); [EMAIL_ADDRESS] (T.A. ); [EMAIL_ADDRESS] (Y.I. ); [EMAIL_ADDRESS] (H.N. ); [EMAIL_ADDRESS] (G.K.); [EMAIL_ADDRESS] (M.W.) Y. Inoue  
Division of Mechanical and Space Engineering, Faculty of Engineering, Hokkaido University, Kita 13 Nishi 8, Kita-ku, Sapporo 060-8628, Hokkaido, Japan; [EMAIL_ADDRESS] (I.T. ); [EMAIL_ADDRESS] (T.A. ); [EMAIL_ADDRESS] (Y.I. ); [EMAIL_ADDRESS] (H.N. ); [EMAIL_ADDRESS] (G.K.); [EMAIL_ADDRESS] (M.  
but is invalid at several conditions, such as low-scattering medium [5]. A target medium is regarded as a scattering medium (continuous medium) with optical properties on the length scale. The optical properties (e.g., scattering and absorption coefficients) specify the strengths of light scattering and absorption. The optical properties have been evaluated by inverse analysis as parameters for biological tissues and agricultural products [6; 7; 8]. The inverse analysis optimizes a difference in light intensity between measured and calculated results using the RTT and incorporates multiple computations of light propagation. This fact suggests that an efficient model of light propagation is desirable in addition to accuracy. Because the validation of the results by inverse analysis is quite difficult for biological tissues and agricultural products, the validation test is necessary for tissue phantoms [9]. As liquid tissue phantoms, colloidal suspensions have been widely used. Colloidal particles correspond to scatterers, and the scattering properties vary with the volume fractions of the particles. The electromagnetic theory (EMT) can calculate the scattering properties for colloidal suspensions on a length scale comparable to the optical wavelength. As the EMT, the independent scattering theory (IST) and dependent scattering theory (DST) have been developed. The IST treats no interaction of the electric fields scattered by particles, while the DST treats the interference of the fields in the far-field [10; 11]. The scattering properties using the IST agree well with those by the inverse analysis at a lower volume fraction than approximately 5%, while the results using the DST do at a high volume fraction up to approximately 20% [12; 13; 14]. For a dilute suspension (low volume fraction), it is easy to adjust values of the scattering properties because of the linear dependence of the scattering properties on the volume fraction. Meanwhile, the adjustment is difficult for a dense suspension (high volume fraction) due to a complicated dependence of the scattering properties on the volume fraction. Hence, clarifying the complicated dependence is significant as fundamental research of optical imaging techniques. Many researchers have examined the scattering properties for dense suspensions by the DST [10; 13; 14; 15; 16; 17; 18; 19]. Meanwhile, research for the dependence of light propagation on the volume fraction has been less reported to the best of our knowledge. In the research field of microwave remote sensing, [PERSON] and co-workers have examined radiative transfer for snow layers using the RTE combined with the DST (RTE-DST) [11]. Recently, some authors have examined the near-infrared light propagation by the RTE-DST for dense colloidal suspensions based on the analytical solutions of the time-dependent RTE [19]. However, the dependence of light propagation on the volume fraction has not been fully clarified. In particular, a range of the volume fraction where the diffusion approximation holds, is unclear, although the length and time scales for the diffusion approximation have been extensively discussed [1; 20; 21; 22]. Because the volume fraction is a control parameter for phantom experiments, the information of the volume fraction range is helpful. In this study, we numerically calculated the steady-state RTE-DST for aqueous alumina suspensions, widely used as a liquid phantom [9], at different volume fractions up to 20%. The numerical schemes for the RTE-DST have been little discussed in previous researches.