* Corresponding author. Tel.: #1-410-516-6210; fax: #1-410-516-4316. E-mail address: kribus@titan.me.jhu.edu (A. Kribus). Journal of Quantitative Spectroscopy & Radiative Transfer 69 (2001) 415}430 Volumetric optical properties of fully anisotropic participating media C. Zhang,A.Kribus*,R.Ben-Zvi Department of Environmental Sciences and Energy Research, Weizmann Institute of Science, Rehovot 76100, Israel Department of Mechanical Engineering, The John Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA Solar Facilities Unit, Weizmann Institute of Science, Rehovot 76100, Israel Received 25 August 1999; accepted 1 May 2000 Abstract The average absorption and scattering properties of participating media (PM) are usually found from experiments,eitheraphysicalmeasurementor,ifpossible,anumericalray-tracingexperiment.Theanalysis oftheexperimentalresultsisnotsimplewhenthemediumisfullyanisotropic,i.e.,extinctiondependsonthe orientation of the incident radiation. Common approaches require a full solution of the radiative transfer equation (RTE) in the sample, and an iterative optimization procedure to "nd the optical properties. We presentanapproximateanalysismethodthatisbasedontreatingthesampleasasinglecontrolvolume.This leadstoadirect,non-iterativesolution,usingasetofalgebraicequationsratherthanafullsolutionofthe RTE. The procedure computes a representation of the optical properties for the most general case of anisotropy,whichiscompatiblewiththediscreteordinatemethodorthe "nitevolumemethodapproaches. Wediscussexperimentalerror,theerrorduetothesinglecontrolvolumeapproximation,andthee!ectofthe optical thickness of the sample. The performance and robustness of the procedure are demonstrated for several test cases.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Discrete ordinates method; Anisotropic extinction; Anisotropic scattering; Inverse problem 1. Introduction Thepropagationofradiationthroughaparticipatingmedium(PM)isanimportantproblemin a large number of research "elds, such as atmospheric sciences, oceanography, remote sensing, 0022-4073/01/$-see front matter  2001 Elsevier Science Ltd. All rights reserved. PII:S0022-4073(00)00090-X