Table 1 Derived equations for distinguishing the natural-VAC-free zone from the pseudo-VAC-free zone in an SMV display.

From: Fatigue-free visual perception of high-density super-multiview augmented reality images

Term

Equation

Term definition

Equation number

\(c_{p} \left( {z_{e} ,N} \right)\)

\(c_{p} = N\frac{e}{{z_{e} }}\frac{{w_{v} \left| {l - z_{e} } \right| + pz_{e} }}{l}\)

Maximum blur width of a voxel consisting of \(N\) views for viewer’s focus distance \(z_{e}\)

(4)

\(c_{o} \left( {d_{obj} ,z_{e} } \right)\)

\(c_{o} = \frac{e}{{z_{e} }}\frac{{W\left| {d_{obj} - z_{e} } \right|}}{{d_{obj} }}\)

Natural true blur width of a voxel with object distance \(d_{obj}\) for \(z_{e}\)

(5)

\(d_{\max } \left( {z_{e} ,N} \right)\)

\(d_{\max } = \frac{{Wlz_{e} }}{{Wl - N\left( {w_{v} \left| {l - z_{e} } \right| + pz_{e} } \right)}}\)

Maximum object distance \(d_{obj}\) of a voxel consisting of \(N\) views in the natural-VAC-free zone for \(z_{e}\)

(6)

\(d_{\min } \left( {z_{e} ,N} \right)\)

\(d_{\min } = \frac{{Wlz_{e} }}{{Wl + N\left( {w_{v} \left| {l - z_{e} } \right| + pz_{e} } \right)}}\)

Minimum object distance \(d_{obj}\) of a voxel consisting of \(N\) views in the natural-VAC-free zone for \(z_{e}\)

(7)