Signal-to-Noise Optimization
Noise Sources Most Commonly Encountered
1. Detector Noise
2. Shot Noise
3. Flicker Noise
Detector Noise
Associated only with the detector, and
therefore constant for a given set of detector
conditions.
Ndetector = Constant
(S/N)det  S
Shot Noise
Noise associated with the random transfer of
electrons across a p-n junction.
Ex: Whether or not a single photon falling on a
detector will actually produce a signal.
Nshot  √2SeΔf
Where:
S = measured signal
e = charge on electron
Δf = frequency bandwidth
Shot noise is usually the limiting source of
noise near the detection limit
S
(S/N)shot = √2SeΔf
(S/N)shot = √S/2eΔf
Δf  1/tc
where tc = time constant
So
(S/N)shot  √Stc
Flicker Noise
Random noise with a 1/f frequency
dependence.
f = sampling frequency
Flicker noise includes slow drifts in signal
intensity caused by such parameters as
temperature, flow rates, etc.
Nflicker = ξ S
where ξ = flicker factor (unit-less)
(S/N)fl = S/ξS = 1/ξ
ξ  1/f
so (S/N)fl  f
and f = frequency of data collection
How do we determine which
type of noise is present?
(S/N)fl = 1/ξ
(S/N)shot  √Stc
(S/N)det  S
Prepare a plot of log(S) vs. log(S/N)
determine the slope (m)
1. m = 1 → Detector Noise
2. m = ½ → Shot Noise
3. m = 0 → Flicker Noise
C
S
N
S /N
lo g S
lo g S /N
0 .0
1 .0
4 .0
6 .5
8 .0
1 0 .0
1 2 .0
1 5 .0
1 8 .0
2 2 .0
2 5 .0
2 7 .0
2 9 .0
3 1 .0
1 0 .1
1 9 .0
4 6 .5
6 6 .5
8 0 .8
9 6 .9
1 1 7 .1
1 4 0 .6
1 6 9 .7
2 0 3 .7
2 2 7 .7
2 4 5 .0
2 6 3 .2
2 8 3 .5
0 .0 1 7 0
0 .0 2 4 0
0 .0 3 7 1
0 .0 4 5 5
0 .0 4 7 2
0 .0 5 1 2
0 .0 5 6 1
0 .0 6 0 8
0 .0 7 2 3
0 .0 8 6 8
0 .0 9 6 1
0 .1 0 5 3
0 .1 1 1 7
0 .1 2 1 6
591
790
1252
1463
1712
1895
2089
2313
2348
2347
2368
2326
2356
2331
1 .0 0
1 .2 8
1 .6 7
1 .8 2
1 .9 1
1 .9 9
2 .0 7
2 .1 5
2 .2 3
2 .3 1
2 .3 6
2 .3 9
2 .4 2
2 .4 5
2 .7 7 1
2 .8 9 8
3 .0 9 8
3 .1 6 5
3 .2 3 4
3 .2 7 8
3 .3 2 0
3 .3 6 4
3 .3 7 1
3 .3 7 0
3 .3 7 4
3 .3 6 7
3 .3 7 2
3 .3 6 8
3 .5
y = -0 .0 0 9 5 x + 3 .3 9 2 8
3 .4
3 .3
3 .2
lo g (S /N )
3 .1
y = 0 .5 1 1 x + 2 .2 5 0 6
3 .0
2 .9
2 .8
2 .7
2 .6
2 .5
1 .0
1 .2
1 .4
1 .6
1 .8
lo g S
2 .0
2 .2
2 .4
S
S/N
N
Other noise sources such as environmental
noise should always be eliminated.
When we measure N experimentally, it is
often a combination of all of the noises present
in the system. The preceding equations are
useful to determine which type of noise
dominates in a certain situation.