Levenberg-Marquardt algorithm with adaptive Tikhonov regularization for bandwidth correction of spectra

Spectrometers are widely used in many fields. However, the spectrum is distorted due to the bandwidth limitations. This study analyzes the problem of using the least square method for bandwidth correction, introduces the common regularization methods and the existing problems of Tikhonov regularization, and proposes a new bandwidth correction method based on Levenberg-Marquardt algorithm with adaptive Tikhonov regularization. The proposed method was used to optimize spectral parameters. White light-emitting diodes and Raman were used as light sources, and a comparative simulation was conducted. Subsequently, the uncertainty and root mean square error of different regularization parameters were calculated. Results show that the proposed method exhibits satisfactory bandwidth correction effect and small estimation error.