Confocal Microscopy in Solution

The detection threshold for this experiment will depend on Pi, the probability that a molecule is present in the probe volume. Taking an analyte concentration of 10 mol 1 , the probability that a molecule is found in the probe volume is 0.0014. The threshold for optimum single molecule detection is 

While the signal-to-noise ratio is similar for this experiment and that of Hirsch-feld, the probability of both a false alarm and a miss is much higher in the confocal microscopy case. The difference reflects the behavior of the Poisson distributed data for small numbers of counts. With a small mean number of photons emitted by a molecule, there is a relatively high probability that the molecule will not emit enough photons to exceed the threshold. 

we can compute thresholds and error rates. Again assuming an analyte concentration of 10 moll Pi becomes 0.36. The threshold is then 

It is interesting that the error rates are much lower for the large sample volume. In this case, the error rates drop because the fluorescence signal is sufficiently large to 

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