Reconstruction method and optimal design of an interferometric spectrometer.

Area of Science:

• Spectroscopy
• Signal Processing
• Optical Engineering

Background:

• Interferometric spectrometers typically use Fourier transforms for spectral recovery.
• Distortions and data gaps in spectrometer fringe patterns hinder traditional Fourier transform application.
• Existing methods struggle with incomplete or noisy interferometric data.

Purpose of the Study:

• To develop a novel spectral estimation method for interferometric spectrometers with corrupted data.
• To address limitations posed by fringe pattern distortions and data loss.
• To improve spectral recovery accuracy using linear inverse problem solving and iterative methods.

Main Methods:

• Combined linear inverse problem solving with iterative methods for spectral estimation.
• Incorporated known spectral responses of individual detectors.
• Utilized iterative methods to compensate for missing input data.
• Employed the condition number of the inversion matrix as an optimization criterion.

Main Results:

• Achieved good spectral estimation for simple spectra (400-point resolution) using fewer than 10 detectors.
• Demonstrated that optimal selection of detector spectral responses significantly impacts spectral recovery quality.
• Showed that maximizing the condition number of the inversion matrix improves spectral restitution within acceptable noise levels.

Conclusions:

• The proposed method offers a viable alternative for spectral estimation when traditional Fourier transforms fail due to data quality issues.
• Careful selection and arrangement of detector spectral responses are crucial for successful spectral recovery.
• The technique shows promise for applications requiring accurate spectral analysis from imperfect interferometric data.