P. Kubelka and F. Munk, Z. Tech. Physik 11, 593–601 (1931).
P. Kubelka, J. Opt. Soc. Am. 38, 448–457 (1948).
T. H. Morton, J. Soc. Dyers Colourists 79, 238–242 (1963).
See Ref. 2, Eqs. (19) and (20).
See Ref. 2, Eq. (22).
See Ref. 2, Eq. (28).
D. B. Judd, J. Res. Natl. Bur. Std. 19, 287–317 (1937); Paper Trade J. 106, 39–46 (1938).
The ratio α can be calculated from a transmittance curve of the dye in a clear substrate which is chemically similar to the substrate used for dyeing. An example is given in a subsequent paragraph. Alternatively, it may be determined from measurements on the dyed sample by a method to be described in a subsequent publication.
A convenient table for the conversion of R∞ to ρ and back, with a spacing of 0.001 in R∞, is given by D. B. Judd, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1952), pp. 358–362.
P. Kubelka, Ref. 2, Eq. (25a).
In the case of paper, for example, owing to inhomogeneity in the sheet, the measured thickness is not the same as the true effective thickness.
E. Allen, Am. Dyestuff Reptr. 48, 27–29 (1959).
S. N. Glarum and S. E. Penner, Am. Dyestuff Reptr. 43, P310–P314 (1954).
Other examples are given in Ref. 12.
Papermaker's brightness is defined by TAPPI as the reflectance through a specifically defined filter in a carefully defined instrument. Often the reflectance at 459 mµ is used as an approximation. The reflectance at 440 mµ, used in this study, is probably slightly lower than the true "brightness" value, but is reliable as a relative indication of "brightness."
E. Allen, J. Opt. Soc. Am. 47, 933–943 (1957); Am. Dyestuff Reptr. 46, 425–432 (1957).