Polynomial defocusing model

The default model used in ThunderSTORM describes the relationship between the axial position of a molecule and its imaged widths along two perpendicular axes by a pair of second degree polynomials

\displaystyle\sigma_{1}\left(z\right) \displaystyle= \displaystyle a_{1}\left(z-c_{1}\right)^{2}+b_{1}\,,
\displaystyle\sigma_{2}\left(z\right) \displaystyle= \displaystyle a_{2}\left(z-c_{2}\right)^{2}+b_{2}\,.

Here a_{1},b_{1},c_{1} and a_{2},b_{2},c_{2} are unknown parameters of the model which can be determined by the calibration process.