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Multilocalization and the van Cittert-Zernike theorem. 1. Theory
1Laboratorio de Optica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina. comastri@df.uba.ar
Summary
This study analyzes interferometers using the van Cittert-Zernike theorem to understand two-beam interferences. It derives a complex coherence degree for periodic sources, detailing fringe properties.
Area of Science:
- Optics and Photonics
- Interferometry
- Coherence Theory
Background:
- The van Cittert-Zernike theorem is fundamental in relating source properties to spatial coherence.
- Amplitude-division interferometers are crucial for various optical measurements.
- Understanding coherence is key to analyzing interference patterns.
Purpose of the Study:
- To analyze the exit of an arbitrary amplitude-division interferometer with two-beam interferences.
- To derive an expression for the complex degree of coherence for a specific source configuration.
- To provide formulas for the characteristics of multilocalized fringes.
Main Methods:
- Employing the complex degree of coherence and the van Cittert-Zernike theorem.
- Analyzing a two-beam interference scenario within an interferometer.
- Considering a source as a periodic array of spatially incoherent slits.
- Assuming negligible aberrations and no vignetting.
Main Results:
- Derived an expression for the complex degree of coherence as a function of exit point position.
- Obtained formulas for the location of multilocalized fringes.
- Provided formulas for fringe spacing and fringe localization depth.
Conclusions:
- The study successfully characterized the complex degree of coherence for the specified interferometer and source.
- The derived formulas offer quantitative insights into the behavior of multilocalized fringes.
- This work contributes to the understanding of interference phenomena in optical systems.