# Some Approaches for Light and Color on the Surface of Mars
## 3 Results
### Colorimetric Characteristics of Lights on Mars' Surface
#### 3.1.5. Color Inconstancy for Samples in the X-Rite ColorChecker(r)  
We computed the corresponding colors [20] for the 24 samples in the X-Rite ColorChecker(r)[15], using the chromatic adaptation transform CIECAT16 [22] with reference condition illuminant D65 and CIE 1964 colorimetric observer for a constant adapting illuminance equivalent to 1000 lx. Next, we computed color inconstancy values [21] in CIELAB units for these samples under some pairs of lights on Mars' surface, as shown in Figures 7-9. Figure 7 shows CIELAB color inconstancies for changes in the solar zenith angle from 0\({}^{\circ}\) to 72\({}^{\circ}\) considering five opacity (Tau) values. For the lowest opacity value (i.e., Tau = 0.1) the average color inconstancy in Figure 7 is 0.06 CIELAB units, and, in principle, none of the 24 samples should exhibit a perceptible color change when the solar zenith angle changes from 0\({}^{\circ}\) to 72\({}^{\circ}\)[23]. However, this change in solar zenith angle does generate average perceptible color changes, which increase with opacity, up to an average value of 3.4 CIELAB units (with a standard deviation of 2.3 CIELAB units) for Tau = 8.1. Similarly, Figure 8 shows CIELAB color inconstancies for changes in opacity from Tau = 0.1 for two values of the solar zenith angle (0\({}^{\circ}\) and 72\({}^{\circ}\)). From Figure 8, average color inconstancies increase in an approximately linear way with the change in opacity, and are highest for the solar zenith angle of 72\({}^{\circ}\) (Figure 8b). Only for a solar zenith angle of 0\({}^{\circ}\), and when opacity changes from 0.1 to 2.1, do some of the samples in the X-Rite ColorChecker(r) appear not to exhibit perceptible color differences, because in this case, 15/24 samples (in particular all 6 achromatic samples in the ColorChecker(r) exhibited color inconstancies below 1.0 CIELAB unit [23]. Figure 6: CIE \(x\),\(y\) chromaticity coordinates for the 3139 lights on Mars’ surface from the COMIMART model [9], in comparison with a part of the Planckian locus (red line) and Earth’s daylight locus (blue line) established by CIE [3]. The color inconstancy is not the same for the 24 samples in the X-Rite ColorChecker(r)[15], numbered here in such a way that the last row of the chart includes the achromatic samples #19 (white) to #24 (black). As an example, Figure 9 shows the color shifts undergone by  
Figure 8: Average color inconstancies [21] and standard deviations (error bars) in CIELAB units for the 24 samples of the X-Rite ColorChecker®[15] and Mars’ lights changing in opacity from Tau = 0.1 to increasing values of Tau up to 8.1, for two solar zenith angles, 0\({}^{\circ}\) (**a**) and 72\({}^{\circ}\) (**b**), using the chromatic adaptation transform CIECAT16 [22]. Figure 7: Average color inconstancies [21] and standard deviations (error bars) in CIELAB units for the 24 samples of the X-Rite ColorChecker®[15] and Mars’ lights changing in solar zenith angle from 0\({}^{\circ}\) to 72\({}^{\circ}\) at five opacity values (Tau = 0.1, 2.1, 4.1, 6.1 and 8.1), using the chromatic adaptation transform CIECAT16 [22]. each of the 24 samples when opacity has a very high change (from Tau = 0.1 to Tau = 8.1) and the solar zenith angle is 72\({}^{\circ}\). Color shifts of six achromatic samples (#19-#24) are not well distinguished in Figure 9, but they are in the range from 1.8 (black sample #24) to 5.2 (white sample #19) CIELAB units, above the human visual threshold (0.55-1.10 CIELAB units [23]). An approximate visualization (Adobe Photoshop 22.1.0) of color shifts indicated in Figure 9 is provided by the two images of the X-Rite ColorChecker(r) shown in Figure 10.  
Figure 10: Approximate colors (Adobe Photoshop 22.1.0) of the 24 samples in the X-Rite ColorChecker®[15] for two light sources on Mars’ surface with a solar zenith angle of 72\({}^{\circ}\) and opacity values (Tau) of 0.1 (**a**) and 8.1 (**b**).