Abstract
One of the most important parameters characterizing imaging systems (neutrons, X-rays, etc.) is their spatial resolution. In magnetic field imaging, the spatial resolution depends on the (magnetic) resolution of the depolarization of spin-polarized neutrons. This should be realized by different methods, but they all have in common that a spin-polarizing and spin-analyzing system is part of the resolution function. First a simple and useful method for determining the spatial resolution for unpolarized neutrons is presented, and then methods in the case of imaging with polarized neutrons. Spatial resolution in the case of polarized neutron imaging is fundamentally different from ‘classical’ spatial resolution. Because of π-periodicity, the shortest path along which a spin-flip can occur is a measure of ‘magnetic’ spatial resolution. Conversely, the largest detectable magnetic field (B-field) within a given path length is also a measure of magnetic spatial resolution. This refers to the spatial resolution in the flight direction of the neutrons (Δy). The Δx and Δz refers to the spatial resolution in x- or z-direction; however, in these cases a different method must be used. Therefore, two independent methods are used to distinguish longitudinal and lateral spatial resolution, one method to determine the modulation transfer function (MTF) by recording the frequency-dependent fringe contrast of magnetic field images of a coil (longitudinal spatial resolution), and the second method, to observe the fringe displacement at the detector as a function of magnetic motion, provided that the accuracy of the motion is much better than the pixel size (at least half the pixel size) of the detector (lateral spatial resolution). The second method is a convolution of the fringe pattern with the pixel array of the detector.
Highlights
To recognize and distinguish small structures, inhomogeneities, defects, etc. in matter, it is necessary to know some basic conditions in neutron imaging regarding spatial resolution, beam divergence, contrast, etc
Spatial resolution principally depends on the incident beam divergence φ, in neutron radiography and tomography it is called L/D ratio, the inverse number of ∼ φ
A thin sample containing a magnetic field preferably requires a longer wavelength for the detection and determination of B and allows for a large ∆λ/λ ≈ 10%. ∆λ/λ determines the contrast in polarized neutron images and one sees in Figure 3 that with increasing B the contrast of spin flips decreases
Summary
To recognize and distinguish small structures, inhomogeneities, defects, etc. in matter, it is necessary to know some basic conditions in neutron imaging regarding spatial resolution, beam divergence, contrast, etc. The first one uses a so-called “Siemens star” and the second method by determining the modulation transfer function (MTF) of the imaging system. Other methods use (absorbing) grids with different line pairs (LP) per unit length and plot the image contrast as a function of LP/unit length or calculate the MTF from the image of an edge. The MTF can be measured directly as the image contrast as a function of the spatial frequency of absorbing gratings with increasing number of line pairs/unit length [9]. We use the image of de-polarized neutrons by special magnetic fields that produces fringe structures with different frequencies in the space domain and the shift of a given pattern with respect to detector pixel array. First, some mathematical basics about conventional spatial resolution are summarized
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