Theoretical framework for soft X-ray Fourier transform spectroscopy using the Wigner function

Area of Science:

• Optics and Spectroscopy
• Interferometry
• Theoretical Physics

Background:

• Fourier transform spectroscopy (FTS) is crucial for high-resolution spectral analysis.
• Mach-Zehnder interferometers are commonly used in FTS but have limitations with partially coherent light.
• Understanding radiation propagation in interferometers is key to improving FTS performance.

Purpose of the Study:

• To develop a theoretical framework for analyzing partially coherent Gaussian radiation in a modified Mach-Zehnder interferometer for FTS.
• To investigate the impact of coherence properties on FTS performance.
• To assess the potential of the proposed setup for high-resolution FTS, particularly in the soft X-ray regime.

Main Methods:

• Utilizing the Wigner function formalism to analytically propagate partially coherent Gaussian radiation.
• Simulating the interference pattern and interferogram generated by the modified interferometer.
• Benchmarking the theoretical results against established models in the diffraction limit.

Main Results:

• The theoretical framework successfully describes radiation propagation through the modified Mach-Zehnder interferometer.
• The analysis indicates that the transverse coherence length requirement for detectable modulation is less stringent than previously thought.
• Theoretical demonstrations show potential for FTS performance across various wavelengths, including the soft X-ray region.

Conclusions:

• The proposed modified Mach-Zehnder interferometer offers a robust theoretical framework for FTS applications.
• The reduced coherence requirement broadens the applicability of FTS systems.
• The interferometer shows significant promise for achieving high-resolution FTS in the soft X-ray spectral range.