## 3 Experiments
### Lateral Magnetic Spatial Resolution  
The spatial magnetic resolution in the case of polarized neutron imaging was also investigated in the case of lateral spatial resolution. In the coil experiment of Figure 11, the B-field increased and the number of spin rotations (spin flips) along the flight path (y-direction) determined. One measures the number of spin flips (number of fringes) as a function of the B-field for a given distance. So one acquires information about the shortest path length a spin-flip can occur (longitudinal magnetic spatial resolution).  
This experiment determines the _largest_ B-field that can be measured with a certain spatial instrumental resolution. However, both the largest and the smallest B-field to be detected depend on the wavelength of the neutron. B and thus the path length for a spin-flip are inverse functions to the neutron wavelength, as given by Equation (6) and seen in Figure 2. Due to knowledge of horizontal and vertical divergences \(\phi_{hor}\) as described in Section 2.3 the fringe pattern must be adapted to the expected resolution. The detector pixel size (also known) must much smaller than the produced fringe pattern, so that the measured convolution provides useful results.  
To determine the lateral spatial resolution, one must measure the spatial resolution with respect to \(\Delta x\) and \(\Delta z\), varying only the position of a fringe pattern on the 2D detector. This was done by a magnetized quadratic coil (I = 3A) placed on a \(\upmu\)m precise stage and moving it up by 50 steps each of one 50 \(\upmu\)m, so that the pattern, generated by the  
Figure 12: The “magnetic MTF” shows 2.9 Line pairs/8 mm\(\sim\)\(\Delta y\) = 345 \(\upmu\)m, red line is fit with error function.  
Figure 13: Part of Figure 11, image I = 6[A], under-laid by the line plot showing the varying contrast in the image.  
magnetized coil and the spin analyzer, is shifted 2.5 mm above the 2D pixel array of the detector. For each step, an image was taken with polarized neutrons. If the fringe pattern moves perpendicular to the detector (horizontal) lines, the movement of the pattern produces different gray values in the detector lines, which can be plotted as a line graph (Figure 14).  
Figure 15 shows five fringe patterns from the radiography image I = 3A, B = 16 mT (Figure 11), four images each shifted by 3 pixel = 81, showing a change from maximum intensity to minimum intensity (spin-flip) for a shift of 12 pixel = 324. A detailed look at different vertical shifts also shows that the distance for a spin-flip varies remarkably. Depending on which part of the image is used, one counts 10 fringes (line pairs, maximum-maximum distance) within 7.6 mm corresponding to 2\(\Delta z\) = 0.76, inner Al block = for a spin-flip or five fringes within 616, inner Al block = for a spin-flip.  
If one plots two different shift positions of the fringe pattern, one obtains Figure 16.  
Figure 14: Vertical movement of the fringe pattern, each step = 50, total shift = 2.5 mm.  
Figure 15: Five fringe pattern produced with of quadratic coil (from Figure 11, I = 3.5A) shifted by 3...18 pixel, pattern and fringes rotated by 90°, length of the coil = 150 mm, inner Al block = 11 mm, outer diameter = 35 mm, wire = Cu, = 0.90(1) mm, resistance = 1.2, 614 windings.  
This was checked in detail with the result that the periodicity of the measured patterns varies from position to position: Table 1 shows mean spin-flip distances for different shift positions. Positions no. 0 and no. 50 show the largest values for a spin-flip and deviations (396(87) \(\upmu\)m and 415(73) \(\upmu\)m, respectively.  
The experimental results of the lateral spatial resolution \(\Delta z\) (380(48) \(\upmu\)m) agree well with the (vertical) geometric spatial resolution (350 \(\upmu\)m) and with the calculated result of the convolution of the fringe pattern with the 2D detector (pixel array) (376 \(\upmu\)m). Due to the vertical beam divergence \(\phi_{vert}=2\phi_{horiz}\), \(\Delta x\) can be given as \(\frac{1}{2}\Delta z=190\)\(\upmu\)m.