William A. Allen

Interaction of Light with a Plant Canopy

The Kubelka–Munk (K–M) theory has been applied to light interaction with leaves stacked in a laboratory spectrophotometer. The theory can also be applied to an actual field plant canopy. The K–M theory is a two-parameter generalization of the one-parameter Bouguer–Lambert, or Beer’s law, relation. The older theory accounts for transmittance of a medium but not for reflectance. The K–M theory, however, yields a theoretical value both for reflectance and transmittance. The K–M theory is applied in this paper to the reflectance and transmittance of stacked mature cotton leaves over the spectral range 0.5–2.5 μ. The standard deviation between theory and experiment, after known biases are calculated and removed from the data, is about 1%—a discrepancy well within experimental error. A procedure is developed to apply the K–M theory to an actual plant canopy. The method involves regression analysis to light flux measurements within a plant canopy. Differential coefficients are derived for use in both stacked-leaf and canopy applications.

Interaction of Isotropic Light with a Compact Plant Leaf

A transparent plate with rough plane-parallel surfaces is used as a theoretical model to explain the interaction of diffuse light with a compact plant leaf. Effective optical constants of a corn leaf have been determined from leaf reflectance and transmittance measured over the spectral range 0.5–2.5 μ with a recording spectrophotometer. The effective index of refraction at 0.5 μ for the corn leaf is not inconsistent with the refractive index of epicuticular wax. The effective absorption spectra of the corn leaf appears to be a superposition of the absorption coefficients of chlorophyll and pure liquid water. Residual spectral data from other leaf constituents are at the resolution limit of the spectrophotometer. The plate model of a leaf is also used to determine moisture content of the corn leaf from reflectance and transmittance measurements.

Dynamics of a Projectile Penetrating Sand

The experiment reported in this paper was designed to obtain data on the dynamics of a nonrotating, conical‐nosed projectile penetrating randomly‐packed sand. Position versus time measurements for the projectile in sand were obtained by means of a photographic‐electronic chronograph developed for the purpose. The striking velocity v0 of all rounds was about 700 m/sec. The negative acceleration of a 5‐in. long, 0.50‐caliber, 80‐gram projectile was found to be roughly expressible by the equation −dv/dt=αv2+βv+γ where the coefficients α, β, and γ are positive constants. This general relation includes as special cases the conventional penetration formulas of Robins‐Euler, Poncelet, and Resal. A new theory of penetration is proposed based on the equations: −dv/dt=αv2,v0>v>vc;−dv/dt=βv2+γ,vc>v>0 where the coefficients α, β, γ are positive constants and α<β. An abrupt transition in the drag force that occurs at the critical velocity vc of about 100 m/sec is believed due to transition from inelastic to quasi‐elas...

Reflectance of cotton leaves and their structure.

Abstract Cotton plants were grown hydroponically with low-, medium-, and high-salinity substrate levels formulated with sodium chloride. Leaves were sampled from third and fourth nodes down from apexes of cotton plants, simulating what an overhead remote sensor would see. A spectrophotometer was used to measure reflectance and transmittance of light impinging on upper surfaces of individual leaves. Total reflectance of light in the 750- to 1300 -mμ spectral range was greater from leaves of cotton plants grown in medium- and high-salinity substrates than from those grown in low-salinity substrates. This increase in reflectance and a lessening in absorptance were consistent with the observed thicker leaves of the saline substrate-grown plants which had larger palisade cells and loosely arranged spongy mesophyll. These structural changes resulted in more intercellular spaces, thus supporting the premise that internal scattering of light is increased by cell wall—air cavity interfaces.

Refractive index of plant cell walls

Air was replaced with media of higher refractive indices by vacuum infiltration in leaves of cucumber, blackeye pea, tomato, and string bean plants, and reflectance of noninfiltrated and infiltrated leaves was spectrophotometrically measured. Infiltrated leaves reflected less light than noninfiltrated leaves over the 500-2500-nm wavelength interval because cell wall-air interfaces were partly eliminated. Minimal reflectance should occur when the average refractive index of plant cell walls was matched by the infiltrating fluid. Although refractive indices that resulted in minimal reflectance differed among the four plant genera, an average value of 1.425 approximates the refractive index of plant cell walls for the four plant genera.

Plant-canopy irradiance specified by the Duntley equations

The Duntley equations for propagation of unidirectionally incident light through a diffusing medium have been generalized and interpreted to account for the diurnal nature of near-infrared radiation measured in an Ithaca, N. Y. corn canopy. The Duntley optical coefficients associated with the specular component of light were assumed to vary as the secant of the sun’s zenith angle. Generalization of the Duntley relations was required in order to predict values of irradiance within the canopy and to account for the effect of background reflectance from the soil. Five independent measurements of canopy irradiance suffice to determine the Duntley parameters. Twenty-four measurements of transmittance within the canopy were used, however, in a least-squares calculation to obtain the best fit of the Duntley equations to irradiance within the corn canopy. The Duntley equations fit the experimental results within a standard deviation of 3.2% for a period from noon to sundown. If the laboratory measurements of optical constants for a single corn leaf are used as constraints, the Duntley equations fit the data to within 3.7%. The best fit to near-ir-transmittance measurements occurs when zero absorptance is assumed for the canopy. The Duntley equations reduce to a three-parameter representation for the special case of no absorptance.

Electrooptical Remote Sensing Methods as Nondestructive Testing and Measuring Techniques in Agriculture

Characteristics of plants that influence reflectance and emission of electromagnetic energy are discussed. Four main spectral regions are influenced by plants. These wavelength bands include the visible region of chlorophyll absorption, very near ir wavelengths, where plant structure is of major importance, the near and middle ir wavelengths, where water and CO(2) absorption predominate, and the far ir region of thermal ir emission. Soil characteristics that influence reflectance and emission of energy are discussed. Nondestructive testing techniques described include laboratory spectrophotometry, field spectrometry, color photography, radiometry, and generation of line scan imagery. Spectrophotometer and spectrometer reflectance data obtained in the laboratory and field are related to interpretation of remote sensing imagery. Model studies that permit predictions of reflectance from plant canopies are described. The principle of multispectral sensing which permits utilization of multiple wavelength channels for establishing unique plant and soil signature is reviewed.

Mean Effective Optical Constants of Cotton Leaves

The plate description of a typical, thin, compact plant leaf, introduced previously, has been generalized to the noncompact case and applied to experimental data including average reflectance and transmittance measurements on 200 mature, field-cotton leaves. A compact leaf has few and a noncompact leaf has many intercellular air spaces in the mesophyll. No statistically significant difference was found between the average leaf thickness and the mean effective water thickness of the leaves. The Kubelka–Munk scattering coefficient s for a typical leaf, measured at the 1-μ spectral region, is approximated by the relation s = r/t, where r and t, respectively, are the reflectance and transmittance of the leaf. The approximate equality of r and t, noted by previous investigators, is explained on the basis of the scattering of diffuse light within the leaf by critical internal reflections. Predictions from the plate (P) model for cotton leaves compare favorably with those of the Kubelka–Munk (K–M) and Melamed (M) theories. Applied to vegetation, all three theories predict a characteristic linear dimension related to the cellular structure of the leaf.

Penetration of a rod into a semi-infinite target

Abstract The penetration of metal rods into semi-infinite metal targets has been investigated experimentally at velocities up to 0.3 cm/μsec. The rods were composed of Au, Pb, Cu, Sn, Al, and Mg; the targets were aluminum. Results are compared with predictions from the hydrodynamic theory of jet penetration. Basic assumptions of the hydrodynamic theory were used to determine an effective yield strength of the target-rod combination. Experimental results indicate that the effective yield strength is relatively independent of the strength of the rod. The hydrodynamic theory of penetration was determined to be generally acceptable except where the density of the jet is much greater than that of the target.A gold jet reveals a new effect of secondary penetration which results in penetration greater than that predicted by theory.

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 artists 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.