The angle dependency in FCPM

Assuming the transition dipole moments for absorption $\vec{M}_{abs}$ and emission $\vec{M}_{em}$ are parallel to the long axis of dye molecules and the excitation light $\vec{E}_0$ is linearly polarized, the absorbed light intensity is given by

Assuming further that the rotational relaxation time $\tau_{rot}$ of the dye is slow compared to the lifetime $\tau_{excite}$ of the excited state, the orientation $\zeta'$ of dye during re-emittance of light can be considered identical to the orientation $\zeta$ during absorption.  The detectable light intensity is then given by

With $\zeta = \zeta'$ follows

In consequence, the detectable light intensity scales with the angle $\zeta$ between the excitation light and the transition dipole moment $\vec{M}$ over the relation