# Concerning Mie scattering and phase function dependance

In general, scattering intensity is written as $I = I_{0} \frac{\pi a^2 Q_{sca} P(\theta)}{r^2 4 \pi}$

It is also written as $I = I_{0} \frac{i_1 + i_2}{2 k^2 r^2}$

I am sort of confused, given the expressions of $i_1$ and $i_2$, is the phase function $P(\theta)$ ONLY dependant on the scattering angle $\theta$?

It is my understanding that the scattering efficiency $Q_{sca}$ incorporates depends on index of refraction, sphere size and wavelength, but the phase function only depends on the scattering angle. Is my understanding correct?

$$I = \underbrace{|{\boldsymbol E}|^2}_{\mathrm{total\,\,\, measured \,\,\,field}} = I_0 \frac{\pi a^2 Q_{\mathrm{sca}} P(\theta)}{4 \pi r^2}$$
$$I_{\mathrm{measured}} = \left| \sum\limits_k {\boldsymbol E}_k + {\boldsymbol E}_{\mathrm{res}}\right|^2$$
for $k$ scatter centers, which makes the problem more computationally taxing. I don't remember if the incoming beam also interferes, but there is some residual effects $({\boldsymbol E}_{\mathrm{res}})$ in the environment. Perhaps this answer will help.