## 3 Experiments  
### Determination of the Spatial Resolution for Unpolarized Neutrons  
The following experiments were performed at PONTO II, an instrument of the University of Applied Sciences, Beuth Hochschule Berlin, dedicated to polarized neutron imaging at the BER II reactor of the Helmholtz-Zentrum fur Materialien und Energie. The first experiments with edge measurements were performed to determine the MTF of the system and thus the spatial resolution for unpolarized neutron imaging. A Cd edge (Figure 8) was placed in a cold neutron beam (\(\lambda=0.32\) nm) and an image taken at a distance of 60 mm from the 2D detector, which had a pixel size = 13.5 \(\upmu\)m (Figure 8). From the fitted shape  
Figure 7: Calculated magnetic field in a coil, length = 150 mm, radius = 9 mm, windings = 614, current = 1 Ampere, B = 5.1 mT inside the coil.  
of the smeared grid e.g., by a Gauss function, the Fourier Transform of the Gauss function, \(\mathcal{FT}\{\text{G}\}\), yields the modulation transfer function MTF, the frequency-dependent contrast function C(f) of the edge image.  
Figure 9 shows steps (a)-(d) to obtain the MTF of the edge image and thus the spatial resolution of the instrument (see also Section 2.1). First the theory (a) is fitted to the experimental edge data (b), then this fit is adjusted to the error function by varying the FWHM of the Gauss function (c). This works better than using the error function itself, and above this, the Gauss function is fitted at the same time. The Fourier transform of the (fitted) Gauss function is then used to calculate the MTF = (\(\mathcal{FT}\)(G(x)) of the edge profile and to determine the 10% contrast \(\text{f}_{max}\) and thus the spatial resolution of the instrument. The correct scanning frequency \(f_{scan}\) is given by \(f_{scan}=2\cdot f_{max}\). The detector pixel size was 13.5 \(\upmu\)m but due to binning = 27 \(\upmu\)m. The best spatial resolution is found at 54 \(\upmu\)m (\(\sim\)\(f_{max}\)), which agrees perfectly with 2 \(\times\) 27 \(\upmu\)m (\(\sim\)\(f_{scan}\)) for \(l_{d}\) = 5 mm. The spatial resolution also depends on the distance \(l_{d}\) of the object to the detector (see Figure 1). The larger \(l_{d}\) the worse is the spatial resolution. This was measured for \(l_{d}\) = 5, 60, 100, 120, 140 and 200 [mm]. If one plots the particular spatial resolution as a function of \(l_{d}\) one obtains the principal limit of the imaging system of \(\sim\)13 \(\upmu\)m for \(l_{d}\) = 0, i.e., the pixel size of the detector 13.5 \(\upmu\)m, which agrees perfectly with the data fit line for \(l_{d}\) = 0 mm (see Figure 10). Comparing the results in Figure 10 one sees the discrepancy between theory based on the \(1/\text{r}^{2}\) law if a pin hole source is used and measured data. The measured data show an entirely different behavior. The explanation is given in [41], there already could be measured that using a mosaic crystal as monochromator the pin hole as source diameter must be replaced by the mosaic structure of the monochromator yielding an improvement of the L/D ratio of a factor \(\sim\)2.7, here a factor 2.2 (Figure 10).  
The spatial resolution can be well derived by plotting the value of the modulation transfer function MTF at 10% contrast as function of the distance of the edge from the detector. For pin hole geometry on observes a \(1/\text{r}^{2}\) behavior, any other geometry, such as using a mosaic crystal as source or a collimator system yields different results (see Figure 10).  
Figure 8: Image of a Cd edge, thickness 0.5 mm, neutron wavelength \(\lambda=0.32\) nm, exposure time = 1800 s, beam divergence \(\phi=0.1^{\circ}\sim\) L/D = 573, [52].