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

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 re...

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Bibliographic Details
Main Authors: Xiong Wang, Chunhui Yan, Zimin Huo, Pengzhang Dai, Dong Yao
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Photonics
Subjects:
Fourier Transform Spectroscopy
phase correction algorithms
instrument phase
cross Teager–Kaiser energy operator
Rao algorithm
Online Access:https://www.mdpi.com/2304-6732/12/3/219
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Summary: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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ψ</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></semantics></math></inline-formula> Energy Operator–Nonlinear Calibration Model (CTKB-NCM) for phase error correction. The algorithm first uses the cross-Teager–Kaiser <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ψ</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></semantics></math></inline-formula> 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 SO<sub>2</sub> gas compared to the conventional Mertz method.
ISSN:2304-6732

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