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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. N detector = Constant (S/N) det  S. Shot Noise.

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signal to noise optimization

Signal-to-Noise Optimization

Noise Sources Most Commonly Encountered

1. Detector Noise

2. Shot Noise

3. Flicker Noise

detector 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

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.

n shot 2se f

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 n shot 2se f s n shot s 2e f

S

(S/N)shot = √2SeΔf(S/N)shot = √S/2eΔf

Δf  1/tc

where tc = time constant

So

(S/N)shot  √Stc

flicker noise

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.

n flicker s

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

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

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

slide14

S

S/N

N

other noise sources such as environmental noise should always be eliminated

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.