Simulates the inverse curve-fitting problem. Contrasts a Naive 2-Layer regression against a Rigorous 3-Layer regression when analyzing noisy experimental data corrupted by physical surface contamination and hardware polarization leakage.
In Variable Angle Ellipsometry (VAE), the dominant error is Model Mismatch rather than random noise. If a student generates experimental data containing a real physical hydration layer (a 3-layer reality) but instructs the statistical solver to fit it using a naive vacuum-to-bulk assumption (a 2-layer model), the solver is trapped. It will mathematically force a fit by artificially skewing the extracted bulk refractive index (nglass) to absorb the physical discrepancy caused by the unacknowledged contamination film.
By plotting the regression residuals for both Ψ and Δ, the experimenter can visually diagnose this mismatch. While the Ψ residuals might look deceptively acceptable when a 2-layer model is forced onto 3-layer data, the Δ residuals will exhibit a massive, highly structured systematic error signature (a sharp spike) exactly at the Brewster angle. This immediately alerts the experimenter that their mathematical model is incomplete. Switching to the Rigorous 3-Layer solver restores the flat residual line and perfectly decouples the bulk material properties from the surface chemistry.
When adjusting the Extinction Ratio (ε) or Analyzer Misalignment (γ) sliders, you will notice the fit lines (and residuals) barely respond, whereas they respond violently to surface contamination (d). This is a mathematically accurate simulation of a profound physical reality:
Result: The solver is mathematically anchored by the immune phase data. It recognizes that to preserve the perfect fit on the Δ curve, it must keep d ≈ 0. It deliberately sacrifices the fit at the very bottom of the Ψ curve to prevent errors in the phase domain. This proves why VAE fundamentally outperforms simple intensity-based Brewster extraction.