2.Įach point in the mesh corresponds to a corrected position in virtual image coordinates ranging from in each direction. The mesh should be high-enough resolution so that the pixel spacing between mesh points is small (2–3 pixels).
The algorithm to correct a pincushion or barrel distortion is as follows: 1.Ĭonstruct a high-resolution rectangular 2D mesh that projects to a screen-space area the size of the input image. Usually the quadratic term dominates the other terms, so approximating with the quadratic term alone often provides good results. The coefficient a is positive for pincushion and negative for barrel distortion. The relationship is usually of the form D = ah 2 + bh 4 + ch 6 + …. Read moreĭistortion is measured as the relative difference of the distance from image center to the distorted position and to the correct position, D = ( h′− h)/ h. is implemented so that this time-consuming step can be avoided (see Chapter “Implementing the homography-based global HR-EBSD/TKD approach” by Ernould et al.). The novel approach proposed in Chapter “Development of a homography-based global DIC approach for high-angular resolution in the SEM” by Ernould et al. Moreover, to date, optical distortions have been corrected by pre-processing the Kikuchi patterns before conducting the HR-EBSD/TKD analysis, when necessary. that some of the conclusions by Britton et al. They consequently stated that a correction for optical distortions is unnecessary when both the reference and the target patterns are distorted in the same way: “ No such correction is needed if both test and reference patterns are recorded from the same specimen with unchanged camera or beam positioning between them.”Īctually, it will be shown in Chapter “Numerical validation and influence of optical distortions on accuracy” by Ernould et al. They noted that the optical distortion causes an error of at most 6.1 × 10 − 4 on one of the elastic strain components, which they said is only about 1.5% of the applied value (2.5° ≈ 4.3 × 10 − 2 rad). For better readability, the authors plotted the difference between the two measurements ( Fig. 14D) were visually close to those obtained without distortion ( Fig.
The experiment was repeated, but with a barrel distortion of 10 − 7 added to all patterns (including the reference.) The results ( Fig. As expected, all the measured components remained close to zero except for the applied rotation in blue squares in Fig. In order to prove the efficiency of the local HR-EBSD technique, undistorted patterns were considered. In a second step, the authors applied a rotation w 12 ranging from 0 to 2.5° in the sample frame, while still considering an unconstrained state. (D) Distorted target and reference patterns. (A) Distorted target pattern and undistorted reference pattern with increasing radial distortion coefficient. The local HR-EBSD method is applied to dynamically simulated patterns. Experimental patterns are all distorted and the use of a simulated reference is to be avoided, mainly due to the uncertainty in the projection geometry ( Maurice et al., 2010).įig. However, this is never the case in practice. Therefore, the authors concluded on the necessity of a correction of optical distortions when the reference is not distorted. They also increased linearly with the amplitude of the applied barrel distortion ( Fig. Although all simulated patterns are associated to a strain-free state, “phantom” elastic strains of the order of 1 to 3 × 10 − 3 were measured. Then, the initial (undistorted) pattern was taken as a reference and compared to the distorted images using the local HR-EBSD/TKD technique. In a first step, the authors dynamically simulated an electron diffraction and added up to 1 × 10 − 7 first order barrel distortion.
The influence of a barrel distortion on the accuracy of the HR-EBSD/TKD technique was investigated by Britton et al.
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