## 2 Methods
### Experimental Setup  
The experiment is carried out using a windshield and set up on a tripod. The viewing angle between the windshield and the horizontal is 45\({}^{\circ}\) at the observer's position. A 9.7-inch iPad (6 th generation) with a black border is placed on a horizontal table, and the windshield is supported by a floor stand, as shown in Figure 1a. The dimensions of the viewing booth are 60 cm (length) \(\times\) 60 cm (width) \(\times\) 60 cm (height), and the interiors are covered with Munsell N7 spectrally neutral paint. Figure 1b shows the experimental setup captured from the observer's eye position, in which the viewing distance is about 65 cm between the eye and the windshield. The white point of the iPad reaches a peak luminance of approximately 560.8 cd/m\({}^{2}\) with chromaticities of ((x, y) = (0.3152, 0.3323)) after a 30-min stabilization period. Additionally, the viewing booth contains the illumination of a four-channel color-adjustable LED device (SkyPanel S60-C, ARRI, Munich, Germany) to produce uniform light sources. The four-channel color-adjustable LED device is adopted to strictly provide a light source by adjusting the illuminance level to 300, 1500, and 9000 lx with an identical CCT of 6500 K. This was measured by the Konica MinoltaChroma Meter CL-200A at the intersection point directly beneath the light source and eye level. The relative spectral power distributions (SPDs) are shown in Figure 2. Table 1 lists the colorimetric characteristics of the lighting conditions measured by a calibrated spectroradiometer (Specbos 1211 TM, JETI Technische Instrumente GmbH, Jena, Germany). In addition, the reflection and the transmission for the windshield (with insulation paper) are around 3% and 31.7%, respectively. The luminance of the booth wall as viewed through the windshield under 300 lx, 1500 lx, and 9000 lx is 5.97 cd/m\({}^{2}\), 29.8 cd/m\({}^{2}\), and 178.3 cd/m\({}^{2}\), respectively. For comparing the colorimetric characteristics of the light directly going to the spectroradiometer (i.e., (x, y) = (0.3085, 0.3228)) and the light going through the windshield (i.e., (x, y) = (0.3037, 0.3183)), it indicates that the color bias for the windshield is close to zero. A total of 61 observers participates in this study, including 20 young adults aged from 18 to 40 years old (mean = 22.9, std. dev. = 4.8), 20 middle-aged adults aged from 40 to 60 years old (mean = 47.3 years, std. dev. = 5.9), and 21 older adults aged 60 years or above (mean = 66.6, std. dev. = 3.9). All of them hold a driving license. Because one older observer \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Illuminance (lx)** & **CCT (K)** & **CRI Ra** & **Duv** \\ \hline
303 & 6502 & 95 & 0.0018 \\
1506 & 6509 & 95 & 0.0026 \\
9025 & 6493 & 95 & 0.0025 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The colorimetric characteristics of ambient lighting conditions. Figure 1: Experimental setup: (**a**) simulation of head-up display; (**b**) an example of viewing field (the chin rest is removed for this photograph). Figure 2: The relative spectral power distribution of the light source (6500 K, 300, 1500, and 9000 lx). does not pass [PERSON]'s test, his data are excluded from the analysis. Therefore, valid data from 60 observers with normal color vision are analyzed. The RGB values of the iPad are adjusted to produce five achromatic colors for different background lightness. Totally 20 text-background lightness combinations are acquired from these five colors, using one for the text and one of the others for the background. These 20 combinations are presented to observers as paired comparisons for estimation, as shown in Figure 3, for a total of 190 pairs. Each observer assesses 20 of the 190 pairs twice for verification. Thus, each observer evaluated the 210 pairs on the head-up display (projected from the iPad) under four illuminance levels.