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Photomultiplier detection system


DC operation (contiuous light beam)              AC operation (chopped light beam)

[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

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References:
Photomultiplier handbook (PDF format)
Getting the best out of photomultiplier detectors (PDF format)
Building your own photomultiplier system


Spreadsheet cell definitions and equations:

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

1. Download the WingZ player application as described above. Launch wingz.exe, then open pmtDC.WKZ.

2. Select Photomultiplier 1, 1 Megohm load resistance, and 1 sec integration time from the pop-up menus (right side of screen). Using the slider controls, set the wavelength to 300 nm, light flux Phi to 10-9 watts (e.g. log(Phi) = -9), percent flicker to .1%, the applied voltage to 800 volts, and the phototube temperature to 300 K.

3. Select different values of load resistor. Note the effect on the signal voltage and noise voltage. The amplifier saturates at 10 volts, so the load resistor must not be so high as to exceed this value. On the other hand, the readout display has a resolution of only 0.001 volt; so the load resistor must not be so low that the

display resolution is a limitation. Does the load resistor have a significant effect on the signal-to-noise ratio (SNR)? Why or why not?

4. Vary the applied voltage. (Select the load resistor as required to make the signal voltage as large as possible without exceeding the saturation level of the amplifier). Does the applied voltage have a significant effect on the signal level? On the SNR? Why or why not?

5. What is the lowest flux F that can be measured by this phototube with an SNR of 3; choose the applied voltage and load resistance in an attempt to improve the SNR as much as possible. Select Photomultiplier 2 and repeat. How does this tube differ from the first one in terms of gain and low light level performance?

6. What is the longest wavelength that can be measured by this phototube (the long wavelength threshold)? Explain. Calculate the cathode work function, in Joules.

7. Can you improve the SNR by cooling the tube (reducing the phototube temperature)? Explain the observed effect.

8. Select Photomultiplier 3 and repeat steps 6 and 7. Why is this phototube called a red sensitive tube? How does cooling the tube effect this tube? Why?

OpenOffice Calc and Excel Versions


Click to see larger graphic

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)


(c) 1991, 2008, Prof. Tom O'Haver , Professor Emeritus, The University of Maryland at College Park. Comments, suggestions and questions should be directed to Prof. O'Haver at toh@umd.edu. Number of unique visits since May 17, 2008: