Spectrum reconstruction based on the constrained optimal linear inverse methods.

Area of Science:

• Optics and Photonics
• Spectroscopy
• Image Processing

Background:

• Birefringent materials in Fourier transform spectrometers cause spectrally varying Nyquist frequencies, complicating spectral retrieval.
• Existing methods like nonuniform fast Fourier transforms have limitations in compensating for dispersion effects.
• Accurate spectral information retrieval is crucial for applications utilizing Fourier transform spectroscopy.

Purpose of the Study:

• To propose and evaluate a novel constrained spectrum reconstruction method for stationary polarization interference imaging spectrometers (SPIIS).
• To address the challenge of spectrally varying Nyquist frequencies caused by material dispersion.
• To provide a robust and effective approach for spectral reconstruction in SPIIS systems.

Main Methods:

• Developed a theoretical model for interferogram generation, incorporating noise and total measurement error.
• Implemented a constrained optimal linear inverse method for spectrum reconstruction.
• Utilized numerical simulations to validate the proposed method's performance.

Main Results:

• The proposed constrained spectrum reconstruction method demonstrates superior effectiveness and robustness compared to non-constrained methods.
• Numerical simulations confirm the method's ability to accurately retrieve spectral information despite dispersion effects.
• The method provides a significant improvement for spectral reconstruction in SPIIS.

Conclusions:

• The constrained spectrum reconstruction method offers a valuable approach for stationary polarization interference imaging spectrometers (SPIIS).
• This method effectively compensates for dispersion-induced errors, enabling accurate spectral retrieval.
• The findings contribute to advancing spectral imaging capabilities in relevant scientific fields.