The point-interaction approximation (or the Foldy–Lax approximation) of the electromagnetic fields generated by a cluster of small-scaled inhomogeneities is derived in the mesoscale (i.e., mesoscopic scale) regime, that is, when the minimum distance \(\varvec{\delta }\) between the particles is proportional to their maximum diameter \({\varvec{a}}\) in the form \(\varvec{\delta }={\varvec{c}}_r \, {\varvec{a}}\) with a positive constant \({\varvec{c}}_r\) that we call the dilution parameter. The small particles are modeled by anisotropic and variable electric permittivities and/or magnetic permeabilities with possibly complex values. We provide the dominating field (the so-called Foldy–Lax field) with explicit error estimates in terms of the dilution parameter \({\varvec{c}}_r\) uniformly in terms of the distribution of these inhomogeneities. Such approximations are key steps in different research areas as imaging and material sciences.

由小尺度不均匀性簇产生的电磁场的点相互作用近似（或Foldy-Lax近似）是在中尺度（即介观尺度）状态下得出的，即最小距离\（\ varvec粒子之间的{\ delta} \）与最大直径\（{\ varvec {a}} \\）成正比，形式为\（\ varvec {\ delta} = {\ varvec {c}} _ r \，{\ varvec {a}} \）具有正常数\（{\ varvec {c}} _ r \）我们称之为稀释参数。通过具有可能复杂值的各向异性和可变的介电常数和/或磁导率对小颗粒进行建模。根据这些不均匀性的分布，我们根据稀释参数\（{\ varvec {c}} _ r \）均匀地为主导字段（所谓的Foldy-Lax字段）提供显式误差估计。这种近似是成像和材料科学等不同研究领域的关键步骤。