# An Analysis of Visibility Requirements and Reaction Times of Near-Field Projections
## 3 Results  
Initially, the used Weber contrasts of the projection system were calculated for the different constellations (projection distance: 1 m/5 m, content: symbol/text). For this purpose, the luminance images recorded at the various constellations and intensity settingsled to the calculation of the Weber contrast. Figure 5 displays the resulting contrast curves. The projector intensity for the present detection study was 1.96-5.88%. The greyscale percentages correspond to an illumination level of 22.98-46.46 lx. Figure 5 shows that the contrast curves are nearly linear over a large range, especially at a distance of 5 m. So, the contrasts at a distance of 5 m are lower than at a distance of 1 m for the same intensity settings, which shows the distance dependency of the Weber contrast. For example, the symbol indicates a maximum contrast of 60.24 at a distance of 1 m and a maximum contrast of 57.99 at 5 m. For the text, the maximum contrast is 73.06 at a 1 m distance and 53.59 at a distance of 5 m.  
The subjects' detection rates for the different contents (symbol, text) at distances of 1 and 5 m were plotted using logistic regression and plotted against the projected contrast. The fitted curves represent the required Weber contrast which presupposes a certain detection probability. To ensure the projection's reliable detection, this study used a 90% detection probability. Figures 6 and 7 show the logistic regression functions of the detection probability over the contrast for the presented object symbol and text in the distances 1 and 5 m averaged for all test persons. For both contents (text, symbol), an increasing contrast is accompanied by higher detection probability, which goes into saturation above a particular contrast value. To obtain a 90% detection probability, a contrast of 0.089 is required for the symbol at a viewing distance of 1 m. The corresponding contrast at a 5 m distance is 0.1253 (Figure 6). Considering the detection probability of the presented text, a 90% detection probability at a 1 m observation distance results in a contrast of 0.111 and 5 m of 0.154 (Figure 7). Here, there is a 38% increase in the detection contrast with increasing distance. By comparing the probability level of 90% for the detection contrasts of the text and symbol at different distances, the 90% detection contrast is significantly higher than that of the symbol at 1 and 5 m. There is an increase of 24% at 1 m distance and 23% at 5 m distance. Looking at the corresponding reaction time of the subjects at the different contrasts of the text- and symbol-based projection, there is a decreasing reaction time for text and symbol at both distances of 1 and 5 m with increasing contrast and increasing detection probability. For both contents at both distances, there is a saturation of the reaction time between 600 and 650 ms before the 90% detection probability has been reached (Figures 6 and 7). Figure 5: Contrast curves for the presented symbol (blue lines) and text (red lines) at distances of 1 m (solid) and 5 m (dashed). depending on the projector intensity. The chi-square test and Cramer's V test were used on the study data to investigate whether the distance or content significantly influences the detection probability [36; 37]. Due to the different shapes of the contents (text, symbol), different Weber contrasts were inherited with the same grey levels for the text-based and symbol-based contents. Since the distance changes the viewing angle and the reflection properties of the pavement vary as a result, these factors influence the measured Weber contrast. To achieve a generally valid statement of the statistical tests, they were determined utilizing the greyscale levels and the resulting illuminance levels. The illuminance levels are independent of the projection content and the viewing distance. The illuminance level is the photometric variable that is ultimately relevant to the design of the projection system.