Willstätter-stoll theory of leaf reflectance evaluated by ray tracing

The widely accepted Willstätter-Stoll (W-S) theory of leaf reflectance has been investigated by extensive ray tracing through a model (W-S model) in which the leaf cellular structure is approximated by circular arcs. Calculations were performed on an IBM 1800 computer. The W-S model is treated as a two-dimensional, uncentered optical system consisting of a single medium and air. Optical properties of the medium are specified by a complex index of refraction. Given an incident ray, new reflected and transmitted rays are produced at each interface with properties determined by the laws of Snell, Fresnel, and Lambert. Calculations indicate that the W-S model, as exemplified by their artist's conception, is too transparent, that is, the magnitude predicted for transmittance is too high. Transmittance is still too high if each interface is treated as a diffusive instead of a smooth surface. The W-S model can be easily improved, however, by introduction of more intercellular air spaces. The modified W-S model promises to be an excellent representation of physical reality. Accurate predictions, however, require an inordinate amount of computer time.