JDETECTOR::JPMTAnalogueSignalProcessor Struct Reference

PMT analogue signal processor. More...

#include <JPMTAnalogueSignalProcessor.hh>

Inheritance diagram for JDETECTOR::JPMTAnalogueSignalProcessor:

Public Types
enum	JThresholdDomain { BELOW_THRESHOLD = -1 , THRESHOLDBAND = 0 , ABOVE_THRESHOLD = 2 }
	Threshold domain specifiers. More...

Public Member Functions
	JPMTAnalogueSignalProcessor (const JPMTParameters &parameters=JPMTParameters())
	Constructor.
void	configure ()
	Configure internal parameters.
double	getDecayTime () const
	Get decay time.
double	getT1 () const
	Get time at transition point from Gaussian to exponential.
double	getY1 () const
	Get amplitude at transition point from Gaussian to exponential.
double	getStartOfLinearisation () const
	Get transition point from a model-dependent to linear relation between time-over-threshold and number of photo-electrons.
double	getAmplitude (const double t1_ns) const
	Get amplitude at given time for a one photo-electron pulse.
double	getRiseTime (const double npe, const double th) const
	Get time to pass from threshold to top of analogue pulse.
double	getDecayTime (const double npe, const double th) const
	Get time to pass from top of analogue pulse to threshold.
double	applySaturation (const double tot_ns) const
	Get time-over-threshold with saturation.
double	removeSaturation (const double tot_ns) const
	Get time-over-threshold without saturation.
double	getDerivativeOfSaturation (const double tot_ns) const
	Get derivative of saturation factor.
double	getGainSpread (int NPE) const
	Get gain spread for given number of photo-electrons.
double	getIntegralOfChargeProbability (const double xmin, const double xmax, const int NPE) const
	Get integral of probability.
double	getIntegralOfChargeProbability (const JThresholdDomain domain, const int NPE) const
	Get integral of probability in specific threshold domain.
void	setPMTParameters (const JPMTParameters &parameters)
	Set PMT parameters.
JThresholdDomain	getThresholdDomain (const double npe) const
	Get threshold domain.
virtual bool	applyQE () const override
	Apply relative QE.
virtual double	getRandomTime (const double t_ns) const override
	Get randomised time according transit-time distribution.
virtual bool	compare (const JPhotoElectron &first, const JPhotoElectron &second) const override
	Compare arrival times of photo-electrons.
virtual double	getRandomCharge (const int NPE) const override
	Get randomised charge according to gain and gain spread.
virtual double	getChargeProbability (const double npe, const int NPE) const override
	Get probability density for given charge.
virtual bool	applyThreshold (const double npe) const override
	Apply threshold.
virtual double	getRiseTime (const double npe) const override
	Get time to reach threshold.
virtual double	getTimeOverThreshold (const double npe) const override
	Get time-over-threshold (ToT).
virtual double	getDerivative (const double npe) const override
	Get derivative of number of photo-electrons to time-over-threshold.
virtual double	getSurvivalProbability (const int NPE) const override
	Probability that a hit survives the simulation of the PMT.
virtual double	getThresholdProbability (const int NPE) const override
	Probability that a hit survives the threshold of the PMT.
virtual double	getNPE (const double tot_ns) const override
	Get number of photo-electrons.
double	getTimeOverThresholdProbability (const double tot_ns, const int NPE) const
	Get probability of having a pulse with specific time-over-threshold.
double	getIntegralOfTimeOverThresholdProbability (const double Tmin, const double Tmax, const int NPE) const
	Get cumulative probability of time-over-threshold distribution.
void	operator() (const JCalibration &calibration, const JPMTData< JPMTSignal > &input, JPMTData< JPMTPulse > &output) const
	Process hits.
virtual void	merge (JPMTData< JPMTPulse > &data) const
	Merging of PMT hits.
const JPMTParameters &	getPMTParameters () const
	Get PMT parameters.
bool	is_valid () const
	Check validity of PMT parameters.
int	getType () const
	Get type for for time-slewing correction.
JProperties	getProperties (const JEquationParameters &equation=JPMTParameters::getEquationParameters())
	Get properties of this class.
JProperties	getProperties (const JEquationParameters &equation=JPMTParameters::getEquationParameters()) const
	Get properties of this class.

Static Public Member Functions
static double	getMaximalRiseTime (const double th)
	Get maximal rise time for given threshold.
static double	getTH0 ()
	Get lower threshold for rise time evaluation.
static double	getTH1 ()
	Get upper threshold for rise time evaluation.
static double	getTmin ()
	Get two photo-electron resolution for time-over-threshold.
static double	getQmin ()
	Get width of charge distribution.
static JEquationParameters &	getEquationParameters ()
	Get equation parameters.
static void	setEquationParameters (const JEquationParameters &equation)
	Set equation parameters.

Public Attributes
double	QE
	relative quantum efficiency
double	gain
	gain [unit]
double	gainSpread
	gain spread [unit]
double	riseTime_ns
	rise time of analogue pulse [ns]
double	TTS_ns
	transition time spread [ns]
double	threshold
	threshold [npe]
double	PunderAmplified
	probability of underamplified hit
double	thresholdBand
	threshold-band [npe]
double	mean_ns
	mean time-over-threshold of threshold-band hits [ns]
double	sigma_ns
	time-over-threshold standard deviation of threshold-band hits [ns]
double	slope
	slope [ns/npe]
double	saturation
	saturation [ns]
bool	slewing
	time slewing of analogue signal

Protected Attributes
double	decayTime_ns
	decay time [ns]
double	t1
	time at match point [ns]
double	y1
	amplitude at match point [npe]
double	x1
	Transition point from a logarithmic to a linear relation between time-over-threshold and number of photo-electrons.

Friends
std::istream &	operator>> (std::istream &in, JPMTAnalogueSignalProcessor &object)
	Read PMT signal from input.

Detailed Description

PMT analogue signal processor.

This class provides for an implementation of the JDETECTOR::JPMTSignalProcessorInterface using a specific model for the analogue pulse of the PMT.
In this, the leading edge of the analogue pulse from the PMT is assumed to be a Gaussian and the tail an exponential.
The width of the Gaussian is referred to as the rise time and the inverse slope of the exponential to the decay time.
The two functions are matched at a point where the values and first derivatives are identical.
Note that the decay time is related to the rise time via the specification JDETECTOR::TIME_OVER_THRESHOLD_NS.

The charge distribution is assumed to be a Gaussian which is centered at the specified gain and truncated by the specified threshold.

The transit times are generated according the specified spread as follows.

• If the specified transit-time spread (TTS) is negative, the transit times are generated according to measurements (see method JDETECTOR::getTransitTime).
  In this, the negated integral value of the TTS corresponds to the option which in turn corresponds to the detector identifier of the measurements.
• If the specified TTS is positive, the transit times are generated according a Gaussian with a sigma equals to the given TTS.
• If the TTS is zero, the transit times are generated without any spread.

Definition at line 52 of file JPMTAnalogueSignalProcessor.hh.

Member Enumeration Documentation

JThresholdDomain

enum JDETECTOR::JPMTAnalogueSignalProcessor::JThresholdDomain

Threshold domain specifiers.

Enumerator
BELOW_THRESHOLD	below threshold
THRESHOLDBAND	inside threshold band
ABOVE_THRESHOLD	above threshold

Definition at line 59 of file JPMTAnalogueSignalProcessor.hh.

                          {
      BELOW_THRESHOLD  = -1,     //!< below  threshold
      THRESHOLDBAND    =  0,     //!< inside threshold band
      ABOVE_THRESHOLD  =  2      //!< above  threshold
    };

Constructor & Destructor Documentation

JPMTAnalogueSignalProcessor()

JDETECTOR::JPMTAnalogueSignalProcessor::JPMTAnalogueSignalProcessor ( const JPMTParameters & parameters = JPMTParameters() )

inline

Constructor.

Parameters

parameters

PMT parameters

Definition at line 71 of file JPMTAnalogueSignalProcessor.hh.

                                                                                     :
      JPMTSignalProcessorInterface(),
      JPMTParameters(parameters),
      decayTime_ns(0.0),
      t1(0.0),
      y1(0.0),
      x1(std::numeric_limits<double>::max())
    {
      configure();
    }

Member Function Documentation

configure()

void JDETECTOR::JPMTAnalogueSignalProcessor::configure ( )

inline

Configure internal parameters.

This method provides the implementations for

• matching of the leading edge of the analogue pulse (Gaussian) and the tail (exponential); and
• determination of number of photo-electrons above which the time-over-threshold linearly depends on the number of photo-electrons (apart from saturation).

Note that this method will throw an error if the value of the rise time (i.e. width of the Gaussian) is too large with respect to the specification JDETECTOR::TIME_OVER_THRESHOLD_NS.

Definition at line 94 of file JPMTAnalogueSignalProcessor.hh.

    {
      static const int    N         = 100;
      static const double precision = 1.0e-4;
 
      // check thresholdband
 
      if (threshold - thresholdBand < getTH0()) {
        THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::configure(): Invalid thresholdband [npe] " << thresholdBand);
      }
 
      // check rise time      
 
      if (riseTime_ns > getMaximalRiseTime(threshold)) {
        THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::configure(): Invalid rise time [ns] " << riseTime_ns);
      } 
 
      // check probability for under-amplified signal
 
      if (PunderAmplified < 0.0) {
        THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::configure(): Invalid probability of under-amplification " << PunderAmplified);
      }
 
      // check invalid combination of zero probability for under-amplified signal and zero gain spread
 
      if (PunderAmplified == 0.0 && gainSpread <= 0.0) {
        THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::configure(): Invalid gain spread " << gainSpread << " for probability of under-amplification " << PunderAmplified);
      }
 
      // decay time
 
      const double y  = -log(threshold);
 
      const double a  =  y;
      const double b  =  riseTime_ns * sqrt(2.0*y) - TIME_OVER_THRESHOLD_NS;
      const double c  =  0.5*riseTime_ns*riseTime_ns;
      const double Q  =  b*b - 4.0*a*c;
 
      if (Q > 0.0) 
        decayTime_ns = (-b + sqrt(Q)) / (2.0*a);
      else
        decayTime_ns =  -b / (2.0*a);
 
      // fix matching of Gaussian and exponential
 
      const double x  =  riseTime_ns / decayTime_ns;
 
      t1 = riseTime_ns*x;
      y1 = exp(-0.5*x*x);
 
      // determine transition point to linear dependence of time-over-threshold as a function of number of photo-electrons
      
      const double xs = saturation;              // disable saturation
 
      saturation = 1.0e50;
 
      x1 = std::numeric_limits<double>::max();   // disable linearisation
 
      double xmin = 1.0;
      double xmax = 1.0 / (getDerivative(1.0) * slope);
 
      for (int i = 0; i != N; ++i) {
 
        const double x = 0.5 * (xmin + xmax);
        const double u = getDerivative(x) * slope;
 
        if (fabs(1.0 - u) < precision) {
          break;
        }
 
        if (u < 1.0)
          xmin = x;
        else
          xmax = x;
      }
 
      x1 = 0.5 * (xmin + xmax);
 
      saturation = xs;                           // restore saturation
    }

getDecayTime() [1/2]

double JDETECTOR::JPMTAnalogueSignalProcessor::getDecayTime ( ) const

inline

Get decay time.

Returns

decay time [ns]

Definition at line 181 of file JPMTAnalogueSignalProcessor.hh.

    {
      return decayTime_ns;
    }

getT1()

double JDETECTOR::JPMTAnalogueSignalProcessor::getT1 ( ) const

inline

Get time at transition point from Gaussian to exponential.

Returns

time [ns]

Definition at line 192 of file JPMTAnalogueSignalProcessor.hh.

    {
      return t1;
    }

getY1()

double JDETECTOR::JPMTAnalogueSignalProcessor::getY1 ( ) const

inline

Get amplitude at transition point from Gaussian to exponential.

Returns

amplitude [npe]

Definition at line 203 of file JPMTAnalogueSignalProcessor.hh.

    {
      return y1;
    }

getStartOfLinearisation()

double JDETECTOR::JPMTAnalogueSignalProcessor::getStartOfLinearisation ( ) const

inline

Get transition point from a model-dependent to linear relation between time-over-threshold and number of photo-electrons.

Returns

number of photo-electrons [npe]

Definition at line 214 of file JPMTAnalogueSignalProcessor.hh.

    {
      return x1;
    }

getAmplitude()

double JDETECTOR::JPMTAnalogueSignalProcessor::getAmplitude ( const double t1_ns ) const

inline

Get amplitude at given time for a one photo-electron pulse.

Parameters

t1_ns

time [ns]

Returns

amplitude [npe]

Definition at line 226 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (t1_ns < t1) {
 
        const double x = t1_ns / riseTime_ns;
        
        return exp(-0.5*x*x);                                // Gaussian
 
      } else {
 
        const double x = t1_ns / decayTime_ns;
 
        return exp(-x) / y1;                                 // exponential
      }
    }

getRiseTime() [1/2]

double JDETECTOR::JPMTAnalogueSignalProcessor::getRiseTime ( const double npe, const double th ) const

inline

Get time to pass from threshold to top of analogue pulse.

In this, the leading edge of the analogue pulse is assumed to be Gaussian.

Parameters

npe	number of photo-electrons
th	threshold [npe]

Returns

time [ns]

Definition at line 251 of file JPMTAnalogueSignalProcessor.hh.

    {
      return riseTime_ns * sqrt(2.0*log(npe/th));            // Gaussian
    }

getDecayTime() [2/2]

double JDETECTOR::JPMTAnalogueSignalProcessor::getDecayTime ( const double npe, const double th ) const

inline

Get time to pass from top of analogue pulse to threshold.

In this, the trailing edge of the analogue pulse is assumed to be exponential.

Parameters

npe	number of photo-electrons
th	threshold [npe]

Returns

time [ns]

Definition at line 265 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (npe*y1 > th)
        return decayTime_ns * (log(npe/th) - log(y1));       // exponential
      else
        return riseTime_ns * sqrt(2.0*log(npe/th));          // Gaussian
    }

getMaximalRiseTime()

static double JDETECTOR::JPMTAnalogueSignalProcessor::getMaximalRiseTime ( const double th )

inlinestatic

Get maximal rise time for given threshold.

Note that the rise time is entirely constrained by the specification JDETECTOR::TIME_OVER_THRESHOLD_NS.

Parameters

th	threshold [npe]

Returns

rise time [ns]

Definition at line 282 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (th > 0.0 && th < 1.0)
        return 0.5 * TIME_OVER_THRESHOLD_NS / sqrt(-2.0*log(th));
      else
        THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::getMaximalRiseTime(): Invalid threshold " << th);
    }

applySaturation()

double JDETECTOR::JPMTAnalogueSignalProcessor::applySaturation ( const double tot_ns ) const

inline

Get time-over-threshold with saturation.

Parameters

tot_ns

time-over-threshold without saturation

Returns

time-over-threshold with saturation

Definition at line 297 of file JPMTAnalogueSignalProcessor.hh.

    {
      return saturation / sqrt(tot_ns*tot_ns + saturation*saturation) * tot_ns;
    }

removeSaturation()

double JDETECTOR::JPMTAnalogueSignalProcessor::removeSaturation ( const double tot_ns ) const

inline

Get time-over-threshold without saturation.

Parameters

tot_ns

time-over-threshold with saturation

Returns

time-over-threshold without saturation

Definition at line 309 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (tot_ns < saturation)
        return saturation / sqrt(saturation*saturation - tot_ns*tot_ns) * tot_ns;
      else
        return std::numeric_limits<double>::max();
      //THROW(JValueOutOfRange, "Time-over-threshold exceeds saturation " << tot_ns << " >= " << saturation);
    }

getDerivativeOfSaturation()

double JDETECTOR::JPMTAnalogueSignalProcessor::getDerivativeOfSaturation ( const double tot_ns ) const

inline

Get derivative of saturation factor.

Parameters

tot_ns

time-over-threshold without saturation

Returns

derivative of saturation factor

Definition at line 325 of file JPMTAnalogueSignalProcessor.hh.

    {
      return saturation * saturation * saturation / ((saturation*saturation + tot_ns*tot_ns) * sqrt(saturation*saturation + tot_ns*tot_ns));
    }

getGainSpread()

double JDETECTOR::JPMTAnalogueSignalProcessor::getGainSpread ( int NPE ) const

inline

Get gain spread for given number of photo-electrons.

Parameters

NPE	number of photo-electrons

Returns

gain spread

Definition at line 337 of file JPMTAnalogueSignalProcessor.hh.

    {
      return sqrt((double) NPE * gain) * gainSpread;
    }

getIntegralOfChargeProbability() [1/2]

double JDETECTOR::JPMTAnalogueSignalProcessor::getIntegralOfChargeProbability ( const double xmin, const double xmax, const int NPE ) const

inline

Get integral of probability.

Parameters

xmin	minimum number of photo-electrons
xmax	maximum number of photo-electrons
NPE	true number of photo-electrons

Returns

probability

Definition at line 351 of file JPMTAnalogueSignalProcessor.hh.

    {
      double zmin = xmin;
      double zmax = xmax;
 
      const double th = threshold - thresholdBand;
 
      if (zmin < th) { zmin = th; }
      if (zmax < th) { zmax = th; }
 
      if        (PunderAmplified <= 0.0) {
 
        const double mu    = NPE * gain;
        const double sigma = getGainSpread(NPE);
 
        const double cumulP = (0.5 * erfc((zmin - mu) / sqrt(2.0) / sigma) -
                               0.5 * erfc((zmax - mu) / sqrt(2.0) / sigma));
        const double norm   =  0.5 * erfc((th   - mu) / sqrt(2.0) / sigma);
 
        return cumulP / norm;
 
      } else if (PunderAmplified < 1.0) {
      
        const double fs  = gainSpread * gainSpread;
 
        double cumulP = 0.0;
        double norm   = 0.0;
        double weight = pow(1.0 - PunderAmplified, NPE);
 
        for (int k = 0; k <= NPE; ++k) {  // k underamplified photo-electrons
 
          const double mu    = (NPE-k) * gain  +  (k) * fs * gain;
          const double sigma = sqrt(mu) * getGainSpread(1);
 
          cumulP += weight * (0.5 * erfc((zmin - mu) / sqrt(2.0) / sigma) -
                              0.5 * erfc((zmax - mu) / sqrt(2.0) / sigma));
          norm   += weight * (0.5 * erfc((th   - mu) / sqrt(2.0) / sigma));
 
          weight *= ((double) (NPE-k) / ((double) (k+1)))  *  PunderAmplified / (1.0 - PunderAmplified);
        }
 
        return cumulP / norm;
 
      } else {
        
        THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::getIntegralOfChargeProbability(): Invalid probability of under-amplification " << PunderAmplified);
      }
    }

getIntegralOfChargeProbability() [2/2]

double JDETECTOR::JPMTAnalogueSignalProcessor::getIntegralOfChargeProbability ( const JThresholdDomain domain, const int NPE ) const

inline

Get integral of probability in specific threshold domain.

Parameters

domain	threshold domain
NPE	true number of photo-electrons

Returns

probability

Definition at line 408 of file JPMTAnalogueSignalProcessor.hh.

    {
      switch (domain) {
 
      case ABOVE_THRESHOLD:
        return 1.0 - getIntegralOfChargeProbability(threshold-thresholdBand, threshold, NPE);
 
      case THRESHOLDBAND:
        return getIntegralOfChargeProbability(threshold-thresholdBand, threshold, NPE);
 
      default:
        return 0.0;
      }
    }

setPMTParameters()

void JDETECTOR::JPMTAnalogueSignalProcessor::setPMTParameters ( const JPMTParameters & parameters )

inline

Set PMT parameters.

Parameters

parameters

PMT parameters

Definition at line 429 of file JPMTAnalogueSignalProcessor.hh.

    {
      static_cast<JPMTParameters&>(*this).setPMTParameters(parameters);
 
      configure();
    }

getThresholdDomain()

JThresholdDomain JDETECTOR::JPMTAnalogueSignalProcessor::getThresholdDomain ( const double npe ) const

inline

Get threshold domain.

Parameters

npe	number of photo-electrons

Returns

threshold domain

Definition at line 460 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (npe > threshold) {
 
        return ABOVE_THRESHOLD;
        
      } else if (npe > threshold - thresholdBand) {
 
        return THRESHOLDBAND;
        
      } else {
 
        return BELOW_THRESHOLD;
      }
    }

applyQE()

virtual bool JDETECTOR::JPMTAnalogueSignalProcessor::applyQE ( ) const

inlineoverridevirtual

Apply relative QE.

Returns

true if accepted; false if rejected

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 482 of file JPMTAnalogueSignalProcessor.hh.

    {
      if      (QE <= 0.0)
        return false;
      else if (QE <  1.0)
        return gRandom->Rndm() < QE;
      else
        return true;
    }

getRandomTime()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getRandomTime ( const double t_ns ) const

inlineoverridevirtual

Get randomised time according transit-time distribution.

Parameters

t_ns

time [ns]

Returns

time [ns]

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 499 of file JPMTAnalogueSignalProcessor.hh.

    {
      if      (TTS_ns < 0.0)
        return t_ns + getTransitTime(gRandom->Rndm(), getType());
      else if (TTS_ns > 0.0)
        return gRandom->Gaus(t_ns, TTS_ns);
      else
        return t_ns;
    }

compare()

virtual bool JDETECTOR::JPMTAnalogueSignalProcessor::compare ( const JPhotoElectron & first, const JPhotoElectron & second ) const

inlineoverridevirtual

Compare arrival times of photo-electrons.

This implementation uses the internal rise time as two photo-electron resolution.

Two (or more) photo-electrons are merged if they are comparable.

Parameters

first	first photo-electron
second	second photo-electron

Returns

true if arrival times of photo-electrons are within two photo-electron resolution; else false

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 520 of file JPMTAnalogueSignalProcessor.hh.

    {
      return second.t_ns < first.t_ns + riseTime_ns;
    }

getRandomCharge()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getRandomCharge ( const int NPE ) const

inlineoverridevirtual

Get randomised charge according to gain and gain spread.

Parameters

NPE	number of photo-electrons

Returns

number of photo-electrons

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 532 of file JPMTAnalogueSignalProcessor.hh.

    {
      double q;
 
      do {
 
        if        (PunderAmplified <= 0.0) {
 
          const double mu    = NPE * gain;
          const double sigma = getGainSpread(NPE);
 
          q = gRandom->Gaus(mu,sigma);
 
        } else if (PunderAmplified < 1.0) {
 
          // Determine which contribution to sample from
          // Method uses inverse transform sampling for a binomial distribution
 
          const double X = gRandom->Uniform();
          double sum_p   = 0.0;
          double weight  = pow(1-PunderAmplified, NPE);
          int k          = 0;  // k underamplified photo-electrons
  
          for (; k <= NPE; ++k) {
      
            sum_p += weight;
            if (sum_p > X) { break; }
      
            weight *= ((double) (NPE-k) / ((double) (k+1)))  *  PunderAmplified / (1.0 - PunderAmplified);
          }
 
          // Sample from chosen contribution
          const double fs    = gainSpread * gainSpread;
          const double mu    = (NPE-k) * gain  +  (k) * fs * gain;
          const double sigma = sqrt(mu) * getGainSpread(1);
 
          q = gRandom->Gaus(mu,sigma);
 
        } else {
 
          THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::getRandomCharge(): Invalid probability of under-amplification " << PunderAmplified);
        }
 
      } while (q < 0.0);
      
      return q;
    }

getChargeProbability()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getChargeProbability ( const double npe, const int NPE ) const

inlineoverridevirtual

Get probability density for given charge.

Parameters

npe	observed number of photo-electrons
NPE	true number of photo-electrons

Returns

probability [npe^-1]

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 588 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (getThresholdDomain(npe) > BELOW_THRESHOLD) {
 
        if        (PunderAmplified <= 0.0) {
 
          const double mu    = NPE * gain;
          const double sigma = getGainSpread(NPE);
 
          const double prob = JMATH::Gauss(npe, mu, sigma);
          const double norm = 0.5 * erfc(((threshold-thresholdBand) - mu) / sqrt(2.0) / sigma);
 
          return prob / norm;
        
        } else if (PunderAmplified < 1.0) {
 
          const double fs = gainSpread * gainSpread;
 
          double norm   = 0.0;
          double prob   = 0.0;
          double weight = pow(1-PunderAmplified, NPE);
 
          for (int k = 0; k <= NPE; ++k) {  // k underamplified photo-electrons
      
            const double mu    = (NPE-k) * gain  +  (k) * fs * gain;
            const double sigma = sqrt(mu) * getGainSpread(1);
      
            prob += weight * JMATH::Gauss(npe, mu, sigma);
            norm += weight * (0.5 * erfc(((threshold-thresholdBand) - mu) / sqrt(2.0) / sigma));
      
            weight *= ((double) (NPE-k) / ((double) (k+1)))  *  PunderAmplified / (1.0 - PunderAmplified);
          }
    
          return prob / norm;
        }
      }
 
      return 0.0;
    }

applyThreshold()

virtual bool JDETECTOR::JPMTAnalogueSignalProcessor::applyThreshold ( const double npe ) const

inlineoverridevirtual

Apply threshold.

Parameters

npe	number of photo-electrons

Returns

true if pass; else false

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 635 of file JPMTAnalogueSignalProcessor.hh.

    {
      return getThresholdDomain(npe) > BELOW_THRESHOLD;
    }

getRiseTime() [2/2]

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getRiseTime ( const double npe ) const

inlineoverridevirtual

Get time to reach threshold.

Note that the rise time is defined to be zero for a one photo-electron signal.

Parameters

npe	number of photo-electrons

Returns

time [ns]

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 649 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (slewing) {
 
        switch (getThresholdDomain(npe)) {
 
        case THRESHOLDBAND:
          return ((getRiseTime(npe, getTH0()) - getRiseTime(npe, threshold-thresholdBand)) -
                  (getRiseTime(1.0, getTH0()) - getRiseTime(1.0, threshold-thresholdBand))) + this->mean_ns;
 
        case ABOVE_THRESHOLD: 
          return ((getRiseTime(npe, getTH0()) - getRiseTime(npe, threshold)) -
                  (getRiseTime(1.0, getTH0()) - getRiseTime(1.0, threshold)));
 
        default:
          THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::getRiseTime: Invalid charge " << npe);
        }
 
      } else {
 
        return 0.0;
      }
    }

getTimeOverThreshold()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getTimeOverThreshold ( const double npe ) const

inlineoverridevirtual

Get time-over-threshold (ToT).

Parameters

npe	number of photo-electrons

Returns

ToT [ns]

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 680 of file JPMTAnalogueSignalProcessor.hh.

    {
      switch (getThresholdDomain(npe)) {
 
      case THRESHOLDBAND: {
        
        return gRandom->Gaus(mean_ns, sigma_ns);
      }
 
      case ABOVE_THRESHOLD: {
        
        double tot = 0.0;
 
        if (npe*y1 <= threshold) { 
          
          tot += getRiseTime(npe, threshold);                           // Gaussian
          tot += getRiseTime(npe, threshold);                           // Gaussian
 
        } else if (npe <= getStartOfLinearisation()) {
 
          tot += getRiseTime (npe, threshold);                          // Gaussian
          tot += getDecayTime(npe, threshold);                          // exponential
 
        } else {
 
          tot += getRiseTime (getStartOfLinearisation(), threshold);    // Gaussian
          tot += getDecayTime(getStartOfLinearisation(), threshold);    // exponential
          
          tot += slope * (npe - getStartOfLinearisation());             // linear
        }
        
        return applySaturation(tot);
      }
        
      default: {
 
        THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::getTimeOverThreshold: Invalid charge " << npe);
      }}
    }

getDerivative()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getDerivative ( const double npe ) const

inlineoverridevirtual

Get derivative of number of photo-electrons to time-over-threshold.

Parameters

npe	number of photo-electrons

Returns

dnpe/dToT [ns^-1]

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 727 of file JPMTAnalogueSignalProcessor.hh.

    {
      switch (getThresholdDomain(npe)) {
 
      case ABOVE_THRESHOLD: {
 
        const double z  = riseTime_ns / sqrt(2.0 * log(npe/threshold));
 
        double y = 0.0;
 
        if (npe*y1 > threshold) {
          
          if (npe <= getStartOfLinearisation())
            y = npe / (z + decayTime_ns);           // Gaussian + exponential
          else
            y = 1.0 / slope;                        // linear
 
        } else {
 
          y = npe / (2.0 * z);                      // Gaussian + Gaussian
        }
 
        const double tot_ns = getTimeOverThreshold(npe);
 
        return y / getDerivativeOfSaturation(removeSaturation(tot_ns));
      }
 
      default:
        return 0.0;
      }
    }

getSurvivalProbability()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getSurvivalProbability ( const int NPE ) const

inlineoverridevirtual

Probability that a hit survives the simulation of the PMT.

The survival probability takes into account the number of photo-electrons, the analogue signal of the PMT and the threshold of the discriminator.

Parameters

NPE	number of photo-electrons

Returns

probability

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 767 of file JPMTAnalogueSignalProcessor.hh.

    {
      using namespace JPP;
 
      if        (QE <= 0.0) {
 
        return 0.0;
 
      } else if (QE <  1.0) {
 
        double P = 0.0;
        
        for (int i = 1; i <= NPE; ++i) {                                             // i corresponds to number of photo-electrons passing relative QE
 
          const double p = (binomial(NPE, i) * pow(QE, i) * pow(1.0 - QE, NPE - i));
 
          P += p * getThresholdProbability(NPE);
        }
 
        return P;
 
      } else {
 
        return getThresholdProbability(NPE);
      }
    }

getThresholdProbability()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getThresholdProbability ( const int NPE ) const

inlineoverridevirtual

Probability that a hit survives the threshold of the PMT.

Parameters

NPE	number of photo-electrons

Returns

probability

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 801 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (NPE > 0) {
 
        if        (PunderAmplified <= 0.0) {
 
          const double mu    = NPE * gain;
          const double sigma = getGainSpread(NPE);
 
          if (sigma > 0.0) {
 
            const double Ptotal = 0.5 * erfc((0.0                       - mu) / (sqrt(2.0) * sigma));
            const double Pabove = 0.5 * erfc((threshold - thresholdBand - mu) / (sqrt(2.0) * sigma));
 
            return Pabove / Ptotal;
 
          } else if (mu >= threshold - thresholdBand) {
 
            return 1.0;
 
          } else {
 
            return 0.0;
          }
 
        } else if (PunderAmplified < 1.0) {
            
          const double fs = gainSpread * gainSpread;                               // amplification factor per stage equals square of relative gain spread
 
          double Ptotal = 0.0;
          double Pabove = 0.0;
          double weight = pow(1.0 - PunderAmplified, NPE);                         // binomial weight - start with all photo-electrons nominal
 
          for (int k = 0; k <= NPE; ++k) {                                         // NPE-k nominal photo-electrons and k underamplified photo-electrons
 
            const double mu    = (NPE-k) * gain  +  (k) * fs * gain;
            const double sigma = sqrt(mu) * getGainSpread(1);
 
            if (sigma > 0.0) {
 
              Ptotal += weight * 0.5 * erfc((0.0                       - mu) / (sqrt(2.0) * sigma));
              Pabove += weight * 0.5 * erfc((threshold - thresholdBand - mu) / (sqrt(2.0) * sigma));
 
            } else if (mu >= threshold - thresholdBand) {
 
              Ptotal += weight;
              Pabove += weight;
            }
 
            weight *= ((double) (NPE-k) / ((double) (k+1)))  *  PunderAmplified / (1.0 - PunderAmplified);
          }
 
          return Pabove / Ptotal;
 
        } else {
 
          THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::getThresholdProbability(): Invalid PunderAmplified " << PunderAmplified);
        }
      }
 
      return 0.0;
    }

getNPE()

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getNPE ( const double tot_ns ) const

inlineoverridevirtual

Get number of photo-electrons.

Parameters

tot_ns

time over threshold [ns]

Returns

number of photo-electrons

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 871 of file JPMTAnalogueSignalProcessor.hh.

    {
      if (tot_ns >= saturation) {
        return std::numeric_limits<double>::max();
      }
 
      const double tot =  removeSaturation(tot_ns);
      const double TOT = (getRiseTime (getStartOfLinearisation(), threshold)  + 
                          getDecayTime(getStartOfLinearisation(), threshold));
      
      if        (tot <= 2*getRiseTime(threshold/y1,threshold)) {              // Gaussian + Gaussian
        
        return threshold * exp(tot*tot/riseTime_ns/riseTime_ns/8.0);
        
      } else if (tot <= TOT) {                                                // Gaussian + Exponential
 
        const double a = decayTime_ns;
        const double b = sqrt(2.0) * riseTime_ns;
        const double c = -(decayTime_ns*log(y1) + tot);
        const double z = (-b + sqrt(b*b - 4*a*c)) / (2*a);
 
        return threshold * exp(z*z);
        
      } else {                                                                // linear
          
        return getStartOfLinearisation() + (tot - TOT) / slope;
      }
    }

getTimeOverThresholdProbability()

double JDETECTOR::JPMTAnalogueSignalProcessor::getTimeOverThresholdProbability ( const double tot_ns, const int NPE ) const

inline

Get probability of having a pulse with specific time-over-threshold.

Parameters

tot_ns	time-over-threshold with saturation [ns]
NPE	true number of photo-electrons

Returns

probability [ns^-1]

Definition at line 908 of file JPMTAnalogueSignalProcessor.hh.

    {
      const double PthBand  = getIntegralOfChargeProbability(THRESHOLDBAND, NPE);
 
      const double npe      = getNPE(tot_ns);
      const double y        = getChargeProbability(npe, NPE);
      const double v        = getDerivative(npe);
      
      const double RthBand  = PthBand * JMATH::Gauss(tot_ns, mean_ns, sigma_ns);
      const double RaboveTh = y * v;
 
      return RthBand + RaboveTh;
    }

getIntegralOfTimeOverThresholdProbability()

double JDETECTOR::JPMTAnalogueSignalProcessor::getIntegralOfTimeOverThresholdProbability ( const double Tmin, const double Tmax, const int NPE ) const

inline

Get cumulative probability of time-over-threshold distribution.

Parameters

Tmin	minimum time-over-threshold (with saturation) [ns]
Tmax	maximum time-over-threshold (with saturation) [ns]
NPE	true number of photo-electrons

Returns

probability [ns^-1]

Definition at line 931 of file JPMTAnalogueSignalProcessor.hh.

    {
 
      const double PthBand  = getIntegralOfChargeProbability(THRESHOLDBAND, NPE);
 
      const double IthBand  = PthBand * (0.5 * erfc((Tmin - mean_ns) / sqrt(2.0) / sigma_ns) -
                                         0.5 * erfc((Tmax - mean_ns) / sqrt(2.0) / sigma_ns)); 
      const double IaboveTh = getIntegralOfChargeProbability(getNPE(Tmin), getNPE(Tmax), NPE);
 
      return IthBand + IaboveTh;
    }

getTH0()

static double JDETECTOR::JPMTAnalogueSignalProcessor::getTH0 ( )

inlinestatic

Get lower threshold for rise time evaluation.

Returns

threshold [npe]

Definition at line 949 of file JPMTAnalogueSignalProcessor.hh.

    {
      return 0.1;
    }

getTH1()

static double JDETECTOR::JPMTAnalogueSignalProcessor::getTH1 ( )

inlinestatic

Get upper threshold for rise time evaluation.

Returns

threshold [npe]

Definition at line 960 of file JPMTAnalogueSignalProcessor.hh.

    {
      return 0.9;
    }

operator()()

void JDETECTOR::JPMTSignalProcessorInterface::operator() ( const JCalibration & calibration, const JPMTData< JPMTSignal > & input, JPMTData< JPMTPulse > & output ) const

inlineinherited

Process hits.

Two (or more) photo-electrons are combined if they are comparable according method compare.
Two (or more) consecutive hits hits maybe merged (according method merge).
A PMT signal with negative number of photo-electrons is not subjected to the quantum efficiency and transit-time distribution.
This feature is used to simulate the singles rate of a PMT when the measured QE is zero.

Parameters

calibration	PMT calibration
input	PMT signals
output	PMT hits

Definition at line 91 of file JPMTSignalProcessorInterface.hh.

    {
      // apply transition time distribution to each photo-electron.
 
      JPMTData<JPhotoElectron> buffer;
      
      for (JPMTData<JPMTSignal>::const_iterator hit = input.begin(); hit != input.end(); ++hit) {
 
        for (int i = 0; i < hit->npe; ++i) {
          if (applyQE()) {
            buffer.push_back(JPhotoElectron(getRandomTime(hit->t_ns)));
          }
        }
 
        for (int i = 0; i > hit->npe; --i) {
          buffer.push_back(JPhotoElectron(hit->t_ns));
        }
      }
 
      if (!buffer.empty()) {
      
        buffer.push_back(JPhotoElectron::getEndMarker());
      
        buffer.sort();
      
      
        // generate PMT hits from time sequence of photo-electrons.
        
        for (JPMTData<JPhotoElectron>::const_iterator q = buffer.begin(), p = q++; q != buffer.end(); ++q) {
          
          while (compare(*p,*q)) {
            ++q;
          }
          
          const double npe = getRandomCharge(distance(p,q));
 
          if (applyThreshold(npe)) {
            output.push_back(JPMTPulse(putTime(p->t_ns + getRiseTime(npe), calibration), getTimeOverThreshold(npe)));
          }
 
          p = q;
        }
        
        // merge overlapping PMT hits.
      
        merge(output);
      }
    }

merge()

virtual void JDETECTOR::JPMTSignalProcessorInterface::merge ( JPMTData< JPMTPulse > & data ) const

inlinevirtualinherited

Merging of PMT hits.

Hits with overlapping time-over-threshold signals should -de facto- be combined. In this, the leading edge is maintained and the time-over-threshold is set to the difference between the overall trailing and leading edges. As a result, the number of PMT hits may be reduced.

Parameters

data	PMT hits (I/O)

Definition at line 311 of file JPMTSignalProcessorInterface.hh.

    {
      using namespace std;
      
      JPMTData<JPMTPulse>::iterator out = data.begin();
      
      for (JPMTData<JPMTPulse>::iterator i = data.begin(); i != data.end(); ) {
        
        double t1 = i->t_ns;
        double t2 = i->t_ns + i->tot_ns;
        
        while (++i != data.end() && i->t_ns < t2 + getTmin()) {
          t2 = max(t2, i->t_ns + i->tot_ns);
        }
        
        out->t_ns   = t1;
        out->tot_ns = t2 - t1;
        
        ++out;
      }
      
      data.resize(distance(data.begin(), out));
    }

getTmin()

static double JDETECTOR::JPMTSignalProcessorInterface::getTmin ( )

inlinestaticinherited

Get two photo-electron resolution for time-over-threshold.

Returns

minimal time [ns]

Definition at line 341 of file JPMTSignalProcessorInterface.hh.

    {
      return 1.0;
    }

getQmin()

static double JDETECTOR::JPMTSignalProcessorInterface::getQmin ( )

inlinestaticinherited

Get width of charge distribution.

Returns

width charge distribution [npe]

Definition at line 352 of file JPMTSignalProcessorInterface.hh.

    {
      return 1.0e-3;
    }

getPMTParameters()

const JPMTParameters & JDETECTOR::JPMTParameters::getPMTParameters ( ) const

inlineinherited

Get PMT parameters.

Returns

PMT parameters

Definition at line 112 of file JPMTParameters.hh.

    {
      return static_cast<const JPMTParameters&>(*this);
    }

is_valid()

bool JDETECTOR::JPMTParameters::is_valid ( ) const

inlineinherited

Check validity of PMT parameters.

Returns

true if valid; else false

Definition at line 134 of file JPMTParameters.hh.

    {
      if (this->QE                 < 0.0 ||
          this->gain               < 0.0 ||
          this->gainSpread         < 0.0 ||
          this->threshold      < 0.0 ||
          this->thresholdBand  < 0.0) {
        return false;
      } 
 
      return true;
    }

getType()

int JDETECTOR::JPMTParameters::getType ( ) const

inlineinherited

Get type for for time-slewing correction.

Returns

type

Definition at line 153 of file JPMTParameters.hh.

    {
      if (this->TTS_ns < 0.0)
        return -lrint(this->TTS_ns);
      else
        return 0;
    }

getEquationParameters()

static JEquationParameters & JDETECTOR::JPMTParameters::getEquationParameters ( )

inlinestaticinherited

Get equation parameters.

Returns

equation parameters

Definition at line 209 of file JPMTParameters.hh.

    {
      static JEquationParameters equation("=", ",", "./", "#");
 
      return equation;
    }

setEquationParameters()

static void JDETECTOR::JPMTParameters::setEquationParameters ( const JEquationParameters & equation )

inlinestaticinherited

Set equation parameters.

Parameters

equation

equation parameters

Definition at line 222 of file JPMTParameters.hh.

    {
      getEquationParameters() = equation;
    }

getProperties() [1/2]

JProperties JDETECTOR::JPMTParameters::getProperties ( const JEquationParameters & equation = JPMTParameters::getEquationParameters() )

inlineinherited

Get properties of this class.

Parameters

equation

equation parameters

Definition at line 233 of file JPMTParameters.hh.

    {
      return JPMTParametersHelper(*this, equation);
    }

getProperties() [2/2]

JProperties JDETECTOR::JPMTParameters::getProperties ( const JEquationParameters & equation = JPMTParameters::getEquationParameters() ) const

inlineinherited

Get properties of this class.

Parameters

equation

equation parameters

Definition at line 244 of file JPMTParameters.hh.

    {
      return JPMTParametersHelper(*this, equation);
    }

Friends And Related Symbol Documentation

operator>>

std::istream & operator>> ( std::istream & in, JPMTAnalogueSignalProcessor & object )

friend

Read PMT signal from input.

Parameters

in	input stream
object	PMT signal

Returns

input stream

Definition at line 444 of file JPMTAnalogueSignalProcessor.hh.

    {
      in >> static_cast<JPMTParameters&>(object);
      
      object.configure();
 
      return in;
    }

Member Data Documentation

decayTime_ns

double JDETECTOR::JPMTAnalogueSignalProcessor::decayTime_ns

protected

decay time [ns]

Definition at line 967 of file JPMTAnalogueSignalProcessor.hh.

t1

double JDETECTOR::JPMTAnalogueSignalProcessor::t1

protected

time at match point [ns]

Definition at line 968 of file JPMTAnalogueSignalProcessor.hh.

y1

double JDETECTOR::JPMTAnalogueSignalProcessor::y1

protected

amplitude at match point [npe]

Definition at line 969 of file JPMTAnalogueSignalProcessor.hh.

x1

double JDETECTOR::JPMTAnalogueSignalProcessor::x1

protected

Transition point from a logarithmic to a linear relation between time-over-threshold and number of photo-electrons.

Measurements by B. Schermer and R. Bruijn at Nikhef.

Definition at line 975 of file JPMTAnalogueSignalProcessor.hh.

QE

double JDETECTOR::JPMTParameters::QE

inherited

relative quantum efficiency

Definition at line 250 of file JPMTParameters.hh.

gain

double JDETECTOR::JPMTParameters::gain

inherited

gain [unit]

Definition at line 251 of file JPMTParameters.hh.

gainSpread

double JDETECTOR::JPMTParameters::gainSpread

inherited

gain spread [unit]

Definition at line 252 of file JPMTParameters.hh.

riseTime_ns

double JDETECTOR::JPMTParameters::riseTime_ns

inherited

rise time of analogue pulse [ns]

Definition at line 253 of file JPMTParameters.hh.

TTS_ns

double JDETECTOR::JPMTParameters::TTS_ns

inherited

transition time spread [ns]

Definition at line 254 of file JPMTParameters.hh.

threshold

double JDETECTOR::JPMTParameters::threshold

inherited

threshold [npe]

Definition at line 255 of file JPMTParameters.hh.

PunderAmplified

double JDETECTOR::JPMTParameters::PunderAmplified

inherited

probability of underamplified hit

Definition at line 256 of file JPMTParameters.hh.

thresholdBand

double JDETECTOR::JPMTParameters::thresholdBand

inherited

threshold-band [npe]

Definition at line 257 of file JPMTParameters.hh.

mean_ns

double JDETECTOR::JPMTParameters::mean_ns

inherited

mean time-over-threshold of threshold-band hits [ns]

Definition at line 258 of file JPMTParameters.hh.

sigma_ns

double JDETECTOR::JPMTParameters::sigma_ns

inherited

time-over-threshold standard deviation of threshold-band hits [ns]

Definition at line 259 of file JPMTParameters.hh.

slope

double JDETECTOR::JPMTParameters::slope

inherited

slope [ns/npe]

Definition at line 260 of file JPMTParameters.hh.

saturation

double JDETECTOR::JPMTParameters::saturation

inherited

saturation [ns]

Definition at line 261 of file JPMTParameters.hh.

slewing

bool JDETECTOR::JPMTParameters::slewing

inherited

time slewing of analogue signal

Definition at line 262 of file JPMTParameters.hh.

---

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

• JPMTAnalogueSignalProcessor.hh