5.3 Glare Perception For Short Light Pulses
5.3.2 Glare Perception For Variable Pulse Form
The section above has shown the general correlation between glare perception, photometric values and pupil metrics for solely rectangular glare pulses. Since the illuminance pulses recorded in real life encounter situations, as shown in section4, in figure4.11, are not rectan-gular, this section is dedicated to the influence of the pulse form on the glare rating. Further-more, the findings here can be used to minimize the glare perception for possible encounters in real life traffic by setting the correct gradient in the cut-off-line of either the low beam or the switched off segments ingfHB.
To break down the influence of pulse form to a simple approach, the setup from above is kept exactly the same. As a reference, rectangle pulses are presented again. To approximate real life pulses, triangle pulses are shown, where the illuminance is linearly increased for half of the pulse duration and then linearly decreased for the rest of the duration. Rectangle and triangle pulses are presented at a random order. Due three different reasons, the values of the pulses shown are changed. Firstly, due to the second pulse form, the amount of pulses is doubled and therefore the test duration would double as well. To keep the test participants vigilant, the duration needs to be kept at the same duration as the previous test. Furthermore, the durations of the pulses need to change for two separate reasons. Firstly the duration and the illuminance values need to change to achieve sets of pulses with the same exposure, illuminance and duration between both pulse forms. Additionally, the values are changed to much lower illuminance values and much higher durations to examine the influence of these settings as well. Since the rest of the setup stayes the same, the results should still be comparable. The used pulse setup is shown in table 5.12. T stands for the pulse duration of rectangle pulses,T△on the other hand, shows the triangle pulses. All photometric values can be grouped. The duration groups are shown by the columns, the illuminance groups are shown in the rows and the exposure groups are displayed on the diagonal sets. The exposure for the triangle pulses is calculated by H = (E·T)/2. This means, that the durations need to be doubled for pulses to get equivalent exposures as shown in table5.12.
152 analysis and optimization of light distributions
Table5.12– Pulse parameters used for the investigation of the influence of the pulse form on the psycholog-ical glare perception. The center of the table gives the exposure calculated by the illuminance and the pulse duration. For rectangle pulses the exposureHis calculated byE·Tand for rectangle pulses the exposure is given by(E·T)/2.
exposure
Illuminance 0.044 lx 0.176 lx 0.705 lx 2.820 lx 11.280 lx
pulseduration
T = 0.300 s 0.013 lx s 0.053 lx s 0.845 lx s 0.845 lx s 3.384 lx s T△ = 0.600 s
T = 1.200 s
0.053 lx s 0.845 lx s 0.845 lx s 3.384 lx s 13.536 lx s T△ = 2.400 s
T = 4.800 s 0.211 lx s 0.845 lx s 3.384 lx s 13.536 lx s 54.144 lx s T△ = 9.600 s
T = 19.200 s
0.845 lx s 3.384 lx s 13.536 lx s 54.144 lx s 246.576 lx s T△ = 38.400 s
For this test setup 17 test subjects with an age between 20 and29years of age, and again either students or working in an office environment, participated in the study. The complete data of the participants including the age distribution and their more detailed information on occupation and more are attached in appendixD.1.1in tableD.9andD.10.
Analogous to the study regarding the correlation between the pupil diameter and the glare perception, the first correlation formed is the correlation between the exposure and the glare perception. This is done separately for the rectangle pulses and the triangle pulses and shown in figure 5.57a and 5.57b. All data is shown by the same symbols and colours as in the previous section with only the pulse duration changing their numeric values.
101 −2 10−1 100 101 102 103 2
3 4 5 6 7 8 9
Exposure in lx · s
inv.deBoerRating
Rectangle Pulses 300 ms 1200 ms 4800 ms 19500 ms
(a)
101 −2 10−1 100 101 102 103 2
3 4 5 6 7 8 9
Exposure in lx · s
inv.deBoerRating
Triangle Pulses 600 ms 2400 ms 9600 ms 38400 ms
(b)
Figure5.57– Glare perception on the inverteddeBoerscale for(a)rectangle and(b)triangle pulses for the different shown pulse durations. Blue squares show the data for 300 ms, red diamonds the data for 1200 ms, green asterisks show the data for 4800 ms and purple circles indicate the data for 19 500 ms pulses.
5.3 glare perception for short light pulses 153 Similar to the data shown before, the glare perception between pulses with different du-rations splits up. Pulses with a shorter duration are perceived as more glaring than pulses with the same exposure, but longer pulse durations. The data for each pulse duration then follows a strictly logarithmic behaviour and the fit data, indicated by the solid lines, for each duration are nearly parallel. This is shown by the fit parameters in the equations 5.15a to 5.15d for the rectangle pulses. Again, the fit statistics are shown in table D.10 in appendix D.1.1. The shown parameters show, that all four fit equations give a very good representation of the data with R2 values above 0.99 for all four fits and only very small fit errors in MSE,
∆W andσ∆W. As previously, wgives the glare perception on the inverteddeBoer scale and H is the exposure in lx s.
w(H/H0)t=300 = 1.0·log10(H/H0) + 6.7 (5.15a) w(H/H0)t=1200 = 1.1·log10(H/H0) + 5.3 (5.15b) w(H/H0)t=4800 = 1.1·log10(H/H0) + 3.9 (5.15c)
w(H/H0)t=19500 = 1.1·log10(H/H0) + 2.6 (5.15d)
The data for the triangle pulses and the corresponding fit equations (5.16a to5.16d) show a slightly different behaviour. While the data is again parallel for the shorter glare pulses of 600 ms and 2400 ms with the same fitted slope parameters as for the rectangle pulses, only a lower axis intercept, the slope for longer pulses decreases down from 1.1 to 0.8 for the longest pulses. Again, all fit parameters are shown in tableD.11in appendixD.1.1, showing that the fitted functions are excellent representations of the recorded data withR2values of over 0.94 for all fits.
w(H/H0)△t=300 = 1.1·log10(H/H0) + 5.4 (5.16a) w(H/H0)△t=1200 = 1.1·log10(H/H0) + 3.7 (5.16b) w(H/H0)△t=4800 = 0.9·log10(H/H0) + 2.4 (5.16c)
w(H/H0)△t=19500 = 0.8·log10(H/H0) + 1.7 (5.16d)
This data shows the first impact of the pulse form on the glare perception. Since for pulses with the same exposure, the intersection with the y-axis at x = 0 is always lower for the tri-angle pulses, the general glare perception of these pulses is lower than the perceived glare of rectangle pulses. A second observation is, that due to the decreasing slope for longer triangle pulses, it can be deducted, that for longer, triangular pulses the duration has a higher impact compared to the maximum illuminance. When looking at rectangle pulses, this behaviour can not be seen and it is thereby deducted, that the slower rise of the illuminance gives the eye the chance to adapt to the to the illuminance level. For short pulses, this adaptation time is too short and thereby no difference in the slope values of the fit data is found.
154 analysis and optimization of light distributions
In the next step, the findings from the study regarding the correlation between the pupil diameter and photometric values are used to rescale the exposure for all data sets. For the rectangle pulses this is shown in figure5.58aand the fit data is shown in equation5.17awith the fit parameters shown in appendixD.1.1in tableD.12. For triangle pulses the data and the fit is shown in figure5.58b, the fit equation in equation5.16and the statistical data is shown in tableD.12as well in the appendixD.1.1.
10−2 10−1 100 101 102 9
8 7 6 5 4 3 2 1
E · T0.47in lx s0.47
inv.deBoerRating
Rectangle Pulses 300 ms
1200 ms 4800 ms 19500 ms
(a)
10−2 10−1 100 101 102 9
8 7 6 5 4 3 2 1
E · T0.47 in lx s0.47
inv.deBoerRating
Triangle Pulses 600 ms
2400 ms 9600 ms 38400 ms
(b)
Figure5.58 – Glare perception on the inverteddeBoerover the scaled exposure for(a)rectangle and(b) triangle pulses for the different shown pulse durations. The Exposure is scaled according to equation5.9 withp = 0.47 and the fit is shown as the red solid line over all data. Blue squares show the data for 300 ms, red diamonds the data for 1200 ms, green asterisks show the data for 4800 ms and purple circles indicate the data for 19 500 ms pulses.
w(H/H0)Mean = 0.9·log10(H/H0) + 5.1 (5.17a) w(H/H0)△Mean = 1.1·log10(H/H0) + 3.7 (5.17b) (5.17c) Again, the fit parameters indicate a very good data representation with R2 values of over 0.8. However, as seen in figure 5.58a and 5.58b respectively, the data does not correlate as well as for the previous study (R2 > 0.98). However, a significant improvement is made when compared to the unscaled exposure. When further investigating this behaviour, an optimized p−valuefor this study is found at p = 0 leading to the best correlation with the illuminance instead of the exposure. This means, that for this study the pulse duration has no influence on the glare perception at all. This is shown for both, rectangle and triangle pulses in the figures 5.59aand5.59b.
5.3 glare perception for short light pulses 155
10−2 10−1 100 101 102 9
8 7 6 5 4 3 2 1
E · T0in lx
inv.deBoerRating
Rectangle Pulses 300 ms
1200 ms 4800 ms 19500 ms
(a)
10−2 10−1 100 101 102 9
8 7 6 5 4 3 2 1
E · T0 in lx
inv.deBoerRating
Triangle Pulses 600 ms
2400 ms 9600 ms 38400 ms
(b)
Figure5.59– Glare perception on the inverted deBoerover the scaled exposure for(a)rectangle and(b) triangle pulses for the different shown pulse durations. The exposure is scaled according to equation5.9 with an optimizedp = 0 thereby showing thedeBoerrating over the illuminance. The fit is shown as the red solid line over all data. Blue squares show the data for 300 ms, red diamonds the data for 1200 ms, green asterix show the data for 4800 ms and purple circles indicate the data for 19 500 ms pulses.
The related fit equations are shown in5.18afor the rectangle pulses and in 5.18bleading to the fit parameters presented in tableD.13 in appendixD.1.1..
w(H/H0)Mean = 1.1·log10(H/H0) + 5.6 (5.18a) w(H/H0)△Mean = 0.9·log10(H/H0) + 4.6 (5.18b) (5.18c) This leads to much better results than the fits with p = 0.47. With R2 values of over 0.95 this correlation is found to be very good. Since this is true for both pulse forms, either the way this part of the study was conducted, with two different pulse forms, influences the rating, or the p−value changes for different pulse durations. This might be the case, since the maximum pulse durations are changed to much longer pulses in order to investigate the influence of those. Therefore, the data from the pulses with durations higher than 2400 ms are left out of the next evaluation and for the short pulses, the fit with p = 0.47 is repeated for rectangle and triangle glare ratings separately. This is shown in figure 5.60. Here, the rectangle pulses are marked by the blue rectangles for 300 ms pulses and red diamonds for the 1200 ms pulses. The correlating fit is shown by the red solid line. The triangle pulses with a duration of 600 ms are represented by the orange triangles and the triangle pulses with a duration of 2400 ms are shown by the purple, upside-down triangles. The correlating fit is shown by the orange, dashed line
156 analysis and optimization of light distributions
10−2 10−1 100 101 102
9 8 7 6 5 4 3 2 1
E · T0.47in lx s0.47
inv.deBoerRating
300 ms 1200 ms Fit Rectangle 600 ms 2400 ms Fit Triangle
Figure5.60– Glare perception on the inverteddeBoerscale for all pulses under 2400 ms over the scaled exposure according to equation5.9with p = 0.47. The rectangle pulses are marked by the rectangles and the diamonds and the correlating fit is shown by the red solid line. The triangle pulses are represented by the two types of triangles and the correlating fit is shown by the orange, dashed line.
This figure again shows, that triangle pulses are, also for the shorter pulses and with the optimized exposure with p = 0.47, triangle pulses are regarded to be less glaring than the rectangle pulses by an average of onedeBoerrating. The fit equations for both fits are shown in the equations5.19aand5.19b
w(H/H0)Mean = 1.0·log10(H/H0) + 5.8 (5.19a) w(H/H0)△Mean = 1.0·log10(H/H0) + 4.6 (5.19b) (5.19c) As shown in tableD.14these fits again lead to a very good representation of the recorded data withR2values over 0.95 and all fit error measures much lower than shown in appendix D.1.1in tableD.12. This means, that for perfect correlation over different pulse durations, a variable p−value needs to be assumed. This will be addressed further in the comparison of the two glare studies.
Firstly, the focus is set to the comparison between the two chosen pulse forms. Therefore, in the next step, the comparison between the de Boer rating for the rectangle pulses and the triangle pulses is done. In the first step, the ratings for all pulses are compared. Since the duration for each triangle pulse is doubled compared to the rectangle pulse, all pulses for each set only contain pulses with equal maximum illuminance and equal exposure. Box plots for both data sets are shown in figure5.61a, and in more detail split up for all exposure values in5.61b. In both figures, glare ratings for the rectangle pulses are shown by blue box plots and glare ratings for the triangle pulses are represented by the red box plots. This is also marked by the symbols at the x-axis of each plot. In figure5.61b, the values set at the x-axix show the exposure values for the rectangle pulse (left) and the triangle pulse (right) for each data set.
5.3 glare perception for short light pulses 157
△
9 8 7 6 5 4 3 2 1
Rectangle Triangle
inv.deBoerRating
(a)
△ △ △ △ 9
8 7 6 5 4 3 2 1
0.3 / 0.6 1.2 / 2.4 4.8 / 9.6 19.5 / 38.4
inv.deBoerRating
(b)
Figure5.61 – Comparison of the glare perception on the inverted deBoer scale between rectangle and triangle pulses.(a)shows box plots for all glare ratings over all rectangle and triangle pulses. The mean ratings are 5.2 for rectangle and 4.3 for triangle pulses.(b)shows the same data split up for the different exposure values. Red box plots indicate the rectangle pulses and blue box plots indicate triangle pulses.
Figure5.61aclearly shows, that even so both data sets contain the same maximum illumi-nance and the same exposure, the triangle pulses are generally rated less glaring. Statistical analysis using the Mann-Whitney-Testshows no significant difference between the rectan-gle and the trianrectan-gle pulses (p > 0.3 for all data sets) due to the large deviation between the different test subjects. However, the median of the rectangle pulses is rated at 5 (just admissible, and thereby directly at the threshold of glaring or not glaring. The triangle pulses however are rated one step lower at 4 betweenjust admissibleandsatisfactoryand thereby not noticeable disturbing. Looking at the single duration sets in figure5.61b, it is obvious, that this trend continues with every duration set of the rectangle pulses being rated onedeBoer rating lower than the correlating rectangle pulse set, even so, the pulse duration is doubled for the triangle pulses.
This leads to the conclusion, that no matter the illuminance or the duration, a light pulse, will be rated lower regarding the discomfort glare, if the edges are sufficiently smooth and the illuminance rises to its maximum value instead of setting the maximum illuminance from the very beginning. This also means, when comparing the glare load from oncoming traffic, neither illuminance nor exposure alone contain sufficient information to calculate the possible glare rating. The pulse form plays a significant role for this as well. Translating this to an automotive use case, the photometric values of two pulses could be identical and without considering the pulse form, the calculated glare perception by Zydek, Lehnert or Kosmaswould lead to identical results. With the results from this study, the smoother light pulses can be rated around one invertedde Boerrating lower than the glare perception for rectangle-like pulses. Furthermore, this part shows, that the modified exposure E·Tp with p = 0.47 is not valid over all durations. Pulses of different durations need to be evaluated differently. The exposure directly correlates to the glare perception only for very short pulses (T < 300 ms) or if all pulses have the same duration. However, if all pulses have the same duration, this is equivalent to the correlation with the maximum illuminance, and to find the correlatingdeBoervalue, the duration needs to be known.
158 analysis and optimization of light distributions
5.3.3 summary and conclusion of glare perception for short light pulses