On the source of non-linear light absorbance in photosynthetic samples

This study presents a mathematical model, which expresses the absorbance of a photosynthetic sample as a non-linear polynomial of selected reference absorbance. The non-linearity is explained by inhomogeneities of a product of pigment concentration and light path length in the sample. The quadratic term of the polynomial reflects the extent of inhomogeneities, and the cubic term is related to deviation of the product distribution from a symmetric one. The model was tested by measurements of suspension of unstacked tobacco thylakoid membranes of different chlorophyll concentrations in cuvettes of different thicknesses. The absorbance was calculated from the diffuse transmittance and reflectance of sample, illuminated by perpendicular collimated light. The evaluated quantity was a sensitivity defined as the relative difference between the sample absorbance and the reference absorbance to the reference absorbance. The non-linearity of sample absorbance was demonstrated by a characteristic deviation of the sensitivity spectrum from a constant value. The absorbance non-linearity decreased on an increase of the product of pigment concentration and cuvette thickness. The model suggests that the sieve and detour effects influence the absorbance in a similar way. The model may be of interest in modeling of leaf or canopy optics including light absorption and scattering.