The fractional Talbot effect in differential x‐ray phase‐contrast imaging for extended and polychromatic x‐ray sources

Abstract

Summary The influence of different physical parameters, such as the source size and the energy spectrum, on the functional capability of a grating interferometer applied for phase‐contrast imaging is discussed using numerical simulations based on Fresnel diffraction theory. The presented simulation results explain why the interferometer could be well combined with polychromatic laboratory x‐ray sources in recent experiments. Furthermore, it is shown that the distance between the two gratings of the interferometer is not in general limited by the width of the photon energy spectrum. This implies that interferometers that give a further improved image quality for phase measurements can be designed, because the primary measurement signal for phase measurements can be increased by enlargement of this distance. Finally, the mathematical background and practical instructions for the quantitative evaluation of measurement data acquired with a polychromatic x‐ray source are given.

Performance and optimization of X-ray grating interferometry

“…The polychromatic fringe visibility can be derived from the polychromatic intensity pattern and its Fourier coefficients, which are given by [15,22] …”

“…A detailed discussion about the difference of a π and a π/2-shifting phase grating for a polychromatic beam is presented. Apart from general and qualitative descriptions [13,14] or simulation case studies [15], the effect of a spectral bandwidth has so far mostly been neglected. However, understanding the dependency of the polychromatic performance of the grating interferometer is crucial for the efficient optimization of dedicated imaging systems based on conventional X-ray tubes.…”

Visibility simulation of realistic grating interferometers including grating geometries and energy spectra

“…The key feature that most work was concerned with is the spectral distribution of the X-ray tube source and its impact on the performance of the grating interferometer [12][13][14] or even the actual simulation of images [15]. Tube sources emit a large range of energies and the understanding of the impact of spectral distributions on the visibility is often driven by increasing the setup performance and thus lowering the dose for patients in medical applications.…”

Boosting phase contrast with a grating Bonse–Hart interferometer of 200 nanometre grating period

“…The opposite approach of reducing the grating period while maintaining the wave propagation distance runs into the situation where the propagation distance becomes many times the Talbot distance. This approach forces the interferometer into the far-field regime, where chromatic dispersion effects and higher order optical aberrations result in low interference fringe amplitude and efficiency [9].…”