Fault detection in dielectric grid scattering

The problem of diagnosing a grid of small (in terms of the probing wavelength) dielectric scatterers is considered. The aim is to detect and locate possible defects occurring within a known grid when one (or more) scatterer is removed/missing (fault). The study is developed for the canonical case of a TM scalar two-dimensional geometry with the scatterers consisting of dielectric cylinders of small circular cross section. The scattering by a fault is modeled by relaying only to a priori information about the complete grid which leads to a numerically effective inversion procedures as the bulk of the numerical effort is to be done only once. Inversion is achieved by a truncated singular value decomposition scheme and results are provided in terms of closed form expressions for the probability of detection and of false alarm. This allows us to foreseen the achievable performance and to highlight the role of scattering configuration parameters. Numerical examples are also enclosed to corroborate theoretical outcomes. The case of two or more faults is considered as well. For such a case it is numerically shown that detection method still works well even though multiple scattering (occurring between faults) is neglected.