What theory is most useful for explaining the characteristics of Afterimages?

1.1. Glare

Glare can be divided into two classes, discomfort and disability glare, respectively. The significant difference is that the latter can strongly obstruct visual performance. Previous studies have investigated the impact of glare induced by LED technology—Ixtaina et al. simulated night-time driving conditions to explore the perturbation or discomfort of glare. The LED signals that were directly visible and with refractors were compared. The findings showed that the higher punctual luminance raised the observers’ perturbation and discomfort [7]. Tyukhova et al. implemented a glare rating experiment to determine how glare source luminance, source positions, source sizes and background luminance influenced pupil size and discomfort glare perception. Their results suggested that an increase of glare source luminance induced more discomfort in the observer [8]. Moreover, the visual data were evaluated with four discomfort glare models. The highest correlation with the observer’s response was achieved by a Unified Glare Rating (UGR) small source extension, and the model was further improved for dark surrounds and night-time applications [9]. Two experiments were carried out by Bullough et al. to test the discomfort from traffic signals, simulated with two distances and three signal colors. The results showed that higher discomfort presented with the increase of signal luminance and a decrease in the viewing distance. Regarding the color signal aspect, the green and yellow signals can easily cause visual discomfort [10]. How the age affected glare recovery, which is the recovery of contrast discrimination after exposure to a high luminance, was discussed by Collins et al. The recovery time was prolonged over 56 years of age [11]. Chen et al. examined the discomfort glare of light sources with different correlated color temperatures (CCTs) from 3100 to 5300 K. The modified UGR model, which took CCT into account, predicted glare perception more accurately and showed a high correlation of determination values [12]. Moreover, Sun et al. developed an image-based measurement system to evaluate the UGR value of fixation points from given panoramic scene images [13].

1.2. Visual Afterimage

Gazing at the high luminance stimulus might bring about a visual afterimage. Depending on the duration time, there were two types of visual afterimage presented, as shown in Figure 1. As the stimulus was removed, a brief positive afterimage was displayed which then gradually changed to a negative one in a relatively slow process [14]. For the positive afterimage, the light and dark parts corresponded to those of the object, whereas complementary colors appeared in the negative one [15]. In general, with a longer fixation duration, a significant negative afterimage is perceived. However, the afterimage’s intense influence was determined by the positive one and was slightly colored [16]. Due to the disadvantages of afterimage on visual performance, many studies have contributed to investigating afterimage characteristics which result from a high luminance stimulus [17,18]. Reidenbach et al. adopted special eye test tasks such as the Landolt C visual test, or a reading task, to investigate the effects of exposure duration on the afterimage and visual impairment using colored LEDs. The results indicated that even exposure durations of less than a second would lead to significant vision impairment [19]. They also studied the characteristics of temporary blinding from various light sources, including LEDs and lasers. The visual acuity and the size of an afterimage as a function of duration caused by a high luminance white LED were quantified and modeled by linear and exponential regression. The experiment revealed that the afterimage size diminished after about 12 min, and the visual acuity was recovered between 30 and 60 s [20]. The visual acuity could be formulated as a logarithmic function depending on the duration of impairment [21]. Stimulus with a lower power laser resulted in a relatively longer duration time of afterimage which might interfere with visual performance up to 300 s [22]. Additionally, two lasers with wavelengths of 632.8 and 542 nm and red, green, blue, and white LEDs with high brightness, were used as the stimuli to establish the relationship between their afterimages and the visual acuity recovery time under low ambient lighting conditions [23]. Comparing the visual acuity recovery times of different light sources indicated that temporary blinding from LEDs impaired the color vision, and the blue LED affected it the most. On the other hand, the visual acuity was severely reduced by the green and white LEDs [24]. Regarding the afterimage’s color appearance, Reidenbach et al. reported the color variation corresponded to the time sequence. The study summarized that the decrease in optical energy was related to the displacement of the perceived colors and would shorten the color variation process [25]. Mikamo et al. proposed a model to describe the color transitions in afterimages based on psychophysical experiments [26]. Furthermore, color discrimination and contrast sensitivity were tested from colored LEDs after displaying a dazzling glare. The result found that a decrease in one level of contrast would extend the identification time by about 4 s [27].

From a review of the previous work, the afterimage’s persistence was found to depend on the luminance of the light source, duration of exposure, surrounding luminance and the location of the effect [28]. Regarding road lighting design for night-time driving tasks, Brémond et al. suggested an index called the visibility level that is highly correlated witho the detection distances [29]. The research revealed that accounting for the impact of visual afterimage characteristics is essential for advanced lighting studies. Determining how to account for the effects of visual afterimage characteristics is an initial step in the study of advanced lighting.

To cope with various LED lighting issues, the International Commission on Illumination (CIE) recently focused on researching the mesopic range of lighting characteristics, especially for night conditions [30,31]. The study aims to investigate the characteristics of visual afterimage caused by high luminance LEDs, including three experiments: (1) duration time of afterimage, (2) color difference between afterimage and background, (3) the impacts of afterimage to text visibility. Different luminance levels of illumination, exposure time, color stimuli and luminance of backgrounds were tested to explore the relationship between afterimage characteristics and influential factors.

2.1. Experimental Setup

A total of 60 test patterns were assessed for each evaluation item (duration of the afterimage, color difference, and visibility) with two luminance levels of illumination, five colors, three luminance levels of background and two exposure times. Figure 2 illustrates an example of a viewing field seen in a completely dark environment. An RGB LED spotlight presents all the stimuli with an IR remote control, enabling the adjustment of colors, transitions, and luminance levels. A half-silvered mirror (50% reflection and 50% transmission) was placed 70 cm in front of the observers to simultaneously acquire the stimulus and different luminance of the background, presented by a 47-inch narrow-bezel transparent display (47TS50MF, LG) with a resolution of 1920 × 1080 pixels. The circular stimulus viewing angle was about 1.35° at the subject’s position, and a cross mark was placed at the center of the half-mirror as a fixation point. Table 1 and Table 2 show the parameter settings. Each LED’s luminance was measured by a spectroradiometer (SR-UL1R, TOPCON) at the observer’s viewing position, and the colorimetric characteristics of the five achromatic colors are listed in Table 3. The black, gray, and white background luminance was 0.02, 9.76, and 29.16 cd/m2, respectively. Figure 3 and Figure 4 illustrate the CIE (International Commission on Illumination) 1976 u’, v’ chromaticity coordinates of the LED color stimuli and the detail of viewing conditions, respectively.

2.2. Experimental Procedures

Three psychophysical experiments were conducted to obtain visual data from observers. Before starting the experiments, a 20-min dark adaptation was required. During the experiment, each observer was seated in front of a half-silvered mirror in a completely dark environment. An experimenter sitting next to the blackout system controlled the display of stimuli in the same order and recorded the observer’s assessments. The transition of the background and the control of exposure time were implemented with Matlab software. Twelve observers with normal vision, including seven males and five females, participated in each experiment. The observers were around 26 years of age (Mean = 25.83, SD = ±1.99), and all of them were Taiwanese. Before starting the experiment, all observers had passed the Ishihara test for color deficiency. Each observer assessed two-fifths of the patterns twice for verification and adapted to the background for 10 s before the stimulus was presented.

3.1. Observer Variability

In previous studies, the coefficient of variation (CV) and correlation coefficient measure (r) were primarily adopted to investigate the agreement between two data sets. The data points can be plotted with a 45o line to reveal the circumstances of two sets of data in variation. The CV values were formulated as Equations (1) and (2) for estimating the inter-observer and intra-observer variability, respectively. The larger CV value means a poorer agreement.

CV =100×1N∑(ΔE−f×ΔV)2(ΔE ¯)2, f=∑ΔE×ΔV∑(Δ V)2

(1)

CV=100y¯×∑(xi−yi)2N

(2)

where ΔV is the estimation of a stimulus from an individual observer, ΔE is the geometric mean of ΔV from all observers and ΔE¯ is the arithmetic mean of all evaluated stimuli N. The scaling factor f was used to adjust the data between ΔV and ΔE. Besides, the observer repeatability was calculated with Equation (2), where y is the arithmetic mean of set yi, and xi and yi represent the first and second judgments from the same observer.

Table 4 and Table 5 show the mean results of the observer variability in each experiment. The observer variability in the color difference and visibility experiments were acceptable except for the duration. The reason is that the partly different retinal photoreceptors of the human eye may lead to higher observer variability. Therefore, the correlation coefficient measure (r) was applied to observer variability of the duration time, which showed better agreement. The r values were 0.86 and 0.85 for inter-observer and intra-observer variability, respectively. The photoconversion process of the afterimages was naturally different among the observers, such that the situation of the afterimages perceived at 5 s showed a significantly poorer agreement, excluding the white background, where the afterimage disappeared within a relatively shorter duration.

3.2. Duration Time of Afterimage

The visual data were obtained by ignoring the data with a worse correlation coefficient of observer variability and averaging the rest of the observers’ responses. Referring to Figure 6a,b, the results indicate that the afterimage duration increased with the higher contrast between the stimulus and backgrounds, where the black one required the longest time for elimination. Furthermore, the higher luminance of illumination and longer exposure time (Pattern 4) lead to a significantly more positive afterimage duration. The duration with different exposure times and luminance levels of the five color stimuli is shown in Figure 6c, where the ordinate represents the mean duration time of three backgrounds. As can be seen, the exposure time and luminance level were the primary factors that influenced the duration time. As the luminance level and exposure time increased, the duration time intensively increased and the luminance level (Level 2) showed a more significant impact on the duration compared with the exposure time (3 s). During the experiment period, a phenomenon was found in that the afterimage reappeared after the observers blinked, and the study from Ito [32] proposed a similar result. Additionally, the Pearson correlation coefficient between different backgrounds is listed in Table 6, presenting a similar tendency under three background levels.

3.3. Color Difference

In discussing the color difference between the afterimage and the background, all visual rating data were first converted to the absolute values. The mean color difference of the afterimage with different backgrounds was analyzed with acceptable visual data which had passed the observer variability exam, as shown in Figure 7a. According to the stacked bar chart, the brighter background, especially when presented with higher luminous stimuli, significantly reduced the color difference. Moreover, the higher luminous stimuli enlarged the color difference perceived by the observers for all background conditions. The impacts of luminance and exposure times were compared, as shown in Figure 7b, where the luminance level produced much more influence on the color difference at 1 s. Furthermore, Table 7 shows the correlation coefficient between different backgrounds on the color difference, and lower correlation was found when compared to the visual response of the white background. However, the black and gray backgrounds were highly correlated with each other.

3.4. Visibility

For visibility, the visual data were analyzed by ignoring the extreme data and averaging the observers’ evaluations. Referring to Figure 8a, the visibility rating level was obviously influenced by backgrounds and decreased with the darker one. As shown in Figure 8b, visibility is significantly reduced with longer exposure time and higher luminance. Furthermore, the higher luminance level showed more potent effects. Throughout the experiment, it was suggested that the positive afterimage seriously obstructed vision. When discussing the correlation coefficient r between the different backgrounds regarding the visibility, high r values in Table 8 were presented by the comparison and similar to the duration.

3.5. Regression Analysis

For the regression analysis, linear regression and a polynomial regression model were utilized to describe the relationship between the visual characteristics of the afterimage resulting from high luminous LEDs under a completely dark environment. Due to there being just a smidgen of visual data for each background condition, only the linear regression was discussed to avoid overfit. However, the polynomial regression, which is typically used to fit the nonlinear dataset, was adopted to build the lighting application model.

The relationship between the duration and the experimental parameters which contained the luminance levels, the background luminance and the exposure time, was investigated. The integral of the luminance contrast of background with the exposure time was regarded as the linear regression feature. It was normalized initially with the highest luminance under each background level. The visual afterimage duration (DT) was formulated as Equation (3), where Ls and Lb are the luminance of the test stimulus and background in units of candela per square meter, and te represents the exposure time of the stimulus in seconds. a0 and a1 are the coefficients equivalent to the linear function intercept and slope, respectively, and their values are listed in Table 9 for different backgrounds. The result of the linear regression model showed highly positive correlations between the prediction and the visual response, where the r values are 0.96 for black, 0.99 for gray, and 0.94 for white backgrounds, as shown in Figure 9.

DT=a1·Ls Lb·te+a0

(3)

The color difference, denoted as CD, between the visual afterimage and background, can be modeled by the integral action from the logarithm of luminance contrast and exposure time as Equation (4). The optimal coefficients of linear regression are shown in Table 10. The r values are 0.96, 0.92 and 0.64 for black, gray and white backgrounds and the scatter plot of the prediction is illustrated in Figure 10. The result clearly showed that the correlations decrease with the raising of contrast, and the brightest background performs the poorest. This might be due to the conversion speed of the afterimage. From the above section of the duration time, the result illustrates the afterimage quickly disappears with the brighter background. Some observers immediately perceived a brighter positive afterimage as the higher luminous stimuli was removed in that process. A darker afterimage was then rapidly generated in 1 s, but some were still situated at the procedure of a positive afterimage. Although the perceived positive afterimage was brighter than the background at 1 s, the level of its color difference was no stronger than its highest level in the negative process. The difference in the personal conversion cycle was considered the main factor leading to a low correlation for a white background.

CD=b1·logLsLb·te+b 0

(4)

In terms of visibility (V), it can also be predicted indirectly by an identical linear function as that of color difference. In other words, the interference of visual performance is a negative presentation of visibility. The higher visibility implies a worse visual performance, which means that the observer cannot clearly recognize the characters. Hence, Equation (5) was used to quantify the degree of visual interference and reveal the opposite tendency with visibility. Following the Weber–Fechner law, the visibility depends on the logarithm of luminance contrast between stimulus and background. Table 11 lists the optimal coefficients of linear regression to predict the visibility. The high negative correlation presents with −0.95, −0.96, and −0.92 for black, gray, and white sets, as shown in Figure 11.

V=c1·logLs Lb·te+c0

(5)