Modeling of Photochemical Reactions in a Focused Laser Beam

Fluorescent materials play a prominent role in the qualitative and quantitative measurement of scientific phenomena of importance in biotechnology and biomedical applications. Photodegradation of fluorophores is a process that determines the accuracy and sensitivity of such measurements. This is the motivation for developing methods for accurately measuring fluorophore photodegradation rates. Recently, illumination consisting of short pulses has been used to examine the decay of photochemical reaction products. However, the time resolved measurements are difficult to interpret since the photodegradation process usually involves multiple time scales. The frequency domain measurement technique discussed here looks at the frequency response of a fluorescent sample to a frequency modulated illuminating light. The photodegradation rate is obtained by interpreting the frequency domain measurements in terms of traditional impedance concepts. In the measurements described in this paper, a focused laser beam is used to illuminate a sample of slowly flowing fluorescent solution. The laser beam is assumed to have a Gaussian power distribution hence illumination is spatially non-uniform in the region of interest. The photochemical reaction rates depend on power, so they will also vary with the position in the beam. However in the case of photodegradation of fluorophores, the measurement of the resulting decrease in fluorescence is given in terms of the radiation emitted from the entire illuminated region. In this work we present a mathematical description of the time evolution of the fluorescence response integrated over a non-uniformly illuminated domain. As a result of our analysis, an experimentally accessible and tractable mathematical model Eq. (19) and Eq. (30) is obtained from a more fundamental description given by Eq. (4) and Eq. (5). The model is used to create a functional form for fitting experimental measurements from a lock-in amplifier.