INFER is an NIST Innovations in Measurement Science (IMS) project that seeks to develop far field neutron interferometers to create multi-scale images (three-dimensional small-angle neutron scattering) and perform precision measurements of fundamental constants and beyond standard model physics.

**Multi-scale Images and Hierarchical Structures**

One of the keys identified by the 2015 DOE report, “Challenges at the Frontiers of Matter and Energy: Transformative Opportunities for Discovery Science” are methods that can study hierarchical systems. Such systems include the propagation of degradation in concrete, fluid transport in geology, ion mobility in battery and fuel cell electrodes, macromolecule transport for drug delivery, and structural biology to improve implants. What these hierarchical systems share in common is that the system function depends on the interplay of the structure across many length scales, for instance the distribution of nanoporosity over centimeter fracture surfaces influence the amount of natural gas recovered in unconventional reservoirs. It is this breadth of length scales – geological systems have pores that range from the nm to the km – presents extreme challenges to characterizing hierarchical systems within a single measurement. Creating tools that can do so are a transformative opportunity, and one that INFER seeks to realize.

INFER forms multiscale images by performing phase imaging with a two-grating far-field neutron interferometer (shown schematically in Figure 1). For INFER, the enabling property of the far field interferometer is that the period of the interference pattern, P, can be easily varied by changing the relative spacing of the two phase gratings, P = L / (F D), where L is the length of the interferometer, F is the frequency of the phase gratings and D is the separation between the two gratings. Typical values are L = 5 m, F = 0.5 µm^{-1} and D = 10 mm, P = 1 mm. An important property of a grating interferometer is the autocorrelation length, ξ, which is determined by ξ = λ Z / P, with λ the neutron wavelength and Z the separation of the sample and detector. As an example, for λ = 1 nm, Z = 10 mm, P = 1 mm, ξ = 10 nm. The fact that the far field geometry allows one to vary P by orders of magnitude, means that ξ can be varied by orders of magnitude. Grating phase imaging yields three image contrasts, the usual transmission image, the phase gradient image, and the visibility image. The transmission image measures the total macroscopic neutron cross section, σ(λ), the phase gradient image measures the coherent scattering length b_{c}, and the visibility measures the pair correlation function, G(ξ). INFER measures G(ξ) over orders of magnitude of ξ, while keeping the sample in a fixed position. All other neutron grating interferometers have a fixed period, requiring one to translate the sample, which sacrifices spatial resolution for large Z. An example is shown in Figure 2.

The pair correlation function measured by INFER is related to the scattered intensity I(q) measured in conventional small angle neutron scattering. With INFER, the mathematics of the visibility image are similar to the transmission image, enabling tomographic reconstruction, so the microstructure is measured at the “voxel” scale, about 50 µm, instead of averaged over the beam and multiple scattering is directly accounted for in tomography reconstruction. INFER’s multiscale data is the pair correlation function, with ξ = [1 nm – 10 µm], averaged over a voxel with linear dimension about 50 µm over a sample size of about 10 cm – 8 orders of magnitude in length!

**Fundamental Constants**

Neutron interferometry has had a long history of combining the unique properties of the neutron (0 charge, 1/2 quantum spin, & magnetic moment) with its diverse set of interactions (nuclear, electromagnetic, & gravity) to study outstanding questions in physics. This has mainly been accomplished by using small 10 cm long crystal interferometers. An interferometer’s sensitivity and precision are a function of its overall length; longer neutron path = larger phase shift = reduction in relative uncertainty. INFER will develop a multi-meter-long, three grating far field interferometer for fundamental physics with greater overall phase sensitivity. This sensitivity allows experiments beyond the scope of the current 10 cm sized interferometers. Our first goal is to measure the local gravitational field which can be accomplished by tilting the gratings such that one neutron path diffracts slightly upward. This upward path, experiencing a slightly less attractive gravitational force, results in a large phase shift proportional to Earth’s field. Ultimately, these 3-grating interferometers (see Figure 1) will be used for a precision measurement of Newton’s gravitational constant, “Big-G”, it being the least well-known fundamental constant.

**Challenges and Opportunities to Realizing INFER**

To obtain microstructural details, requires multiple tomographic acquisitions at multiple ξ. We seek to obtain 100 ξ measurements over 3D in one day, requiring advances in data acquisition, neutron optical components, image reconstruction, and data analysis. The INFER collaboration seeks to develop:

- High Aspect Ratio Phase Gratings [Link to 685 page on grating development]
- Dynamic Neutron Transmission Grating
- Simulations of imaging with phantom objects for instrument calibration purposes
- Imaging Dose Reduction and SNR maximization for 3D Tomographic Reconstructions
- Uncertainty estimation of measurements from 3D tomographic reconstruction
- Automatic volume segmentation and pair correlation function fitting
- Multi-scale data visualization

[1] D. A. Pushin *et al.*, “Far-field interference of a neutron white beam and the applications to noninvasive phase-contrast imaging,” *Phys. Rev. A*, vol. 95, no. 4, 2017.

[2] D. Sarenac *et al.*, “Three Phase-Grating Moiré Neutron Interferometer for Large Interferometer Area Applications,” *Phys. Rev. Lett.*, vol. 120, no. 11, p. 113201, 2018.

Created March 24, 2021, Updated February 17, 2022