The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry

Area of Science:

• Medical Imaging
• X-ray Optics
• Interferometry

Background:

• X-ray differential phase contrast imaging (XDPCi) using Talbot interferometry can simultaneously provide attenuation, phase, and dark-field contrast from single projection data.
• The dark-field contrast is believed to be influenced by small-angle x-ray scattering and the second-order phase derivative.

Purpose of the Study:

• To derive analytic formulae characterizing the second-order phase derivative's contribution to dark-field contrast.
• To validate these formulae through computer simulations.
• To investigate the potential of second-order differential phase contrast imaging for broader applications.

Main Methods:

• Theoretical derivation based on paraxial Fresnel-Kirchhoff theory, decomposing refractive index decrement into smooth and fine structures.
• Computer simulations using numerical phantoms with an XDPCi system employing Talbot interferometry.
• Evaluation of a proposed retrieval method for second-order differential phase contrast and its robustness.

Main Results:

• Analytic formulae and simulations confirm that the second-order derivative significantly contributes to dark-field contrast, alongside small-angle scattering.
• This contrast is substantially magnified by the ratio of detector cell dimension to grating period.
• The proposed method for retrieving second-order differential phase contrast was validated.

Conclusions:

• The derived analytic formulae are significant for understanding dark-field contrast in Talbot interferometry-based XDPCi.
• These findings may spur further research and development in XDPCi.
• This work holds potential for advancing preclinical and clinical applications of x-ray differential phase contrast imaging.