Theory of differential phase fluorometry: Detection of anisotropic molecular rotations

A general description of transformations in the excited state is employed to derive the general equations for the differential delay and the modulation ratio of the fluorescence owing to different pairs of excited species present. These equations yield directly the differential delay and the modulation ratio of the polarized components of the fluorescence from a rotating spherical molecule. Similar equations for a rotating irregular molecule are then derived from the sine and cosine transforms of the impulse response of the polarized components of the fluorescence emission. It is shown that for excitation at a wavelength at which the limiting polarization is high, namely, 1/2 to 3/11, the maximum differential tangent observed for anisotropic rotations is uniformly lower than the value for the sphere. The magnitude of this tangent defect permits an estimate of the minimum standard deviation of the principal rotational rates of the ellipsoid of inertia that describes the rotations of the molecule.