Edge phase retrieval for dispersion measurements with wavelet decomposition and reconstruction

We propose a new method, to our knowledge, to retrieve phase in spectrally resolved interferometry for dispersion measurements using the discrete wavelet transform. The original interferogram is decomposed and reconstructed for signal denoising by adopting the Daubechies-4 (db4) wavelet. This process enhances the clarity of edge fringes in the reconstructed interferogram, enabling accurate retrieval of the edge phase. We demonstrate the accuracy of the proposed method through dispersion measurements of SF66 glasses with different thicknesses. By quantitatively analyzing the measurement accuracy and uncertainty in the whole available spectral range, we further improve the performance of our method. The maximum relative error of group delay dispersion does not exceed 1.1% for the 10 mm thick SF66 and 0.15% for the 200 mm thick SF66. The measurement system exhibits high robustness against noise and environmental perturbations. Benefiting from the advantages of edge preservation and high accuracy, this approach shows reasonable potential in the field of nonlinear optics and ultrafast lasers.