Table 1. Equations of the simple and balanced multi-point displacement encoding strategies.

		Encoding	Decoding
Simple	Two-point	$$\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 1& 1\end{array}\right]\left[\begin{array}{c}{k}_e\Delta x\\ \Delta {\theta }_b\end{array}\right]$$ Eq. [5]	$$\left[\begin{array}{c}{k}_e\Delta x\\ \Delta {\theta }_b\end{array}\right]=\left[\begin{array}{cc}-1& 1\\ 1& 0\end{array}\right]\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\end{array}\right]$$ Eq. [6]
	Three-point	$$\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\end{array}\right]=\left[\begin{array}{ccc}0& 0& 1\\ 1& 0& 1\\ 0& 1& 1\end{array}\right]\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ \Delta {\theta }_b\end{array}\right]$$ Eq. [7]	$$\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ \Delta {\theta }_b\end{array}\right]=\left[\begin{array}{ccc}-1& 1& 0\\ -1& 0& 1\\ 1& 0& 0\end{array}\right]\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\end{array}\right]$$ Eq. [8]
	Four-point	$$\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\\ {\phi }_4\end{array}\right]=\left[\begin{array}{cccc}0& 0& 0& 1\\ 1& 0& 0& 1\\ 0& 1& 0& 1\\ 0& 0& 1& 1\end{array}\right]\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ k_e\Delta z\\ \Delta {\theta }_b\end{array}\right]$$ Eq. [9]	$$\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ k_e\Delta z\\ \Delta {\theta }_b\end{array}\right]=\left[\begin{array}{cccc}-1& 1& 0& 0\\ -1& 0& 1& 0\\ -1& 0& 0& 1\\ 1& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\\ {\phi }_4\end{array}\right]$$ Eq. [10]
Balanced	Two-point	$$\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\end{array}\right]=\left[\begin{array}{cc}1& 1\\ -1& 1\end{array}\right]\left[\begin{array}{c}{k}_e\Delta x\\ \Delta {\theta }_b\end{array}\right]$$ Eq. [11]	$$\left[\begin{array}{c}{k}_e\Delta x\\ \Delta {\theta }_b\end{array}\right]=\left[\begin{array}{cc}1/2& -1/2\\ 1/2& 1/2\end{array}\right]\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\end{array}\right]$$ Eq. [12]
	Three-point	$$\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\end{array}\right]=\left[\begin{array}{ccc}1& 0& 1\\ -1/2& \sqrt{3}/2& 1\\ -1/2& -\sqrt{3}/2& 1\end{array}\right]\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ \Delta {\theta }_b\end{array}\right]$$ Eq. [13]	$$\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ \Delta {\theta }_b\end{array}\right]=\left[\begin{array}{ccc}2/3& -1/3& -1/3\\ 0& \sqrt{3}/3& -\sqrt{3}/3\\ 1/3& 1/3& 1/3\end{array}\right]\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\end{array}\right]$$ Eq. [14]
	Four-point	$$\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\\ {\phi }_4\end{array}\right]=\left[\begin{array}{cccc}-\sqrt{3}/3& -\sqrt{3}/3& -\sqrt{3}/3& 1\\ \sqrt{3}/3& \sqrt{3}/3& -\sqrt{3}/3& 1\\ \sqrt{3}/3& -\sqrt{3}/3& \sqrt{3}/3& 1\\ -\sqrt{3}/3& \sqrt{3}/3& \sqrt{3}/3& 1\end{array}\right]\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ k_e\Delta z\\ \Delta {\theta }_b\end{array}\right]$$ Eq. [15]	$$\left[\begin{array}{c}{k}_e\Delta x\\ k_e\Delta y\\ k_e\Delta z\\ \Delta {\theta }_b\end{array}\right]=\left[\begin{array}{cccc}-\sqrt{3}/4& \sqrt{3}/4& \sqrt{3}/4& -\sqrt{3}/4\\ -\sqrt{3}/4& \sqrt{3}/4& -\sqrt{3}/4& \sqrt{3}/4\\ -\sqrt{3}/4& -\sqrt{3}/4& \sqrt{3}/4& \sqrt{3}/4\\ 1/4& 1/4& 1/4& 1/4\end{array}\right]\left[\begin{array}{c}{\phi }_1\\ {\phi }_2\\ {\phi }_3\\ {\phi }_4\end{array}\right]$$ Eq. [16]