Journal of Quantitative Spectroscopy & Radiative Transfer 73 (2002) 111–120 www.elsevier.com/locate/jqsrt Dierential approximations for transient radiative transfer through a participating medium exposed to collimated irradiation C.-Y. Wu * , N.-R. Ou Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC Received 10 April 2001; accepted 1 June 2001 Abstract First, we apply the modied dierential approximation (MDA) suggested by Chandrasekhar to transient radiative transfer in a scattering planar medium exposed to collimated pulse irradiation. Next, a hybrid method of the P 1=3 approximation suggested by Olson and the MDA is developed. The hybrid method may be referred to as the modied P 1=3 approximation (MP 1=3 A) and is also applied to the same example. Comparisons of the results obtained by solving the MDA, the MP 1=3 A and the exact integral equation are made. The comparisons show that the temporal distribution of the transmissivity obtained by the MDA contains a small protuberance or an abrupt slope change, which decreases with the decrease of the scattering albedo. The results obtained by the MP 1=3 A are more accurate than those obtained by the MDA for most of the cases considered, because the MP 1=3 A corrects the propagation speed of the transmitted radiation. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Time-dependent radiation transport; Modied dierential approximation; Collimated irradiation; Integral equation; Scattering media 1. Introduction Scattering and propagation of a laser pulse through a participating medium is of impor- tance in many elds, including lidar and optical communication [1], remote sensing [2], com- puter tomography [3] and photodynamic therapy [4]. Recently, Pham and coworkers [5] used frequency-domain measurements to estimate the optical properties of tissue-like media for * Corresponding author. Fax: +886-6-235-2973. E-mail address: cywu@mail.ncku.edu.tw (C.-Y. Wu). 0022-4073/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S0022-4073(01)00174-1