Theoretical Study on Radiative Properties of an Optically Thick Painted Layer Containing Spherical Pigment : Case of Normal Incidence

An analysis is presented for the radiative transfer in the semi-infinite medium of an absorbing vehicle containing thee absorbing and anisotropically scattering particles of the pigment to predict the reflection properties of an optically thick painted layer in the wave length range of 0.35-20μm. The effects of the volume concentration (v=0.005-0.55) and the optical property of the pigments (TiO_2, Fe_2O_3) on the bidirectional and hemispherical reflectance are examined. A generalized relation between the hemispherical reflectance and the scattering albedo is obtained. The procedure of expressing the bidirectional reflection intensity as a continuous function of cosine of polar angle and the interpolation method to obtain the hemispherical reflectance at the intermediate optical thickness between the small and the infinitive ones are presented.