Comparison between discrete dipole and exact techniques

AbstractFour computer codes based on the Discrete Dipole Approximation are compared againsteach other and against exact solutions for five di erent scattering geometries. The interestis in the accuracy of intensity and linear polarization values the codes produce and in thecomputational time needed. 1 Introduction Most of the existing light scattering programs can be divided into three physically di erent categories:ray-optics (RO), geometrical optics (GO) and wave optics (WO) approaches. A classical example of theray-optics treatment is the Radiative Transfer Equation (RTE), see, e.g., van de Hulst [1]. The GO methodsare basically the same as the RO complemented only by the di raction correction close to the forwardscattering. Finally, the WO methods can be derived more or less directly from the Maxwell’s equationsand are, in principle, exact. As a qualitative recipe it can be stated that the RO methods can be appliedto sparsely packed geometries where the packing density is less than about 10%. GO approach suits forlarge solid particles and in all the other cases the exact WO methods are a must. Our long standing interesthas been to analyze light scattering by planetary regoliths and products from the paper industry. In theseapplications the WO methods are the only possible ones because the packing density in both these casescertainly exceeds 10%.Among the WO methods the discrete dipole approximation (DDA), also known as the coupled dipoleapproximation, has several special advantages over all the other existing approaches. These are that they canbe applied to quite arbitrary shaped geometries which can be inhomogeneous and anisotropic. As alreadyexplicitly in its name the DDA has a major drawback in being an approximation although if infinite CPUtime would be possible the results should become exact. The other smaller drawback comes from the factthat if orientation averages are needed then the computationally demanding linear equations must be solvedrepeatedly.