Christoph Florian Schaller - FU Berlin, FB MI

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Christoph Schaller - STORMicroscopy 20 Additionally we veriy that the average error caused by numerical integration tting is independent of the position of the spot center within the pixel now. This can be seen in Figure 4.6. We add a Poisson distributed background noise with an average of 130 photons per pixel, all other parameters remain unchanged. Figure 4.6: Average error according to spot diameter, pixel size 100 nm, 10000 photons, average of 130 photons/pixel background noise. Figure 4.7: Average error according to photon number, pixel size 100 nm, spot diameter 500 nm, average of 130 photons/pixel background noise. Finally we have a look at the relation of the average error and the photon number. We choose a constant spot size of 500 nm for which both algorithms are performing ne when using the common pixel size of 100 nm. Then we generate 2000 images for several photon numbers and add an average of 130 photons per pixel background noise. In Figure 4.7 we obtain decreasing errors for both algorithms, however the numerical integration tting again performs better. Especially it ts the expected N −1/2 -dependancy very well, resulting in an average error converging straight to zero in contrast to the Gaussian mask t. 4.4 Quantication of occuring shifts caused by pixelation In Chapter 3.2 we analyzed the occuring systematic errors due to pixelation in the extreme case of tting the perfect Gaussian distribution, which equals the limit of observing an innite number of photons stemming from one spot. Now we want to x dierent photon numbers and analyze the occuring shifts. Thus for every xed photon number we generate 200 equally distributed spot centers and 200 STORM images respectively (40.000 STORM images altogether) and t those. To increase the number of samples we consider x- and y-coordinate as independent, which is reasonable because a 2D Gaussian is only the combination of 1D Gaussians in each coordinate direction. Then we calculate the 1D shifts towards the spot center. Last but not least we need to be sure, which part of the error is caused by pixelation. Therefore we apply numerical integrations as a cross-check to the Gaussian mask ts. The results for a spot size of 500 nm and a pixel size of 100 nm, for which both algorithms are performing ne, can be found in Figure 4.8 on the next page. No background noise is added here as it would only make our results less clear. We observe that the shifts for the NI algorithm are centered around 0, while the GM ts are unambiguously biased in direction of the spot center. As expected the distribution becomes less broad for an increasing photon number.
Christoph Schaller - STORMicroscopy 21 Figure 4.8: Distribution of 1D shifts, spot size 500 nm, pixel size 100 nm, no background noise.
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Christoph Florian Schaller - FU Berlin, FB MI

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