Analysis of reflectance and transmittance measurements on absorbing and scattering small samples using a modified integrating sphere setup.

The aim of the present paper is to analyze reflectance and transmittance measurements on small scattering and absorbing samples. The long term goal is to perform quantitative, spectroscopic in vivo measurements of pigments in small samples of plant material. Small samples such as small leaves constitute a special experimental challenge in cases in which the sample beam has a larger cross-sectional area than the sample. The experimental errors introduced when measuring reflectance and transmittance on small absorbing and scattering samples are investigated theoretically and experimentally by using a blue polyester sample as an appropriate test sample. The experiments are performed with either a mask or a lens setup combined with a mask inserted in the sample beam. In particular, the errors introduced in the reflectance measurements can be very large and larger than 100%. It is shown that any direct illumination of the mask must be avoided. To obtain more accurate values for the reflection coefficient it is necessary to combine the mask with a focusing lens system, adjust the mask and sample very carefully, and choose the ratio between the aperture of the mask and the beam area as large as possible. In the case of transmittance measurements, it is shown that the combination of a special sample fixture and a lens system gives rise to smaller errors compared to the errors introduced by the mask alone or the mask combined with a focusing lens system.