Predicting visibility of interference fringes in X-ray grating interferometry.

Area of Science:

• X-ray optics and interferometry
• Coherent diffractive imaging
• Phase contrast imaging

Background:

• Interference fringe visibility is crucial for x-ray grating-based interferometers.
• Predicting visibility for polychromatic sources currently requires extensive computer simulations.
• Existing methods lack general applicability for diverse interferometer designs and source spectra.

Purpose of the Study:

• To develop a general quantitative theory for predicting intensity fringe patterns in x-ray interferometers.
• To provide closed-form formulas for fringe visibility that incorporate key physical effects.
• To offer a more efficient alternative to computer simulations for interferometer design.

Main Methods:

• Fourier expansion of the intensity fringe pattern.
• Development of a general quantitative theory.
• Incorporation of partial spatial coherence, spectral averaging, and detector pixel re-binning effects.

Main Results:

• Derivation of closed-form formulas for predicting fringe patterns.
• Demonstration of the formulas' ability to account for partial coherence and spectral properties.
• Validation of the theory for Talbot-Lau interferometers with arbitrary configurations and source spectra.

Conclusions:

• The developed theory provides a powerful analytical tool for x-ray interferometer design.
• The closed-form formulas significantly simplify the prediction of fringe visibility.
• This work facilitates the optimization of interferometers for polychromatic x-ray sources.