The static object resolution

This three equations show that the allowed sampling distances of all three directions are depth dependent. The depth sampling index is given by iz. If three-dimensional objects or their surfaces are given with respect to a equidistant sampling coordinates or constant Nyquist frequencies. These object information datas must be filtered and resampled. Therefore the necessary filtering operations will be derived below.

The sampling resolutions given by equations $\left( \ref{Eq_Zobs3} \right)$, $\left( \ref{Eq_Zobs4} \right)$, $\left( \ref{Eq_Zobs5} \right)$ can be achieved as long as the lenticular focus line is smaller than the horizontal sub-pixel width of one image view on the focal point plane (cf. fig. 1). This view-pixel width is given by (cf. equ. $\left( \ref{Eq_Zobs0} \right)$)

$$\Delta X_{view}=\frac{FP_{pitch}}{N_{view}}$$ (22)

This highest depth dependent 3D resolution is valid for a fixed observer position. Therefore the resolution of objects given by equ. $\left( \ref{Eq_Zobs3} \right)$ to $\left( \ref{Eq_Zobs5} \right)$ is called the static resolution. In case the observer makes a horizontal movement there has to be taken into account another resolution scale which is described in the following.

The observer sampling point distance shown in fig. 2 is given by $\Delta X_{obs}$ (equ. $\left( \ref{Eq_Zobs6} \right)$). The x-positions of the viewing point might be given by

$$X_{view}\left( i\right) =i\cdot \Delta X_{view} \mbox{, } I_{min}<i<I_{min}+N_{view}$$ (23)

Let now the viewing position move

$$X_{view}=\left( i-\frac{1}{2}\right) \cdot \Delta X_{view}$$ (24)

$$X'_{view}=\left( i+\frac{1}{2}\right) \cdot \Delta X_{view}$$ (25)

In the ideal case of a highest matching optical focus no changing of views happens. But crossing the point $X_{view} \left( i+ \frac{1}{2} \right)$ the neighbored view appears. Consequently the objects structure jumps into the z-plane to the correct position. This jumping step is given by

$$\Delta X_{objjump}\left( i_{z}\right) =\left[ Z_{obj}\left( ... ...ft( 0\right) \right] \cdot \frac{\Delta X_{view}} {Z_{screen}}$$ (26)

if $\Delta X_{objjump}\left( i_{z}\right) <\Delta X_{obj}\left( z\right)$ then no jump takes place. In the other cases the jump is quantized by $X_{obj} \left( i_{z} \right)$.