We present the analysis of interferometry diagnostics with the user-friendly Talbot Numerical Tool (TNT), a Fourier-based postprocessing code that enables real-time assessment of plasma systems. TNT performance was explored with visible and infrared interferometry in pulsed-power-driven $Z$ -pinch configurations to expand its capabilities beyond Talbot X-ray interferometry in the high-intensity laser environment. TNT enabled accurate electron density characterization of magnetically driven plasma flows and shocks through phase-retrieval methods that did not require data modification or masking. TNT demonstrated enhanced resolution, detecting below 4 % fringe shift, which corresponds to 8.7 × 10¹⁵ cm ⁻² within 28 μ m, approaching the laser probing system limit. TNT was tested against a well-known interferometry analysis software, delivering an average resolving power nearly ten times better ( ∼ 28 μ m versus ∼ 210 μ m) when resolving plasma ablation features. TNT demonstrated higher sensitivity when probing sharp electron density gradients in supersonic shocks. A maximum electron areal density of 4.1 × 10¹⁷ cm ⁻² was measured in the shocked plasma region, and a minimum electron density detection of ∼ 1.0 × 10¹⁵ cm ⁻² was achieved. When probing colliding plasma flows, the calculations of the effective adiabatic index and the associated errors were improved from γ∗=2.6 ± 1.6 – 1.4 ± 0.2 with TNT postprocessing, contributing valuable data for the interpretation of radiative transport. Additional applications of TNT in the characterization of pulsed-power plasmas and beyond are discussed.