Dark noise
Dark noise is due to the generation of thermal dark electrons
N
d
, irrespective of whether the sensor is irradiated. N
d
sta-
tistically fluctuates about
N
d
. Dark noise is specified for a
PMT voltage of 1000 V; with lower voltages it progressively
loses significance.
Dark noise can be reduced by cooling the sensor. However,
the reduction is significant only if N
≤
N
d
, e.g. in object-free
areas of a fluorescence specimen. In addition, the dark noise
must be the dominating noise source in order that cooling
effects a signal improvement; in most applications, this will
not be the case.
Additional sources of noise to be considered are amplifier
noise in sensor diodes and readout noise in CCD sensors. In
the present context, these are left out of consideration.
The mean square deviation
∆
N from the average (N + N
d
) of
the photoelectrons and dark electrons registered,
so that the total signal-to-noise ratio can be given as
where
N
= number of photoelectrons per pixel time
(sampling time)
se
= multiplication noise factor of secondary emission
q
= peak-to-peak noise factor of the laser
N
d
= number of dark electrons in the pixel or sampling time
Example:
For N =1000, N
d
=100, se = 1.2, and q = 0.05
Sources of noise effective in the LSM exist everywhere in the
signal chain – from the laser unit right up to A/D conversion.
Essentially, four sources of noise can be distinguished:
Laser noise q
Laser noise is caused by random fluctuations in the filling of
excited states in the laser medium. Laser noise is propor-
tional to the signal amplitude N and therefore significant
where a great number of photons (N < 10000) are detected.
Shot noise (Poisson noise)
This is caused by the quantum nature of light. Photons with
the energy
h
·
υ
hit the sensor at randomly distributed time
intervals. The effective random distribution is known as
Poisson distribution. Hence,
where N = number of photons detected per pixel time
(= photoelectrons = electrons released from the PMT cathode
by incident photons). With low photoelectron numbers
(N < 1000), the number N of photons incident on the sensor
can only be determined with a certainty of
±
N
.
N can be computed as
where QE (
λ
)
= quantum yield of the sensor at wavelength
λ
;
1 photon = h·c/
λ
; c = light velocity; h = Planck’s constant
Secondary emission noise
Caused by the random variation of photoelectron multipli-
cation at the dynodes of a PMT. The amplitude of secondary
emission noise is a factor between 1.1 and 1.25, depending
on the dynode system and the high voltage applied (gain).
Generally, the higher the PMT voltage, the lower the sec-
ondary emission noise; a higher voltage across the dynodes
improves the collecting efficiency and reduces the statistical
behavior of multiplication.
V
Sources of Noise
Details
SNR
≈
N
Poisson
= N
N =
photons
QE
(
)
.
pixel time
N
= se
.
(N+N
d
) (1+q
2
)
SNR =
N
2
se
2
(N+N
d
) (1+q
2
)
SNR =
1000
2
1.2
2
(1000+100) (1+0.05
2
)
= 25.1
337_Grundlagen_Infoboxen_e 25.09.2003 16:17 Uhr Seite 5
