Beyond Beer's Law: Spectral Mixing Rules

Mayerhöfer, Thomas G.; Popp, Juergen

doi:10.1177/0003702820942273

Cited by 23 publications

(24 citation statements)

References 28 publications

(47 reference statements)

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“…In section 3.1 we also touched upon what happens when the heterogeneities are no longer small compared to wavelength, but the onset of scattering is only one effect that leads to deviations from the Beer-Lambert law. If we assume samples that consist of two different constituents, the simplest mixing rule according to the Lorentz-Lorenz model would be that [89,90] ð26Þ where φ 1 and φ 2 are the volume fractions of the constituents 1 and 2. This corresponds to the simplified form of eqn.…”

Section: Sample Heterogeneity and Mixing Rulesmentioning

confidence: 99%

“…The corresponding form to eqn. (24) would be [89] ð27Þ and the form related to the Lorentz-Lorenz relation (22) is [89,91] ð28Þ It is obvious that these mixing rules are no longer compatible with Beer's law, and not only because we use the volume fraction (which is connected to the molar concentration in ideal systems via c i = φ i • d i /M i with density d i of the neat compound and its molar mass M i ), cf. Figure 9.…”

Section: Sample Heterogeneity and Mixing Rulesmentioning

confidence: 99%

“…In other words, if spectra taken with a microscope from different locations of the sample differ significantly from each other, then these mixing rules are not sufficient (micro-heterogeneous sample). The reason is that the transmittance T and reflectance R of a larger area or volume of the sample are always area or volume averaged quantities: [89,95] ð29Þ Here φ i represents either the volume fraction (transmittance) or the fraction of the surface area (reflectance) of microscopically large domains completely consisting of either component 1 or 2. If components 1 and 2 are not completely immiscible or if the domains are not or not all larger than the resolution limit, then the mixing rules become even more complicated, whereas if the conditions are fulfilled, eqn.…”

Section: Sample Heterogeneity and Mixing Rulesmentioning

confidence: 99%

“…Figure 9). [89] In this case, the bands strongly flatten for micro-heterogeneous samples compared to micro-homogeneous samples with the same composition (this might explain the band flattening which is often erroneously explained with shadowing, cf. section 3.1).…”

Section: ð30þmentioning

confidence: 99%

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

2020

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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.

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Section: Sample Heterogeneity and Mixing Rulesmentioning

confidence: 99%

Section: Sample Heterogeneity and Mixing Rulesmentioning

confidence: 99%

Section: Sample Heterogeneity and Mixing Rulesmentioning

confidence: 99%

Section: ð30þmentioning

confidence: 99%

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

2020

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“…FTIR microscopy thus has been applied successfully in characterizing the disease state of tissue samples of different types from several different organs 1–4 . However, the raw spectra obtained from FTIR imaging experiments inherently suffer from scattering and the effect that Beer–Lambert's law is not applicable to such spectra, since the samples are heterogeneous 5,6 . Following the chemical information cannot be obtained from the measured spectra without correction.…”

Section: Introductionmentioning

confidence: 99%

A representation learning approach for recovering scatter‐corrected spectra from Fourier‐transform infrared spectra of tissue samples

Raulf

Butke

Menzen

et al. 2020

Journal of Biophotonics

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Infrared spectra obtained from cell or tissue specimen have commonly been observed to involve a significant degree of scattering effects, often Mie scattering, which probably overshadows biochemically relevant spectral information by a nonlinear, nonadditive spectral component in Fourier transform infrared (FTIR) spectroscopic measurements. Correspondingly, many successful machine learning approaches for FTIR spectra have relied on preprocessing procedures that computationally remove the scattering components from an infrared spectrum. We propose an approach to approximate this complex preprocessing function using deep neural networks. As we demonstrate, the resulting model is not just several orders of magnitudes faster, which is important for real‐time clinical applications, but also generalizes strongly across different tissue types. Using Bayesian machine learning approaches, our approach unveils model uncertainty that coincides with a band shift in the amide I region that occurs when scattering is removed computationally based on an established physical model. Furthermore, our proposed method overcomes the trade‐off between computation time and the corrected spectrum being biased towards an artificial reference spectrum.

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The Negative Solvatochromism of Reichardt‘s Dye B30 – A Complementary Study

Spange

Mayerhöfer

2022

ChemPhysChem

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The UV/Vis spectra of a hypothetical negative solvatochromic dye in a solvent are theoretically calculated assuming the classical damped harmonic oscillator model and the Lorentz‐Lorenz relation. For the simulations, the oscillator strength of the solvent was varied, while for the solute all oscillator parameters were kept constant. As a result, a simple change of the oscillator strength of the solute can explain the redshift and intensity increase of the UV/Vis band of the solute. Simulated results are compared with measured UV/Vis spectroscopic data of 2,6‐diphenyl‐4‐(2,4,6‐triphenylpyridinium‐1‐yl) phenolate B30 (Reichardt‘s dye) Significant correlations of the absorption energy (1/λmax) with the molar absorption coefficient ϵ as function of solvent polarity are demonstrated for several derivatives of B30. The approach presented is only applicable to negative solvatochromism. Therefore, while the approach is vital to fully understand solvatochromism, it needs to be complemented by other approaches, e. g., to describe the changes of the chemical interactions based on the nature of the solvent, to explain all its various aspects.

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Beyond Beer's Law: Spectral Mixing Rules

Cited by 23 publications

References 28 publications

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

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

A representation learning approach for recovering scatter‐corrected spectra from Fourier‐transform infrared spectra of tissue samples

The Negative Solvatochromism of Reichardt‘s Dye B30 – A Complementary Study

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