2 INTEGRATING SPHERES WITH AN INTERVENING SCATTERING SAMPLE

Two integrating spheres placed so that the exit port of one and the entry port of the other are adjacent, with only a sample intervening, will permit the simultaneous determination of the reflectance and the transmittance of the sample. Such a geometry permits measurements to be made as the sample undergoes some external stimulation, such as heat, pressure, or a chemical change. To determine the sample reflectance and the transmittance from the measured values of irradiance within each sphere requires the calculation of the exchange of light through the sample between the spheres. First the power collected by a detector situated in the wall of an integrating sphere is calculated as a function of the area and the reflectance of the wall, the holes, the sample, and the detector for both diffuse and collimated light incident upon the sample and for a sample located at either the exit port (reflectance) or the entry port (transmittance) of the sphere. Next, by using the single-sphere equations, we calculate the effect of the multiple exchange of light between two integrating spheres arranged so that the sample is placed between them. In all the cases of two integrating spheres the power detected is greater than or equal to that for the single sphere and depends on both the reflection and the transmission properties of the sample. Additionally, the effect of a baffle placed between the sample and the detector or of a nonisotropic detector is to reduce the power detected.