Then, the image quality metric was evaluated as a function of precision error in $B$ and rotational error in $X$, which are the two main errors affecting STRATUS image quality. We considered nine variables: rotational and translational errors in $B$, and rotational errors in $X$. For each dimension, the step was 0.1 mm or degree for the translation and rotation components, respectively. To display a three-dimensional (3-D) matrix, both dimensions of rotation and translational errors in $B$ were compressed to a single precision dimension using the relationship map shown in Appendix ^{2}. The precision’s range in $B$ is set to vary from 0 to 1 mm, while the rotational error’s range in $X$ varied from 0 to 2 deg. For each value in the precision’s range, all possible corresponding rotational and translational components, according to the distribution map shown in Fig. 11, were taken into consideration, and their corresponding simulation image quality values were averaged. As mentioned earlier, the rotational error dimension shown in Fig. 6 represents the norm of the rotational error components. Thus, different rotational vectors can share the same norm value. Similarly, different translational vectors can share the same norm. To consider the variation of vectors, we run the simulation algorithm and acquire data from 18 independent trials with varying rotational and translational error vectors while maintaining the same corresponding norm values. As a result, Fig. 6 shows the mean, the worst-case, and the best-case scenarios of this image-quality analysis. The best-case scenario means that the highest value in each matrix is shown through 18 trials, and the worst-case scenario means that the lowest value is shown. The raw image quality metric is shown in Fig. 6(a), while Fig. 6(b) is rescaled to only show values larger than 1, which corresponds to the image quality of the single pose case. Any color other than the dark blue can be regarded as an image quality improvement compared to the single pose case. The value for each trial has a variation, and it indicates that the same magnitude of $X$ and $B$ can result in different image quality. The accumulation of multiple randomized errors in the process to simulating images from five poses can be one of the reasons to explain this phenomenon. However, a more important factor is that each Euler angle in the rotational error in $X$ has a different contribution to image quality. Axial direction misalignment between multiple poses is the most influential factor, and the rotation in elevation axis is the dominant component in causing misalignment between multiple poses in the axial direction. Therefore, the image quality can be degraded when the error in the elevational axis of rotation is significant even if the overall rotational error in $X$ is small. The error in $X$ is more tolerant than the error in $B$, because the error in $X$ is constant for five poses, while the error in $B$ varies for each pose. Nevertheless, it does not mean that the error in $X$ is not important compared to that in $B$ because the rotational error in $X$ depends on the performance of ultrasound calibration that has room for improvement, while the error in $B$ is a predefined factor based on what tracking system is used.