# Cold and Thermal Neutron Single Grating Dark-Field Imaging Extended to an Inverse Pattern Regime
## 1 Introduction  
Advanced and multimodal imaging techniques with neutrons and X-rays that go beyond conventional attenuation contrast imaging have recently experienced a rapid growth in applications. Amongst them, techniques that offer differential phase contrast (DPC) and dark-field (DF) contrast simultaneously, and in addition to the attenuation signal, have attracted particular interest. Phase contrast imaging is sensitive to phase shifts induced by local variations in the real part of the refractive index. Compared to the conventional attenuation signal, X-ray phase contrast imaging can provide significantly better contrast for visualizing small electron density variations in a sample, and it has shown potential for dose reduction, which is particularly important for clinical applications [1, 2]. The feasibility of phase contrast imaging has also been demonstrated for neutrons and applied for mapping not only phase shifts induced by bulk materials [3, 4], but also by magnetic fields [5, 6]. Dark-field contrast imaging, in turn, has the potential to quantitatively probe spatially resolved small-angle scattering of investigated materials [4, 7]. Grating interferometry (GI) is the most efficient technique for this multimodal imaging approach that delivers both the phase contrast and the dark-field signals in addition to the attenuation. It is based on measuring the local modulation of an interference pattern induced in the beam by the grating interferometer. A conventional neutron GI setup is typically comprised of a set of three line gratings with defined periods, typically on the order from a few to a few tens of micrometers, which produce an interference pattern through the Talbot-Lau effect. The first is an absorption grating that is placed downstream of the source and creates a partially coherent beam. The second is a phase grating that creates a sinusoidal interference pattern. The last one is another absorption grating, which is required to translate the interference pattern that cannot be directly resolved by the detector system into a pixel-wise modulation upon a phase stepping approach [8; 9]. For this, one of the gratings is scanned in several steps across the beam using a precision stepping motor. This is repeated both with (sample scan) and without (reference scan) the sample in the beam. Fitting the sinusoidal modulation created in every pixel by the phase-stepping and correlating the sample and reference scans delivers the attenuation, differential phase and dark-field images of the sample, as described in [4]. In contrast, a non-interferometric single grating (SG) approach for neutron dark-field imaging was recently demonstrated [10], which simplifies the instrumentation requirements. For this, only single-shot exposures of an absorption grating with and without the sample in the beam are required, and complex alignment procedures and optimization for a single wavelength are eliminated. As we show, single gratings can be used in a straightforward manner at cold and thermal neutron beamlines. With the use of conventional 1D grating patterns, DPC and DF are sensitive to refraction and scattering in the direction perpendicular to the grating lines only. Recent studies have shown that multi- and omni-directional scattering imaging can be achieved by using two gratings with 2D periodical patterns creating a pattern of macroscopic circular beam modulations [11]. The key parameters of a dark-field imaging setup are the autocorrelation length and the visibility. The instrumental autocorrelation length probed is related to the scattering vector amplitude, analogous to the spin echo length in a spin echo SANS experiment, and its details are described in [7]. Its value determines the length scales accessible by the technique, which today lies in the range from a few tens of nanometers to about ten micrometers [12; 10; 13; 14; 15; 16].