Christoph Florian Schaller - FU Berlin, FB MI

Christoph Schaller - STORMicroscopy 19
Finally we try to conrm the dependency of
the average error on the number of photons in a
spot in the form △x ∼ √ 1
N
for large enough N,
which we introduced in Chapter 3.1, see (3.3).
Our simulation results seem to agree with the
estimated proportionality in the logarithmic plot
in Figure 4.4 pretty well at rst, however the
decay is damped and thus the average error does
not converge to zero.
Figure 4.4: Average error according to photon number,
pixel size 100 nm, spot diameter 500 nm, average
of 130 photons/pixel background noise.
4.3 Eect of numerical integrations
As we hope to avoid unnecessary approximations, we use random generated data with known spot
centers to check whether our algorithm is more precise, i.e. yields a t that is signicantly closer to
the true center. First, we x the number of photons at 10000 and generate 1000 frames respectively
for the occuring spot sizes. The pixel size is kept at 100 nm, the background noise is set to zero here
as we want to compare with the minimal possible error, i.e. the error caused by coarse- and niteness
of the data, which is according to (3.3) given by
〈△x min 〉 =
√
σ 2 + a2
12
N .
In Figure 4.5 we observe that at least 10%
of the error can be avoided by using numerical
integration tting. Especially at small spot sizes
the algorithm outperforms the Gaussian mask t
as the error keeps linearly decreasing here. This
agrees with the theory, even if the error is still
larger than the unavoidable one.
Figure 4.5: Average error according to spot diameter,
pixel size 100 nm, 10000 photons, no background
noise.