Dual-wavelength Fourier Ptychographic Topography

Abstract

We introduce a dual-wavelength Fourier ptychographic topography (FPT) method that extends the lambda/2 height-range limit of single-wavelength FPT. By reconstructing complex fields at two illumination wavelengths and exploiting their phase difference, the method achieves an effective synthetic wavelength lambda_s and an unambiguous range of lambda_s/2 without reducing lateral resolution. A noise-robust wrapped-number search is used to select per-pixel integer pairs (k1, k2), and a global refinement with circular TV regularization and soft bounds improves stability and preserves height discontinuities. The approach is validated through rigorous scattering-model-based simulations and experiments on structured silicon samples, demonstrating accurate height recovery in regimes where single-wavelength FPT exhibits phase wrapping. We analyze the limits of the FPT forward model and identify aspect ratio (AR) and phase modulation transfer function (ph-MTF) as key predictors of reconstruction fidelity. Simulations and experiments show that increasing AR beyond a practical threshold causes loss of high-frequency phase transfer and destabilizes dual-wavelength unwrapping. Within this AR range, dual-wavelength FPT provides robust, high-resolution topography suitable for semiconductor and industrial metrology.