To improve the accuracy of the method, particularly for targets with high refractive indices or for fine discretizations, various corrections to <math>\alpha_j</math> are applied. These include: the lattice dispersion relation (LDR) polarizability (Draine & Goodman, 1993), which adjusts <math>\alpha_j</math> to ensure that the dispersion relation of an infinite lattice of dipoles matches that of the continuous material; the radiative reaction (RR) correction, which compensates for the fact that each dipole radiates energy and is influenced by its own radiation field.▼
The Clausius–Mossotti polarizability for each dipole is given by
where <math>\varepsilon_j</math> is the relative permittivity of the material at the dipole’s position. The dipole volume <math>V_\mathrm{dipole}</math> is constant across all dipoles.
▲To improve the accuracy of the method, particularly for targets with high refractive indices or for fine discretizations, various corrections to <math>\alpha_j</math> are applied. These include: the lattice dispersion relation (LDR) polarizability (Draine & Goodman, 1993), which adjusts <math>\alpha_j</math> to ensure that the dispersion relation of an infinite lattice of dipoles matches that of the continuous material; the radiative reaction (RR) correction, which compensates for the fact that each dipole radiates energy and is influenced by its own radiation field.
==Fast Fourier Transform for fast convolution calculations==
