Saving energy, White-light LED plays a main role in solid state lighting system. Find the best energy saving driven solution is the engineer endless hard work. Besides DC and AC driving, LED using Pulse Width Modulation (PWM) operation is also a valuable research topic. The most important issue for this work is to find the drive frequency and duty for achieving both energy saving and better feeling on the human vision sensation. In this paper, psychophysics of human vision response to the lighting effect, including Persistence of vision, Bloch's Law, Broca-Sulzer Law,
Ferry-Porter Law, Talbot-Plateau Law, and Contrast Sensitivity, will be discussed and analyzed.
From the human vision system, we found that there are three factors: the flash sensitivity, the illumination intensity and the background environment illumination, that are used to decide the frequency and duty of the PWM driving method. A set of controllable LED lamps with adjustable frequency and duty is fitted inside a non-closed box is constructed for this experiment.
When the background environment illumination intensity is high, the variation of the flash sensitivity and illumination intensity is not easy to observe. Increasing PWM frequency will eliminate flash sensitivity. When the duty is over 70%, the vision sensitivity is saturated. For warning purpose, the better frequency range is between 7Hz to 15Hz and the duty cycle can be lower down to 70%. For general lighting, the better frequency range is between 200Hz to 1000Hz and the duty cycle can also be lower down to 70%.
Keywords: PWM, White-light LED, Psychophysics of vision.
General lighting consumes about 18% in the whole world energy. Improving lighting system efficiency will save energy and reduce carbon emissions. The energy saving issue becomes the most widely research topic.
White-light LED (WLED) is generally driven by using DC power. To save more energy, PWM (Pulse-width modulation) is a feasible technique. PWM is a period square wave voltage, with two parameters namely frequency and duty.
Frequency is the number of period waves per second, and duty is high voltage part in a square wave in proportion, sometimes also call duty ON, the low voltage in square wave call duty OFF. At the duty ON period, the LED lamp is lit.
While during duty OFF, the LED lamp has no power.
To find the best driving frequency, we need to connect the phenomenon of Psychophysics of vision and PWM control technique. Many researchers keep on working in this topic. In [1], the result shows that set frequency to 1000 hertz and duty equals to 60%, then the best luminescence efficiency of white LED will be obtained. In [2], they got the same effect as DC driving by setting frequency of PWM to 1K hertz, and the duty cycle equal to 80%.
These are important results. However, many physiological characteristics of human vision and environmental factor are been ignored. Besides, there is no exact theoretical basis to support the experimental result. After all, the lighting is for human vision. These parameters (frequency and duty) must be carefully studied based on human vision.
Based on the Psychophysics of vision and Broca-Sulzer effect, a WLED experiment was conduct by Masafumi JINNO.
He concluded that the brightness can be doubled than that of DC driven when the WLED is driven by PWM pulse with frequency equal to 60 hertz and duty is 95%. A more detailed inspection was carried out and concluded that the use of

blue LED brightness can be felt at 1.5 ~ 1.9 times, the green LED is 2.0 ~ 2.2 times, the red LED is 1.0 ~ 1.3 times.
Using this concluding remark, we can use a 50lm/W WLED to replace a 100lm/W WLED [12]. However, this method use a frequency near the flicker fusion frequency to driver LED, make the wrong impression to feeling a strong light sense, but still don’t know applicability in normal lighting system.
This paper will propose the best parameters of PWM to drive White-light LED based on physiological responses of human vision medical data and theory.
Follow this short introduction, the theory of Psychophysics of vision for light system will be discussed in section 2. The experimental design, flash experiments and DC lighting experiments will be conducted in section 3. The experimental results obtained by using the best parameters of PWM to driving White-light LED in normal lighting system will be given in section 4. Finally is a short concluding remark.
In time domain, based on Persistence of vision, Bloch’s Law describes the vision experience stimulated by a periodically glitter, while the Broca-Sulzer Law describes the vision experience stimulated by a non-periodically glitter.
Ferry-Porter Law describes what frequency will not feeling flicker. Talbot-Plateau Law describes after the disappearance of perception of light flashes response. The Contrast Sensitivity deals with spatial and temporal domain vision experience.
2.1 Persistence of vision
Image or light appears and disappears repeatedly, if repeatedly frequency greater than the threshold will not feel flicker, feel image or light are continuous. This effect is widely used in movie, TV and lighting system. The experimental results of Arthur C. Hardy; red light presence of fovea is 0.0209 second; yellow-green light presence of fovea is 0.0179 second; blue-violt light presence of fovea is 0.0349 second. Conclusion is light stay time between 0.04 second to 0.028 second
[4]. So set the frequency between 25 hertz to 35 hertz or more, human eye will not feel flicker, this is also the film, television, etc. The origin of the frame rate set. However, in light background will feel the flicker, and therefore the lighting system in order to apply to the extent possible, to really increase the frequency to twice the power frequency.
Persistence of vision is only a crude simple experimental result, indicate more than threshold frequency will not feel flicker. With the subsequent development of ophthalmic medical research, the Persistence of vision phenomenon has been insufficient, research methods on the update, and only by Persistence of vision phenomenon to study parameters of
PWM technique is no longer used.
2.2 Bloch’s Law
To discuss flicker behavior, first is what vision response, when flicker from appeared to disappear. It was found that in the past, used a enough light stimulation, observer will feel a certain degree of brightness; if used half stimulation, then observer will feel a half degree of brightness. If want to feel the same brightness, then the lighting duration time need used double times. Such as photographic film as the process, if the external light intensity is not enough, then you need increase the exposure time. This process is called temporal summation. Bloch’s Law [5] proposed a simple formula:
Bt = k (1)
In Eq (1), flash light strength is B, duration time is t, and the product k keeps in constant. In other words, the flash time with energy is a constant relationship. In addition, Bloch’s Law describes the shorter the stimulus duration time, the stronger the stimulus powerful. The higher the contrast ratio represents the stimulus needed to be stronger, be able to identify the presence of light. Contrast is defined as follows, where
L
and
1
L
are the two different light sources.
2
C=
L
1
L
1
L
2
L
2
(2)
As described in Eq. (2), the contrast of two different light sources constitutes the average luminance [7], the test area in the flash brightness is L , the background brightness is
1
L
2
. The range of C is between 0.0 and 1.0, representing different size ratio between two light sources, if the brightness difference between the background and the light be greater, then the C value will be greater.

Experiments are done by Andrei Gorea, and the results said that when the duration time in 10ms or less, the required contrast of 0.5, while the duration time more than 50ms, the required contrast will be reduced to 0.1[6]. The duration time of the PWM operation is often less than 50ms, so the light source must be designed to select the contrast of 0.5 or more.
2.3 Broca-Sulzer Law
This theorem is also under study in the vision response to flash phenomenon. Different points are when light indubitable, what response of vision will be. This experiment is to find the vision response using difference duration time, taken between 50 milli-second to 200 milli-second. When flash appeared, vision will reaction quickly, but this time there will be a perception of stimuli beyond the actual weighting, drop to reflect the actual brightness. Experimental results, on dark background, the highest response in 0.046 second if the stimulus brightness used 170 lux, if the stimulus brightness is 126 lux, then the highest response in 0.062 second [8]. It should be noted that when the flash duration time when more than 0.125 second effect will be substantially weakened. If more than 0.5 second, Broca-Suzler effect will not exist.
2.4 Ferry-Porter Law
When the flicker frequency keeps increasing, flashes phenomenon will gradually disappear. Such as persistence of vision happened in 35 hertz, when flashes of feeling disappeared, at this time enter the flicker fusion. This frequency point called flicker fusion frequency. Also called critical flicker fusion (CFF) frequency, because the sense is feeling flicker or not flicker. Ferry-Porter [9][10] found that high stimulus intensity will increases CFF. Experiment done by Tyler and
Hamer, the difference between stimulus intensity and background intensity increase, will enhance the relative CFF [11].
So when the needs of different lighting design, has different CFF. Usually when the lighting environment, the greater the contrast with the background, the higher is required to CFF, which explains why people read high-frequency lamps will be comfortable.
2.5 Talbot-Plateau Law
At the time when flicker fusion occurs, the Talbot-Plateau Law scope of operation is started. When the flashing light continued to stimulate the vision, the frequency increased gradually let the flicker sense disappeared, then the brightness will fall into a sense of the average state. This behavior is also a temporal summation. For example, a lighting system of the PWM, driver duty at 50%, brightness sense will equivalent to 50% of DC-driven. It is noteworthy that when the gap between two different duty values is not large, vision can not distinguish the difference. Experiment by Hsien-Liang Liu and J-J Junz Wang, at 1KHz driven, duty difference of 20% can not be distinguished [2]. Experiment by Masafumi
JINNO, duty difference of 5% can not be distinguished [3].
In this paper, we want to find the best drive methods in white-light LED PWM operation, and to verify the theory described in Section II for the white-light LED lighting on the suitability. The Experiment we report is not working at the dark environment, because the environment is not the completely dark room, the room is often with much external ambient light. For the above reasons, we design a similar lighting environment to the real, and we want to find the operation range that we can work.
There are three main experiments will be conducted, they are flash, CFF and DC lighting experiments. The purpose of the flash experiment is to find the frequency threshold for the eye can’t feel flickered. The lighting frequency of lighting system need higher than the value in this experiment reported for avoiding the eye feel uncomfortable. In this experiment, we also find the highest sensitivity for eye to design the warning lighting.
Before the DC lighting experiments, we must find the frequency let human feel no flicker. This experiment is work for general lighting, a general lighting must provide a steadily lights, let human eye feel smooth and comfortable. This experiment want to find the highest CFF.
In the DC lighting experiments, we want to find the method can reduce the drive current but not cause the light-sensitive approach loss. The method is created by the affect for sensitivity impact with different duty when the visual feel no flickered, and the relationship between the frequency and the environment.

Based on the purpose for experiment, we design a simple test equipment of lighting, detect the phenomenon by eye. This equipment is a box with one side opened light, the size of length and breadth are the same, and pasting the white paper inside to produce non-direct lighting, this equipment is shown in Figure 1.
Figure 1-A is the equipment side view. Outside the light box, there is a light barrier face to the observation point to avoid the eyes look straight. The x, y are length and width for the light box, all of them are 20cm, and the d is 50cm. A and B are observation points, the point A at the light box edge, and the point B distance the light box edge length d. both A and are at the central line of y.
Figure 1-B is the top view with equipment, there is a LED lights as the test light source installed on the light box on the central. The test light source is a row of white-light LED of the composition, there are seven white-light LED lights form a group size of length 6.5cm width 0.5cm,
Figure 1-C is a real picture taken from box façade. In order to show the location of LED lamp deliberate use of low-angle shot, but the experiment will not look directly at the LED lamp, light barrier will obstruct the direct light.
Light barrier y A B
LED lamp y x
Figure 1-A. Experiment side view x
A
Figure 1-B. Experiment top view d d
B
Figure 1-C. Experiment front view
Table 1. Experiment environment (Lux)
Lamp OFF
LED OFF
Lamp ON
LED OFF
Lamp OFF
LED DC ON
Lamp ON
LED DC ON
A
0
100
780
780
B
3
142
20
172
Most of the lighting systems are operated in the indoor environment with some light or no light environments.
Considerations for the ambient light will affect the visual effects, the observed point A represents the low environmental impact, and the observed point B represents a high degree of environmental impact.
Before the experiment, measuring the illumination by lux meter at point A and point B uses to be as the base environment data for light environment and no light environment. The data are recorded in Table 1, whose unit is Lux.
The human eye detect the phenomenon at view point A and B. This observation can be ignored spatial frequency effects, because this perspective is no spatial variation within one visual angle.
In the test environment, the first environment illuminance with interior lights is 142 Lux, and the second environment illuminance without interior lights is 3 Lux.
When the light is driven using DC-source, the environment illuminance is 780 Lux at point A. at point B, 50cm away from the light box, the measured illuminance is 172 Lux as listed in Table 1.

First, using a single light box do the flash experiment, change the duty to test sensitivity response and CFF changes at different illuminance. Then use two sets of the same light box be independently operation of the LED lamps, use different PWM operations, record observer’s interactive response and compare them. Second, do DC-source driven experiment on both sets based on flashing the CFF data. Then one set keep on DC driven, while another set is for comparing, which is applied by PWM modulating. We need to find the PWM frequency which is done by slowly varying the frequency until the observer feel the two test sets has the same result. Now we got the operating of the PWM that have the same effect as DC driven. Finally, to find the best PWM duty, apply the obtained frequency on both test box and slowly varying the duty value and to observe interactive response and compare the different results of two test boxes.
The experiments are flickering test and DC test. The observers are use eye watching experiments and describe the feeling, but feeling is a very vague thing that not easy be digitized, and different people has different feeling, only five observers in our experiments cannot be the requirement of medical statistics, but all the record of observers reaction after finish, that changes of response are similar. So the following only show one of observer results, to illustrate the effects that we found.
4.1 Flash experiments
The purpose of twinkle light is for warning and not for lighting. To find the best PWM parameters of frequency value and duty value that give somebody rise to attention. In the preliminary experiment with the driven duty is a 50% square-wave, we found the frequency in the 17 hertz can occur maximum sensitivity at observation point B. Setting the frequency at 17 hertz, we found that the sensitivity will vary with duty change. Because the different duty affects the brightness sense to cause the different warning, the proportion between the appropriate ratio and the warning lights should be carefully observed. To find this proportion, change the duty from 10% and 90% with the frequency and record the highest sensitivity. Based on the different frequency that has highest sensitivity in different duty ratio to compare the frequency of the strongest sensitivity with other duty can find the best matching range.
Lighting-A Lighting-B Dark-A Dark-B
14
12
10
8
6
4
2
0
20
18
16
10% 20% 30% 40% 50%
Duty
60% 70% 80%
Figure 2-A. High sensitivity frequency
90%

Lighting Dark
7
6
5
4
3
2
1
0
10% 20% 30% 40% 50% 60% 70% 80% 90%
Duty
Figure 2-B. Sensitive intensity
Fix duty, and adjust frequency to find the highest sensitivity, the experiment results are shown in Figure 2-A. In Figure
2-A, Lighting-A and Lighting-B is fluorescent light ON environment of observation points A and B, and Dark-A and
Dark-B is in the fluorescent light OFF observation points A and B. From the figure we can find that the highest sensitivity range is between 7Hz to 18Hz. However, under different duty values we can find that any two different sets of high sensitivity frequency comparison, the intensity is different. In order to identify the strength, find the weakest sensitivity of the strength of a duty, set this intensity value to 1. Set the second weakest intensity value to 2. Following this method, we can test different strength duty ratio. The observation is location at B, because it is compare two light boxes. The results are shown in Figure 2-B, The Lighting is the fluorescent lights turned ON, and the Dark is the fluorescent lights turned OFF. It can be found that with different Duty to produce the highest sensitivity of frequency are differences, affecting the high sensitivity frequency is not only with duty, but also with the light on the external environment. When the environment is with the extra bright, the high sensitivity frequency change is low. When the environment brightness is reduced, the high sensitivity frequency change is high. If the duty become large and make the sensitivity become strong, it will cause the ratio of the sensitivity and low duty to be reduced. In Figure 2-B, there are the intensity recorded with different duty. The brightness is increased when the duty is also increases, so that is difficult to identify the high sensitivity frequency. This is the no lighting test found that when duty after 60%, the possible reasons for non-linear changes in Figure 2-A the Dark-A line and Dark-B line. Broca-Suzler Law explains the stimulus duration time (lighting
ON time) upper 0.062 second will reduce the sensitivity, but never discuss lighting OFF time. Our experimental results showed that, duration time from the 0.022 second to 0.035 second, and the LED OFF time need a little larger than the
ON time will produce the most sensitivity.
Integrated experimental findings, set frequency 7Hz to 18Hz and the duty between 40-50% in no extra light environment, the sensitivity can be the strongest. The sensitivity of observation point A is greater than that of observation point B. If the environment is bright, the sensitivity on observation point A is still greater than the observation point B, but the overall feeling is decreased. This is the ambient light reduces the contrast, and reduces sensitivity. But, increase duty will not enhance sensitivity.
4.2 CFF experiments
In the CFF testing, we use a similar approach with the flash experiments. Because the brightness impact on the CFF, duty must be different, adjustment frequency points, respectively. Point A and B are observed in different positions.
Record the frequency value when the observer feels the flicker disappeared. The same procedures are done at ON and
OFF lights environment. The results are shown in Figure 3. Lighting-A line and Lighting-B line are ON light environment observation points A and B records, Dark-A line and Dark-B line are OFF light environment observation points A and B records. We can find when the duty value is at 50%, the CFF of ON light is 58Hz to 67Hz but the CFF

value is increased to between 65Hz to 72Hz when OFF light. When the illuminance difference between the environment and lighting LED is increased, the CFF value is increased also. When the duty value is increased, the CFF value is decreased.
Lighting-A Lighting-B Dark-A Dark-B
50
40
30
20
10
80
70
60
0
10% 20% 30% 40% 50%
Duty
60% 70%
Figure 3. Critical fusion frequency (CFF)
80% 90%
Experiments also found that if only pay attention to the observation point A around and watch the LED light, does not reach the flashing frequency increases, the internal edge of the area will flicker slightly. Experiments also found that if only pay attention to the observation point A around and watch the LED light, increases frequency to no flicker, the internal edge of the light box will still feel flicker slightly. From Figure 3, we found that brightness will determine the
CFF. In real world, if the human eye is closer to lighting a stronger brightness felt, on the other hand, a weaker brightness felt. The CFF value found in short distance will not apply to long distance. Experiment result shows that the largest CFF is 75Hz. In order to comply with any room lighting use, the drive frequency to be increased to at least double that is 150 hertz or more can be guaranteed not to feel flicker.
4.3 DC lighting experiments
Based on Talbot-Plateau Law and Bloch's Law, the energy intensity will decide light feeling that is different duty equal to the different brightness sense. Preliminary experiments have found that visual for the slight differences are not very accurate, and this inaccurate response may help energy saving design. In this subsection, we want to find how much difference in duty value that our visual sensing will not be stimulated.
First, the driving frequency is increased to 150Hz for the operation is much greater than CFF. Then, one light box for the control group, another light box is comparison group; adjust the duty to pursue the perceived brightness of the control group by observer. The observation in point B that distance is 50cm. The duty difference is absolute of control group duty subtract comparison group duty. For example, if control group is forty percent and comparison group is thirty-seven percent, than duty difference is three percent.
The results are shown in Figure 4. From Figure 4, we can find that when the duty value is smaller, our visual system can easier to detect the change in duty value, on the other hand, when the duty value is larger, our visual system is more difficult to detect the change in duty value. The test light ON when the ambient brightness of 142 Lux, the duty in control group is 70% or more, then comparison group will more difficult to identify, resulting in Figure 4, the Dark line

after the 70% have nonlinear curve, it is lighting brightness too high then sense will saturate. In light ON experiment, duty increases the scope of cannot recognition were within 5%. In other words, when the environment and lighting system have large difference, the slight change in lighting is not easy to detect.
Lighting Dark
20%
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
4%
1%
5%
2%
12%
2%
13%
1%
10%
5%
19%
5%
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Duty
Figure 4. Duty difference
If use one light box, the observation in point A, that is reduce the environmental impact on this test. Fixed the duty and observe, increases duty slowly, when observer feel brightness change and record it. Similar tests can be found in Figure 4
Lighting line results, but there will not be fluctuations in the posterior segment. The duty from 10% to 30%, 2% variation will not be noticed. When duty from 40% to 60%, 5% variation will not be noticed. When duty from 70% to 100%,
10% variation will not be noticed. Either light ON or light OFF experimental have the same results.
Fixed control group duty, use the same duty in comparison group and adjust frequency, or fixed control group frequency, use the same frequency in comparison group and adjust duty, if frequency more than CFF many, flicker fusion does occur, then the brightness sense only have related with the duty, not related with frequency.
Based on the above results we can find that the larger the difference of Lux value between environment and LED brightness, the easier to detect the change of duty value. Fixed duty and varying the frequency will not cause the change in brightness. The luxmeter value shows when duty is increased, the brightness is increased also.
4.4 Compare experimental results
Based on the previous relevant theory, the experimental environments are to be set on no light in background. The actual lighting, need consider the possible impact of the background light. When the lighting and background brightness difference is very small, and many effects will be reduced, so to really take advantage of these effects, lighting and background light must be the difference widened to be effective. Our results also confirm this point.
The human visual identifies different brightness capability is that the greater the brightness the weaker the capability. For example, the difference of the brightness is 80Lux, changing the brightness from 400Lux to 500Lux is difficult to identify, while changing the brightness from 120Lux to 200Lux is easy to identify.

To design the Warning lights, we use the Broca-Sulzer law can achieve the effect of the perceived brightness increasing, and the sensitive can be promote when the light is flashing continuous, it can enhance the warning effect. We advocate the range of the using frequency between 7 Hz to 18 Hz, because the bright sensitive for every people are different.
According to the difference of ambient light decided the bright of light, the warning light brightness must be greater with the ambient light higher. The effect is the best when the duty is operated between 40% and 50%, and the duty need to be increased with the ambient light become brighter.
In general lighting, the frequency needs to be increased higher than the range of flicker fusion frequency. The flicker fusion frequency is different for every people, so increasing the frequency higher than 150 Hz can cause the sensitive of flash is disappear. This way can be used to increase the bright. Because the environmental bright effect the eye to discern the duty, when the environmental bright is much light, it’s much default to identify the duty vary.
If we don’t consider the effect of environmental bright in indoor lighting system, the ability of duty identify will become much low when the bright is increase. By our experiments, when the illuminance more than 500 Lux than sense will saturate, more than this brightness is usually ineffective, the range from 300Lux to 500Lux the duty difference cannot be identified almost to 5%, if less than 250Lux dropped to 2%.
This work was supported in part by the National Science Council under grant NSC 99-2221-E-214-057.
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