text: In 1966, Harry G. Hecht (with Wesley W. Wendlandt) published a book entitled "Reflectance Spectroscopy", because "unlike transmittance spectroscopy, there were no reference books written on the subject" of "diffuse reflectance spectroscopy", and "the fundamentals were only to be found in the old literature, some of which was not readily accessible". Hecht describes himself as a novice in the field at the time, and said that if he had known that Gustav Kortüm "a great pillar in the field" was in the process of writing a book on the subject, he "would not have undertaken the task".  Hecht was asked to write a review of Kortüms book and their correspondence concerning it led to Hecht spending a year in Kortüms laboratories.  Kortüm is the author most often cited in the book.
  One of the features of the remission function emphasized by Hecht was the fact that
  should yield the absorption spectrum displaced by .  While the scattering coefficient might change with particle size, the absorption coefficient, which should be proportional to concentration of an absorber, would be obtainable by a background correction for a spectrum.  However, experimental data showed the relationship did not hold in strongly absorbing materials.  Many papers were published with various explanations for this failure of the Kubelka-Munk equation.  Proposed culprits included: incomplete diffusion, anisotropic scatter ("the invalid assumption that radiation is returned equally in all directions from a given particle"), and presence of regular reflection. The situation resulted in a myriad of models and theories being proposed to correct these supposed deficiencies.  The various alternative theories were evaluated and compared.
  In his book, Hecht reported the mathematics of Stokes and Melamed formulas (which he called “statistical methods”).  He believed the approach of Melamed, which “involve a summation over individual particles” was more satisfactory than summations over “plane parallel layers”.  Unfortunately, Melamed's method failed as the refractive index of the particles approached unity, but he did call attention to the importance of using individual particle properties, as opposed to coefficients that represent averaged properties for a sample.  E.L. Simmons used a simplified modification of the particle model to relate diffuse reflectance to fundamental optical constants without the use of the cumbersome equations.  In 1975, Simmons evaluated various theories of diffuse reflectance spectroscopy and concluded that a modified particle model theory is probably the most nearly correct.
  In 1976, Hecht wrote a lengthy paper comprehensively describing the myriad of mathematical treatments that had been proposed to deal with diffuse reflectance. In this paper, Hecht states that he assumed (as did Simmons) that in the plane-parallel treatment, the layers could not be made infinitesimally small, but should be restricted to layers of finite thickness interpreted as the mean particle diameter of the sample. This is also supported by the observation that the ratio of the Kubelka–Munk absorption and scattering coefficients is  that of corresponding ratio of the Mie coefficients for a sphere.  That factor can be rationalized by simple geometric considerations, recognizing that to a first approximation, the absorption is proportional to volume and the scatter is proportional to cross sectional surface area.  This is entirely consistent with the Mie coefficients measuring absorption and scatter at a point, and the Kubelka–Munk coefficients measuring scatter by a sphere.
  To correct this deficiency of the Kubelka–Munk approach, for the case of an infinitely thick sample, Hecht blended the particle and layer methods by replacing the differential equations in the Kubelka–Munk treatment by finite difference equations, and obtained the Hecht finite difference formula:
  Hecht apparently did not know that this result could be generalized, but he realized that the above formula "represents an improvement … and shows the need to consider the particulate nature of scattering media in developing a more precise theory".