# Spatial Resolutions of On-Axis and Off-Axis Transmission Kikuchi Diffraction Methods
## 3 Results and Discussion
### Difference in Spatial Resolution between the On-Axis and Off-Axis TKD Methods  
By using the above method, the spatial resolutions of the on-axis and off-axis TKD methods were measured in the same SEM at the same sample position. The data obtained at different voltages and sample thicknesses are presented in Figure 3. The intensity and contrast of the pattern for the 169-nm-thick sample were too low to identify at the same parameters used for the other two samples. Therefore, results are presented only for the two samples.  
Figure 1: **(A)** Schematic of the ferritic steel lamella used for the determination of the spatial resolutions of the on-axis and off-axis transmission Kikuchi diffraction (TKD). Kikuchi patterns across the grain boundary at an accelerating voltage of 30 kV and thickness of 91 nm, acquired by (**B**) on-axis TKD (the regions of interest (ROIs) are outlined by the red annular rings) and (**C**) off-axis TKD (the ROIs are outlined by the red circles).  
Figure 2: Correlation coefficient profiles at the accelerating voltage of 30 kV and thickness of 91 nm (**A**) determined by using the digital image correlation (DIC) technique by comparing the sampling patterns with the left (blue curve) and right patterns (red curve) in order and (**B**) after average filtering. (**C**) Sum of the normalized correlation coefficients as a function of the distance.  
The spatial resolution of the on-axis TKD was better than that of the off-axis TKD at the same accelerating voltage and thickness; the largest gap was 8 nm. The only difference between the two configurations was the intersection angle between the phosphor screen and incident beam (\(\alpha\)) [5]. In the off-axis TKD, the intersection angle had a magnitude of only a few degrees, which led to a high gnomonic distortion and low diffraction intensity. On the contrary, no pattern distortion and high diffraction intensity were observed in the on-axis TKD because the angle \(\alpha\) was close to 90\({}^{\circ}\). Consequently, in the off-axis TKD, the probe current and/or exposure time have to be increased to produce an equivalent pattern quality. In this study, we increased both current and exposure time. Nonetheless, the increase in current leads to larger probe size and interaction volume, which inevitably increase the spatial resolution. Therefore, at their optimal parameters, the beam current used in the off-axis TKD method should be higher than that in the on-axis TKD method, which leads to a larger spatial resolution. Similarly, if we set equal parameters for both TKD methods, the pattern quality in the off-axis TKD method would be worse owing to its lower intensity. Therefore, the spatial resolution of the off-axis TKD would still be worse than that of the on-axis TKD.  
Another reason for the difference is the smaller net scattering angle in the on-axis TKD because of the detector geometry. At a given depth, the path length through the sample is smaller for the on-axis TKD, which implies that fewer scattering events may occur before the electrons reach the detector. Therefore, the on-axis TKD has a thicker source region of detected intensity, which is beneficial to the lateral spatial resolution, but detrimental to the depth spatial resolution [5; 22].