# Dimensional Threshold of Fluorescence

The dimensional threshold of fluorescence is a property that is not currently controlled by the specifications but appears to largely determine the sensitivity of a fluorescent penetrant. A. L. Walters and R. C. McMaster conducted an experiment that led to the understanding of this condition. Two optically flat plates of glass were clamped tightly together. A drop of fluorescent penetrant was placed at the interface of the plates. The penetrant could be seen migrating in between the plates but when exposed to black light, no fluorescence was seen. The phenomenon was not fully understood until 1960 when Alburger introduced the concept of thin-film transition of fluorescent response.

The dimensional magnitudes of typical crack defects correspond to the dimensional thresholds of fluorescence response which are characteristic of the available penetrant. Alternately stated, the degree of fluorescence response, under a given intensity of ultraviolet radiation, is dependent on the absorption of ultraviolet radiation, which in turn depends on dye concentration and film thickness. Therefore, the ability of a penetrant to yield an indication depends primarily on its ability to fluoresce as a very thin film. The performance of penetrants based on the physical constraints of the dyes can be predicted using Beer's Law equation. This law states that the absorption of light by a solution changes exponentially with the concentration of the solution. This equation does not hold true when very thin layers are involved but works well to establish general relationships between variables.

$I=I_{0}xe^{-lCt}$

Where:

I = Transmitted light intensity
Io = Incident light intensity
l = Absorption coefficient per unit of concentration
C = Dye concentration
t = Thickness of the absorbing layer trolled to a certain degree by the concentration of the fluorescent tracer dye in the penetrant.

This equation states that the intensity of the transmitted energy is directly proportional to the intensity of the incident light and varies exponentially with the thickness of the penetrant layer and its dye concentration. Therefore, when the dye concentration is increased, the brightness of the thin layer of penetrant generally increases. However, the dye concentration can only be increased so much before it starts to have a negative effect on brightness. A Meniscus-Method Apparatus can be used to measure the dimensional threshold of fluorescence.

References:

• Alburger, J.R., Notes on the History of Testing Panels for Inspection Penetrants, Paper Summaries, Nations Spring Conference, New Orleans, LA, Published by ASNT, April 1978, pp. 257-270.
• Alburger, J.R., Dimensional Transition Effects in Visible Color and Fluorescent Dye Liquids, Proceedings, 23rd Annual Conference, Instrument Society of America, Vol. 23, Part I, Paper No. 564.
• Gram, B., Mechanisms Contributing to Fluorescence and Visibility of Penetrants, Proceedings of the Fifth International Conference on Nondestructive Testing, May 1967, pp 225-233.