| A Cramer-Rao bound (CRB) is developed to characterize the information content about scattering parameters through the wave scattering information contained in reflective (R), transmissive (T), and combined R plus T data. The analysis is developed for scalar wave scattering systems in one-dimensional space, paying particular attention to elastic scatterers, which simplifies the signal model (relative to more general scattering systems), thereby allowing closed-form expressions for the CRB for special cases. The derived CRB results quantify the effect of multiple scattering, be it in enhancing or in diminishing imaging capabilities, relative to the Born approximation model which is customarily used as the standard reference for resolution limits (the so-called "diffraction limit"). The work also discusses the role of the measurement configuration for scatterer information extraction (e.g., reflective data applicable to monostatic radar, versus transmissive data applicable to bistatic radar). In particular, we show that certain natural parameters control the enhancement in the estimation performance from scattering data. Additionally, we discuss how specific sensing configurations enhance the estimation associated to those parameters. |
