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Proposing measures of flicker in the low frequencies for lighting applications.


Light flicker from 60 Hz magnetically-ballasted fluorescent, metal halide, and high pressure sodium lamps has been an ongoing concern of the lighting practice community because of the possible connection to headaches, distraction, fatigue, lower productivity, and annoyance in a small but significant population. Since the 1990's high-frequency electronic ballast specifications and replacements primarily based on energy efficiency have essentially eliminated low frequency flicker from most workplaces. Now, with the increasing adoption of LEDs as a light source, various forms of flicker have been reintroduced to the lighting market in many products. Even a steady-output LED luminaire can be turned into a source of flicker if not carefully matched with a compatible dimmer.

At this point in time the specifier and manufacturer have no reliable metrics to separate problematic LED products from those with flicker-free operation. This paper addresses how flicker that affects humans could be quantitatively characterized, and gives some examples of how LED lighting and control systems can be evaluated to mitigate undesired flicker.


There has been emerging concern about health effects in lighting due to "invisible" flicker (IEEE P1789, 2010). Most humans are unable to perceive flicker in light above 60 Hz, but there still remain measurable biological effects above the critical fusion frequency. ERG (electroretinogram) responses indicate that invisible flicker is transmitted through the retina, even up to 200 Hz (Berman,1991). Some visual stress researchers have suggested that this flicker may lead to headaches and eye strain (see (IEEE P1789, 2010) for extensive reference list on health effects of flicker). Older magnetic ballast fluorescent lighting is known to have flicker at twice the AC Mains line frequency (100 Hz/ 120 Hz). This is also the case with some new LED lighting technologies. IEEE Standards P1789 group on LED flicker is examining these concerns and providing recommended practices to the community. This paper represents important concepts that are emerging from IEEE Standards P1789 that may be necessary to define how to measure flicker.

A difficulty with existing definitions of flicker is that they do not decipher between low frequency and high frequency flicker. For example, percent flicker (see definition below) of a pwm (pulse width modulated) signal is independent of its frequency (see Example 1, below). However, for high enough frequency, there are no retinal biological effects due to flicker. Thus, it is important to change the concepts of how to measure flicker in lighting to include frequency dependence. This paper provides the following:

* Explanation as to why existing definitions of flicker are inadequate to give recommendations on safe flicker frequencies.

* ntroduction of new flicker definitions more suitable for lighting designers.

* Examples and experiments to substantiate the relationships between the new measures of flicker.

Although this paper does not give recommendations for safe modulating frequencies or depth of flicker modulation, it provides the first, important step to doing so for the LED lighting industry by proposing precise flicker measures.


According to the IES (Illuminating Engineering Society), there are two measures of flicker that have commonly been proposed by lighting designers. The Flicker Index (Eastman and Campbell, 1952; Kaufman, 1984) is often used to measure the relative cyclic variation of the output of different light sources. Referring to Fig. 1 the Flicker Index is defined as the area above the line of average light divided by the total area of the light output curve for a single cycle.

Mathematically, this leads to the relation in Fig. 1 of Flicker Index = (Area 1)/(Area 1 + Area 2) (1)

According to the IES Lighting Handbook (Kaufman, 1984), the Flicker Index is preferred over Percent Flicker, which has the relation

Percent Flicker = 100 (Max Min)/(Max + Min) (A-B)/(A + B). (2)

However, Percent Flicker is more commonly found, compared to Flicker Index in research fields such as photobiology and visual science/stress (Wilkins, 1995; Boyce, 2003). This is alternatively called Peak-to-Peak Contrast, Michelson Contrast, or Modulation in the literature (Wilkins, 1995).


However, none of the definitions of flicker in the literature directly provides the necessary information on whether the associated flicker is in the frequency range of health effects or risks. Specifically, above a certain frequency, light may not induce human biological effects, and therefore it is not necessary to limit flicker for all frequencies of modulations. It is common that a signal be may be composed of several signal frequencies, particularly when switching power supplies are used to drive LED strings. Thus, the above definitions need to be expanded upon before they can be used to assess health effects and risks in LED lighting. See (IEEE Standards P 1789 public report, 2010) for introduction on how flicker may occur in LED lighting.


By decomposing a periodic time signal into its Fourier Series components, it is possible to analyze individual frequency components of the flicker. Visual stress research suggests (Wilkins, 1995; de Lange, 1961; Campbell and Robson, 1967; De Valois, 1980) that it is the amplitude of the low frequency flicker components that must be considered in its relation to the average illuminance. For example, in response to flickering stimuli, the temporal modulation transfer function (TMTF) of the human eye behaves similarly to a low pass filter where the higher frequency Fourier components of a waveform are severely suppressed (Kelly, 1969). Furthermore, for the human TMTF, there is a gradual downward suppression of all components above 20 Hz continuing to somewhere about 90 to 100 Hz where visible flicker is no longer perceived. The amount of suppression in the 20 to 100 Hz range depends on the frequency, light level and size of the flickering source and to a certain extent the age of the observer. For example, a large visual target of mean luminance 450 cd/m2 flickering at 60 Hz with a modulation of 30 percent can be seen as flickering while the same target at the lower light level of 40 cd/sq m is below the threshold even for 100 percent modulation. Similarly, modeling of the ERG response to flickering light, extending well above the perceivable flicker frequency, for example, up to 200 Hz, can be modeled in several stages. The first stage of the photoreceptors is a temporal low pass filter with cutoff frequency in the vicinity of 50 Hz. After this filter, there is subsequent nonlinear process (Burns, 1992). The results in (Berman, 1991) also indicate that there is no measurable ERG output above 200 Hz (ignoring saccade movement).

Therefore, since the beginning stage of the retina response is modeled as low pass filter, the signal after this filter will have reduced high frequency harmonics. When such processes occur, it is standard to consider modeling the input signal by its truncated Fourier Series that contains the harmonic components that are of interest and ignoring the input harmonic content that would be severely attenuated at the output. Specifically, assume that a signal is periodic with period T= 1/f where f is the frequency of the signal. Defining [omega] = 2[pi]f, the signal may be represented by the Fourier Series:


where [X.sub.avg] is the average value of x(t), [c.sub.m] are the Fourier amplitude coefficients and corresponding to angular frequency [omega]*m, and [phi]m represent the angular phase shift for this frequency

From this Fourier Series decomposition, it is possible to define flicker in terms of low frequency signal components that may be of health risk concern. Because we are concerned with the low frequency components of the signal and their relation to an average value, it is proposed to consider a truncated Fourier Series that keeps only the terms within the frequency range 0 < n*f <[f.sub.threshold], where the [f.sub.threshold] may depend on application and n is an integer. Specifically, [f.sub.threshold] is defined by the user as the upper frequency limit above which has negligible influence on the output. Then, the signal x(t) may be approximated by the n-term truncation [X.sub.trunc](t)

Xtrunc (t) = Xavg + [c.sub.1] cos ([omega]t + [[phi].sub.1]) + [c.sub.2] cos (2[omega]t + [[phi].sub.2])+...+[c.sub.n] cos (n[omega]t + [[phi].sub.n])(4)

As the number of Fourier terms increases the approximation of x(t) by [X.sub.trunc](t) improves.


Flicker Index and Percent Flicker can now be defined in terms of [X.sub.trunc](t) as can other concepts to measure the amount of potentially harmful flicker in a lamp. Specifically, define the following

Consider the truncated Fourier Series representation of x(t) represented by [X.sub.trunc](t) as in (4) with n terms (n*f <[f.sub.threshold], where f = 1/T is the frequency of signal x(t)).

Low frequency flicker index (LFFI): The Flicker Index of the signal [X.sub.trunc](t) which is composed of only the low frequency harmonic range of index.

Low frequency percent flicker (LFPF): The Percent Flicker of the signal [X.sub.trunc](t) which is composed of only the low frequency harmonic range of index. Specifically, if [X.sub.trunc](t) is given in (4), then

LFPF = max {Xtrunct (t)}-min{Xtrunct (t)}/max {Xtrunct (t)}+min{Xtrunct (t)} x 100 (5)

It is possible to define flicker in terms of the energy or power of each harmonic component. This leads to concepts similar to Total Harmonic Distortion or Total Unwanted Distortion (Krein, 1998):

Low frequency flicker distortion (LFFD): The ratio of {the square root of the sum of the squares of the unwanted harmonic coefficients} divided by {the average value of the signal}.

LFFD = [square root of ([C.sub.1.sup.2] + [C.sub.2.sup.2] +... [C.sub.n.sup.2])/Xavg (6)

LFFD appears to be the simplest to measure experimentally, especially when there are multiple Fourier coefficients to be considered. This is because there is no phase shift dependence on LFFD. Further, we may also consider replacing the denominator of the LFFD by [X.sub.rms] of the entire signal, and this may give similar measures for flicker. None of these above definitions have been proposed by lighting designers for measures of flicker yet, but they seem natural to power electronic designers when multiple low frequencies are present.


For the case when there is only one single harmonic of interest, then only the [c.sub.1] term is used:

1) Low Frequency Flicker Index can be calculated independent of the phase shift [phi]1, and therefore, without loss of generality this phase shift can be assumed zero. Then with noticing the symmetry of cosine functions, the Low Frequency Flicker Index will satisfy:


This leads directly to

LFFI = Low Frequency Flicker Index = 1/[pi] ([c.sub.1]/Xavg)

2) Low Frequency Percent Flicker also simplifies noting that the max and min values of [X.sub.trune](t) are equal to [X.sub.avg]+[c.sub .l] and [X.sub.avg]-[c.sub.1], respectively. Therefore,

LFPF = Low Frequency Percent Flicker = ([c.sub.1]/Xavg)100.

3) Low Frequency Flicker Distortion yields similar answer to Low Frequency Percent Flicker (divided by 100) also

LFFD = Low Frequency Flicker Distortion = ([c.sub.1]/Xavg)

Example: Consider a simple periodic PWM waveform for the luminous flux output of an LED lamp as shown in Fig. 2. Suppose we define [f.sub.lamp] = 1/T as the frequency of the flicker. The duty cycle, D, varies between 0 and 1 and represents LFFD = Low Frequency Flicker Distortion = a fraction of on-time for the PWM signal. The Fourier Series of the PWM waveform is given by



For the purpose of illustration, suppose that we are only interested in the first term of the Fourier series, perhaps because 2*[f.sub.lamp] > [f.sub.threshold]. Then the truncated Fourier series is given by

Xtrunc(t) = [X.sub.max] * (D + 2 sin ([pi]D)/[pi] cos([omega](t-0.5DT)))

Therefore: LFFD = Low Frequency Flicker Distortion = [c.sub.1]/Xavg =2 sin ([pi]D)/[pi]D

For example, if D = 0.5, then the LFFD = 4/[pi] = 1.27, or equivalently, the Low Frequency Percent Flicker is equal to 127 percent. It should be noted that the PWM example represents luminance intensity of common LED lamps on the market. Some modulate at frequencies as low as twice the line frequency (120 Hz in US and 100 Hz in Europe), while others modulate at frequencies near 1kHz. By defining measures such as above, it is possible to carefully analyze the influences of the individual frequency harmonics on human health and decipher the differences between the different lamps with different frequencies. That is, health effects may not be noticeable at the higher frequencies, as noted in (IEEE P1789, 2010).


It may be suggested that for very low frequencies, there is no need to limit harmonic content. In this case, we may define a range of frequencies that are of concern [f.sub.low] < f < [f.sub.threshold]. Then it is possible to define a modified measure of distortion that only includes the Fourier terms in the frequency range of interest. For example, it is possible to define

TUFD = [square root of ([c.sub.k.sup.2]+[c.sub.k+1.sup.2]+...[c.sub.n.sup.2])]/Xavg

where the undesirable terms in Xtrunc(t) of (6) are the terms associated with {[c.sub.k], [c.sub.k+1],...[c.sub.n]} where n is as defined in (6), n > k, and f*(k-1) < [f.sub.low] but f*k > [f.sub.low]. Of course, in order to make the proposed definitions more meaningful to lighting standards, it is important to define and justify [f.sub.threshold], the upper frequency limit after which lighting may not impose biological concerns. This document does not suggest such a frequency.


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Boyce PR. 2003. Human factors in lighting. 2nd Edition. New York: Taylor and Francis. 584 p.

Bums SA, Elsner AE, Kreitz MR. 1992. Analysis of nonlinearities in the flicker ERG. Optom Vis Sci. 69(2):95-105.

Campbell F, Robson J. 1968. Application of fourier analysis to the visibility of gratings. J. Physiol. 197:551-566.

de Lange Dzn H. 1961. Eye's Response at flicker fusion to square-wave modulation of a test field surrounded by a large steady field of equal mean luminance. J Opt Soc Am. 51(4):415-421.

De Valois RL, De Valois KK. 1980. Spatial vision. Annu Rev Psychol. 31:309-341.

Eastman AA. Campbell JH. 1952. Stroboscopic and flicker effects from fluorescent lamps. Illum Eng. 47(1):27-33.

IEEE. 2010. IEEE Standards P 1789 -Biological effects and health hazards from flicker, including flicker that is too rapid to see. Editors: Lehman B, Wilkins A.

Kaufman J, editor. 1984. IES lighting handbook. New York: Illuminating Engineering Society of North America.

Kelly DH. 1969. Diffusion model of linear flicker responses. J Opt Soc Am. 59(12): 1665-1670.

Krein PT. 1998. Elements of power electronics. New York: Oxford University Press. 766 p.

Wilkins AJ. 1995. Visual stress. New York: Oxford University Press.

Brad Lehman (1), Arnold Wilkins (2), PhD, Sam Berman (3) PhD, Michael Poplawski (4) and Naomi Johnson Miller (4)

(1.) Department of Electrical & Computer Engineering, Northeastern University, Boston MA; (2.) Visual Perception Unit, University of Essex, Colchester, UK; (3.) Berkeley CA; (4.) Pacific Northwest National Laboratory, Portland OR

doi: 10.1582/LEUKOS.2010.07.03004
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Author:Lehman, Brad; Wilkins, Arnold; Berman, Sam; Poplawski, Michael; Miller, Naomi Johnson
Article Type:Report
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Date:Jan 1, 2011
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