Transformation Kubelka-Munk

Fig-1 Absorption spectra, obtained through the Kubelka-Munk transformation of diffuse reflectance spectra, of indolinonaphthospiropyran adsorbed onto silica gel. Spectra are shown for coverages of (A) 2.35, (B) 9.49, (C) 34.2, and (D) 46.7 /ig/m2. (Data adapted from Ref. 12.)... 

In systems where there are optically active reaction products held in transparent reagent carriers between the incident light and the reflecting background (e.g. Kodak or Fuji systems), the Kubelka-Munk transformation is... 

The DRIFT spectra were taken in a Nicolet 510P instrument in which a diffuse reflectance cell (Spectra-Tech) was fitted. For obtaining a reasonable signal-to-noise ratio. 200 interferograms were collected with a resolution of 4 cm. All the spectra are presented without manipulation and only Kubelka-Munk transformations are employed for ensuring quantitivity. 

Figure 7. Kubelka-Munk transformed diffuse reflectance spectrum of (A) untreated and (B) calcined catalyst 10-wt% Au on aluminium oxide "C" calcination conditions 400°C, air, 4 h. The change in the plasmon absorbance of the supported gold colloid due to change in particle size can be clearly seen c.f. Figure 2 curves B and C. (the Kubelka-Mumk function F(R) is not the simple absorbance spectrum but is divided by the scattering spectrum of the white alumina support, which is normally assumed to be monotonic F(R) = K/S)...

Dahm and Dahm [22] have shown that both log(l/R) and the Kubelka-Munk transformation are nonlinear functions of concenfrafion. The log(l/K) transformation is nonlinear because the absorbance coefficient is considered the additive sum of the absorbance coefficients of all absorbing species in the sample, and it does not consider that scattering varies as a function of wavelengfh. The nonlinearity of the Kubelka-Munk relationship is due... 

Diffusive reflectance infrared spectroscopy (DRIFT, presented as the Kubelka-Munk transformation) was used to identify the nature of the carbon and hydrogen species of the polymer-deriv amorphous products. The spectra of the pyrolyz PNMS and PCMS are... 

In the diffuse reflectance mode, samples can be measured as loose powders, with the advantages that not only is the tedious preparation of wafers unnecessary but also diffusion limitations associated with tightly pressed samples are avoided. Diffuse reflectance is also the indicated technique for strongly scattering or absorbing particles. The often-used acronyms DRIFT or DRIFTS stand for diffuse reflectance infrared Fourier transform spectroscopy. The diffusely scattered radiation is collected by an ellipsoidal mirror and focussed on the detector. The infrared absorption spectrum is described the Kubelka-Munk function ... 

If the scattering coefficient does not depend on the infrared frequency, the Kubelka-Munk function transforms the measured spectrum RJ V) into the absorption spectrum K v). In situ cells for DRIFT studies of catalysts have been described [10] and are commercially available. 

Diffuse reflectance R is a function of the ratio K/S and proportional to the addition of the absorbing species in the reflecting sample medium. In NIR practice, absolute reflectance R is replaced by the ratio of the intensity of radiation reflected from the sample and the intensity of that reflected from a reference material, that is, a ceramic disk. Thus, R depends on the analyte concentration. The assumption that the diffuse reflectance of an incident beam of radiation is directly proportional to the quantity of absorbing species interacting with the incident beam is based on these relationships. Like Beer s law, the Kubelka-Munk equation is limited to weak absorptions, such as those observed in the NIR range. However, in practice there is no need to assume a linear relationship between NIRS data and the constituent concentration, as data transformations or pretreatments are used to linearize the reflectance data. The most used linear transforms include log HR and Kubelka-Munk as mathemati-... 

Fig. 1. (a) Diffuse reflectance spectra of P25 (thin line), TH (thick line), 3% [PtClJ/P25 (dashed line) and 4.0% H2[PtCl6]/TH (dotted line). The Kubelka-Munk function, F(R00), is used as the equivalent of absorbance, (b) Transformed diffuse reflectance spectra of P25 (thin line), TH (thick line), 3% [PtCl4]/P25 (dashed line) and 4.0% H2[PtCl6]/TH (dotted line). The bandgap energy was obtained by extrapolation of the linear part. 

Diffuse reflectance IR spectroscopy has become an attractive alternative to mulls with the introduction of DRIFT cell by Griffiths,29 later modified by Yang.30 Since materials are dispersed in a nonabsorbing medium and not subjected to thermal or mechanical energy during sample preparation, DRIFT spectroscopy is especially suitable for the qualitative/quantitative analysis for polymorphs, which are prone to solid-state transformations. The Kubelka-Munk (K-M) equation,31 which is analogous to Beer s law for transmission measurements, is used to quantitatively describe diffusely-reflected radiation ... 

The DRIFT spectra were recorded by a FTS 165 spectrometer of BIO-RAD Laboratories (Philadelphia, USA) using the praying-mantis-diffuse-reflection attachment. Unmodified metal or metal oxide particles were used as reference. The spectra were measured in Kubelka-Munk units collecting 32 scans. For data post processing the spectra were transformed in ASCII-files and processed in Origin 5.0. Smoothing was not done. 

The motivation for transforming reflectance data into the Kubelka-Munk function is to obtain a representation of the absorption spectrum of the sample, which also allows one to relate intensities directly to concentration. It is sometimes debated as to whether the transformation should be performed, as described below. 

If for a scanner a monochromator drive is disposable and controllable by a computer, like for example with the instrument KM 3 Zeiss, spectra and their derivatives can be recorded. A spectrum can be obtained by taking the difference between substance- and background spectrum after a logarithmic transformation or a transformation by the Kubelka-Munk-function. 

V wide-line NMR spectra were collected on a Bmker MSL 300 FT NMR spectrometer operating at 78.9 MHz and equipped with a special probe head for measurements in the absence of air. UV-Visible-NIR diffuse reflectance spectra (DRS) were measured in air using a Perkin Elmer Lamda 19 instrument after transformation of reflectivity (R) according to the Kubelka-Munk function F(R) = (l-R)V2R.o. BaS04 was used as a reference. 

Figure 77. A Kubelka-Munk contour-plot, measured with a diode-array device. The sample-peak at 33.9 mm separation distance can be identified as flupirtine, a centrally acting non-opioid analgesic substance. Flupirtine shows absorptions between 200 and 350 nm and an additional fluorescence quenching signal between 500 and 530 nm. The weak signal at 400 nm is the flupirtine fluorescence spectrum which would be invisible if evaluated using equation (2). A transformation of the raw-data using equation (3) would show this signal only to reveal it as a fluorescence emis-...

Figure 10.18 Spectra by reflection, (a) From a sample of plexiglass, three types of reflection are displayed. Left, crude spectra and right, spectra after correction. Above, crude signal of specular reflection and the result in units of K following application of the Kramers-Kronig (transformation of the reflectance) calculation middle, spectrum obtained by diffused hght comparison of the crude spectrum with the Kubelka-Munk correction below, spectrum obtained by ATR, the latter requiring a fine correction to reduce the absorbance at higher wavelengths which would be overestimated (b) comparison of two spectra of benzoic acid, one obtained through transmission, the other by diffused reflection and subsequent K-M correction.

When diffuse reflectance measurements are taken of the adsorbed tetrahedral species and the transmittance data are transformed into Kubelka-Munk units (Eq. 1), a plot versus loading affords a linear correlation analogous to the... 

In practical cases, Kubelka-Munk, 1/T, absorbance ratios, derivatives, and other transforms have been applied to data with scattering properties. Continued research on the interaction of radiation reflected from different types of solid surfaces would be extremely useful. A summary of the measurement characteristics and their effects on reflected energy from solid surfaces is delineated in Table 1. 

Solution and gas phase spectra are usually presented in absorbance mode but can easily be transformed to transmittance using the Beer-Lambert law. Solid state spectra are presented as diffuse reflectance, the Kubelka-Munk function, or % reflectance, as described above. However, first, second, and even high, derivative spectra are also quite common. These higher derivative spectra are usefiil in picking out structure in spectra, showing vibrational shoulders etc., or components in mixtures [21]. 

The Fourier transformed interferograms provide IR spectra that can be recorded at will in normalized reflectance spectra (reflectance units R) (Fig. 17A), in quasi-absorbance units that are not proportional to concentration (-log/ ) (Fig. 17B), or in Kubelka-Munk units that are proportional to concentration (Fig. 17C). The substances can be localized on the TLC plate by using either spectral windows chosen at will (Fig. 18A and also dashed line in B) or the Gram-Schmidt technique (Fig. 18 dotted line in B). The first method can be used to increase selectivity (e.g., the spectral window can be chosen so as to detect only compounds with carbonyl groups), while the latter is universally applicable and independent of wave number. 

Diffuse reflection spectra are often transformed to Kubelka-Munk units as defined below, just as spectra measured in transmission are converted to absorbance ... 

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