## 1 Introduction
Ambient illuminance and screen luminance are frequently examined separately in different studies, and only a few investigations have studied the impact of ambient illuminance and screen luminance levels on visual fatigue and visual performance. For example, [PERSON] et al. (2014) explored the combined effects of these two factors on visual fatigue and performance by manipulating the ambient illuminance (5 and 85 lx) and screen luminance (20 and 140 cd/m\({}^{2}\)) simultaneously between subjects. They found that although subjective visual fatigue was not affected by either screen luminance or ambient illuminance, objective visual fatigue evaluated by blink frequency increased under high luminance conditions (140 cd/m\({}^{2}\)) [22]. Using limited levels of ambient illuminance and screen luminance, this line of research provides a relatively better solution for visual fatigue. However, with regard to practical settings, the levels of illuminance and luminance employed would vary significantly, and some levels may be easily neglected by this line of research. To solve this problem, multiple levels of illuminance and/or screen luminance, with a wide range, need to be manipulated to determine the optimal screen luminance under different ambient illuminances. The related studies are summarized in Figure 1. [PERSON] et al. (2013) investigated the optimum screen luminance of mobile phones (Samsung S5660, 3.2 inch TFT-LCD screen, 480\(\times\)320 pixels) under ambient illuminance by measuring task performance, CFF and subjective ratings of comfort, visual fatigue and overall satisfaction. The results of these studies showed that optimum screen luminance under ambient illuminance levels of 0, 100 and 500 lx corresponded to 11, 68 and 257 cd/m\({}^{2}\), respectively [23]. Using the same mobile phone, [PERSON] et al. (2013) revealed that optimum screen luminance levels under outdoor illuminance levels of 10k, 20k and 50k lx were 354, 734 and 1375 cd/m\({}^{2}\), respectively [24]. In a study by [PERSON] et al. (2014), participants were required to evaluate the display quality and visual fatigue associated with three different mobile phones (Samsung Galaxy S3, Nokia 920 and iPhone 45) to investigate the optimal luminance under variable levels of ambient illuminance. They found that the optimal luminance levels for 0, 150, 300, 400, 600 and 800 lx were 55, 170, 308, 436, 470 and 496 cd/m\({}^{2}\), respectively [25]. [PERSON] et al. (2018) found that the optimal luminance for short-term reading was 58.5, 66, and 84 cd/m\({}^{2}\) for 100, 150, and 300 lx, respectively [26]. Recently, [PERSON] et al. (2017) identified the comfort zone of display luminance under different ambient illuminances [27]. In a follow-up study, [PERSON] et al. extended the reading duration and found that the optimal luminance zones were 45-90 cd/m\({}^{2}\) under 100 lx and 45-270 cd/m\({}^{2}\) under 230 lx [28]. These findings indicated that optimum screen luminance increased with increasing ambient illuminance, which was in accordance with Weber-Fechner's Law of brightness perception [29; 30]. More specifically, brightness perception, an attribute of visual perception in which a source appears to be radiating or reflecting light, depends on the relative weight between screen luminance and ambient illuminance. It is essential to increase the screen illuminance accordingly with the incensement of ambient illuminance to keep the brightness perception unchanged. Light brings multiple benefits to both individuals and society [31; 32]; however, inappropriate light exposure (both ambient light and the light emitted from screens of digital devices), especially at night, can also potentially damage human biological functioning (i.e., circadian rhythm and nighttime sleep) [33; 34; 35; 36]. This is the so-called nonvisual function of light, which has attracted much attention in the field of chronobiology and lighting.