Analytical relations for luminescence intensities accounting for reabsorption

Abstract

Mathematical relations defining distortions from true values of photoluminescence intensities that arise during measurements due to absorption at the luminescence frequencies are derived for various experimental designs. The adequacy of the derived relations is confirmed by special experiments. The relations allow one to define correctly the contours, widths, and maximum frequencies of luminescence bands of absorbing media and to deduce absorption coefficients of substances from luminescence measurements.Introduction. Luminescent methods are commonly used to solve scientific and practical problems [1,2]. A mathematical relation describing the law of formation of a photoluminescence (PL) spectrum of each of the components in a substance that have overlapping absorbance bands was obtained without limitations on the optical density [3]. The resulting relation makes it possible to determine absorption coefficients of components (including those without luminescence), absorption contours, and ratios of PL quantum yields. Use of these capabilities requires measurements of actual PL intensities, which may be made in relative units. However, they should not be distorted by any associated factors, for example, absorption in the PL frequency range.PL and absorption bands of different components and a single component may overlap under actual conditions of scientific research and analytical measurements although the total optical density of absorption is not negligible compared with unity. Under such conditions the measured PL intensity does not correspond to the true intensity. Therefore, absorption may produce errors in the determination of contours, central frequencies of PL bands, and calculations that use the intensities. This problem has been discussed relative to various experimental designs in all monographs on luminescent methods for studying a substance (e.g., [1, 2, 4]). Certain qualitative empirical recommendations are given in those references. It is also concluded that methods for accurate determination of corrections that would allow distortions of PL intensities caused by absorption to be taken into account do not exist [2,4]. A fundamental solution of the situation proposes performing investigations at low optical densities of absorption, which in many instances is impossible. For example, optical densities of absorption were several units for investigations of color centers in dielectrics even for sample thicknesses of the order of 1 mm [5].Herein mathematical relations allowing distortions of PL intensities arising from absorption effects to be taken into account are derived. Various experimental designs that were classified [2, 4] as illumination at a right angle, illumination in line, and frontal illumination are examined. The adequacy of the resulting relations is demonstrated by measurements of Rhodamine 6G luminescence, the fluorescence and absorption spectra of which overlap considerably. The relations are used in studies of radiation color centers in lithium fluoride crystals to determine the conto...

Quantitative luminescent analysis methods

“…Such relations have been obtained recently for photoluminescence and photoluminescence excitation (PLE) spectra. In the first case, equations are used that determine the changes in the photoluminescence intensities as a result of re-absorption of photoluminescence in the analyte medium [5]. In the second case, the methods are based on the dependence of the photoluminescence intensity on the absorption coefficients of a multicomponent medium, [6,7].…”

“…In the second case, the methods are based on the dependence of the photoluminescence intensity on the absorption coefficients of a multicomponent medium, [6,7]. From the relations obtained in [5][6][7], equations are derived that make it possible to find the absorption coefficients of a medium from the measured intensity.The problem of finding the absorption coefficients according to the procedure outlined above is an inverse problem. In order to properly solve inverse problems with original data obtained experimentally with random errors,…”

“…Changes in the photoluminescence intensity as a result of re-absorption in the analyte medium depend on the relative orientation of the directions of propagation of the exciting radiation and the detected radiation. The simplest relation for these changes is obtained in the case when photoluminescence is detected at a right angle to the direction of propagation of the exciting radiation [5]:…”

“…In such a case, we should measure the luminescence intensity of the substance whose photoluminescence spectrum overlaps the absorption spectrum of the analyte component. In the following, we call such a substance a luminescent probe [5]. In determining the absorption coefficients using a probe, the function ϕ L (ν) in Eqs.…”

“…In [5], relations are given describing the changes in the photoluminescence intensity as a result of re-absorption for other measurement variants classified as in-line illumination and frontal illumination. Based on these relations, in analogy with (2), (3), we can obtain transcendental equations allowing us to determine the absorption coefficients.…”