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.

Mean effective optical constants of thirteen kinds of plant leaves

Plant leaves grown in a greenhouse and leaves collected from the field have been analyzed to obtain mean effective optical constants based upon diffuse reflectance and transmittance measurements taken over the 0.5-2.5-micro spectral range. These optical constants are used in a generalized flat-plate model to describe the phenomena of leaf reflectance. Analysis procedures developed led to measures of the amount of water and intercellular air spaces in the leaves. Over the 1.4-2.5-micro spectral range, the absorption spectra of leaves are not statistically different from that of pure liquid water. Leaf reflectance differences among the plant leaves over the 0.5-1.4 micro range are caused principally by Fresnel reflections at external and internal leaf surfaces and by plant pigment absorption. Reflectance over the 1.4-2.5-micro range results largely from Fresnel reflections and absorption by water. Data are presented in the form of dispersion curves with 95% confidence bands and tabulated plant leaf absorption spectra. The dispersion curves were assumed to be cubic equations of the form n = Sigmaa(i)lambda(i) (i = 0, 1, 2, 3), where lambda is wavelength. Reflectance measurements at 1.65 micro have been associated with the equivalent water thickness and the intercellular air spaces in the leaf. Accuracy of the plate theory based upon a cubic dispersion curve is shown to be within experimental error.

Relation of light reflectance to histological and physical evaluations of cotton leaf maturity

Cotton plants were grown hydroponically with controlled environment. Third, growth chamber grown true leaves of cotton plants were tagged on the day they became macroscopically visible. Beginning 3.0 days after tagging,five leaf harvests representing maturity dates were made at successive 2- or 3-day intervals. Measurements with a spectrophotometer made on the leaves showed that the largest increase in reflectance, about 5%, and decrease in transmittance, about 8%, occurred between average values for after-tagging-ages of 3.5 days and 8.0 days over the 0.75-1.35-micro wavelength interval. Between after-tagging-ages of 3.5 days and 8.0 days, leaves expanded approximately fivefold, numbers of intercellular spaces approximately doubled, and thicknesses increased 14%. The theory of diffuse reflectance and transmittance of a compact leaf of equivalent water thickness (EWT) specified by D is generalized to include also the noncompact leaf characterized by many intercellular air spaces, can be regarded as a pile of N compact layers separated by infinitesimal air spaces. The void area index (VAI) of a noncompact leaf is given by N - 1, where N is not necessarily an integer. Predictions from the generalized theory include a measure of the water, air, and plant pigments in a leaf. An effective dispersion curve associated with the leaf surfaces is also obtained. A derived parameter D/N largely determines the reflectance and transmittance of a typical leaf over the 1.40-2.50-micro spectral range. A cotton leaf is highly compact when it first unfolds. At this point D/N ~ 180 micro. This value is essentially the leaf thickness. Intercellular air spaces develop rapidly during the next few days, and D/N decreases in value to about 130 micro Subsequently, the leaf cells increase in size with no substantial further increase in the number of intercellular air spaces. This final growth phase is characterized by a slight increase in D/N to a maximum value of about 140 micro. Maximum reflectance of the leaf corresponds to a minimum value of D/N. The parameter D/N is highly correlated with the amount of intercellular air spaces in a leaf.