A simplified two layer model for light diffuse reflectance in thin skin fruits

Abstract

A simple model of light diffuse reflectance in thin skin fruits is presented. The model is based in a semi-infinite two-layer geometry (skin and flesh) and introduces simplifications due to the fact that the first layer is very thin. The flesh is described in terms of the usual reduced scattering and absorption coefficients µs′ and µa but the skin is modeled by simple reflection (R), absorption (A) and transmission (T) coefficients. The problem of diffuse reflectance is thus reduced to the problem of determining the four constants µs′, µa, R and T. It is shown that the problem can be solved by using absolute reflectance and spatially resolved reflectance measurements simultaneously. The coefficients µs′ and µa are determined by the usual fit of the diffuse reflectance profile (photons re-emitted from the flesh far from the incidence point) to the diffusion approximation. The coefficients R and T are determined by a second fit involving the total reflectance profile (photons reemitted both from skin and flesh), the incident beam profile and the diffuse reflectance profile calculated according to the previously determined values of µs′ and µa. The anisotropy of the light re-emitted by the fruit can also be roughly compared with the Lambertian expected behavior. In order to test the model we have followed a population of 22 ‘Rocha’ pears along a period of two weeks. We have then performed the population averages along the time and checked the plausibility of the values obtained for µs′, µa, R and T according to the expected fruit physiological changes along ripening. The results show that all parameters are physically acceptable and evolve in time according to the expected fruit ripening physiology.