given in Appendix \[matrixnorm\].

For $\mu_1=\mu_2=1$, $\mathcal{M}=M+  m= \textstyle \sum_o PC_o^2$, and the D-optimal and norm-optimal problems and are transferred respectively to $$\begin{aligned}
\begin{aligned}\label{D-opt2}
& \underset{\upsilon_o,~o=1,\ldots,O}{\text{minimize}}
& & -\mbox{det}\Big(\mbox{PC}_o^2(\upsilon_o)\Big) \\
& \text{subject to}
& & \underline{\upsilon}_o \leq \upsilon_o \leq \overline{\upsilon}_o\\
& & & \mathcal{M}=M+m\\
\end{aligned}\end{aligned}$$ and, $$\begin{aligned}
\begin{aligned}\label{norm-opt2}
& \underset{\upsilon_o,~o=1,\ldots,O}{\text{minimize}}
& & -\left\| \mbox{PC}_o^2(\upsilon_o) \right\| \\
& \text{subject to}
& & \underline{\upsilon}_o \leq \upsilon_o \leq \overline{\upsilon}_o\\
& & & \mathcal{M}=M+m\\
\end{aligned}\end{aligned}$$

Differences between the optimization sets { and } and { and } are the followings.

-   In order to solve or , at each iteration of the optimization, the PC matrices of all orientations and $\mathcal{M}$ must be computed. Solving and does not require $\mathcal{M}$ at each iteration of the optimization.

-   The solution to or results in one optimal parameter vector for all orientations. The solution to or results in $O$ numbers of optimal parameter vectors (one optimal vector for each orientation).

A Sub-Optimal Solution to the Norm-Optimal Problem
--------------------------------------------------

In order to avoid the computation of $\mathcal{M}$ at each iteration of the optimization, a sub-optimal criterion of is derived, which optimizes the parameter vector separately at each orientation. Note that the results of this subsection are valid 