**Appendix**

#### **A. Dynamic comparison of the state change agility between the activities of focusing, fixation, and images fusion**

**Figure 5** shows three graphs of Eq. (2), which is the analytical solution of state change in a first-order linear model. The graphs were obtained by replacing the time constant (τ) by the time constants (τC, τR, and τS) according to Eq. (3). The relation was defined from the numerical analysis compatibility, associated with the agility for object visualization.

**Figure 5.**

*Muscle contraction percentage graph, Eq. (2), (C) Ciliary muscle contraction (time constant τC). (R) Rectus muscle contraction (time constant τR). (S) Superior oblique muscle contraction (time constant τS).* 

$$\mathbf{f(t) = 100 \times (1 - e^{-t/\tau})} \tag{2}$$

$$
\mathbf{\mathcal{B}}\mathbf{\tau}\,\mathbf{C} = \mathbf{\tau}\,\mathbf{R} = \mathbf{\tau}\,\mathbf{S}/\mathbf{\mathcal{B}}\tag{3}
$$

#### **A.1 Analysis of the relationship τ<sup>C</sup> = τR/3**

Voluntary action, in order to observe an object of interest, requires the movement of the eyes toward it, under the rectus muscles control (τR). For this, it is necessary, in the first place, to focus on the object (τC) at the moment of its projection in the fovea. Therefore, focalization agility is then considered to be three times higher

than fixation agility. The effect of the variation of the projection of the image on the retina, due to the accommodation of the lens, occurs more rapidly than the effect of the angular displacement of the eyeball, because the amount of mass displaced by the eyeball is much larger than the amount of mass that is moved to crystalline accommodation. Graph 3 shows that at time t = τC = τR/3, the focus had completed 63% of the work, while the displacement is 28%. That is, the numerical result is compatible with the associated analysis between the focus and fixation agility.
