This paper presents a scatterer information estimation method for both E- and H-polarizations based on a time-domain saddle-point technique (TD-SPT). The method utilizes numerical data of the response waveforms of the reflected geometric optical ray (RGO) series, which constitute the backward transient scattering field components when a line source and an observation point are at the same location. A scatterer selected in the paper is a two-dimensional (2-D) coated cylinder. The three types of scatterer information are the relative permittivity of a coating medium layer and its thickness, and the outer radius of a coated cylinder. Specifically, the scatterer information estimation formulas are derived by applying the TD-SPT represented in RGO series to the amplitude intensity ratios (AIRs) of adjacent RGO components. By focusing on the analytical results that the AIRs are independent of polarization, we analytically clarify that all the estimation formulas derived here denote polarization independence. The estimates are obtained by substituting numerical data of the peaks of the response waveforms of the RGO components and their arrival times, as well as numerical parameters of a pulse source, into the estimation formulas and performing iterative calculations. We derive approximations to the estimation errors that are useful in quantitatively evaluating the errors of the estimates. The effectiveness of the scatterer information estimation method is substantiated by comparing the estimates with the set values. The polarization independence of the estimation formulas is validated numerically by contrasting the estimates for E- and H-polarizations. The estimation errors are discussed using the approximations to the errors of the estimates when a line source and an observation point are at the same location. Thereafter, the discrepancies that arise between the estimation errors when a line source and an observation point are at different locations are discussed. The methods to control the estimation accuracy and the computational time are also discussed.