3 Theoretical Models of Light Scattering and Absorption
59
the scatter-corrected absorbance and the absorption coefficient do not change significantly if the process of halving the thickness is continued beyond this point. This,
then, is an example in which the effects of absorption and scatter have been successfully separated, and the calculated absorption coefficient truly represents the ability
of the material to absorb light.
By contrast, suppose the A, R, and T data in Table 3.1 were obtained from a sample
composed of particles that are 0.25 cm, or 250 mm, in diameter. The calculated
absorption coefficient for a layer of thickness 0.25 cm is significantly different from
the converged value of ~ 2.98 cm
−1 . Subdividing a particle creates new surfaces, and
scattering is a surface phenomenon. (The significance of surface area to volume ratio
in absorption and scattering was introduced in Sect. 3.9.) Consequently, one cannot
plausibly expect a layer with a thickness of 0.01 or 0.001 cm to be “representative”
of the original sample. In this scenario, one might regard all rows of Table 3.1 with
d < 0.25 cm as mathematical constructs that have no physical significance. Notice
that according to Table 3.1, R = 0.189 when d = 0.25 cm. A plausible interpretation
of this result is that even if the layer is only one particle thick, almost 19% of the
incident light is remitted by a single interaction, and this 19% has no opportunity to
be absorbed. In such a case, separating the effects of absorption and scatter is likely
not a realistic goal.
References
1. W. E. Knowles Middleton, Bouguer, Lambert, and The Theory of Horizontal Visibility. Isis 51,
no. 2 (1960): 145–49. https://www.jstor.org/stable/226845.
2. W.W. Wendlandt, H.G. Hecht, Reflectance Spectroscopy (John Wiley and Sons, New York,
1966)
3. J.M. Chalmers, P.R. Griffiths, Handbook of Vibrational Spectroscopy (John Wiley & Sons Ltd.,
Chichester, UK, 2002)
4. C.V. Raman, A new radiation. Indian J. Phys. 2, 387–398 (1928)
5. M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, Handbook of Optics, 2 nd ed., vol.
1, McGraw-Hill, Inc., New York (1995
6. G.G. Stokes, On the intensity of the light reflected from or transmitted through a pile of plates.
Proceedings of the Royal Society of London 11, 545 (1862)
7. A. Schuster, Radiation Through a Foggy Atmosphere. Astrophysical J.21 , 1 (1905)
8. G. Kortüm, Reflectance Spectroscopy (Springer, Berlin, 1969)
9. P. Kubelka, F. Munk, Ein Beitrag zur Optik der Farbanstriche. Z.Tech. Phys. (Leipzig), 12
(1931)
10. P. Kubelka, New Contributions to the Optics of Intensely Light-Scattering Materials. Part I J.
Optical Soc. America 38, 5 (1948)
11. T. Burger, J. Kuhn, R. Caps, J. Fricke, Quantitative Determination of the Scattering and Absorption Coefficients from Diffuse Reflectance and Transmittance Measurements: Application to
Pharmaceutical Powders. Appl. Spectrosc. 51(3), 309–322 (1997)
12. R.G. Giovanelli, Reflection by Semi-infinite Diffusers. Optica Acta: International Journal of
Optics 2(4), 153–162 (1955)
13. F. Benford, Radiation in a Diffusing Medium. J. Optical Soc. America 36, 524–554 (1946)
14. D. J. Dahm, K.D. Dahm, Bridging the continuum-discontinuum gap in the theory of diffuse
reflectance. J. Near Infrared Spectroscopy 7, 47-53 (1999)
59
the scatter-corrected absorbance and the absorption coefficient do not change significantly if the process of halving the thickness is continued beyond this point. This,
then, is an example in which the effects of absorption and scatter have been successfully separated, and the calculated absorption coefficient truly represents the ability
of the material to absorb light.
By contrast, suppose the A, R, and T data in Table 3.1 were obtained from a sample
composed of particles that are 0.25 cm, or 250 mm, in diameter. The calculated
absorption coefficient for a layer of thickness 0.25 cm is significantly different from
the converged value of ~ 2.98 cm
−1 . Subdividing a particle creates new surfaces, and
scattering is a surface phenomenon. (The significance of surface area to volume ratio
in absorption and scattering was introduced in Sect. 3.9.) Consequently, one cannot
plausibly expect a layer with a thickness of 0.01 or 0.001 cm to be “representative”
of the original sample. In this scenario, one might regard all rows of Table 3.1 with
d < 0.25 cm as mathematical constructs that have no physical significance. Notice
that according to Table 3.1, R = 0.189 when d = 0.25 cm. A plausible interpretation
of this result is that even if the layer is only one particle thick, almost 19% of the
incident light is remitted by a single interaction, and this 19% has no opportunity to
be absorbed. In such a case, separating the effects of absorption and scatter is likely
not a realistic goal.
References
1. W. E. Knowles Middleton, Bouguer, Lambert, and The Theory of Horizontal Visibility. Isis 51,
no. 2 (1960): 145–49. https://www.jstor.org/stable/226845.
2. W.W. Wendlandt, H.G. Hecht, Reflectance Spectroscopy (John Wiley and Sons, New York,
1966)
3. J.M. Chalmers, P.R. Griffiths, Handbook of Vibrational Spectroscopy (John Wiley & Sons Ltd.,
Chichester, UK, 2002)
4. C.V. Raman, A new radiation. Indian J. Phys. 2, 387–398 (1928)
5. M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, Handbook of Optics, 2 nd ed., vol.
1, McGraw-Hill, Inc., New York (1995
6. G.G. Stokes, On the intensity of the light reflected from or transmitted through a pile of plates.
Proceedings of the Royal Society of London 11, 545 (1862)
7. A. Schuster, Radiation Through a Foggy Atmosphere. Astrophysical J.21 , 1 (1905)
8. G. Kortüm, Reflectance Spectroscopy (Springer, Berlin, 1969)
9. P. Kubelka, F. Munk, Ein Beitrag zur Optik der Farbanstriche. Z.Tech. Phys. (Leipzig), 12
(1931)
10. P. Kubelka, New Contributions to the Optics of Intensely Light-Scattering Materials. Part I J.
Optical Soc. America 38, 5 (1948)
11. T. Burger, J. Kuhn, R. Caps, J. Fricke, Quantitative Determination of the Scattering and Absorption Coefficients from Diffuse Reflectance and Transmittance Measurements: Application to
Pharmaceutical Powders. Appl. Spectrosc. 51(3), 309–322 (1997)
12. R.G. Giovanelli, Reflection by Semi-infinite Diffusers. Optica Acta: International Journal of
Optics 2(4), 153–162 (1955)
13. F. Benford, Radiation in a Diffusing Medium. J. Optical Soc. America 36, 524–554 (1946)
14. D. J. Dahm, K.D. Dahm, Bridging the continuum-discontinuum gap in the theory of diffuse
reflectance. J. Near Infrared Spectroscopy 7, 47-53 (1999)