Physics and Engineering of Radiation Detection

6.5. Photodetectors 397

In the two subsequent sections we will look at the theoretical considerations
of the signal-to-noise ratio computations in the analog and digital modes of PMT
operation.

A.17NoiseinAnalogMode

We saw earlier that in analog mode of operation, an average photoelectric current
is measured at the anode. The measured average photocurrent also has an AC shot
noise component superimposed on its instantaneous value. There are several factors
that contribute to this noise, the most important of which are described below.

Statistical Fluctuations: The production of photoelectrons in the photo-

cathode, like all other quantum mechanical processes, has certain statistical

uncertainty. This implies that, even if we shine the PMT with monochro-

matic light having constant intensity, the production rate of photoelectrons will

have some fluctuations characterized by the probabilistic nature of the process.

Furthermore, the multiplication of these photoelectrons also has statistical un-

certainty associated with it. These two fluctuations introduce uncertainty or

noisein the system. The shot noise currentσstcorresponding to the overall

statistical fluctuations in the photocathode and the dynodes can be written as

σst=μ

√

2 eIpeFB. (6.5.24)

Hereμis the PMT gain,Ipeis the photoelectric current,Bis the bandwidth

of the measuring electroncis, andF is the PMT noise figure, which can be

calculated for a PMT havingndynodes with individual gainsδiwithi=1, ..., n

by

F=1+

1

δ 1

+

1

δ 1 .δ 2

+.....+

1

δ 1 .......δn

. (6.5.25)

A point worth stressing here is thatIpeshould not be confused with the anode

current since it represents the photoelectric current, that is, the total charge

being produced by the photocathode and collected by the first dynode per unit

time. The termsF,B,andμtransform this current into the anode current.

The photoelectric current can be obtained from the relation

Ipe=Nγe(QE)(CE), (6.5.26)

whereNγis the number of photons incident on the photocathode per unit time,

eis the electronic charge,QEis the quantum efficiency of the photocathode,

andCEis the collection efficiency of the first dynode.

Background Light: Photomultiplier tubes are very sensitive devices and

therefore unless the system has been made extremely light tight, there are

always some background photons contributing to the signal. The correspond-

ing shot noise can be written as

σbg=μ

√

2 eIbgFB. (6.5.27)