Photomultiplier detection system
DC operation (contiuous light beam) AC operation (chopped light beam)
[Cell definitions and equations] [Student assignment handout]
[Cell definitions and equations] [Student assignment handout]
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 continous 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-activitated on-screen sliders, pop-up menus, and radio buttons.
Download links: pmtDC.wkz; pmtAC.wkz.
Wingz player application and basic set of simulation modules, for
windows PCs or Macintosh
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
Light Measurement with Photomultiplier Tubes
An Interactive Computer Simulation
1. 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?