PMT analogue signal processor. More...

#include <JPMTAnalogueSignalProcessor.hh>

Inheritance diagram for JDETECTOR::JPMTAnalogueSignalProcessor:

Public Types
enum	JThresholdDomains { BELOW_THRESHOLDBAND = -1, IN_THRESHOLDBAND = 0, ABOVE_THRESHOLD = 2 }
	Threshold domain specifiers. More...

Public Member Functions
	JPMTAnalogueSignalProcessor (const JPMTParameters &parameters=JPMTParameters())
	Constructor. More...

void	configure ()
	Configure internal parameters. More...

double	getDecayTime () const
	Get decay time. More...

double	getT1 () const
	Get time at transition point from Gaussian to exponential. More...

double	getY1 () const
	Get amplitude at transition point from Gaussian to exponential. More...

double	getStartOfLinearisation () const
	Get transition point from a model-dependent to linear relation between time-over-threshold and number of photo-electrons. More...

double	getAmplitude (const double t1_ns) const
	Get amplitude at given time for a one photo-electron pulse. More...

double	getRiseTime (const double npe, const double th) const
	Get time to pass from threshold to top of analogue pulse. More...

double	getDecayTime (const double npe, const double th) const
	Get time to pass from top of analogue pulse to threshold. More...

double	applySaturation (const double T) const
	Get time-over-threshold with saturation. More...

double	removeSaturation (const double tot_ns) const
	Get time-over-threshold without saturation. More...

double	getDerivativeOfSaturation (const double T) const
	Get derivative of saturation factor. More...

double	getGainSpread (int NPE) const
	Get gain spread for given number of photo-electrons. More...

virtual double	getChargeProbability (const double npe, const int NPE) const override
	Get probability density for given charge. More...

double	getIntegralOfChargeProbability (const double xmin, const double xmax, const int NPE) const
	Get integral of probability. More...

double	getIntegralOfChargeProbability (JThresholdDomains domain, const int NPE) const
	Get integral of probability in specific threshold domain. More...

void	setPMTParameters (const JPMTParameters &parameters)
	Set PMT parameters. More...

virtual bool	applyQE () const override
	Apply relative QE. More...

virtual double	getRandomTime (const double t_ns) const override
	Get randomised time according transition time distribution. More...

virtual bool	compare (const JPhotoElectron &first, const JPhotoElectron &second) const override
	Compare (arrival times of) photo-electrons. More...

virtual double	getRandomCharge (const int NPE) const override
	Get randomised charge according to gain and gain spread. More...

virtual double	getNPE (const double tot_ns, const double eps=1.0e-3) const
	Get number of photo-electrons. More...

virtual JThresholdDomains	applyThreshold (const double npe) const override
	Apply threshold. More...

virtual double	getRiseTime (const double npe) const override
	Get time to reach threshold. More...

virtual double	getTimeOverThreshold (const double npe) const override
	Get time-over-threshold (ToT). More...

virtual double	getDerivative (const double npe) const override
	Get derivative of number of photo-electrons to time-over-threshold. More...

double	getTimeOverThresholdProbability (const double tot_ns, const int NPE) const
	Get probability of having a pulse with specific time-over-threshold. More...

double	getIntegralOfTimeOverThresholdProbability (const double Tmin, const double Tmax, const int NPE) const
	Get cumulative probability of time-over-threshold distribution. More...

virtual double	getSurvivalProbability (const int NPE) const override
	Probability that a hit survives the simulation of the PMT. More...

void	operator() (const JCalibration &calibration, const JPMTData< JPMTSignal > &input, JPMTData< JPMTPulse > &output) const
	Process hits. More...

virtual void	merge (JPMTData< JPMTPulse > &data) const
	Merging of PMT hits. More...

const JPMTParameters &	getPMTParameters () const
	Get PMT parameters. More...

bool	is_valid () const
	Check validity of PMT parameters. More...

JProperties	getProperties (const JEquationParameters &equation=JPMTParameters::getEquationParameters())
	Get properties of this class. More...

JProperties	getProperties (const JEquationParameters &equation=JPMTParameters::getEquationParameters()) const
	Get properties of this class. More...

Static Public Member Functions
static double	getMaximalRiseTime (const double th)
	Get maximal rise time for given threshold. More...

static double	getTH0 ()
	Get lower threshold for rise time evaluation. More...

static double	getTH1 ()
	Get upper threshold for rise time evaluation. More...

static double	getTmin ()
	Get two photo-electron resolution for time-over-threshold. More...

static double	getQmin ()
	Get minimal width of charge distribution. More...

static JEquationParameters &	getEquationParameters ()
	Get equation parameters. More...

static void	setEquationParameters (const JEquationParameters &equation)
	Set equation parameters. More...

Public Attributes
double	QE
	relative quantum efficiency More...

double	gain
	gain [unit] More...

double	gainSpread
	gain spread [unit] More...

double	riseTime_ns
	rise time of analogue pulse [ns] More...

double	TTS_ns
	transition time spread [ns] More...

double	threshold
	threshold [npe] More...

double	PunderAmplified
	probability of underamplified hit More...

double	thresholdBand
	threshold-band [npe] More...

double	mean_ns
	mean time-over-threshold of threshold-band hits [ns] More...

double	sigma_ns
	time-over-threshold standard deviation of threshold-band hits [ns] More...

double	slope
	slope [ns/npe] More...

double	saturation
	saturation [ns] More...

bool	slewing
	time slewing of analogue signal More...

Protected Attributes
double	decayTime_ns
	decay time [ns] More...

double	t1
	time at match point [ns] More...

double	y1
	amplitude at match point [npe] More...

double	x1
	Transition point from a logarithmic to a linear relation between time-over-threshold and number of photo-electrons. More...

double	MAX_CHARGE
	Maximum charge [npe]. More...

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

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 transition times are generated according the specified spread as follows.

If the specified transition-time spread (TTS) is negative, the transition times are generated according to measurements (see method JDETECTOR::getTransitionTime).
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 transition times are generated according a Gaussian with a sigma equals to the given TTS.
If the TTS is zero, the transition times are generated without any spread.

Definition at line 52 of file JPMTAnalogueSignalProcessor.hh.

Member Enumeration Documentation

enum JDETECTOR::JPMTSignalProcessorInterface::JThresholdDomains

inherited

Threshold domain specifiers.

Enumerator
BELOW_THRESHOLDBAND	below threshold band
IN_THRESHOLDBAND	inside threshold band
ABOVE_THRESHOLD	above threshold band

Definition at line 89 of file JPMTSignalProcessorInterface.hh.

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

Constructor & Destructor Documentation

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

inline

Constructor.

Parameters

parameters PMT parameters

Definition at line 61 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

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 84 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);
       } 
 
       // 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;
     }

double JDETECTOR::JPMTAnalogueSignalProcessor::getDecayTime ( ) const

inline

Get decay time.

Returns: decay time [ns]

Definition at line 160 of file JPMTAnalogueSignalProcessor.hh.

     {
       return decayTime_ns;
     }

double JDETECTOR::JPMTAnalogueSignalProcessor::getT1 ( ) const

inline

Get time at transition point from Gaussian to exponential.

Returns: time [ns]

Definition at line 171 of file JPMTAnalogueSignalProcessor.hh.

     {
       return t1;
     }

double JDETECTOR::JPMTAnalogueSignalProcessor::getY1 ( ) const

inline

Get amplitude at transition point from Gaussian to exponential.

Returns: amplitude [npe]

Definition at line 182 of file JPMTAnalogueSignalProcessor.hh.

     {
       return y1;
     }

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 193 of file JPMTAnalogueSignalProcessor.hh.

     {
       return x1;
     }

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 205 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
       }
     }

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 230 of file JPMTAnalogueSignalProcessor.hh.

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

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 244 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
     }

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 261 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);
     }

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

inline

Get time-over-threshold with saturation.

Parameters

T	time-over-threshold without saturation

Returns: time-over-threshold with saturation

Definition at line 276 of file JPMTAnalogueSignalProcessor.hh.

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

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 288 of file JPMTAnalogueSignalProcessor.hh.

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

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

inline

Get derivative of saturation factor.

Parameters

T	time-over-threshold without saturation

Returns: derivative of saturation factor

Definition at line 300 of file JPMTAnalogueSignalProcessor.hh.

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

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 312 of file JPMTAnalogueSignalProcessor.hh.

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

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 325 of file JPMTAnalogueSignalProcessor.hh.

     {
       if (applyThreshold(npe) > BELOW_THRESHOLDBAND) {
 
         const double f = gainSpread * gainSpread;
 
         double norm   = 0.0;
         double prob   = 0.0;
         double weight = (PunderAmplified > 0.0 ? pow(PunderAmplified, NPE) : 1.0);
 
         for (int k = (PunderAmplified > 0.0 ? 0 : NPE); k <= NPE; ++k) {
           
           const double mu    = ((NPE-k) * f * gain) + (k * gain);
           const double sigma = sqrt((NPE-k) * f + k) * getGainSpread(1);
           
           norm += weight * (0.5 * TMath::Erfc(((threshold-thresholdBand) - mu) / sqrt(2.0) / sigma));
           prob += weight * TMath::Gaus(npe, mu, sigma, kTRUE);
           
           weight *= ( (NPE - k) / ((double) (k+1)) *
                       (1.0 - PunderAmplified) / PunderAmplified );
         }
         
         return prob / norm;
       }
 
       return 0.0;
     }

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 362 of file JPMTAnalogueSignalProcessor.hh.

     {
       double zmin = xmin;
       double zmax = xmax;
 
       const double th = threshold - thresholdBand;
       const double f  = gainSpread * gainSpread;
 
       if (zmin < th) { zmin = th; }
       if (zmax < th) { zmax = th; }
       
       double norm   = 0.0;
       double cumulP = 0.0;
       double weight = (PunderAmplified > 0.0 ? pow(PunderAmplified, NPE) : 1.0);
 
       for (int k = (PunderAmplified > 0.0 ? 0 : NPE); k <= NPE; ++k) {
 
         const double mu    = ((NPE-k) * f * gain) + (k * gain);
         const double sigma = sqrt((NPE-k) * f + k) * getGainSpread(1);
 
         norm   += weight * (0.5 * TMath::Erfc((th   - mu) / sqrt(2.0) / sigma));
         cumulP += weight * (0.5 * TMath::Erfc((zmin - mu) / sqrt(2.0) / sigma) -
                             0.5 * TMath::Erfc((zmax - mu) / sqrt(2.0) / sigma));
 
         weight *= ( (NPE - k) / ((double) (k+1)) *
                     (1.0 - PunderAmplified) / PunderAmplified);
       }
 
       return cumulP / norm;
     }

double JDETECTOR::JPMTAnalogueSignalProcessor::getIntegralOfChargeProbability	(	JThresholdDomains	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 401 of file JPMTAnalogueSignalProcessor.hh.

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

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

inline

Set PMT parameters.

Parameters

parameters PMT parameters

Definition at line 421 of file JPMTAnalogueSignalProcessor.hh.

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

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

inlineoverridevirtual

Apply relative QE.

Returns: true if accepted; false if rejected

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 451 of file JPMTAnalogueSignalProcessor.hh.

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

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

inlineoverridevirtual

Get randomised time according transition time distribution.

Parameters

t_ns time [ns]

Returns: time [ns]

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 468 of file JPMTAnalogueSignalProcessor.hh.

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

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

inlineoverridevirtual

Compare (arrival times of) photo-electrons.

Parameters

first	first photo-electron
second	second photo-electron

Returns: true if arrival times of photo-electrons are within rise time of analogue pulses; else false

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 486 of file JPMTAnalogueSignalProcessor.hh.

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

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 498 of file JPMTAnalogueSignalProcessor.hh.

     {
       double q;
       do {
 
         // Determine which contribution to sample from
         int k = NPE;
         if (PunderAmplified > 0.0) {
 
           const double X = gRandom->Uniform();
           double weight  = pow(1.0 - PunderAmplified, NPE);
         
           for (double sum_p = 0.0; k > 0; --k) {
             
             sum_p += weight;
             if (sum_p > X) { break; }
             
             weight *= ( k / ((double) (NPE - (k-1))) *
                         PunderAmplified / (1.0 - PunderAmplified) );
           }
         } 
 
         // Sample from chosen contribution
         const double f     = gainSpread * gainSpread;
         const double mu    = ((NPE-k) * f * gain) + (k * gain);
         const double sigma = sqrt((NPE-k) * f + k) * getGainSpread(1);
 
         q = gRandom->Gaus(mu,sigma);
 
       } while (q < 0.0);
       
       return q;
     }

virtual double JDETECTOR::JPMTAnalogueSignalProcessor::getNPE	(	const double	tot_ns,
		const double	eps = `1.0e-3`
	)		const

inlinevirtual

Get number of photo-electrons.

Parameters

tot_ns	time over threshold [ns]
eps	precision

Returns: number of photo-electrons

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 540 of file JPMTAnalogueSignalProcessor.hh.

     {
       const double t = removeSaturation(tot_ns);
 
       double npe;
       if (t <= 2*getRiseTime(threshold/y1,threshold)) {   // Gaussian + Gaussian
         
         npe = threshold * exp(t*t/riseTime_ns/riseTime_ns/8.0);
         
       } else if (t <= (getRiseTime(getStartOfLinearisation(), threshold) +
                        getDecayTime(getStartOfLinearisation(), threshold))) {
                                                           // Gaussian + Exponential
 
         const double A = decayTime_ns;
         const double B = sqrt(2.0) * riseTime_ns;
         const double C = -(decayTime_ns*log(y1) + t);
         const double z = (-B + sqrt(B*B - 4*A*C)) / (2*A);
 
         npe = threshold * exp(z*z);
         
       } else {                                            // linear
 
         const double T = (getRiseTime(getStartOfLinearisation(), threshold) + 
                           getDecayTime(getStartOfLinearisation(), threshold));
                                 
         npe = getStartOfLinearisation() + (t - T) / slope;
       }
 
       return (npe <= MAX_CHARGE ? npe : MAX_CHARGE);
     }

virtual JThresholdDomains 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 579 of file JPMTAnalogueSignalProcessor.hh.

     {
       if (npe > threshold) {
 
         return ABOVE_THRESHOLD;
         
       } else if (npe > threshold - thresholdBand) {
 
         return IN_THRESHOLDBAND;
         
       } else {
 
         return BELOW_THRESHOLDBAND;
       }
     }

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 604 of file JPMTAnalogueSignalProcessor.hh.

     {
       if (slewing) {
 
         switch (applyThreshold(npe)) {
         case IN_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;
       }
     }

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 634 of file JPMTAnalogueSignalProcessor.hh.

     {
 
       switch (applyThreshold(npe)) {
       case IN_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);
       }}
     }

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 681 of file JPMTAnalogueSignalProcessor.hh.

     {
       switch(applyThreshold(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;
       }
     }

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 721 of file JPMTAnalogueSignalProcessor.hh.

     {
 
       const double PthBand  = getIntegralOfChargeProbability(IN_THRESHOLDBAND, NPE);
 
       const double npe      = getNPE(tot_ns);
       const double y        = getChargeProbability(npe, NPE);
       const double v        = getDerivative(npe);
       
       const double RthBand  = PthBand * TMath::Gaus(tot_ns, mean_ns, sigma_ns, kTRUE);
       const double RaboveTh = y * v;
 
       return RthBand + RaboveTh;
     }

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 745 of file JPMTAnalogueSignalProcessor.hh.

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

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

inlineoverridevirtual

Probability that a hit survives the simulation of the PMT.

Parameters

NPE	number of photo-electrons

Returns: probability

Reimplemented from JDETECTOR::JPMTSignalProcessorInterface.

Definition at line 764 of file JPMTAnalogueSignalProcessor.hh.

     {
       if        (QE <= 0.0) {
 
         return 0.0;
 
       } else if (QE <= 1.0) {
 
         double P = 0.0;
         
         const double f = gainSpread * gainSpread;
 
         for (int i = 1; i <= NPE; ++i) {
 
           const double p = (TMath::Binomial(NPE, i) *
                             TMath::Power(QE, i) * TMath::Power(1.0 - QE, NPE - i));
           
           double Ptotal = 0.0;
           double Pabove = 0.0;
           double weight = (PunderAmplified > 0.0 ? pow(PunderAmplified, i) : 1.0);
 
           for (int k = (PunderAmplified > 0.0 ? 0 : NPE); k <= NPE; ++k) {
 
             const double mu    = ((i-k) * f * gain) + (k * gain);
             const double sigma = sqrt((i-k) * f + k) * getGainSpread(1);
 
             Ptotal += weight * (0.5 * TMath::Erfc((      0.0 - mu) / sqrt(2.0) / sigma));
             Pabove += weight * (0.5 * TMath::Erfc((threshold - mu) / sqrt(2.0) / sigma));
 
             weight *= ( (i - k) / ((double) (k+1)) *
                         (1.0 - PunderAmplified) / PunderAmplified );
           }
 
           P += p*Pabove/Ptotal;
         }
         
         return P;
 
       } else {
 
         THROW(JValueOutOfRange, "JPMTAnalogueSignalProcessor::getSurvivalProbability: Invalid QE " << QE);
       }
     }

static double JDETECTOR::JPMTAnalogueSignalProcessor::getTH0 ( )

inlinestatic

Get lower threshold for rise time evaluation.

Returns: threshold [npe]

Definition at line 814 of file JPMTAnalogueSignalProcessor.hh.

     {
       return 0.1;
     }

static double JDETECTOR::JPMTAnalogueSignalProcessor::getTH1 ( )

inlinestatic

Get upper threshold for rise time evaluation.

Returns: threshold [npe]

Definition at line 825 of file JPMTAnalogueSignalProcessor.hh.

     {
       return 0.9;
     }

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

inlineinherited

Process hits.

Parameters

calibration	PMT calibration
input	PMT signals
output	PMT hits

Definition at line 103 of file JPMTSignalProcessorInterface.hh.

     {
       // apply transition time distribution to each photo-electron.
 
       buffer.clear();
       
       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)));
           }
         }
       }
 
       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) > BELOW_THRESHOLDBAND) {
             output.push_back(JPMTPulse(putTime(p->t_ns + getRiseTime(npe), calibration), getTimeOverThreshold(npe)));
           }
 
           p = q;
         }
         
         // merge overlapping PMT hits.
       
         merge(output);
       }
     }

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

Definition at line 294 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));
     }

static double JDETECTOR::JPMTSignalProcessorInterface::getTmin ( )

inlinestaticinherited

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

Returns: minimal time [ns]

Definition at line 380 of file JPMTSignalProcessorInterface.hh.

     {
       return 1.0;
     }

static double JDETECTOR::JPMTSignalProcessorInterface::getQmin ( )

inlinestaticinherited

Get minimal width of charge distribution.

Returns: minimal charge [npe]

Definition at line 391 of file JPMTSignalProcessorInterface.hh.

     {
       return 1.0e-3;
     }

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

inlineinherited

Get PMT parameters.

Returns: PMT parameters

Definition at line 111 of file JPMTParameters.hh.

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

bool JDETECTOR::JPMTParameters::is_valid ( ) const

inlineinherited

Check validity of PMT parameters.

Returns: true if valid; else false

Definition at line 133 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;
     }

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

inlinestaticinherited

Get equation parameters.

Returns: equation parameters

Definition at line 192 of file JPMTParameters.hh.

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

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

inlinestaticinherited

Set equation parameters.

Parameters

equation equation parameters

Definition at line 205 of file JPMTParameters.hh.

     {
       getEquationParameters() = equation;
     }

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

inlineinherited

Get properties of this class.

Parameters

equation equation parameters

Definition at line 216 of file JPMTParameters.hh.

     {
       return JPMTParametersHelper(*this, equation);
     }

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

inlineinherited

Get properties of this class.

Parameters

equation equation parameters

Definition at line 227 of file JPMTParameters.hh.

     {
       return JPMTParametersHelper(*this, equation);
     }

Friends And Related Function Documentation

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 436 of file JPMTAnalogueSignalProcessor.hh.

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

Member Data Documentation

double JDETECTOR::JPMTAnalogueSignalProcessor::decayTime_ns

protected

decay time [ns]

Definition at line 832 of file JPMTAnalogueSignalProcessor.hh.

double JDETECTOR::JPMTAnalogueSignalProcessor::t1

protected

time at match point [ns]

Definition at line 833 of file JPMTAnalogueSignalProcessor.hh.

double JDETECTOR::JPMTAnalogueSignalProcessor::y1

protected

amplitude at match point [npe]

Definition at line 834 of file JPMTAnalogueSignalProcessor.hh.

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 840 of file JPMTAnalogueSignalProcessor.hh.

double JDETECTOR::JPMTSignalProcessorInterface::MAX_CHARGE

protectedinherited

Maximum charge [npe].

Definition at line 398 of file JPMTSignalProcessorInterface.hh.

double JDETECTOR::JPMTParameters::QE

inherited

relative quantum efficiency

Definition at line 233 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::gain

inherited

gain [unit]

Definition at line 234 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::gainSpread

inherited

gain spread [unit]

Definition at line 235 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::riseTime_ns

inherited

rise time of analogue pulse [ns]

Definition at line 236 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::TTS_ns

inherited

transition time spread [ns]

Definition at line 237 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::threshold

inherited

threshold [npe]

Definition at line 238 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::PunderAmplified

inherited

probability of underamplified hit

Definition at line 239 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::thresholdBand

inherited

threshold-band [npe]

Definition at line 240 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::mean_ns

inherited

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

Definition at line 241 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::sigma_ns

inherited

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

Definition at line 242 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::slope

inherited

slope [ns/npe]

Definition at line 243 of file JPMTParameters.hh.

double JDETECTOR::JPMTParameters::saturation

inherited

saturation [ns]

Definition at line 244 of file JPMTParameters.hh.

bool JDETECTOR::JPMTParameters::slewing

inherited

time slewing of analogue signal

Definition at line 245 of file JPMTParameters.hh.

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

JPMTAnalogueSignalProcessor.hh

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Attributes

Friends

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation