Contrast in the FCPM

• The efficiency of light absorption is determined by the angle between the polarization of incident light and the direction of the absorption transition dipole of the dye molecule. The intensity of detected light depends on the angle between the polarization direction of the polarizer and the emission transition dipole of the dye.

• Suppose, the transition dipole (both for excitation and fluorescence) of the dye molecule is parallel to n. Light (blue sinusoidal line) with linear polarization P parallel to n excites a fluorescent signal (red sinusoidal line) of the same polarization and some amplitude I₀. If n is perpendicular to P, the fluorescence signal vanishes, (b and c). For an intermediate angle 0<α<π/2 between P and the transition dipole, the intensity of fluorescent light is intermediate between I₀ and zero, (d).

IFCPM ~ I0cos4α

Why       I_FCPM ~ I₀cos⁴α      ?????

The efficiencies of both absorption I_abs and fluorescence I_em at some small woxel characterized by spatial coordinate r are proportional to the scalar product of the two vectors, the transition dipole d || n and electric field of light wave E || P:

For used dyes the fluorescence lifetime τ_f ~ 1ns
For most LCs the rotational diffusion time τ_D  ~ 10ns

Since τ_D > τ_f, the FCPM signal is:

I_FCPM ~ I₀cos⁴α