	Angular acceptance of PMT.

double(*	km3 )(const double ct)
	Model specific function to describe light scattering in water.

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 (C-like interface)

Definition at line 275 of file JLED.hh.

Constructor & Destructor Documentation

◆ JLED_C()

JPHYSICS::JLED_C::JLED_C	(	const double	Area,
		const JAbstractLED *	LED,
		double(*	QE )(const double),
		double(*	Pmt )(const double),
		const double	L_abs,
		const double	L_s,
		double(*	Km3 )(const double),
		const double	P_atm,
		const double	wavelength,
		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

Area	photo-cathode area [m^2]
LED	pointer to interface for emission profile from LED
QE	pointer to function for quantum efficiency of PMT
Pmt	pointer to function for angular acceptance of PMT
L_abs	absorption length [m]
L_s	scattering length [m]
Km3	pointer to model specific function to describe light scattering in water
P_atm	ambient pressure [atm]
wavelength	wavelength of light [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 298 of file JLED.hh.

                                                :
      JLED(wavelength, Tmin_ns, Tmax_ns, engine, numberOfPoints, epsilon),
      JDispersion(P_atm),
      A    (Area ),
      led  (LED  ),
      qe   (QE   ),
      l_abs(L_abs),
      ls   (L_s  ),
      pmt  (Pmt  ),
      km3  (Km3  )
    {}

Member Function Documentation

◆ getLightFromLED()

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

inlineoverridevirtual

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]

Implements JPHYSICS::JAbstractLED.

Definition at line 338 of file JLED.hh.

    { 
      return led->getLightFromLED(ct, phi, dt);
    }

◆ getPhotocathodeArea()

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

inlineoverridevirtual

Photo-cathode area of PMT.

Returns: photo-cathode area [m^2]

Implements JPHYSICS::JAbstractPMT.

Definition at line 351 of file JLED.hh.

    { 
      return A;
    }

◆ getQE()

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

inlineoverridevirtual

Quantum efficiency of PMT (incl.

absorption in glass, gel, etc.).

Parameters

lambda wavelenth [nm]

Returns: QE

Implements JPHYSICS::JAbstractPMT.

Definition at line 363 of file JLED.hh.

    { 
      return qe(lambda);
    }

◆ getAngularAcceptance()

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

inlineoverridevirtual

Angular acceptance of PMT.

Parameters

ct	cosine angle of incidence

Returns: relative efficiency

Implements JPHYSICS::JAbstractPMT.

Definition at line 375 of file JLED.hh.

    { 
      return pmt(ct);
    }

◆ getAbsorptionLength()

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

inlineoverridevirtual

Absorption length.

Parameters

lambda wavelenth [nm]

Returns: absorption length [m]

Implements JPHYSICS::JAbstractMedium.

Definition at line 387 of file JLED.hh.

    { 
      return l_abs;
    }

◆ getScatteringLength()

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

inlineoverridevirtual

Scattering length.

Parameters

lambda wavelenth [nm]

Returns: scattering length [m]

Implements JPHYSICS::JAbstractMedium.

Definition at line 399 of file JLED.hh.

    { 
      return ls;
    }

◆ getScatteringProbability()

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

inlineoverridevirtual

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

Parameters

ct	cosine scattering angle

Returns: probability

Implements JPHYSICS::JAbstractMedium.

Definition at line 412 of file JLED.hh.

    { 
      return km3(ct);
    }

◆ getDirectLightFromLED()

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

inlineinherited

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

inlineinherited

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::JDispersion::getIndexOfRefractionPhase ( const double lambda ) const

inlinevirtualinherited

Index of refraction (phase velocity).

Parameters

lambda wavelenth [nm]

Returns: index of refraction

Implements JPHYSICS::JDispersionInterface.

Definition at line 51 of file JDispersion.hh.

    {
      const double x = 1.0 / lambda;
 
      return a0  +  a1*P  +  x*(a2 + x*(a3 + x*a4));
    }

◆ getDispersionPhase()

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

inlinevirtualinherited

Dispersion of light for phase velocity.

Parameters

lambda wavelength of light [nm]

Returns: dn/dlambda

Implements JPHYSICS::JDispersionInterface.

Definition at line 65 of file JDispersion.hh.

    {
      const double x = 1.0 / lambda;
      
      return -x*x*(a2 + x*(2.0*a3 + x*3.0*a4));
    }

◆ getDispersionGroup()

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

inlinevirtualinherited

Dispersion of light for group velocity.

Parameters

lambda wavelength of light [nm]

Returns: dn/dlambda

Implements JPHYSICS::JDispersionInterface.

Definition at line 79 of file JDispersion.hh.

    {
      const double x = 1.0 / lambda;
 
      const double n   = getIndexOfRefractionPhase(lambda);
      const double np  = getDispersionPhase(lambda);
      const double npp = x*x*x*(2.0*a2 + x*(6.0*a3 + x*12.0*a4));
      const double ng  = n / (1.0 + np*lambda/n);
      
      return ng*ng * (2*np*np - n*npp) * lambda / (n*n*n);
    }

◆ 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);
    }

◆ 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);
    }

Member Data Documentation

◆ A

const double JPHYSICS::JLED_C::A

protected

photo-cathode area [m2]

Definition at line 421 of file JLED.hh.

◆ led

const JAbstractLED* JPHYSICS::JLED_C::led

protected

Pointer to interface for emission profile from LED.

Definition at line 426 of file JLED.hh.

◆ qe

double(* JPHYSICS::JLED_C::qe) (const double lambda)

protected

Quantum efficiency of PMT (incl.

absorption in glass, gel, etc.)

Parameters

lambda wavelenth [nm]

Returns: QE

Definition at line 434 of file JLED.hh.

◆ l_abs

double JPHYSICS::JLED_C::l_abs

protected

Absorption length.

Definition at line 439 of file JLED.hh.

◆ ls

double JPHYSICS::JLED_C::ls

protected

Scattering length.

Definition at line 444 of file JLED.hh.

◆ pmt

double(* JPHYSICS::JLED_C::pmt) (const double ct)

protected

Angular acceptance of PMT.

Parameters

ct	cosine angle of incidence

Returns: relative efficiency

Definition at line 452 of file JLED.hh.

◆ km3

double(* JPHYSICS::JLED_C::km3) (const double ct)

protected

Model specific function to describe light scattering in water.

Parameters

ct	cosine scattering angle

Returns: probability

Definition at line 460 of file JLED.hh.

◆ wavelength

double JPHYSICS::JLED::wavelength

protectedinherited

Definition at line 261 of file JLED.hh.

◆ tmin

double JPHYSICS::JLED::tmin

protectedinherited

Definition at line 263 of file JLED.hh.

◆ tmax

double JPHYSICS::JLED::tmax

protectedinherited

Definition at line 264 of file JLED.hh.

◆ main_engine

JQuadrature JPHYSICS::JLED::main_engine

protectedinherited

Definition at line 266 of file JLED.hh.

◆ beta_engine

JQuadrature JPHYSICS::JLED::beta_engine

protectedinherited

Definition at line 267 of file JLED.hh.

◆ phi_engine

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

protectedinherited

Definition at line 268 of file JLED.hh.

◆ P

const double JPHYSICS::JDispersion::P

inherited

Dispersion parameters (x = 1/lambda)

ambient pressure [atm]

Definition at line 95 of file JDispersion.hh.

◆ a0

const double JPHYSICS::JDispersion::a0

inherited

offset

Definition at line 96 of file JDispersion.hh.

◆ a1

const double JPHYSICS::JDispersion::a1

inherited

dn/dP

Definition at line 97 of file JDispersion.hh.

◆ a2

const double JPHYSICS::JDispersion::a2

inherited

d^1n/(dx)^1

Definition at line 98 of file JDispersion.hh.

◆ a3

const double JPHYSICS::JDispersion::a3

inherited

d^2n/(dx)^2

Definition at line 99 of file JDispersion.hh.

◆ a4

const double JPHYSICS::JDispersion::a4

inherited

d^3n/(dx)^3

Definition at line 100 of file JDispersion.hh.

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

JLED.hh

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ JLED_C()

Member Function Documentation

◆ getLightFromLED()

◆ getPhotocathodeArea()

◆ getQE()

◆ getAngularAcceptance()

◆ getAbsorptionLength()

◆ getScatteringLength()

◆ getScatteringProbability()

◆ getDirectLightFromLED()

◆ getScatteredLightFromLED()

◆ getIndexOfRefractionPhase()

◆ getDispersionPhase()

◆ getDispersionGroup()

◆ getIndexOfRefractionGroup()

◆ getKappa()

◆ getKmin()

Member Data Documentation

◆ A

◆ led

◆ qe

◆ l_abs

◆ ls

◆ pmt

◆ km3

◆ wavelength

◆ tmin

◆ tmax

◆ main_engine

◆ beta_engine

◆ phi_engine

◆ P

◆ a0

◆ a1

◆ a2

◆ a3

◆ a4