Sufficiency of individual versus collections of DIGP maps for inverse scattering

Determine whether an individual double-indexed geometric-phase (DIGP) map for a fixed index pair $(p,q)$ is sufficient for inverse-scattering problems, or whether a collection of DIGP maps generated from multiple $(p,q)$ pairs and the same polarimetric measurements is required.

Background

The paper introduces the double-indexed geometric phase (DIGP) as a family of polarization-state observables parameterized by real indices $p$ and $q$. For thin films and three-dimensional scattering objects, the authors compute multiple DIGP maps from the same underlying polarimetric data and suggest that these maps may support inverse retrieval of morphological and electromagnetic parameters.

The unresolved issue is whether one DIGP map, corresponding to a single $(p,q)$ pair, contains enough information for reliable inverse scattering, or whether several maps are needed. A preliminary principal component analysis indicates substantial redundancy among collections of DIGP maps, but the analysis does not establish the minimum sufficient collection or settle whether an individual map can provide robust parameter retrieval.