Theoretical aspects of Fourier Transform Spectrometry and common path triangular interferometers

Area of Science:

• Earth remote sensing
• Optical interferometry
• Spectroscopy

Background:

• Imaging interferometry is advancing for Earth remote sensing.
• Sagnac configurations are increasingly used for new imaging interferometers.
• A need exists for a comprehensive theory of triangular Fourier transform spectrometers (FTSs).

Purpose of the Study:

• To develop a self-contained theory for triangular FTS signal description and processing.
• To investigate disadvantages of multiplexing and compare FTS with dispersive instruments.
• To address phase error correction and non-unitary transformations in Sagnac interferometers.

Main Methods:

• Theoretical development of signal processing for triangular FTS.
• Analysis of multiplexing disadvantages.
• Comparison of Fourier transform spectrometers (FTS) and dispersive instruments.
• Investigation of phase error correction methods.
• Analysis of non-unitary transformations in Sagnac interferometers.
• Discussion of noise effects on spectral estimations.

Main Results:

• A self-contained theory for triangular FTS signal processing has been developed.
• Disadvantages of multiplexing were investigated.
• Comparisons between FTS and dispersive instruments were made.
• Methods for correcting phase errors and non-unitary transformations were addressed.
• The impact of noise on spectral estimations was discussed.

Conclusions:

• The developed theory provides a framework for understanding and processing signals from triangular FTS instruments.
• The study offers insights into optimizing Sagnac interferometer performance for Earth remote sensing applications.
• Addressing phase errors and noise is crucial for accurate spectral estimations.