# Experimental verification of the matrix formulation of the Schuster-Kubelka-Munk theory of diffusing layers

TL;DR: In this article, the authors tested the validity of the theory experimentally using a few diffusing multilayers, each consisting of three distinct layers, as samples and measured the reflectances of each layer with (R) and without (R0) itself as its backing layer under identical conditions of illumination and measurement.

Abstract: The authors tested the validity of the theory experimentally using a few diffusing multilayers, each consisting of three distinct layers, as samples. The reflectances of each layer with (R) and without (R0) itself as its backing layer were separately measured for different wavelengths under identical conditions of illumination and measurement. After conversion of the relative values of R and R0 into absolute ones, it was possible to calculate the matrix elements of each layer and hence those of the multilayered samples. From those matrix elements, the reflectances of the multilayered samples could be calculated for different wavelengths. Also, the spectral reflectances of the multilayers as such were measured in the manner indicated. Comparison of the calculated reflectance vs. wavelength curves with experimental ones for the multilayered sample demonstrated good agreement between the theory and the experimental results within the limits of experimental accuracy.

##### References

More filters

••

TL;DR: It is shown by theory and experiment that reflectance and absorption of a nonhomogeneous specimen depend on the direction of illumination, whereas transmittance does not.

Abstract: The derived laws apply to layers whose scattering coefficient S and absorption coefficient K vary vertically to the surface of the layer. In the general case the differential equations of the preceding paper [ P. Kubelka , J. Opt. Soc. Am.38, 448 ( 1948)] must be used; the coefficients, however, hitherto constant, now are functions of the distance x from the surface. In the practically important case in which K/S is constant, one may introduce the variable p, such that p≡∫0x(x)dx. One reduces thereby the nonhomogeneous to the previously treated homogeneous case.Transmittance T1,2 and reflectance R1,2 of two nonhomogeneous sheets can be calculated by the following equations: T1,2=T1T21-R1R2, R1,2=R1+T12R21-R1R2,where T1, T2, R1, R2 are the transmittances and reflectances of the single sheets, and R1 represents the reflectance of the first sheet when illuminated in the inverse direction. Analogous formulas for more sheets and formulas relating transmittance, reflectance for specimens upon black, gray or white backing surfaces, and contrast ratio, are derived.It is shown by theory and experiment that reflectance and absorption of a nonhomogeneous specimen depend on the direction of illumination, whereas transmittance does not.

777 citations

••

TL;DR: In this paper, a 4° square, two-part photometric field, symmetrical about a vertical division and viewed through a pupil 3 mm in diameter, is illuminated in both parts by artificial sunlight at a constant brightness of about 3 or 4 millilamberts (retinal illumination, 70 to 90 photons) with a surrounding field of about 0.5 millilambert.

Abstract: A 4° square, two-part photometric field, symmetrical about a vertical division and viewed through a pupil 3 mm in diameter, is illuminated in both parts by artificial sunlight at a constant brightness of about 3 or 4 millilamberts (retinal illumination, 70 to 90 photons) with a surrounding field of about 0.5 millilambert. Homogeneous light is added to one-half, and sunlight simultaneously subtracted so that the field remains matched in brightness. Two adjustments of the mixture are made: (1) the least purity perceptible with certainty (pmax), and (2) the greatest imperceptible purity (pmin). The purity of these mixtures is then measured, increased accuracy being obtained by measuring a known large multiple of the homogeneous brightness. Values of pmax and pmin have been obtained as a function of the wave-length of the homogeneous component; these values are reported in detail, and some discussion of their interpretation is given.

64 citations

••

TL;DR: In this article, the total reflection of a light diffuser with nonuniform absorption is considered in the two-beam model, and a series solution is obtained for the Kubelka-Munk equations that describe an opaque layer characterized by a constant scattering coefficient and an absorption coefficient with an exponential distribution.

Abstract: The total reflection of a light diffuser with nonuniform absorption is considered in the two-beam model. A series solution is obtained for the Kubelka–Munk equations that describe an opaque layer characterized by a constant scattering coefficient and an absorption coefficient with an exponential distribution. Numerical results are graphically shown and applications to photochemical studies are discussed. An analytic solution is given for a special composite diffuser that has a uniform layer of finite thickness on its surface.

48 citations

••

TL;DR: In this paper, the reflectances of a number of different barium sulfate substances were measured and a correlation between the reflectance and chemical impurities as well as their grain sizes was found.

Abstract: The reflectances of a number of different barium sulfate substances were measured. The measurements show a correlation between the reflectance and chemical impurities as well as their grain sizes. In view of the problem of developing better working white standards, the importance of these results is discussed with respect to the magnesium oxide white standard, as well as the perfect diffuser which the CIE recently recommended for ultimate adoption as the reference standard.

38 citations