# Spatial Resolutions of On-Axis and Off-Axis Transmission Kikuchi Diffraction Methods
## 1 Introduction  
Electron back-scattering diffraction (EBSD) is a powerful technique in material science for microstructural analyses [1]. The use of nanomaterials has rapidly increased with the development of nanotechnologies. Nevertheless, the limited spatial resolution of the EBSD may not be sufficient to reveal the substructures and this may hamper its application in nanomaterial analyses.  
To improve the spatial resolution of the EBSD, [PERSON] and [PERSON] changed the EBSD configuration so that the Kikuchi patterns formed by transmitted electrons can be acquired [2]. The resultant electron diffraction technique is referred to as transmission EBSD or off-axis transmission Kikuchi diffraction (off-axis TKD). However, the pattern center is distant from the center of the detector in the off-axis TKD method, which leads to a considerable distortion. In 2016, [PERSON] et al. proposed an on-axis TKD method, in which the incident beam, sample, and detector are collinear [3]. Compared to the off-axis TKD, the new configuration provides higher signal intensity and lower distortion. Furthermore, either the electron dose or acquisition time can be reduced 20 times to yield an equivalent pattern quality as that in the off-axis TKD method [4; 5; 6].  
In recent years, both off-axis and on-axis TKD methods have been extensively used to analyze nanocrystalline and ultrafine-grain materials [6; 7; 8; 9; 10; 11]. The spatial resolution is one of the key factors in the EBSD-based orientation microscopy, as it determines the accuracy of grain size investigations and phase identifications. Although Kikuchi patterns are commonly used to provide two-dimensional information about the microstructure of a material, they are a product of the three-dimensional electron interaction volume [12]. Consequently, when the electron beam is scanned across a grain boundary, the interaction volumes of both sides overlap, which leads to overlapping and unindexable Kikuchi patterns. [PERSON] defined two types of spatial resolution, physical spatial resolution (PSR) and effective spatial resolution (ESR) [13]. The PSR corresponds to the smallest distance from a large-angle grain boundary where the overlapping pattern of both crystals appears, while the ESR indicates the smallest distance across a boundary where the patterns are still indexable by a software algorithm [13; 14]. [PERSON] et al. compared the on-axis and off-axis TKD methods in many aspects, including the spatial resolution [5]. They investigated the effect of working distance in spatial resolution at detector-typical microscope parameters and demonstrated that the PSR of the on-axis TKD was slightly improved compared to that of the off-axis TKD. However, no extensive studies have been carried out on the PSR changes with other microscope parameters and sample parameters for on-axis and off-axis TKDs in the same scanning electron microscope (SEM). In addition, the low signal-to-noise ratio of the TKD pattern leads to errors in the calculation of the PSR, which has been neglected in previous research.  
In this study, the evaluation method for the PSR was improved by considering only the effective parts of the patterns, while the noisy parts were eliminated during the calculation. Additionally, we introduced average filtering to remove low-frequency noise, and thus, precisely calculate the spatial resolution. Furthermore, the spatial resolution difference between the off-axis and on-axis TKDs was investigated at different accelerating voltages and specimen thicknesses. We aimed to analyze the limitations of the instruments for an optimal analysis of each sample.