Photomultiplier detection system
DC operation (contiuous light beam) AC operation (chopped light beam)
[Cell definitions and equations] [Student assignment handout] [OpenOffice and Excel Version]
[Cell definitions and equations] [Student assignment handout] [OpenOffice and Excel Version]
A simulation of measurement of light intensity by a photomultiplier tube (PMT). Includes the effect of load resistance, integration time, wavelength, light flux, applied voltage, and phototube temperature on signal and signal-to-noise ratio of light intensity measurement with photomultiplier tubes. Students compare difference types of phototubes, measure spectral characteristic, observe effects of amplifier overload, display resolution limits, phototube overload, determine lowest flux that can be measured, attempt to improve the SNR by cooling the phototube. There are versions for DC operation (with a continuous light beam) and AC operation (with a chopped light beam). The DC version shows the signal and signal-to-noise ratio numerically; the AC version shows the signal and signal-to-noise ratio graphically.
When used in a lecture-demonstration environment with a computer video projection system, where it is often difficult to use the keyboard data entry in a darkened room, these models can be operated using only the mouse-activated on-screen sliders, pop-up menus, and radio buttons.
Download links.
WingZ versions:
DC operation (with a continuous light beam):
pmtDC.wkz;
AC operation (with a chopped light beam):
pmtAC.wkz.
Wingz player application and basic set of simulation modules, for
windows PCs or Macintosh
OpenOffice and Excel Version
Other simulations that employ a photomultiplier detection system:
Signal-to-noise ratio of absorption spectrophotometry
Fluorescence Spectroscopy Signal-to-Noise Ratio
Comparison of Calibration Curve Fitting Methods in Absorption Spectroscopy
Effect of Slit Width on Signal-to-Noise Ratio in Absorption Spectroscopy
Scanning Fluorescence Spectrometer
U.V.-Visible Spectrophotometer
Dual Wavelength Spectrophotometer
Effect of Slit Width on Emission Spectroscopy SNR
Spectroscopy of Atomic Absorption
References:
Photomultiplier handbook (PDF format)
Getting the best out of photomultiplier detectors (PDF format)
Building your own photomultiplier system
Inputs (table below display portion of the spreadsheet):
lambda wavelength, nm (controlled by on-screen slider)
Phi radiant flux, watts (controlled by on-screen slider)
flicfac flicker factor (0-1) (controlled by on-screen slider)
Kmax Max. Klam
LamMax Max. wavelength
block 1=on 0=off
k number of stages
V total applied voltage, volts (controlled by on-screen slider)
Klam quantum efficiency at lambda
Ec cathode work function, Joule
eta collection efficiency
excess excess noise current, amps
RL Load resistance, ohms (controlled by on-screen pop-up menu)
t integration time, sec (controlled by on-screen pop-up menu)
Tr Temperature (K) of load resistor
Tc Temperature (K) of photocathode (controlled by on-screen slider)
Ac Area of photocathode, cm2
C thermionic constant
Calculated quantities: freq =(2.998E+17)/lambda Hz E =(6.6261E-34)*freq Joule Flux =Phi/E electrons/sec Klam =Kmax*exp(-((lambda-LamMax)/thresh*3.5)^2) quantum efficiency at lambda Vd =V/k voltage per dynode, volts m =g^k multiplication factor rcp =Klam*Flux*block photoelectron emission rate rt =ict/1.602E-19 cathode thermionic emission rate Rlam =(Klam*1.602E-19)/E radiant cathode responsivity (amps/watt) g =0.17*Vd^0.7 gain per stage ic =rcp*1.602E-19*block cathode photocurrent ia =eta*m*Rlam*Phi*block anode photocurrent ict =C*Ac*Tc*Tc*exp(-Ec/(Tc*1.3805E-23)) cathode thermionic current iat =ict*m*eta anode thermionic (dark) current Es =RL*(ia+iat) signal voltage alpha =1/(g-1)~ secondary emission factor deltaf =1/(2*t)~ noise bandwidth, Hz sigmai =sqrt(2*1.602E-19*(1+alpha)*m*ia*deltaf) photosignal shot noise current sigmat =sqrt(2*1.602E-19*(1+alpha)*m*iat*deltaf) thermionic shot noise current sigmad =sqrt(sigmat^2+excess^2) total dark noise current sigma =sqrt(sigmad^2+sigmai^2) total shot noise current sigmaJ =sqrt(4*1.38E-23*Tr*RL*deltaf) Johnson noise voltage sigman =sqrt((RL*sigma)^2+sigmaJ^2+sigmaf^2) total noise voltage sigmav =RL*sigma total shot noise voltage sigmaf =flicfac*(Es-iat*RL) flicker noise voltage (displayed) SNR =ia*RL/sigman signal-to-noise ratio (displayed) sigmadt =sqrt((RL*sigmad)^2+sigmaJ^2) total dark noise voltage (displayed) thresh =6.626E-34*29980000000*10000000/Ec long wavelength threshold, nm Display (DC System): Signal Voltage=Es+sigman*2*(rand()-rand()+rand()-rand()+rand()-rand()) Noise Voltage = sigman SNR = SNR flicker noise = sigmaf photon noise = sigmai*RL dark noise = sigmadt Sheet script: on recalc if ia > .001 put "Anode current exceeds 1 mA maximum; phototube may be damaged by excessive current." into B1 else put " " into B1 end if if ic > .000001 put "Cathode current exceeds 1 ľA maximum; phototube may exhibit fatigue." into B2 else put " " into B2 end if if lambda > thresh put 0 into block else put 1 into block end if end recalc on idle put count+2 into count if count = 10 recalc range H2 if signal > 10 put 10 into H4 else put signal into H4 end if put 0 into count end if end idle
Student handout (WingZ Version)
Light Measurement with Photomultiplier Tubes
Computes the detector signal current and signal-to-noise ratio, given the phototube characteristics and the incident light power (watts) on the photocathode. Includes source flicker, photon, and thermionic emission noise.
Assumptions: Quantum efficiency of photocathode, gain per stage, and collection efficiency are independent of light level and detector current.
View Equations (.pdf)
Download spreadsheet in OpenOffice format (.ods)
Download spreadsheet in Excel format (.xls)