# Resolution Aspects for Near-Field Projections
## 3 Results
### Analysis of the Perceived Resolution  
The studies executed in this work enhance the current awareness of near-field projections by focusing on the impact of projection content, viewing distance and various ambient \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario** & **Compared Items** & **Text** & **Symbol** \\ \hline \multirow{4}{*}{Distance PGS} & \(1\) m \(\times\) 3 m & \(\chi 2(9)=2.53\), \(p>0.05\), & \(\chi 2(9)=4.29\), \(p>0.05\), \\  & \(\text{V}=0.06\) & & \(\text{V}=0.07\) \\  & \(1\) m \(\times\) 5 m & \(\chi 2(8)=15.09\), \(p>0.05\), & \(\chi 2(9)=18.48\), \(p<0.05\), \\  & \(\text{V}=0.13\) & & \(\text{V}=0.14\) \\  & \(3\) m \(\times\) 5 m & \(\chi 2(9)=11.89\), \(p>0.05\), & \(\chi 2(9)=9.71\), \(p>0.05\), \\  & \(\text{V}=0.11\) & & \(\text{V}=0.10\) \\ \hline \multirow{4}{*}{Distance DDS} & \(1\) m \(\times\) 3 m & \(\chi 2(8)=16.72\), \(p<0.05\), & \(\chi 2(9)=16.96\), \(p<0.05\), \\  & \(1\) m \(\times\) 5 m & \(\chi 2(8)=72.43\), \(p<0.05\), & \(\chi 2(9)=68.47\), \(p<0.05\), \\  & \(\text{V}=0.19\) & & \(\text{V}=0.17\) \\  & \(3\) m \(\times\) 5 m & \(\chi 2(8)=32.74\), \(p<0.05\), & \(\chi 2(8)=22.39\), \(p<0.05\), \\  & \(\text{V}=0.12\) & & \(\text{V}=0.10\) \\ \hline \multirow{4}{*}{Ambient Lighting} & \(1\) m \(\times\) 1 m & \(\chi 2(8)=30.39\), \(p<0.05\), & \(\chi 2(9)=29.70\), \(p<0.05\), \\  & DDS & \(\text{V}=0.17\) & \(\text{V}=0.14\) \\  & \(3\) m \(\text{PGS}\) \(\times\) 3 m & \(\chi 2(9)=24.19\), \(p<0.05\), & \(\chi 2(8)=20.72\), \(p<0.05\), \\  & DDS & \(\text{V}=0.13\) & & \(\text{V}=0.11\) \\  & \(5\) m \(\text{PGS}\) \(\times\) 5 m & \(\chi 2(8)=17.01\), \(p<0.05\), & \(\chi 2(9)=21.79\), \(p<0.05\), \\  & DDS & \(\text{V}=0.10\) & & \(\text{V}=0.11\) \\ \hline \multirow{4}{*}{Projection Content} & \multicolumn{2}{c}{PGS} & \multicolumn{2}{c}{DDS} \\ \cline{2-4}  & Text 1 m \(\times\) & \(\chi 2(9)=5.73\), \(p>0.05\), & \(\chi 2(9)=15.65\), \(p>0.05\), \\ \cline{1-1}  & Symbol 1 m & \(\text{V}=0.08\) & \(\text{V}=0.09\) \\ \cline{1-1}  & Text 3 m \(\times\) & \(\chi 2(9)=10.49\), \(p>0.05\), & \(\chi 2(8)=23.23\), \(p<0.05\), \\ \cline{1-1}  & Symbol 3 m & \(\text{V}=0.11\) & & \(\text{V}=0.11\) \\ \cline{1-1}  & Text 5 m \(\times\) & \(\chi 2(9)=11.53\), \(p>0.05\), & \(\chi 2(8)=23.96\), \(p<0.05\), \\ \cline{1-1}  & Symbol 5 m & \(\text{V}=0.11\) & & \(\text{V}=0.10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Effects of viewing distance, ambient lighting and projection content statistically analyzed with a chi-square test and the corresponding effect size (Cramer’s V). lighting concerning the perceived resolution. Henceforth, the resolution is specified in pixels per degree (px/\({}^{\circ}\)) to ensure a technology-independent specification for the effective resolution on the ground by considering the average height of the participants (DDS: 1.79 m; PSD: 1.77 m). Thereupon, the average height of the subjects h of each study, the viewing distance d for either 1 m, 3 m, or 5 m and the calculated resolution of the logistic regression DPI define the effective resolution RES on the ground:  
\[RES=\frac{1}{\tan^{-1}\Big{(}\frac{25.4\ mm}{DPI_{LogReg.}}\cdot\sqrt{h^{2}+d^{2 }}\Big{)}} \tag{4}\]  
Before the application of the equation above, the 90% threshold level is extracted from the continuous logistic regression \(DPI_{LogReg. }=\alpha\cdot\sqrt[6]{\frac{1}{0.9}-1}\) to achieve the corresponding effective resolution \(RES\) on the ground, which is illustrated in Table 2 for all possible combinations of viewing distance, projection content, or ambient lighting (PGS, DDS). For every combination, the corresponding confidence intervals are included in brackets to display the lower bound (left number) and the upper bound (right number) of the perceived resolution in pixels per degree. The detailed logistic regression is displayed in Figure 4a,b for the PGS's symbol- and text-based projection content.