Research on Fourier Transform Spectral Phase Correction Algorithm Based on CTKB-NCM

In Fourier Transform Spectrometers, phase errors in spectral measurement induce distortion in reconstructed spectra. Existing phase correction algorithms demonstrate insufficient precision in addressing both linear phase and instrumental phase components, resulting in limited applications for the restored spectra in the field of precision measurement. This paper proposes an algorithm called the Cross-Teager–Kaiser ψB Energy Operator–Nonlinear Calibration Model (CTKB-NCM) for phase error correction. The algorithm first uses the cross-Teager–Kaiser ψB energy operator (CTKB) method to correct linear phase errors, then applies the Nonlinear Calibration Model (NCM) to solve for the instrument phase correction parameters at each wavenumber, and finally uses the instrument phase correction parameters to correct the residual phase after the linear phase error has been corrected. The Rao algorithm is used to determine the optimal instrument phase correction parameters. Simulation experiments demonstrate that the CTKB-NCM method achieves an order-of-magnitude improvement in normalized reconstructed spectral accuracy for SO2 gas compared to the conventional Mertz method.