Inverse geometry for grating-based x-ray phase-contrast imaging

Abstract

Phase-contrast imaging using conventional polychromatic x-ray sources and grating interferometers has been developed and demonstrated for x-ray energies up to 60 keV. Here, we conduct an analysis of possible grating configurations for this technique and present further geometrical arrangements not considered so far. An inverse interferometer geometry is investigated that offers significant advantages for grating fabrication and for the application of the method in computed tomography ͑CT͒ scanners. We derive and measure the interferometer's angular sensitivity for both the inverse and the conventional configuration as a function of the sample position. Thereby, we show that both arrangements are equally sensitive and that the highest sensitivity is obtained, when the investigated object is close to the interferometer's phase grating. We also discuss the question whether the sample should be placed in front of or behind the phase grating. For CT applications, we propose an inverse geometry with the sample position behind the phase grating.

Performance and optimization of X-ray grating interferometry

“…The former can be solved by using curved gratings [24]. The latter represents a problem owing to the object positiondependent sensitivity [20,25], where α min is proportional to the distance from the object to G1. In the extreme case, where the distance between the source and G1 is comparable to the sample size, the position-dependent α min in the sample ranges from σ α = ∞ (at source) to σ α,min (at G1).…”

“…As the sensitivity has also been defined differently [10,20], here α min is just referred to as the smallest detectable refraction angle. The proportionality of α min to p 2 /d suggests using a small analyser grating pitch and long experimental arrangements, which can be achieved with higher Talbot order designs.…”

Toward Clinically Compatible Phase-Contrast Mammography

“…Firstly, the arrangement of the breast tissue holder and the phase grating downstream of the X-ray beam were exchanged [7]. Thus, a saving of approximately 33% mean glandular dose was achieved (value corresponds to a sample compression of 4 cm), by utilizing the wafer-substrate (silicon) as an effective absorber of low energy photons and increasing the source-tosample distance (Fig 1A).…”

“…Thus, a saving of approximately 33% mean glandular dose was achieved (value corresponds to a sample compression of 4 cm), by utilizing the wafer-substrate (silicon) as an effective absorber of low energy photons and increasing the source-tosample distance (Fig 1A). Note that this optimization step only altered the effective pixel-size, whilst maintaining the overall photon statistics and only slightly decreasing the interferometer sensitivity, contingent on the fact that the sample holder was placed directly downstream of the phase grating (distance of 2.5 cm) [7].…”

Clinical boundary conditions for grating-based differential phase-contrast mammography

“…and have periodicities p 0 , p 1 and p 2 , respectively. For convenience, we put together the relations that hold between these periodicities and the distances l = G 0 G 1 and d n = G 1 G 2 [27]. The nth order Talbot distance D n for a parallel beam geometry and the correction for cone beam geometry are given by…”