## 1 Introduction  
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 theory to this subject is well established and described in detail in [1, 2, 3, 4, 5]. The spatial resolution of a neutron imaging system can be measured by several methods, two of them are frequently used and commonly accepted. The first one uses a so-called \"Siemens star\" and the second method by determining the modulation transfer function (MTF) of the imaging system. The determination with the \"Siemens star\" is simple because one can directly read the resolution from an image of the Siemens star. The disadvantage is that it does not cover the frequency range continuously.  
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 more common method uses opaque edges, because absorbing grids with different line pairs (LP) per unit length yield only a discrete Fourier spectrum, different to an absorbing edge. There is a large number of publications showing up all advantages and disadvantages of this method, but using an edge is a simple but very straightforward method to derive the modulation transfer function of a digital radiography system from an edge image. The image examined with the point spread function (PSF) method must have a high contrast-to-noise ratio, so it is (for clinical studies) often inappropriate for describing the MTF as well as with the edge spread function (ESF) method [6,7]. A technique for rendering the ESF method robust to image noise is presented where the noisy ESF is smoothed out through multiple stages of filtering [8]. The MTF can be also 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].  
The spatial detector resolution approaches the 1 \(\upmu\)m size, driven by different techniques such as micro-channel plate (MCP), microscope-like devices, gadolinium oxysulfide scintillators, absorbing grids, observing tracks from neutron capture events, hybrid pixel detector (Medipix [10]), coded source imaging (CSI) system [11], fiber optics taper (FOT), etc. [8,12,13,14,15,16,17,18,19,20,21], and inaccuracies associated with use of precision test objects, such as a slit or an edge can be reduced [22,23] and misalignment of an edge with respect to detector pixel columns or rows can be taken into account [6]. A collection of test devices was developed for neutron imaging that can be used to quantify pixel and voxel size, resolution of the imaging system, and beam divergence. [24]. In 2014 the spatial resolution in neutron imaging reached with 7.8 \(\upmu\)m = 63.2 line pairs/mm a level, which is comparable with \(\uplambda\)-ray imaging, [25]; however, today already a resolution of X-ray imaging is obtained [26,27,28,20,21,26,27].  
For radiography (and tomography) using polarized neutrons the magnetic spatial resolution is always associated with change of the neutron spin orientation due to a magnetic field. Polarized neutron imaging is used in many experiments and has been published, e.g., [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], but all have in common a spin analysis system which determines the resolution of the imaging system.  
In this paper, first a simple and powerful method is proposed to determine the spatial resolution in the case of imaging with un-polarized neutrons. Then we describe how to determine the spatial resolution in the case of imaging with polarized neutrons. We use the image of de-polarized neutrons by special magnetic fields that produces fringe structures with different frequencies in the space domain and additionally the shift of a given pattern with respect to detector pixel array. However, first, some mathematical basics about conventional spatial resolution are summarized.