Raman signal extraction from CARS spectra using a learned-matrix representation of the discrete Hilbert transform

Area of Science:

• Spectroscopy
• Computational Chemistry
• Data Analysis

Background:

• Quantitative analysis of Coherent Anti-Stokes Raman Scattering (CARS) spectra is crucial.
• Nonresonant background (NRB) interference distorts CARS spectra, complicating analysis.
• Existing methods like Kramers-Kronig and maximum entropy can introduce errors, especially with spectral windows.

Purpose of the Study:

• To develop a novel computational method for improving the accuracy of Raman spectral retrieval.
• To address the limitations of current techniques in handling spectral distortions caused by NRB.
• To present an easily implementable and fast approach for accurate CARS spectral analysis.

Main Methods:

• A learned matrix approach to the discrete Hilbert transform was developed.
• This method was applied to correct for NRB interference in CARS spectra.
• The technique was evaluated for its accuracy and ease of implementation.

Main Results:

• The learned matrix approach significantly improves the accuracy of Raman retrieval.
• The method effectively removes distortions caused by NRB interference.
• The approach is computationally efficient and easy to implement.

Conclusions:

• The learned matrix discrete Hilbert transform offers a superior method for quantitative CARS spectral analysis.
• This technique overcomes limitations of existing computational approaches, particularly regarding spectral window boundaries.
• The developed method provides a fast, accurate, and practical solution for spectral distortion correction.