Mathematics

The calculation of the cross-section is done using a PiMieScatt library. It uses Mie theory to determine the effeciences and cross-section using the dielectric functions of the metals. There is an automatic determination weither to use rayleigh based on the size of the particle.

Calculation cross-section

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are \[x = {-b \pm \sqrt{b^2-4ac} \over 2a}.\]

Beer lambert adaptation

To determine the transmission and scattering intensities, the Beer-lambert equations are adapted as follows: \[ I_{trans} = I_0 \, e^{\sigma_{ext} \, n \, x} \] \[ I_{scatt} = \frac{1}{2} \,\beta \,I_0 \,\frac{\sigma_{sca}}{\sigma_{ext}} (1-e^{-2 \, \sigma_{ext} \, n \, x}) \]

Dielectric functions