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Database: ingentaconnect
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TY - ABST
AU - Loyalka, S. K.
AU - Riggs, C. A.
TI - Inverse Problem in Diffuse Reflectance Spectroscopy: Accuracy of the Kubelka-Munk Equations
JO - Applied Spectroscopy
PY - 1995-08-01T00:00:00///
VL - 49
IS - 8
SP - 1107
EP - 1110
KW - Analytical methods
KW - Reflectance spectroscopy
KW - Transmittance spectroscopy
KW - Optics
N2 - In diffuse reflectance spectroscopy the Kubelka-Munk equations have been used extensively. These equations provide simple solutions to the inverse problem of obtaining information on the scattering and absorption cross sections from reflected light. Proof is provided that the basic
Kubelka-Munk equation

(d*r*(*x*)/*s*d*x*) = *r*
^{2}(*x*) - 2*ar*(*x*) + 1

should be replaced by the equation

(d*r*(*x*)/*s*d*x*) = *r*
^{2}(*x*) - 2(2*a* - 1)*r*(*x*) +
1

and that the Kubelka-Munk function

(*k*/*s*) = ((1 - *R*
_{∞})^{2}/2*R*
_{∞})

should be replaced by the function

(*k*/*s*) = ((1 - *R*
_{∞})^{2}/4*R*
_{∞}).

Here
*r*(*x*) is the reflectance; *s* is the scattering cross section (cm^{-1}); *a* = (*k* + *s*)/*s*, where *k* is the absorption cross section (cm^{-1}); and *R*
_{∞} is the reflection coefficient of an infinitely thick
sample. We note, however, that because of a redefinition of *a* carried out by Kubelka and Munk in the process of their calculations, the scattering cross section *s* calculated from their expression

*sd* = 1/(1/2(1/*R*
_{∞} - *R*
_{∞}))(coth^{-1}((1/2(1/*R*
_{∞}
+ *R*
_{∞}) - *r*(*d*))/(1/2(1/*R*
_{∞} - *R*
_{∞}))) - coth^{-1}((1/2(1/*R*
_{∞} + *R*
_{∞}))/(1/2(1/*R*
_{∞} - *R*
_{∞}))))

is correct. But
the Kubelka-Munk theory still overestimates *k* by a factor of two.
UR - http://www.ingentaconnect.com/content/sas/sas/1995/00000049/00000008/art00008
M3 - doi:10.1366/0003702953964976
UR - http://dx.doi.org/10.1366/0003702953964976
ER -