The Kubelka-Munk Equation The relationship between absorption and scattering coefficients (K and S)...
1
The Kubelka-Munk Equation The relationship between absorption and scattering coefficients (K and S) and the diffuse reflection R versus the wavelength is given by the Kubelka-Munk function F(R): The coefficients differ in their spectral behaviour. S exhibits a steady increase towards the UV-regime. The slope mainly depends on the mean particle size and the the particle size distribution of the sample. As noted above, chemical information is carried by K. Due to the manifold of constituents the UV-region usually lacks of discrete absorption bands. The overlap of bands results in a absorption continuum with a steap increase towards shorter wavelengths, which is suggested to be an indicative of organic carbon content. Spectra obtained within a soil profile (“Steinkreuz; Steigerwald”) 1 are shown in figure one, clearly demonstrate that the spectral response of K dominates in this region. However, direct correlation of the TOC with the Kubelka-Munk values fails (inset of Fig. 1). Moving to the NIR-regime (Fig.2) the spectral background due to scattering becomes spiked with discrete absorption bands (mainly –OH and –CH). Again there is no simple correlation between the K- M values and neither the carbon content nor the humidity. Separation of the coefficients is inevitable. Diffuse reflectance spectroscopy of forest soils: Scattering and absorption coefficients in dependence of moisture and organic matter content Gerald Hörner , Steffen Lau, Frank Schael*, Hans-Gerd Löhmannsröben Institute of Chemistry, Physical Chemistry, University Potsdam, Karl-Liebknecht Str. 24 – 25, D-14476 Golm *Current address: Ehrfeld Mikrotechnik AG, D-55234 Wendelsheim Acknowledgement We gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (Priority program 1090 „Böden als Quellen und Senken für CO 2 “). References [1] L. Schober, H.-G. Löhmannsröben, J. Environ. Monit. 2 (2000) 651-655. [2] G. Hörner, F. Schael, H.-G. Löhmannsröben, manuscript in preparation. [3] C. Rumpel, I. Kögel-Knabner, Org. Geochem., 33 (2002) 393- 399. S K R R R F 2 ) 1 ( ) ( 2 Footnote 1 Several ground samples of a depth profile from Steinkreuz/Steigerwald, provided and characterized by C. Rumpel, TU München. S K S K R F dye ) ( 0,0 0,4 0,8 1,2 1,6 0 40 80 120 160 200 K , S /cm -1 Vol .[H 2 O ]/m l Results and conclusions Experiments corresponding to Fig.3 with a number of other soils and pure inorganic matrices (Al 2 O 3 , kaolinite) verified that scattering is strongly correlated with the water content (Fig. 6), while the absorption coefficient remains untouched. As shown in the inset of Fig. 5 for hydrated alumina, this conclusion in principle also holds for the NIR-region in absence of specific absorption. Plots of the reciprocal K-M values (S/K) at 1700nm coincide with the humidity dependence of the isolated S values at 520 nm. [2] 0,0 0,4 0,8 1,2 1,6 0 100 200 300 400 500 S 520nm /cm -1 Al 2 O 3 IIC v SdBv 1 Vol .[H 2 O ]/m l Fig. 6: Scattering coefficients of two soils and alumina at 520 nm as a function of water content (Vol. [H 2 O] per 10 g of solid). Data for different experimental series of alumina underline the accuracy Of the method. Inset: Reciprocal Kubelka -Munk values S/K of alumina at 1700 nm vs. water content. 0,0 0,5 1,0 1,5 2,0 5 6 7 8 9 10 ( S / K ) 1700nm Vol.[H 2 O ]/m l 0 20 40 60 80 100 120 140 0 10 20 30 40 50 0 30 60 90 120 150 0,1 1 10 0 25 50 75 100 125 150 K 520nm /cm -1 TOC /% TOC /% K /cm -1 depth /cm Fig. 6: Total organic carbon TOC and measured absorption coefficient K at 520 nm within a depth profile. Inset: Logarithmic correlation of K and TOC . Data for TOC 0,19 and 3,50 % obtained with reference materials. horizo n depth/ cm TOC/% S/cm -1 K/cm -1 IVCv 115- 140 0,09 80 31 IIICv 85-115 0,11 91 38 SdBv 2 50-80 0,14 108 44 SdBv 1 24-50 0,30 115 61 Bv 5-24 0,98 112 92 Ah 0-5 8,26 - - IICv - 0,19 364 58 Ah [1] - 3,50 20 130 kaolinite - 0,00 263 1 Tab. 1: Summary of optical parameters at 520 nm and TOC [3] within a depth profile in comparison with reference materials (in italics). S obtained at a soil humidity of 2,4 %. 0 20 40 60 80 0,8 1,6 2,4 3,2 0,50m l 0,75m l 1,00m l 1,25m l 1,50m l F(R) 520nm K d /cm -1 400 500 600 700 800 900 0 2 4 6 8 10 L (44,45% ) O h (22,95% ) A h (8,26% ) B v (0,98% ) S dB v2 (0,30% ) S dB v1 (0,14% ) IIIC v (0,11% ) IV C v (0,09% ) 0 10 20 30 40 50 0 4 8 12 425 nm 355 nm F(R') C arbon content /% F(R) /nm Diffuse reflectance spectroscopy as analytical tool in soil science Analysis of heterogeneous systems in general resists simple experimental approaches, since classical chemical analysis demands for complicated and often time consuming separation steps. Furthermore, destruction of the original sample is inevitable. Inspired by promising results mainly in food and pharmaceutical analysis, the indestructive optical technique diffuse reflectance spectroscopy, especially in the n ear i nfrar ed regime (NIR; 800 nm 2500 nm), became a widely used tool also in soil science. Sample preparation procedures are minimized or even completely bypassed. Usually supported by chemometric data processing, a number of both chemical and physical parameters can be extracted from the spectra simultaneously. However, reliable correlations between the spectra and the parameters of interest are restricted to samples of related origin and constitution. More general correlation functions valid for different soil types, sampling depths, and areas have not been reported yet. Direct spectral analysis has to overcome problems of a different kind. In terms of Kubelka-Munk theory, chemical constitution and physical texture in the spectra are reflected by the absorption coeffient K and the scattering coefficient S, respectively. Inevitably, only the ratio K/S is obtained. Herein we present an efficient method of coefficient separation in the UV-Vis region (300 nm 800 nm) by dye-doping. Using alumina as a solid matrix and eosine as a dopant, the potential of the method has been demonstrated. Based on these results, for the horizons of a real world profile the absorption and scattering properties have been determined. The dependencies of K and S on soil humidity and organic matter content will be discussed. Coefficient separation For independent determination of K and S soils were spiked with different concentrations of a dye (eosin), varying the overall absorption while keeping S of the matrix constant. [1] Plots of F(R) versus the absorption coefficient of the dye therefore yield linear correlations (inset Fig. 3). From slope and intercept the coefficients are calculated at different degrees of humidity (Fig.3). UV-Vis NIR Fig. 1: UV-Vis diffuse reflectance spectra of the horizons of a podsole profile; inset: Plot of K-M values versus the TOC for two wavelengths. 1400 1600 1800 2000 2200 2400 0,04 0,08 0,12 0,16 0,20 0,24 0,28 0,32 -CH com b. -OH m ineral -OH com b. -OH overtone F(R) = K / S /nm Fig. 2: NIR diffuse reflectance spectra of the horizons of a podsole profile; Boxes define the spectral regions of specific absorption (colour code: see Fig. 1) Fig. 3: Absorption and scattering coefficients of a podsole horizon in dependency of humidity; Inset: Linear plots of K-M values of spiked soils versus dye loading at variable humidity Fig. 4: Typical vertical profile of a european pseudogley 1400 1600 1800 2000 2200 2400 0,0 0,2 0,4 0,6 0,8 1,0 1,2 = 1700nm F(R) = K / S /nm Fig. 5: Diffuse reflectance spectra of alumina with increasing water load in the NIR. Bands at 1450 and 1950 nm correspond to –OH vibrations. Inset: Reciprocal Kubelka -Munk values S/K of alumina at 1700 nm vs. water content. While for a given material the scattering coefficient defines the humidity of the sample, knowledge of the absorption coefficient K seems to allow direct insight into the carbon budget of the soil (at constant humidity). Contrary to the situation in Fig.1, a steady decrease of K with the sampling depth is observed, which results in a simple correlation with the TOC itself. isolated coefficients Coefficient ratio
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Transcript of The Kubelka-Munk Equation The relationship between absorption and scattering coefficients (K and S)...
The Kubelka-Munk Equation
The relationship between absorption and scattering coefficients (K and S) and the diffuse reflection R versus the wavelength is given by the Kubelka-Munk function F(R):
The coefficients differ in their spectral behaviour. S exhibits a steady increase towards the UV-regime. The slope mainly depends on the mean particle size and the the particle size distribution of the sample. As noted above, chemical information is carried by K. Due to the manifold of constituents the UV-region usually lacks of discrete absorption bands. The overlap of bands results in a absorption continuum with a steap increase towards shorter wavelengths, which is suggested to be an indicative of organic carbon content. Spectra obtained within a soil profile (“Steinkreuz; Steigerwald”)1 are shown in figure one, clearly demonstrate that the spectral response of K dominates in this region. However, direct correlation of the TOC with the Kubelka-Munk values fails (inset of Fig. 1).
Moving to the NIR-regime (Fig.2) the spectral background due to scattering becomes spiked with discrete absorption bands (mainly –OH and –CH). Again there is no simple correlation between the K-M values and neither the carbon content nor the humidity. Separation of the coefficients is inevitable.
Diffuse reflectance spectroscopy of forest soils: Scattering and absorption coefficients in dependence of
moisture and organic matter content Gerald Hörner, Steffen Lau, Frank Schael*, Hans-Gerd Löhmannsröben
Institute of Chemistry, Physical Chemistry, University Potsdam, Karl-Liebknecht Str. 24 – 25, D-14476 Golm
*Current address: Ehrfeld Mikrotechnik AG, D-55234 Wendelsheim
Acknowledgement
We gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (Priority program 1090 „Böden als Quellen und Senken für CO2“).
References
[1] L. Schober, H.-G. Löhmannsröben, J. Environ. Monit. 2 (2000) 651-655. [2] G. Hörner, F. Schael, H.-G. Löhmannsröben, manuscript in preparation.[3] C. Rumpel, I. Kögel-Knabner, Org. Geochem., 33 (2002) 393-399.
S
K
R
RRF
2
)1()(
2
Footnote1 Several ground samples of a depth profile from Steinkreuz/Steigerwald, provided and characterized by C. Rumpel, TU München.
S
K
S
KRF dye)(
0,0 0,4 0,8 1,2 1,60
40
80
120
160
200
K, S
/ cm
-1
Vol. [H2O] / ml
Results and conclusionsExperiments corresponding to Fig.3 with a number of other soils and pure inorganic matrices (Al2O3, kaolinite) verified that scattering is strongly correlated with the water content (Fig. 6), while the absorption coefficient remains untouched. As shown in the inset of Fig. 5 for hydrated alumina, this conclusion in principle also holds for the NIR-region in absence of specific absorption. Plots of the reciprocal K-M values (S/K) at 1700nm coincide with the humidity dependence of the isolated S values at 520 nm. [2]
0,0 0,4 0,8 1,2 1,60
100
200
300
400
500
S52
0nm /
cm-1
Al2O
3
IICv
SdBv1
Vol. [H2O] / ml
Fig. 6: Scattering coefficients of two soilsand alumina at 520 nm as a function of water content (Vol. [H2O] per10 g of solid). Data for different experimental series of alumina underline the accuracyOf the method.Inset: Reciprocal Kubelka -Munk values S/K of alumina at 1700 nm vs. water content.
0,0 0,5 1,0 1,5 2,05
6
7
8
9
10
(S/K
) 1700
nm
Vol. [H2O] / ml
0 20 40 60 80 100 120 1400
10
20
30
40
50
0
30
60
90
120
150
0,1 1 100
25
50
75
100
125
150
K52
0nm
/ cm
-1
TOC / %TO
C /
%
K /
cm-1
depth / cm
Fig. 6: Total organic carbon TOC and measured absorption coefficient K at 520 nm within a depth profile.Inset: Logarithmic correlation of K and TOC . Data for TOC 0,19 and 3,50 % obtained with reference materials.
horizon depth/cm TOC/% S/cm-1 K/cm-1
IVCv 115-140 0,09 80 31
IIICv 85-115 0,11 91 38
SdBv2 50-80 0,14 108 44
SdBv1 24-50 0,30 115 61
Bv 5-24 0,98 112 92
Ah 0-5 8,26 - -
IICv - 0,19 364 58
Ah [1] - 3,50 20 130
kaolinite - 0,00 263 1
Tab. 1: Summary of optical parameters at 520 nm and TOC [3] within a depth profile in comparison with reference materials (in italics). S obtained at a soil humidity of 2,4 %.
0 20 40 60 80
0,8
1,6
2,4
3,2
0,50ml 0,75ml 1,00ml 1,25ml 1,50ml
F(R
) 520n
m
Kd / cm-1
400 500 600 700 800 9000
2
4
6
8
10 L (44,45%) Oh (22,95%) Ah (8,26%) Bv (0,98%) SdBv2 (0,30%) SdBv1 (0,14%) IIICv (0,11%) IVCv (0,09%)
0 10 20 30 40 500
4
8
12
425 nm
355 nm
F(R
')
Carbon content / %
F(R
)
/ nm
Diffuse reflectance spectroscopy as analytical tool in soil scienceAnalysis of heterogeneous systems in general resists simple experimental approaches, since classical chemical analysis demands for complicated and often time consuming separation steps. Furthermore, destruction of the original sample is inevitable. Inspired by promising results mainly in food and pharmaceutical analysis, the indestructive optical technique diffuse reflectance spectroscopy, especially in the near infrared regime (NIR; 800 nm 2500 nm), became a widely used tool also in soil science. Sample preparation procedures are minimized or even completely bypassed. Usually supported by chemometric data processing, a number of both chemical and physical parameters can be extracted from the spectra simultaneously. However, reliable correlations between the spectra and the parameters of interest are restricted to samples of related origin and constitution. More general correlation functions valid for different soil types, sampling depths, and areas have not been reported yet. Direct spectral analysis has to overcome problems of a different kind. In terms of Kubelka-Munk theory, chemical constitution and physical texture in the spectra are reflected by the absorption coeffient K and the scattering coefficient S, respectively. Inevitably, only the ratio K/S is obtained.Herein we present an efficient method of coefficient separation in the UV-Vis region (300 nm 800 nm) by dye-doping. Using alumina as a solid matrix and eosine as a dopant, the potential of the method has been demonstrated. Based on these results, for the horizons of a real world profile the absorption and scattering properties have been determined. The dependencies of K and S on soil humidity and organic matter content will be discussed.
Coefficient separation
For independent determination of K and S soils were spiked with different concentrations of a dye (eosin), varying the overall absorption while keeping S of the matrix constant. [1] Plots of F(R) versus the absorption coefficient of the dye therefore yield linear correlations (inset Fig. 3). From slope and intercept the coefficients are calculated at different degrees of humidity (Fig.3).
UV-Vis
NIR
Fig. 1: UV-Vis diffuse reflectance spectra of the horizons of a podsole profile; inset: Plot of K-M values versus the TOC for two wavelengths.
1400 1600 1800 2000 2200 2400
0,04
0,08
0,12
0,16
0,20
0,24
0,28
0,32 -CH comb.
-OH mineral
-OH comb.
-OH overtone
F(R
) =
K/S
/ nm
Fig. 2: NIR diffuse reflectance spectra of the horizons of a podsole profile; Boxes define the spectral regions of specific absorption (colour code: see Fig. 1)
Fig. 3: Absorption and scattering coefficients of a podsole horizon in dependency of humidity; Inset: Linear plots of K-M values of spiked soils versus dye loading at variable humidity
Fig. 4: Typical vertical profile of a european pseudogley
1400 1600 1800 2000 2200 24000,0
0,2
0,4
0,6
0,8
1,0
1,2
= 1700nm
F(R
) =
K/S
/ nm
Fig. 5: Diffuse reflectance spectra of alumina with increasing water load in the NIR. Bands at 1450 and 1950 nm correspond to –OH vibrations.Inset: Reciprocal Kubelka -Munk values S/K of alumina at 1700 nm vs. water content.
While for a given material the scattering coefficient defines the humidity of the sample, knowledge of the absorption coefficient K seems to allow direct insight into the carbon budget of the soil (at constant humidity). Contrary to the situation in Fig.1, a steady decrease of K with the sampling depth is observed, which results in a simple correlation with the TOC itself.
isolated coefficientsCoefficient ratio
