Causes of numerical pathology in formulas for reflectance factor (R), transmittance factor (T), and reflectance factor over a perfectly black background (R-0) under the Kubelka-Munk model are posited, and alternate formulas believed less prone to these pathologies are introduced. Suggestions are offered not only for R, T, and R-0, but also for intermediate or adjunct quantities used in the main formulas. Computational experiments were performed to verify that the new models produce the same results as the existing ones under non-pathological conditions, exhibit acceptable levels of precision in a customary floating-point environment, and are more robust with respect to edge cases where an input quantity is zero. The new formulas performed well, with some evidence that the new hyperbolic forms provide better accuracy than their exponential counterparts. (C) 2021 Society for Imaging Science and Technology.
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