Another look at magic-angle-detected fluorescence and emission anisotropy decays in fluorescence microscopy.

It is shown that in contrast to a traditional fluorescence spectroscopy with the parallel beams of light, in which the kinetic fluorescence decays are collected at the so-called magic-angle of thetamag=54.7 degrees, in the fluorescence microscopy, the value of the magic-angle depends on the numerical aperture (NA) of a microscope objective and on the refractive index (n) of an immersion liquid used. Two methods enabling the determination of the magic-angle values corresponding to different values of NA/n, are discussed. It is shown that thetamag changes from a value of 54.7 degrees at the NA/n-->0, to a value of 45 degrees with NA/n-->1. Also in contrast to a traditional fluorescence spectroscopy, in the fluorescence microscopy the term I parallel(t)+2I perpendicular (t) does not represent the total fluorescence intensity Itot(t), because the resulting fluorescence decay I parallel(t)+2I perpendicular (t) is contributed by the dynamic evolution of excited fluorophores. A correctly defined total fluorescence intensity solely represents the kinetic evolution of excited fluorophores, and in the fluorescence microscopy it equals Itot(t)=3Imag(t), where Imag(t) represents the fluorescence intensity detected at thetamag corresponding to a particular NA/n value. If the correct (true) decay of Itot(t) is substituted into the denominator in the expression for the emission anisotropy r(t), r(t) is a (multi)exponential function of time and it accounts for the high-aperture excitation-detection conditions.