Neutron interferometry using a single modulated phase grating

Abstract

Neutron grating interferometry provides information on phase and small-angle scatter in addition to attenuation. Previously, phase grating moiré interferometers (PGMI) with two or three phase gratings have been developed. These phase-grating systems use the moiré far-field technique to avoid the need for high-aspect absorption gratings used in Talbot–Lau interferometers (TLI) that reduce the neutron flux reaching the detector. We first demonstrate, through theory and simulations, a novel phase grating interferometer system for cold neutrons that requires a single modulated phase grating (MPG) for phase-contrast imaging, as opposed to the two or three phase gratings in previously employed PGMI systems. The theory shows the dual modulation of MPG with a large period and a smaller carrier pitch P, resulting in large fringes at the detector. The theory was compared to the full Sommerfeld–Rayleigh diffraction integral simulator. Then, we proceeded to compare the MPG system to experiments in the literature that use a two-phase-grating-based PGMI with best-case visibility of around 39%. The simulations of the MPG system show improved visibility in comparison to that of the two-phase-grating-based PGMI. An MPG with a modulation period of 300 µm, the pitch of 2 µm, and grating heights with a phase modulation of ([Formula: see text], illuminated by a monochromatic beam produces visibility of 94.2% with a comparable source-to-detector distance (SDD) as the two-phase-grating-based PGMI. Phase sensitivity, another important performance metric of the grating interferometer, was compared to values available in the literature, viz. the conventional TLI with the phase sensitivity of 4.5 × 103 for an SDD of 3.5 m and a beam wavelength of 0.44 nm. For a range of modulation periods, the MPG system provides comparable or greater theoretical maximum phase sensitivity of 4.1 × 103 to 10.0 × 103 for SDDs of up to 3.5 m. This proposed MPG system appears capable of providing high-performance PGMI that obviates the need for the alignment of two phase gratings.

X-ray Interferometry Using a Modulated Phase Grating: Theory and Experiments

“…The theory of the 1-dimensional MPG was originally derived in [24], which will hold for a 2-dimensional MPG if the grating is constant in one dimension. However, for this study, multiple MPGs were produced by Microworks GmbH, Germany, where the grating bars were staggered for improved structural stability, following a Bridge design, [29], as shown in Figure 2.…”

“…First, we will briefly review the theory of the 1-dimensional MPG [24], then detail the modifications necessary for 2 dimensions. For the 1-dimensional MPG, the grating transmission function is given as…”

“…We then compare the results with experiments performed in the Keck Imaging Laboratory at Pennington Biomedical Research Center (PBRC). In a previous study, we presented the theory of the 1-dimensional MPG with comparisons to simulations performed using the Sommerfeld Rayleigh Diffraction Integral (SRDI) simulator, with several orders of magnitude of decreased simulation time and comparable results [24]. In this paper, we will extend the 1dimensional MPG theory to account for the staggering of the grating bars that are implemented during fabrication for grating stability.…”

“…There are presently several grating interferometers in the literature, including the Talbot-Lau Interferometer (TLI) [16,17,18], Dual Phase Grating Interferometer (DPGI) [19,20], and Modulated Phase Grating Interferometer (MPGI) [21,22,23,24,25]. The TLI has a phase grating, G1, that produces interference fringes that are not directly resolvable by typical detectors, meaning an analyzer grating, G2, is required to create visible Moiré patterns, resolvable at the detector.…”

“…The modulated phase grating interferometer (MPGI), originated by our group [21,22,23,24], consists of a single grating where the heights of the grating bars follows an envelope function, with a relatively large period, W . The envelope function is sampled at a high-frequency pitch, p, to meet the coherence requirements similar to that of the TLI and DPGI systems.…”