## Abstract

An overlap term is used in fluorescence theory to account for the spectrally distributed interaction between laser radiation and molecular transitions. We present a dimensionless overlap fraction formulation. Compared with the more common dimensional overlap term [in units of inverse wave number (1/cm^{−1})], this form of expression of the interaction between a laser and an absorption transition has a much more practical interpretation and simplifies the equations that describe fluorescence measurements.

© 1995 Optical Society of America

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### Equations (5)

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(1)
$$D(\mathrm{\nu})=S{\left\{1+{\left[\frac{2(\mathrm{\nu}-{\mathrm{\nu}}_{0})}{\mathrm{\Delta}\mathrm{\nu}}\right]}^{2}\right\}}^{-1},$$
(2)
$${I}_{\mathrm{\nu}}(\mathrm{\nu},t)={{I}_{\mathrm{\nu}}}^{0}{T}_{L}(t){L}_{L}(\mathrm{\nu}),$$
(3)
$${{I}_{\mathrm{\nu}}}^{0}=\frac{1}{\mathrm{\Delta}{\mathrm{\nu}}_{L}\mathrm{\Delta}{t}_{L}}{\int}_{-\infty}^{+\infty}{\int}_{-\infty}^{+\infty}{I}_{\mathrm{\nu}}(\mathrm{\nu},t)\text{d}\mathrm{\nu}\text{d}t,$$
(4)
$${{I}_{\mathrm{\nu}}}^{0}=\frac{{P}_{L}}{{A}_{L}{R}_{L}\mathrm{\Delta}{\mathrm{\nu}}_{L}\mathrm{\Delta}{t}_{L}}=\frac{{E}_{L}}{{A}_{L}\mathrm{\Delta}{\mathrm{\nu}}_{L}\mathrm{\Delta}{t}_{L}}.$$
(5)
$${\mathrm{\Gamma}}_{lu,L}={\int}_{-\infty}^{+\infty}{Y}_{A}(\mathrm{\nu}){L}_{L}(\mathrm{\nu})\text{d}\mathrm{\nu},$$