Huang’s defocusing model

An alternative model of the defocusing curves is described by Huang et al. [1]. The relationship between the axial position of a molecule and its imaged widths along two perpendicular axes is given by

\displaystyle\sigma_{1}\left(z\right) \displaystyle= \displaystyle\frac{w_{01}}{2}\,\sqrt{1+\left(\frac{z-c_{1}}{d_{1}}\right)+a_{1% }\left(\frac{z-c_{1}}{d_{1}}\right)^{2}+b_{1}\left(\frac{z-c_{1}}{d_{1}}\right% )^{4}}\,,
\displaystyle\sigma_{2}\left(z\right) \displaystyle= \displaystyle\frac{w_{02}}{2}\,\sqrt{1+\left(\frac{z-c_{2}}{d_{2}}\right)+a_{2% }\left(\frac{z-c_{2}}{d_{2}}\right)^{2}+b_{2}\left(\frac{z-c_{2}}{d_{2}}\right% )^{4}}\,.

Here w_{01},a_{1},b_{1},c_{1},d_{1} and w_{02},a_{2},b_{2},c_{2},d_{2} are unknown parameters of the model which can be determined by the calibration process.

References

  • [1] B. Huang, W. Wang, M. Bates and X. Zhuang(2008) Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, Science 319 (5864), pp. 810–3. External Links: Document. Cited by: Huang’s defocusing model.