Leonid Fukshansky

Light gradients in plant tissue

In this paper we suggest a method for calculating light gradients in scattering and absorbing media. The method is based on the Kubelka-Munk theory and involves computational modeling of light fluxes in a multilayered object, when every layer satisfies the prerequisites of the Kubelka-Munk theory. The model also includes specular reflection that may contribute strongly to internal photon fluence rates for diffuse light. To illustrate the possible effects of light gradients, a cotyledon of Cucurbita pepo is described in terms of this model. It is argued that a number of results in in vivo spectroscopy cannot be correctly interpreted unless light gradients or optics in general are included in the discussion, i.e., the light flux at the site of the pigment has to be known. To outline the difficulties involved some methods of measuring light gradients or internal photon fluence rates are critically considered.

ABSORPTION SPECTRA OF LEAVES CORRECTED FOR SCATTERING and DISTRIBUTIONAL ERROR: A RADIATIVE TRANSFER and ABSORPTION STATISTICS TREATMENT

A comprehensive treatment of light propagation through intact leaves based on the theories of radiative transfer and absorption statistics was used to calculate the theoretical absorption spectra of the chlorophyll‐containing particles under conditions of multiple scattering and pigment spatial distribution equivalent to those in a leaf. These spectra were compared with the experimental in vivo spectra of leaves and in vitro spectra of chlorophyll‐protein complexes extracted form these leaves. We conclude that the main discrepancies between the in vivo and in vitro spectra are apparently due to the optical artifacts specific for light propagation in leaves‐multiple scattering and distributional error. Alterations of the pigment properties upon extraction significantly contribute to these discrepancies. The method has an estimated accuracy of about 10% and can be applied to derive the intrinsic optical properties of the photosynthetic mechanism in a leaf, as well as for the systematic study of their changes in the course of light adaptation.

Extension of the Kubelka–Munk theory of light propagation in intensely scattering materials to fluorescent media

The Kubelka–Munk theory of light propagation in intensely scattering materials is extended for application to fluorescing media. As an example, the extended theory is applied to the plant sensory pigment system phytochrome that is masked by chlorophyll.

Estimation of optical parameters in a living tissue by solving the inverse problem of the multiflux radiative transfer

Calculations of radiative transfer require knowledge of the absorption and scattering coefficients and the asymmetry factor of scattering in the medium. A method is presented for estimating these coefficients in living plant leaves from fiber-optic measurements. We consider the plant leaf as consisting of two layers of different refractive indices and with reflecting surfaces. Light intensities at the boundaries of these layers in several irradiated plant leaves have been measured using a thin (70-microm) glass fiber connected to a photomultiplier. The diffuse reflection and transmission were measured with an integrating sphere. From these values we derive an estimation of the scattering and absorption coefficients and the asymmetry factor of scattering applying an inversion of the multiflux theory of light propagation in turbid media. In addition, we compare these coefficients with those obtained by using the Kubelka-Munk theory.

On the interpretation of absorption spectra of leaves - II. The non-absorbed ray of the sieve effect and the mean optical pathlength in the remainder of the leaf.

Abstract— The sieve effect and scattering within leaves are analysed by the use of a simple model. By plotting the leaf transmittance (corrected for light not entering the leaf) vs the transmittance of an equivalent amount of homogeneous plastid pigments, an intercept is found where the latter is zero. This minimum transmittance represents the fraction of the leaf area devoted to the ray of the sieve effect which strikes no chloroplasts. It varied between 7% and 0.2% in non‐senescent leaves. When this was subtracted from the leaf spectrum, the peak absorbance was greater than that of the homogeneous leaf pigments in all cases. The ratio of the leaf absorbance to that of the homogeneous pigments, at the same wavelength, is the apparent optical pathlength, which increases with decreasing absorbance. By plotting this ratio vs the absorbance of the equivalent homogeneous pigment, an intercept is found where the latter is zero. This intercept is interpreted as an estimate of the true mean scattering pathlength. Leaves with high chlorophyll contents had low pathlengths (mean and SD = 2.30 ± 0.25); with moderate and low contents, the values were higher (2.75 ± 0.28, 3.95 ± 0.77). Another application of the model gave values between 3 and 4 for the true scattering pathlength.

On the interpretation of absorption spectra of leaves. I, Introduction and the correction of leaf spectra for surface reflection

Abstract— Reflectance and transmittance spectra of leaves and their sum can be corrected to relate only to the light actually entering the leaf, if the reflectance of the epidermal surface is known. The latter is found if the leaf reflectances at several wavelengths near the transmittance minimum in the red are plotted vs the transmittances of a homogeneous suspension of the native pigment‐proteins at the same chlorophyll content per unit area and at the same wavelengths. With non‐senescent leaves, the relation is linear and the extrapolation of the pigment transmittance to zero gives the value for the surface reflection. Surface reflectance data (both adaxial and abaxial) are given for the leaves of a number of trees and a few herbs, plus examples of the raw and corrected spectra. With normal, glaucous leaves, the adaxial reflectance averaged 4.5% of the incident light (n= 23, range = 3.7 −5.9, standard deviation = 0.4). The reflectances of the abaxial surfaces ranged between 7 and 13% since additional near‐surface reflection occurred at the inside of the epidermis and in the spongy mesophyll. Reflectance and transmittance data demonstrated strong absorption in the epidermis below 480 nm.

OPTICS OF A BIFACIAL LEAF: 1. A NOVEL COMBINED PROCEDURE FOR DERIVING THE OPTICAL PARAMETERS

Abstract— A novel experimental‐theoretical procedure, deriving optical parameters of a bifacial leaf, is presented and analyzed. Its theoretical basis is the four‐flux approximation of the radiative transfer theory. Its experimental basis is three‐dimensional measurements of internal radiances at different depths and in different directions within a leaf by using optical microprobes. The intrinsic instrumental error of the microprobe measurements is accounted for by a special correcting theory. The treatment yields the spectral curves for attenuation, scattering and absorption coefficients as well as for the asymmetry of scattering in both palisade and spongy tissue layers. The values of obtained optical parameters were verified by comparing calculated transmission and remission of a leaf with those measured with the integrating sphere. It is concluded that the treatment provides a sound basis for the analysis of the light microenvironment as a function of leaf structure and the nature of incident light.

Absorption statistics in turbid media

Abstract The influence of the spatial pattern of absorption on a measured absorbance is known as the distributional error or sieve-effect. This phenomenon distorts the absorption spectra of objects with an inhomogeneous pigment distribution (e.g. intact biological tissues) compared to those with an evenly-spaced pigment. A quantitative treatment of the sieve-effect is proposed for intensely scattering objects based on a variational principle. The basis for this treatment is hierarchical statistics, a similar but more complex contruction than the derivation of the most probable distribution in classical statistical mechanics.

Correcting remission and transmission spectra of plant tissue measured in glass cuvettes: a technique.

A method for measuring transmittance and reflectance of plant material in glass cuvettes using a single-beam spectrophotometer with an integrating sphere attachment is described. This method requires extensive processing of the originally measured values as these are distorted by multiple reflections of the diffusely transmitted or reflected light. Most of the theories on light interaction with scattering materials require data processing to meet the theorys prerequisites. Therefore, the complicated evaluation does not restrict the applicability of the method. Special attention is given to the 60 degree/diffuse incidence requirement of the Kubelka-Munk theory. It is argued that the 60 degree/diffuse requirement is not essential for thick scattering layers. It is further stressed that a better knowledge of the optical properties should be of great help in many fields of biology.

Optics of a Bifacial Leaf: 2. Light Regime as Affected by the Leaf Structure and the Light Source

Abstract— This paper presents a theoretical analysis of the light regime in a bifacial leaf performed on the basis of optical parameters estimated from the measurements of internal light fluxes with optical microprobes. Pathlength distributions, absorptances and gradients of absorption rates are calculated as affected by different aspects of leaf optics and morphology: scattering of tissue layers, overall scattering, surface reflection, thickness and absorption to attenuation ratio in single tissue layers. The in vivo measured transmission spectrum of a leaf is correlated with the in vitro chlorophyll spectrum by accounting for two main disturbing factors: multiple scattering (pathlength statistics) and distributional error (absorption statistics).