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

I_{abs}\propto\left(\vec{M}_{abs} \vec{E}_0\right)^2=\left(\left|\vec{M}_{abs}\right|\left|\vec{E}_0\right|cos\left(\zeta\right)\right)^2

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

I_{det}=I_{abs}\left(\vec{M}_{em} P\right)^2=I_{abs}\left(\left|\vec{M}_{abs}\right|\left|\vec{E}\right|\cos^2\left(\zeta'\right)\right)

With \zeta = \zeta' follows

I_{det}=\left(\left|\vec{M}_{abs}\right|\left|\vec{M}_{em}\right|\left|\vec{E}_0\right|\left|\vec{E}\right|\right)^2\cdot \cos^4\left(\zeta\right)

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

I_{det}\propto \cos^4\left(\zeta\right)