Closed-form expressions to fit data obtained with a multipass Fabry-Perot interferometer

Area of Science:

• Optics and Spectroscopy
• Interferometry
• Physical Chemistry

Background:

• Multipass Fabry-Perot interferometers (FP) are used to analyze scattering lines.
• Analyzing the line shapes produced by multipass FP systems can be computationally complex.
• Understanding the impact of experimental parameters like collecting pinholes is crucial.

Purpose of the Study:

• To develop a simplified method for deriving closed-form expressions for line shapes in multipass FP systems.
• To reduce the convolution problem in multipass FP analysis to a single-pass problem.
• To investigate the effect of a collecting pinhole on sharp lines in multipassing.

Main Methods:

• Developed a novel analytical method to derive closed-form expressions for multipass FP line shapes.
• Reduced the mathematical complexity of multipass spectral analysis.
• Applied the method to Lorentzian and damped-harmonic-oscillator line shapes across single, triple, and quintuple passes.

Main Results:

• Successfully derived a closed-form expression for ideal multipass FP line shapes.
• Demonstrated the method's effectiveness with various line types and pass numbers.
• Quantified the effect of the collecting pinhole on sharp spectral lines in multipass configurations.

Conclusions:

• The developed method simplifies the analysis of scattering lines obtained with multipass Fabry-Perot interferometers.
• This approach facilitates accurate spectral fitting and a deeper understanding of interferometer performance.
• The findings are applicable to optimizing experimental setups and interpreting spectral data.