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 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  √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 = √2SeΔf (S/N) shot = √S/2eΔf Δf  1/t c where t c = time constant So (S/N) shot  √St c S

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 = 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  √St c (S/N) det  S

determine the slope (m) 1. m = 1 → Detector Noise 2. m = ½ → Shot Noise 3. m = 0 → Flicker Noise Prepare a plot of log(S) vs. log(S/N)

S/N N S

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. Other noise sources such as environmental noise should always be eliminated.