Correction to the Beer-Lambert-Bouguer law for optical absorption

Abstract

The Beer-Lambert-Bouguer absorption law, known as Beer's law for absorption in an optical medium, is precise only at power densities lower than a few kW. At higher power densities this law fails because it neglects the processes of stimulated emission and spontaneous emission. In previous models that considered those processes, an analytical expression for the absorption law could not be obtained. We show here that by utilizing the Lambert W-function, the two-level energy rate equation model is solved analytically, and this leads into a general absorption law that is exact because it accounts for absorption as well as stimulated and spontaneous emission. The general absorption law reduces to Beer's law at low power densities. A criterion for its application is given along with experimental examples.

Deep learning predicts function of live retinal pigment epithelium from quantitative microscopy

“…Absorption imaging has been reported in the literature (26)(27)(28), but the QBAM technology developed here can be implemented on any standard bright-field microscope, and it uses real-time, automated, statistically robust methods to provide high confidence in image quality and reproducibility. The advantage to using absorbance rather than raw pixel intensities is that absorbance is an absolute measure of light attenuation (29). Raw pixel intensities can vary with microscope configuration and settings (e.g., uneven lighting, bulb intensity and spectrum, camera, etc.)…”

Modelling and simulation of atmospheric conditions impact on photovoltaic production in Saint Louis area

“…According to the Bouguer-Lambert law, better known as Beer's Law, the attenuation of light through a medium is proportional to the distance covered in the medium and the radiation flux where k is an attenuation coefficient (Abitan et al, 2008). 1Where, is the radiation attenuated; : is the incidental radiation; is the attenuation coefficient; : is the covered distance.…”

Is the current selective laser trabeculoplasty paradigm a myth?

“…The Beer-Lambert-Bouguer law states absorption is proportional to the thickness of the absorbing medium, but once cavitation occurs this law no longer applies. 4 Because the founding paradigm of SLT is that it is effective at settings where no visible sign of cavitation occurs, extinction effects should apply in vivo. Clinical studies have failed to demonstrate a relationship between angle pigmentation and treatment response 5 for SLT, suggesting that the considerable contradiction and confusion in the SLT literature over the last 15 years may resolve into error if the paradigm is revised.…”