The Bouguer‐Beer‐Lambert Law: Shining Light on the Obscure

Abstract

The Beer‐Lambert law is unquestionably the most important law in optical spectroscopy and indispensable for the qualitative and quantitative interpretation of spectroscopic data. As such, every spectroscopist should know its limits and potential pitfalls, arising from its application, by heart. It is the goal of this work to review these limits and pitfalls, as well as to provide solutions and explanations to guide the reader. This guidance will allow a deeper understanding of spectral features, which cannot be explained by the Beer‐Lambert law, because they arise from electromagnetic effects/the wave nature of light. Those features include band shifts and intensity changes based exclusively upon optical conditions, i. e. the method chosen to record the spectra, the substrate and the form of the sample. As such, the review will be an essential tool towards a full understanding of optical spectra and their quantitative interpretation based not only on oscillator positions, but also on their strengths and damping constants.

Mechanistic model: Analysis of diffusion dynamics of Lugol’s chromoendoscopy in Basal layer-type squamous cell carcinoma in situ via Euler’s method and Law of mass action

“…However, at the tissue level, the effect of it is almost imperceptible on Lugol’s Chromendoscopy, more critical, the inputs and outputs of Iodine are both passive diffusion, which suggests the free diffusion dynamic of Iodine has continuity characteristics, so we ignore the viscosity and make an approximation which describes “dry water”(Feynman, Leighton et al 1963) rather than natural state inside the cell. According to Beer-Lambert law(Mayerhöfer, Pahlow et al 2020), we have where A iodine is the absorbance of normal esophageal mucosa after iodine staining;k iodine is attenuation is attenuation coefficient of normal esophageal mucosa after iodine staining; C omplex is the density of Iodine- glycogen complex; l esophagus is the length of esophageal epithelium which contain glycogen granules along the y-axis(note: let us first assume that C omplex is low concentration in our model).…”

In Situ Synchrotron X‐Ray Absorption Spectroscopy Studies of Anode Materials for Rechargeable Batteries

“…For higher energies on the other hand, such as the Sn and Sb K‐edges, either Al or Cu tapes will work well. One should carefully take into account that the fraction of the photon intensity that makes it through the sample is exponentially dependent on the number of absorption lengths present (Bouguer's Law) [41] …”

“…One should carefully take into account that the fraction of the photon intensity that makes it through the sample is exponentially dependent on the number of absorption lengths present (Bouguer's Law). [41] Other cell components are similar to conventional coincells, but care must be taken to the as-synthesized working electrodes. Firstly, with regard to current collectors used for in situ hard XAS study, carbon cloths are versatile substrates for coating anode materials as the working electrode with negligible absorption of photon intensity for hard X-ray.…”

Beer–Lambert law for optical tissue diagnostics: current state of the art and the main limitations

“…Therefore, Beer's empiric law at small concentrations will work properly. 38 Some chemical interactions within large concentrations can influence the Beer law accuracy, as well. Tang et al 39 analyzed chiral composition with different concentrations.…”

“…Despite the fact that organic and biological substances have relatively low absorption, they may have some bands that are much stronger, even 2.5 times higher than the limit. 38…”