The Kubelka-Munk functions is given by:

F (R) = (1–R)²/2R = k/s = Ac/s

where, R = reflectance; k = absorption coefficient; s = scattering coefficient; c = concentration of the absorbing species; A = absorbance.

It gives a correlation between the reflectance and the concentrations of absorbing species in weak absorbing samples, something like the Lambert-Beer law for absorbance.

The Kubelka-Munk function was develop to analyse paint coated surfaces and therefore is expected that the analyzed surface is totally plane and with infinitesimal thickness. One limitation of the technique is its use in samples with different particle size were light scattering is high.

You can get some information is the text below:

Diffuse Reflectance Spectroscopy

JOSÉ TORRENT and VIDAL BARRÓN

http://www.uco.es/organiza/departamentos/decraf/pdf-edaf/DRS08.pdf

The Kubelka-Munk functions is given by:

F (R) = (1–R)²/2R = k/s = Ac/s

where, R = reflectance; k = absorption coefficient; s = scattering coefficient; c = concentration of the absorbing species; A = absorbance.

It gives a correlation between the reflectance and the concentrations of absorbing species in weak absorbing samples, something like the Lambert-Beer law for absorbance.

The Kubelka-Munk function was develop to analyse paint coated surfaces and therefore is expected that the analyzed surface is totally plane and with infinitesimal thickness. One limitation of the technique is its use in samples with different particle size were light scattering is high.

You can get some information is the text below:

Diffuse Reflectance Spectroscopy

JOSÉ TORRENT and VIDAL BARRÓN

http://www.uco.es/organiza/departamentos/decraf/pdf-edaf/DRS08.pdf

Mathias

One question to you: you say the K-B is used for weaky absorbing materials but it is also used in printing with black ink on paper whihc is a strongly absorbing medium

We used diffuse reflectance spectroscopy to differentiate between water and ice on different roads (see attached patent). Proof of principle was performed together with the Porsche Company in the Alpes. Within milliseconds also the thickness of ice and water on the street was measured during driving. Of course corrections for different surface roughness and reflectivities were performed.

Ata I just noticed:

You do not specify your question you only ask about "the" problems with the K-B approach. What is YOUR problem

Altough, I do not know what Ata might willing to ask exactly, but I do know about several computational problems related to two-constant Kubelka-Munk theory. Most of these computational problems are related to calibration procedures (i.e. related system of linear equations derived from two constant KM-theory). The main issues, up to my best knowledge, are the ill-conditionedness of these equations especially for low wavelength that may cause problems when the two constant KM-theory is applied for color matching problems.

I have an old operations research paper not really recognized by the color research community. If you want to read the paper please go to

http://www.sciencedirect.com/science/article/pii/0377221794900647

If anyone is interested on more details related to computational problems arising during the calibration procedure please contact me.

I don't know what is the problem with his samples, but, a problem to me is for exemple: in the end moment to determination of band gap I should plot [F(R∞)hv]2 against hv and take the zero for extrapolation of the linear portion of the curve. But, this "2" is relative a nature of optical transition. If I don't have this information in the literature, what should I do?

I have a question though about the KM function. If the k in KM function is the absorption coefficient, is this the same as the absorption coefficient (alpha) used in Tauc plot method for attaining the band gap? Where we plot (ahv)^p vs hv to obtain the intersect

How do the k and s in the Kubelka-Munk function relate to the index of refraction -- specifically the real and imaginary parts (k,n) of the index? 

@ Nahum: no direct relationship you could establish.

For a few more points discussed, see link below and links therein.

https://www.researchgate.net/post/diffuse_reflectance_of_reduced_graphene_oxide#576ceddddc332d0e5a317d71

@ Nahum Gat: the attempts to relate the constants in KM theory with the optical properties of powder/porous material are sometimes made, although the theory itself does not make use of these relations. Kubelka-Munk, as it is, requires only measured values of reflectance from the coatings of different thickness and completely disregards the physics behind. If you still want to find out how refractive index influences the k and s constants, there are two major parameters you need to know - the size of scatterers (particle size for powders, pore size for porous solids) and their arrangment in space (volume fraction). Depending on whether the geometric mean of particle/pore sizes is larger or smaller than the wavelength of interest, different approximations can be applied. If you are interested, you can follow the derivations in Sections 4.1 and 4.2 of my paper:

https://www.researchgate.net/publication/259717755_Nanophosphor_Coatings_Technology_and_Applications_Opportunities_and_Challenges

there, Equations 70 and 71 show k and s for the case of independent scattering of light by single scatterers. For nanostructured materials, the case of dependent scattering must be considered (that is, use dependent efficiencies of absorption and scattering from Section 4.2 in Equations 70 and 71).

On a primitive level, if we could assume that the size of scatterers and their arrangement in space are fixed, an increase of either the real or the imaginary part of  refractive index should cause an increase of s or k, respectively. However, without knowledge of the size distribution of scatterers and their volume density, no quantitative prediction can be made. If we would want to compare two materials with unknown size distribution of pores/particles and/or their volume fraction, I would not dare even a qualitative prediction.

Article Nanophosphor Coatings: Technology and Applications, Opportun...

@Roman

The questioner never responded on our questions what HIS problem is

As so many question at RG: absolutely unclear what he means

Did you read his question BTW: do you understand what it means?

Could it be that he was looking for exemplatory problems to exercise in maths? If he does not answer, we should not care much and develop the discussion in our own interests. Researchgate does not often provide us with good topics for exchanging our thoughts.

The list of tags is also "interesting", to say the least.

Karl Camman's example is nicely showing that you can well use something (a type of optical measurement) as a diagnostic tool, even though you do not access the "physical content" of the measured quantity. But I would also think that in this case applying the KM formula is neither really necessary nor applicable since the (angle integrated) total DR is most probably not the measured quantity.

Hello there, does anyone know if the modelling done by Eldridge (2008 - Determination of Scattering and Absorption Coefficients for Plasma-Sprayed Yttria-Stabilized Zirconia Thermal Barrier Coatings) to fit the absorption and scattering coefficients  of YSZ into the measured values of reflectance and transmittance of the same material are valid to other materials?

The author uses the Kubelka-Munk model (four-fluxes) to correlate the coefficients with the measurements, then start from an initial guess for both values and proceed with iterations, until a pre-determined minimum error is achieved.

I wasn't able to understand some parts of the deductions done by Eldridge on his paper and assumed that the "values" used by him came from the modelling and math themselves, other than from material-dependent sources, but my goal is to use the same model to predict other materials (oxides) transmittance and reflectance.

Am I wrong in doing so? Can anyone help me out with any thoughts on that?

From The Kubelka-Munk functions is given by:

F (R) = (1–R)²/2R = k/s = Ac/s

where, R = reflectance; k = absorption coefficient; s = scattering coefficient; c = concentration of the absorbing species; A = absorbance.

so,

how can we calculate the Scattering Coefficient? and pls explain the c value concentration of the absorbing species?

@ Ramamoorthy Sengan:

The idea and ansatz behind the KR "formalism" leading to the equation is overly simplistic.

Assuming that there is some species in your material which is responsible for both absorption and scattering, then the rates of both processes vary proportionally to its concentration (disregarding multiple scattering.) This is analogous to Lamberts law.

Even assuming that the KM ansatz were correct: F(R) depends on two quantities (k & s) through their ratio. Therefore the DS measurement, interpreted in the KM framework, does only provide the spectral dependence of this ratio. It would take further reasoning to try disentangling the two. 

@ Ramamoorthy Sengan:

"how can we calculate the Scattering Coefficient?" - this is depend on the other parameters which you can measure or estimate. However, some review of estimation methods for Kubelka-Munk parameters K & S you can find in our paper: https://www.researchgate.net/publication/260152617_Comparative_analysis_of_radiative_transfer_approaches_for_calculation_of_diffuse_reflectance_of_plane-parallel_light-scattering_layers

Article Comparative analysis of radiative transfer approaches for ca...

can you give me the download link of the following article----

Kubelka, P. and Munk, F. (1931) Ein Beitrag Zur Optik Der Farbanstriche. Zeitschrift für Technische Physik, 12,593-601.

I do not have such link, but you can download two following main articles by Kubelka:

https://www.osapublishing.org/josa/abstract.cfm?uri=josa-38-5-448

https://www.osapublishing.org/josa/abstract.cfm?uri=josa-44-4-330

For my understanding, these two articles of 1948 and 1954 years are completely cover 1931 article and go much further...

we need more informations about you issue in this question

Sapan Kumar Sen

I am attaching the paper

Kubelka, P. and Munk, F. (1931) Ein Beitrag Zur Optik Der Farbanstriche. Zeitschrift für Technische Physik, 12,593-601.

Unfortunately it is in deutsch

To expand a little bit on Kai Fauth 's comment: Only a minority of materials has cubic symmetry. For the rest, it is important to realize that there is a crystallite size effect. Once the crystallites are larger than about a tenth of the wavelength, it is no longer possible to describe the optical properties with a scalar dielectric function. Consequently, you can't describe them with a scalar absorption index either. SeeArticle Optical isotropy in polycrystalline Ba_ {2} TiSi_ {2} O_ {8}...

thank you

To estimate the bandgap energy by Kubelka-Munk Theory, does it differentiate the direct and indirect transition?.

The Kubelka-Munk theory is similar to the Tauc theory. So it depend on the kind of transition.