# Perceived Brightness and Resolution of Holographic Augmented Reality Retinal Scan Glasses
## 3 Results
### Perceived Resolution Study Results  
This study was conducted in a controlled environment which allowed us to determine the pupil size directly. We measured the pupil diameter of all participants right before the experiment while they faced the monitor on the chinrest and found a mean \(\pm\) sd pupil diameter of 3.3 \(\pm\) 0.4 mm within a range from 2.5 mm to 4.0 mm. With the optical measurement values from the glasses, we determined LRS according to Equation (14). We then used the luminance of the LED monitor backgrounds for L\({}_{A}\) and the transmittance of the combiner \(\tau_{C}\) to calculate ACRRS according to Equation (17). Table 1 provides the trial parameters and results from the perceived resolution study. The left side of the table shows the trial parameters including the ambient contrast ratio ACRRS for the retinal scan stimuli and the LED monitor background. Since ACRRS stayed well above 0.5 for all trials, we can now assume that the perceived resolution threshold is only a function of the spatial frequency and not the contrast. The right side of the table shows the number of participants that successfully passed each staircase level. \"Passing\" a staircase level means that the participant provided three correct answers in a row at that level during the staircase algorithm. The level number corresponds to the digital pixel width of the line patterns. All 20 participants were able to complete horizontal level 4H (3.59 cyc/deg) and vertical level 5V (3.20 cyc/deg) in all trials. No participant was able to complete horizontal level 1H (14.35 cyc/deg) or vertical level 1V (16.01 cyc/deg) in any trial. The endpoints of the staircase algorithm provide an overview over the results but do not represent all individual datapoints. We therefore additionally fitted sigmoidal psychometric functions to the trial data. We determined the perceived resolution threshold from the inflection point of the functions and calculated the 95% confidence intervals. Figure 6 shows two separate fits for horizontal and vertical lines. This gives us a perceived resolution of 7.09 cyc/deg (95% CI: 6.91 to 7.27) for horizontal and 7.43 cyc/deg (95% CI: 7.02 to 7.89) for vertical lines. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \multirow{2}{*}{**Trial**} & \multicolumn{8}{c}{**Trial Parameters**} & \multicolumn{8}{c}{**Number of Participants That Passed Staircase Resolution Level Horizontal [H] and Vertical [V]**} \\ \cline{2-11}  & **Classes** & **Monitor** & **Lss** & **ACRRS** & **4H** & **3H** & **2H** & **1H** & **4V** & **3V** & **2V** & **1V** \\  & **Classes** & **Monitor** & **[cd/m2]** & **ACRRS** & 3.59 \(\sigma\)_/_d_ & _4.78 \(\sigma\)_/_d_ & _7.17 \(\sigma\)_/_d_ & _14.35 \(\sigma\)_/_d_ & _4.00 \(\sigma\)_/_d_ & _5.34 \(\sigma\)_/_d_ & _8.01 \(\sigma\)_/_d_ & _16.01 \(\sigma\)_/_d_ \\ \hline
1 & red & black & 83 & 92 & 20 & 17 & 0 & 0 & 20 & 17 & 0 & 0 \\ \hline
3 & red & red & 83 & 3 & 20 & 19 & 0 & 0 & 19 & 19 & 0 & 0 \\
4 & green & black & 929 & 1032 & 20 & 20 & 4 & 0 & 20 & 20 & 0 & 0 \\ \hline
5 & green & black & 83 & 92 & 20 & 20 & 5 & 0 & 20 & 20 & 0 & 0 \\ \hline
6 & green & red & 929 & 38 & 20 & 20 & 5 & 0 & 20 & 20 & 0 & 0 \\ \hline
7 & green & red & 83 & 3 & 20 & 20 & 6 & 0 & 20 & 20 & 0 & 0 \\ \hline
8 & green & green & 929 & 38 & 20 & 20 & 6 & 0 & 20 & 20 & 0 & 0 \\ \hline
9 & green & green & 83 & 3 & 20 & 20 & 5 & 0 & 20 & 20 & 0 & 0 \\ \hline
10 & blue & black & 91 & 101 & 20 & 20 & 4 & 0 & 20 & 20 & 0 & 0 \\ \hline
11 & blue & black & 83 & 92 & 20 & 20 & 5 & 0 & 20 & 20 & 2 & 0 \\ \hline
12 & blue & orange & 91 & 4 & 20 & 20 & 3 & 0 & 20 & 20 & 1 & 0 \\ \hline
13 & blue & orange & 83 & 3 & 20 & 20 & 4 & 0 & 20 & 20 & 1 & 0 \\ \hline
14 & blue & blue & 91 & 4 & 20 & 20 & 5 & 0 & 20 & 20 & 1 & 0 \\ \hline
15 & blue & blue & 83 & 3 & 20 & 20 & 5 & 0 & 20 & 20 & 1 & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: Trial parameters and results from staircase algorithm in perceived resolution study.