Inverse problem approaches for stationary Fourier transform spectrometers

Area of Science:

• Optics and Photonics
• Spectroscopy
• Instrument Development

Background:

• Miniaturized Fourier transform infrared (FTIR) spectrometers are crucial for portable spectral analysis.
• Two-dimensional interferograms generated by these devices can be affected by optical imperfections.
• Standard Fourier transforms are insufficient for accurate spectral estimation due to these defects.

Purpose of the Study:

• To develop a processing methodology for accurate spectral estimation from 2D interferograms produced by a miniaturized FTIR spectrometer.
• To address and correct for deterministic defects such as parasitic interferences and pixel wavelength disparities.

Main Methods:

• Design and development of a miniaturized stationary Fourier transform infrared spectrometer.
• Implementation of inversion methods to account for measured deterministic defects.
• Inclusion of a regularization term in the processing algorithm.

Main Results:

• Successful generation of two-dimensional interferograms.
• Demonstration of a processing methodology capable of correcting for optical defects.
• Validation of the approach through initial experimental results.

Conclusions:

• The developed processing methodology is effective for spectral estimation from imperfect 2D interferograms.
• This approach enables accurate spectral analysis using miniaturized FTIR spectrometers despite inherent optical limitations.
• The study validates the efficiency of inversion methods and regularization for correcting deterministic defects in spectral data.