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Lighting Res. Technol. 2012; 0: 1–14
Characterising the effective intensity of
multiple-pulse flashing signal lights
JD Bullough PhD, NP Skinner MSc and RT Taranta BSc
Lighting Research Center, Rensselaer Polytechnic Institute, Troy, NY, USA
Received 23 December 2011; Revised 14 March 2012; Accepted 16 March 2012
Flashing lights used in aviation signal applications can be characterised by the
luminous intensity of a steady-burning signal light with the same visual
effectiveness. Different formulae exist for calculating the effective intensity of
flashing signal lights that use multiple brief pulses of light within each flash. The
results of a laboratory study conducted to test these calculation methods revealed
that a formulation based on the Blondel–Rey–Douglas effective intensity method
was more predictive of judgments of overall visibility than a different formulation
published in recent aviation authority guidance. A follow-up experiment yielded
confirmation of these findings. Different aspects of visibility resulted in very
different judgments, and the limitations of the effective intensity concept to
characterise the visibility of a flashing light are also discussed.
1. Introduction
Flashing lights are used in aviation signal
lighting because they are thought to produce
higher conspicuity than steady-burning signal
lights, and a substantial body of experimental
evidence confirms this expectation.1–7 Some
authors have reported that very short pulses
of light can appear brighter than a steady
light having an intensity the same as the
maximum of the light pulse,8 the so-called
Broca-Sulzer effect.5 Despite their generally
higher conspicuity than steady-burning lights,
flashing lights can result in difficulty maintaining fixation and in judging the relative
location or direction of the flashing signal9–11
or can create distractions.6 Wienke12 found
that when the location of a flashing light
signal was unknown in advance, it needed to
be flashed about three times before it was
detected.
Address for correspondence: JD Bullough, Lighting Research
Center, Rensselaer Polytechnic Institute, 21 Union St., Troy,
NY 12180, USA
E-mail: bulloj@rpi.edu
Flashing lights are used in a variety of
transportation applications, each with its own
terminology and technical language.13 One
method used extensively across transportation modes to quantify the visual effectiveness
of flashing signal lights has been through the
luminous intensity of a steady-burning signal
light with equal effectiveness, a concept
known as effective intensity. One of the most
commonly used formulations for effective
intensity is the Blondel–Rey formulation
based on studies conducted by Blondel and
Rey.14 According to this formulation, the
effective intensity (Ie, in cd) of a flashing
signal light at near-threshold viewing conditions is defined as follows:
Z t2
Ie ¼
I dt=ða þ t2 t1 Þ
ð1Þ
t1
where I is the instantaneous luminous intensity (in cd) at any moment between times t1
and t2 (both represented in seconds); and a is
a constant (in units of seconds) determined
experimentally by Blondel and Rey14 to have
a value near 0.2.
ß The Chartered Institution of Building Services Engineers 2012
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10.1177/1477153512444494
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Various studies on the perception of flashing lights have confirmed that the Blondel–
Rey formulation is reasonably predictive of
the effectiveness of flashing light signals (such
as visual range or relative brightness) under a
wide range of conditions.15–20 This is significant because different light source technologies can produce a wide range of temporal
waveforms of light output as a function of
time.21 Values for the constant a in equation
(1) have been found to be different depending
upon factors such as the overall intensity of
the light (i.e., for suprathreshold rather than
threshold conditions),15,22–26 the colour of
light25,27 and spatial configurations of the
light.25,28,29
Not all of the research findings into the
relationships between the value of a in equation (1) and the equivalent steady-burning or
effective intensities have been consistent.
Many authors have stated that the value of
a decreases as the overall intensity
increases,22,24–26 but sometimes an opposite15
or no relationship30 was apparent. Despite
these conflicts, the effective intensity formulation proposed by Blondel and Rey14
remains largely accepted for use in a wide
variety of contexts,19 although it may not be
suitable for predicting the relative effectiveness of very complex waveforms, such as a
rapidly alternating high–low sequence superimposed onto a sinusoidal temporal waveform of lower frequency.31
Another factor that can influence the
perception of a flashing light is the presence
of very brief, multiple pulses within a cycle of
a flashing signal light. Although sensitivity to
differences in light flash onset or frequency is
relatively high,32 with onset differences of
10 ms being able to be reliably detected,33
sensitivity to pulses presented in temporal
sequence appears to be lower. For a series of
very short flash pulses separated by dark
intervals of 100 ms or less,34–36 the visual
system will perceive only a single flash.
Sometimes, the dark interval could be even
larger and the pulses would be seen as a single
flash.37 Douglas38 proposed and the
Illuminating Engineering Society39 accepted
a formulation for the effective intensity of
multiple-pulse flashes that is identical to
equation (1), but where t1 is the starting
time of the first pulse in the train of pulses
making up the flash and t2 is the ending
time of the last pulse in the train. There is
some evidence40,41 that this so-called Blondel–
Rey–Douglas formulation38 for effective
intensity provides good agreement with
empirical data.
In comparison, the formulation for multiple-pulse flashing lights (when the frequency
of the pulses is at least 50 Hz, corresponding
to an interval between pulses of approximately 0.01 s) used in some signal lights
specified by the U.S. Federal Aviation
Administration42 uses a modified version of
equation (1). In this version, the integration in
equation (1) is performed individually for
each pulse in the flash, and the effective
intensities for each pulse are summed to arrive
at the effective intensity (Ie, in cd) for the
entire multiple-pulse flash, as follows:
Z ta
Z tc
Ie ¼
I dt=ða þ ta t1 Þ þ
I dt=ða þ tc tb Þ
t1
Z
tb
te
I dt=ða þ te td Þ
þ
td
Z
t2
þ ...
I dt=ða þ t2 tz Þ
ð2Þ
tz
where I is the instantaneous luminous intensity
(in cd) at any moment between times t1 and t2
(both represented in seconds); ta is the end time
for the first pulse in the flash, tb is the start time
for the second pulse, tc is the end time for the
second pulse, td is the start time for the third
pulse, te is the end time for the third pulse and
so on; tz is the start time of the last pulse and t2
is the end time of the last pulse (all values of tn
are in seconds) and a is a constant (in units of
seconds) with a value of 0.2.
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Multiple-pulse flashing light effective intensity
Only a single experimental investigation43
has been identified in which the Blondel–
Rey–Douglas formulation38 was compared
directly with the one specified in equation
(2).42 A limited field trial of various multiplepulse flashing lights resulted in responses that
appeared to be more consistent with the
Blondel–Rey–Douglas method38,39 than that
described by equation (2),42 but there was
substantial variability in the results.43 For this
reason, some authorities have proposed using
the Blondel–Rey–Douglas method38 rather
3
than equation (2)42 to quantify the effective
intensity of multiple-pulse flashing lights,44
particularly at a time when new light source
technologies, such as light-emitting diodes
(LEDs), with a wide variety of onset times
and possible temporal profiles, are being
deployed in aviation signal light systems.
The present paper summarises two laboratory experiments designed to compare the
relative utility of the Blondel–Rey–Douglas
formulation38,39 for effective intensity and the
method described by equation (2)42 at predicting the visual effectiveness of multiplepulse flashing lights.
Pinhole apertures
2. Method: Experiment 1
10 cm
Experiment 1 was conducted in the Levin
Photometric Laboratory of the Lighting
Research Center (LRC). Two white LED
Figure 1 Schematic of the apparatus used to present
flashing light stimuli in the experiment
(a)
Dark interval = 0.03 s
(b)0.875
0.875
0.75
luminous intensity (cd)
luminous intensity (cd)
0.75
0.625
0.5
0.375
0.25
0.125
0
–0.1
Dark interval = 0.01 s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.625
0.5
0.375
0.25
0.125
0
–0.1
0.9
0
0.1
0.2
0.3
(c)
(d)
Dark interval = 0.003 s
0.875
0.6
0.7
0.8
0.9
0.6
0.7
0.8
0.9
0.75
luminous intensity (cd)
luminous intensity (cd)
0.5
Dark interval = 0.001 s
0.875
0.75
0.625
0.5
0.375
0.25
0.125
0
–0.1
0.4
time (s)
time (s)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.625
0.5
0.375
0.25
0.125
0
–0.1
0
0.1
0.2
0.3
0.4
0.5
time (s)
time (s)
Figure 2 Temporal waveforms for the multiple-pulse flashing light conditions. Each pulse has a duration of 0.01 s.
Intervals between pulses are (a) 0.03 s, (b) 0.01 s, (c) 0.003 s and (d) 0.001 s. Each train of pulses repeated every s at a
frequency of 1 Hz
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1
0.8
0.6
0.4
0.2
0
0.01
(c)
Proportion judged more
attention-getting
(b)
Dark interval = 0.03 s
Proportion judged more
attention-getting
Proportion judged more
attention-getting
(a)
1
0.1
Steady light intensity (cd)
0.8
0.6
0.4
0.2
0.1
0.8
0.6
0.4
0.2
(d)
Dark interval = 0.003 s
1
0
0.01
Dark interval = 0.01 s
1
0
0.01
10
Proportion judged more
attention-getting
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Steady light intensity (cd)
0.1
1
Steady light intensity (cd)
10
Dark interval = 0.001 s
1
0.8
0.6
0.4
0.2
0
0.01
0.1
1
Steady light intensity (cd)
10
Figure 3 Proportion of times subjects judged the steady-burning signal light as more attention-getting than each of
the flashing light signals, plotted as a function of the steady-burning light intensity. Each panel corresponds to a
different dark interval between light pulses. Also shown are the best-fitting sigmoid functions to the data constrained
to have the same slope. Goodness-of-fit values are a: r2 ¼ 0.73, b: r2 ¼ 0.47, c: r2 ¼ 0.59, d: r2 ¼ 0.74
light sources were placed behind 0.6-mm
diameter pinhole apertures (Figure 1) and
viewed from a distance of 2 m. One of the
sources was operated on a constant current
power supply so that it produced an illuminance of 15 mlx, 22 mlx, 29 mlx, 37 mlx or 44
mlx (so that its luminous intensity was 0.059
cd, 0.089 cd, 0.118 cd, 0.147 cd or 0.177 cd,
respectively) at the viewing distance.
The other source was operated to produce
a flash every second (at a frequency of 1 Hz),
which contained three distinct, rectangular
light pulses each having a duration of 0.01 s,
with the pulses separated by 0.03 s, 0.01 s,
0.003 s or 0.001 s. During the light pulses, the
illuminance that was produced 2 m away was
206 mlx, with an instantaneous luminous
intensity of 0.825 cd. Temporal profiles of
each waveform are shown in Figure 2.
Waveforms were verified using a fastresponse photocell and an oscilloscope.
According to the effective intensity formulation in equation (2),42 the effective intensity
of each of the four waveforms shown
in Figure 2 is 0.118 cd. Using the Blondel–
Rey–Douglas formulation38,39 based on equation (1), and setting the start (t1) and end (t2)
times as the start and end times for the entire
train of pulses, the calculated effective intensities are as follows:
0.03 s dark interval: 0.085 cd
0.01 s dark interval: 0.099 cd
0.003 s dark interval: 0.105 cd
0.001 s dark interval: 0.107 cd
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Multiple-pulse flashing light effective intensity
(b)
Dark interval = 0.03 s
Proportion judged higher
average brightness
Proportion judged higher
average brightness
(a)
1
0.8
0.6
0.4
0.2
0
0.01
Dark interval = 0.01 s
1
0.8
0.6
0.4
0.2
0
0.1
1
10
0.01
Proportion judged higher
average brightness
Proportion judged higher
average brightness
(d)
Dark interval = 0.003 s
1
0.8
0.6
0.4
0.2
0
0.01
0.1
1
0.1
1
10
Steady light intensity (cd)
Steady light intensity (cd)
(c)
5
10
Steady light intensity (cd)
Dark interval = 0.001 s
1
0.8
0.6
0.4
0.2
0
0.01
0.1
1
10
Steady light intensity (cd)
Figure 4 Proportion of times subjects judged the steady-burning signal light as having higher average brightness
than each of the flashing light signals, plotted as a function of the steady-burning light intensity. Each panel
corresponds to a different dark interval between light pulses. Also shown are the best-fitting sigmoid functions to
the data constrained to have the same slope. Goodness-of-fit values are a: r2 ¼ 0.73, b: r2 ¼ 0.83, c: r2 ¼ undefined,
d: r2 ¼ 0.67
The luminous intensities of the steadyburning light signals were centred around
0.118 cd, the calculated effective intensity
using equation (2).42 The other four luminous
intensity values for the steady-burning light
signal were 50%, 75%, 125% and 150% of this
value. They also included values lower and
higher than the range of calculated effective
intensity values based on the Blondel–Rey–
Douglas formulation38,39 in equation (1). Each
of the flashing signals could be presented
simultaneously with one of its corresponding
five steady-burning light signals, for a total of
20 experimental conditions.
Ten subjects (5 female/5 male, age 23–62
years, mean age 38 years) participated in the
experiment. After signing a consent form
approved by Rensselaer’s Institutional
Review Board (IRB), subjects were seated in
position and the height of the signal light
apparatus was confirmed to closely match the
eye height of each subject. An experimenter
read the following instructions to each subject: ‘In this experiment, you will be asked to
compare pairs of simulated signal lights
viewed side by side. One will be a flashing
light and one will be a steady light. First, you
will be asked to judge which one would be
more likely to capture your attention if you
were not looking directly at it. Second, you
will be asked to judge the relative average
brightness of the two lights. By average
brightness, we mean: over the duration of
several cycles of the flashing light, which one
looks like it produces more total light?
Finally, you will be asked to judge the relative
overall visibility of the lights. Visibility may
be a combination of how easy it is to detect,
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identify, and locate a signal light. Taking all
of these factors into account, which light do
you think is more visible? Try to keep your
method of judging each pair of lights the same
for each pair of lights you will see.’
Then the room lights were switched off. In
a randomised order, each pair of steadyburning and flashing light signals was presented to each subject twice, and subjects were
instructed to respond on a laptop computer
(with a screen luminance of 2 cd/m2) to each
of the three questions described in the
instructions:
Which light is more attention-getting?
Which light
brightness?
has
a
higher
average
Which light is more visible overall?
After subjects entered their responses, the
next signal light pair was presented until they
completed all 40 trials (2 repetitions of the 20
conditions). Sessions took about 30 minutes
for each subject to complete.
3. Results: Experiment 1
The results of Experiment 1 are shown in
Figures 3–5, with the percentages corresponding to each response plotted as a function of
the luminous intensity of the steady-burning
light. Also shown in these figures are the bestfitting sigmoid functions to the data in each
panel, having the form:
y ¼ ða cÞ= 1 þ ðx=bÞd þ c
ð3Þ
where a (not the same as a in equations (1)
and (2)) and c are the minimum and maximum values of the function (fixed at 0 and 1,
respectively, representing the minimum and
maximum proportion of times the steady light
could be chosen), b is the luminous intensity
(in cd) where the proportion would be 0.5 and
d is the relative slope of the functions.
Although the data in Figures 3–5 could in
principle be represented by simpler functions
(e.g., linear or logarithmic), it is reasonable to
suppose that if the intensity of the steadyburning light were reduced to a very low
value, the proportion of people judging it to
be a stronger stimulus would approach zero.
Similarly, if the steady-burning light’s intensity were increased to a very high value, the
proportion of people judging it to be a
stronger stimulus would approach one.
(Values less than zero or greater than one
would, of course, be nonsensical.) For this
reason, the sigmoid function in equation (3),
which asymptotes to zero and one for very
low and high values, respectively, was selected
for curve fitting.
3.1. Attention-getting properties
Figure 3 shows, for each of the four
flashing light waveforms (each with a different dark interval), the proportion of
responses that the steady-burning light was
judged more attention-getting than the flashing light, as a function of the luminous
intensity of the steady-burning light. Each
panel of Figure 3 shows five data points,
representing the five steady-burning luminous
intensities compared to each flashing signal
light. For the data in Figure 3, the average
best-fitting value of d, the relative slope, was
1.262 using equation (3), so this was fixed in
subsequent curve fitting, and b was the only
free parameter. For each dark interval, the
value of b leading to the best-fitting sigmoid
function was:
0.03 s dark interval: b ¼ 0.277 cd
0.01 s dark interval: b ¼ 0.345 cd
0.003 s dark interval: b ¼ 0.512 cd
0.001 s dark interval: b ¼ 0.406 cd
In each case there was at least a moderate
correlation45 between the observed data and
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Multiple-pulse flashing light effective intensity
(b)
Dark interval = 0.03 s
1
0.8
0.6
0.4
0.2
0
0.01
0.1
1
10
Proportion judged more visible
Proportion judged more visible
(a)
Dark interval = 0.01 s
1
0.8
0.6
0.4
0.2
0
0.01
Steady light intensity (cd)
(d)
Dark interval = 0.003 s
1
0.8
0.6
0.4
0.2
0
0.01
0.1
1
Steady light intensity (cd)
10
Proportion judged more visible
Proportion judged more visible
(c)
7
0.1
1
Steady light intensity (cd)
10
Dark interval = 0.001 s
1
0.8
0.6
0.4
0.2
0
0.01
0.1
1
Steady light intensity (cd)
10
Figure 5 Proportion of times subjects judged the steady-burning signal light as having higher overall visibility than
each of the flashing light signals, plotted as a function of the steady-burning light intensity. Each panel corresponds to
a different dark interval between light pulses. Also shown are the best-fitting sigmoid functions to the data
constrained to have the same slope. Goodness-of-fit values are a: r2 ¼ 0.80, b: r2 ¼ 0.89, c: r2 ¼ 0.56, d: r2 ¼ 0.72
the best-fitting function. The values of b listed
above correspond to the steady-burning luminous intensity that would be predicted to be
judged as equally attention-getting as each of
the four flashing light conditions.
in the best-fitting sigmoid functions for each
flashing light condition were:
3.2. Average brightness
Figure 4 shows the proportion of responses
that the steady-burning light was judged as
having higher average brightness than the
flashing light, as a function of the luminous
intensity of the steady-burning light. The
slopes of the sigmoid functions in Figure 4
were constrained to their average value
(d ¼ 1.559) when this was a free parameter
for each set of data. The values of b resulting
0.003 s dark interval: b ¼ 0.091 cd
0.03 s dark interval: b ¼ 0.046 cd
0.01 s dark interval: b ¼ 0.066 cd
0.001 s dark interval: b ¼ 0.085 cd
Except for the dark interval of 0.003 s,
where the goodness of fit could not be
determined to be better than a straight line
of zero slope, there was always a strong
correlation45 between the observed data and
the best-fitting function. The values of b listed
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Table 1 Summary of visibility responses for Experiment 2
Conditions in each pair
Condition judged more
visible more frequently
Number of times condition
was judged more visible
(out of 20)
Dark interval ¼ 0.03 s and
Dark interval ¼ 0.01 s
Dark interval ¼ 0.03 s and
Dark interval ¼ 0.003 s
Dark interval ¼ 0.03 s and
Dark interval ¼ 0.001 s
Dark interval ¼ 0.01 s and
Dark interval ¼ 0.003 s
Dark interval ¼ 0.01 s and
Dark interval ¼ 0.001 s
Dark interval ¼ 0.003 s and
Dark interval ¼ 0.001 s
Dark interval ¼ 0.01 s
15/20 (p50.05)
Dark interval ¼ 0.003 s
16/20 (p50.01)
Dark interval ¼ 0.001 s
14/20 (n.s., p40.05)
Dark interval ¼ 0.01 s
12/20 (n.s., p40.05)
Dark interval ¼ 0.001 s
15/20 (p50.05)
Dark interval ¼ 0.003 s
11/20 (n.s., p40.05)
above correspond to the steady-burning luminous intensity that would be predicted to be
judged as having equal average brightness as
each of the four flashing light conditions.
judged as having equal overall visibility as
each of the four flashing light conditions.
3.3. Overall visibility
Figure 5 shows the proportion of responses
that the steady-burning light was judged as
having greater overall visibility than the
flashing light, as a function of the luminous
intensity of the steady-burning light. The
slopes of the best-fitting sigmoid functions
in Figure 5 were constrained to their average
value (d ¼ 1.313) when this was a free parameter for each set of data. The values of b
resulting in the best-fitting sigmoid functions
for each flashing light condition were:
Experiment 2 was conducted in the same
laboratory and used the same apparatus as
Experiment 1, except only the four flashing
light conditions illustrated in Figure 2 were
used. Ten subjects (3 female/7 male, aged
23–61 years, mean age 37 years) participated
in the experiment. After entering the laboratory, signing a consent form approved by
Rensselaer’s Institutional Review Board, and
sitting in their position, the height of the
apparatus was adjusted to match each subject’s eye height. An experimenter read the
following instructions: ‘In this experiment,
you will be asked to compare pairs of flashing
signal lights viewed one after another. You
will be asked to judge the relative overall
visibility of the lights. Visibility may be a
combination of how easy it is to detect,
identify, and locate a signal light. Taking all
of these factors into account, which light do
you think is more visible? Try to keep your
method of judging each pair of lights the same
for each pair of lights you will see.’
After this, the room lights were extinguished and subjects were presented each
0.03 s dark interval: b ¼ 0.069 cd
0.01 s dark interval: b ¼ 0.072 cd
0.003 s dark interval: b ¼ 0.081 cd
0.001 s dark interval: b ¼ 0.093 cd
In each case there was at least a strong
correlation45 between the observed data and
the best-fitting function. The values of b listed
above correspond to the steady-burning luminous intensity that would be predicted to be
4. Method: Experiment 2
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Times condition judged more visible (%)
Multiple-pulse flashing light effective intensity
9
100%
80%
*
60%
40%
*
20%
0%
0.03 s
0.01 s
0.003 s
0.001 s
Dark interval (s)
Figure 6 Percentage of times each flashing light was judged more visible, out of the total number of times it was
presented. Asterisks (*) indicate percentages that differ reliably (p50.05) from chance
combination of signal lights in sequential
pairs, one after another. The first in the pair
was called ‘A’ and the second was called ‘B.’
Subjects were given the opportunity to view
each of the lights as often as needed to make
their judgments before stating verbally
whether they believed ‘A’ or ‘B’ was more
visible. Each pair was viewed twice in a
randomised order, and the lights in each
pair were presented in opposite order for each
trial featuring a given pair of lights. An
experimenter recorded the verbal judgment of
each subject during each trial. Each experimental session was completed in approximately 15 minutes.
5. Results: Experiment 2
The results of Experiment 2 are presented in
two ways. Table 1 shows, for each pair of
conditions, the number of times (out of 20: 10
subjects and 2 trials each) each condition was
judged as more visible. Figure 6 shows the
number of times each condition was chosen,
as a percentage of the total number of times it
could have been chosen.
For each pair of conditions in Table 1, the
rightmost column also indicates whether the
proportion of times a given condition was
judged as more visible is statistically significant (p50.05) based on a Chi-square test, and
assuming a 50% probability of being chosen
under chance conditions. Of the three pairs of
conditions in Table 1 that resulted in statistically significant differences, the direction of
the difference always favoured the condition
with the shorter interval between multiple
pulses.
In Figure 6, the percentages of time each
flashing light condition was judged as more
visible (out of the total number of times it
was presented) increase monotonically as
the dark interval between the pulses in each
flash decreased. For the dark intervals of
0.03 s and 0.001 s, Chi-square tests revealed
that the percentages were statistically significantly different (p50.05) from chance.
The condition with the dark interval of
0.03 s was judged more visible reliably less
than half the time, whereas the condition
with the dark interval of 0.001 s was judged
more visible reliably more than half the
time.
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6. Discussion
6.1. Differences among response types in
Experiment 1
The results from Experiment 1 shown in
Figures 3–5 were relatively noisy. The
observed proportions along the y-axes in
these figures did not always increase monotonically with the x-axis values. Goodnessof-fit values for the best-fitting sigmoid
functions were usually moderately high (i.e.,
r240.5) but sometimes yielded rather poor
correlations between the steady-burning
light’s intensity and the response proportions
for each question. Although as described
above, a sigmoid function reasonably reflects
the expected behaviour for very low or very
high steady-burning signal intensities, it seems
clear that the questions in Experiment 1 could
be difficult to answer and that the precision of
the resulting equivalent intensity values is
therefore limited.
Even taking into account the limited precision of the present data, inspection of
Figures 3–5 indicates that the three responses
elicited in Experiment 1 were very different.
Figure 3 shows the relative attention-getting
characteristics of the steady-burning lights
compared to the flashing lights. All of the
proportions in Figure 3 are less than 0.5,
which suggests that on average, the flashing
lights were all judged to be more attentiongetting than the steady-burning lights used in
the study. This finding is consistent with
previously published studies on the conspicuity of flashing lights.1–7 It also suggests that
neither the Blondel–Rey–Douglas formulation38,39 for effective intensity nor the one
described by equation (2)42 are very predictive
of the attention-getting characteristics of
flashing lights.
In Figure 4, most of the proportions are
greater than 0.5, suggesting that on average,
people generally judged the steady-burning
lights to have higher time-averaged brightness
than the flashing lights. These are much
different responses from those based on
attention-getting characteristics. Of the three
response types, the data in Figure 5 for
overall visibility are most balanced in terms
of the number of proportions greater than or
lower than 0.5. These differences underscore
the importance of understanding the different
responses needed in detecting, identifying and
locating flashing signal lights. A flashing light
that is more conspicuous than a particular
steady-burning light may not be judged as
having greater average brightness nor as
being more visible than the same steadyburning light.
It is worth noting, however, that notwithstanding some imprecision in the measured
responses, the steady-burning luminous intensities predicted to produce equivalent attention-getting, average brightness and overall
visibility characteristics seem to increase as
the dark interval decreases from 0.03 s to
0.001 s. This is more consistent with the
Blondel–Rey–Douglas formulation38,39 than
with the one in equation (2),42 which predicts
the same effective intensity for all four
conditions.
6.2. Agreement between experiments
The results of both experiments were consistent. Based on the overall visibility
response data in Figure 5, the steady-burning
luminous intensities predicted to have equivalent visibility as each flashing light increased
as the dark interval was decreased in
Experiment 1, and similarly, the overall percentages of time that each flashing light was
judged as more visible in Experiment 2
increased as the dark interval was decreased.
Again, despite imprecision in the measured
responses, both sets of data indicate that the
visual effectiveness for the four flashing light
conditions was highest when the dark interval
between pulses of light in the flash was
shortest. Since the effective intensity formulation in equation (2)42 predicts each of these
conditions to have the same effective
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intensity, the results from these experiments
call into question the use of this as a means to
compare multiple-pulse flashing lights.
Based on equation (1) (using t1 to represent the starting time for the train of three
pulses and t2 to represent the ending time
for the train of pulses), the predicted
effective intensity values using the Blondel–
Rey–Douglas method38,39 for the four
experimental conditions (see Section 2) are
strongly correlated45 with the estimated
equivalent intensities for overall visibility in
Experiment 1 (see Section 3.3; r2 ¼ 0.68) and
with the overall visibility percentages listed
from Experiment 2 (Figure 6; r2 ¼ 0.98).
However, only the data from Experiment 1
can be used to make absolute comparisons
between the Blondel–Rey–Douglas predictions38,39 and measured visibility assessments. On average, the empirical equivalent
steady-burning intensities for equal overall
visibility were about 20% lower than the
predictions using the Blondel–Rey–Douglas
formulation38,39 for multiple-pulse flashing
lights. Although a 20% difference is rather
small, and could possibly be caused by the
imprecision in measured responses in the
present study, the disagreement can be
lessened using a slightly different value of a
in equation (1). For example, if the value of
a is 0.25 rather than 0.20, the calculated
effective intensities for each condition are:
0.03 s dark interval: 0.073 cd
0.01 s dark interval: 0.083 cd
0.003 s dark interval: 0.087 cd
0.001 s dark interval: 0.088 cd
As reported above (see Section 1), Neeland
et al.15 suggested that for suprathreshold
conditions, the value of a increases as the
overall intensity increases. However, this
finding has not been found consistently in
11
the literature. Other authors22,24,25 came to
the opposite conclusion.
6.3. Conclusions
In general, the results of both experiments
described here agree with the notion that the
formulation for effective intensity of multiplepulse flashing lights in equation (2),42 which is
based on the sum of the effective intensity
values for each individual pulse, will not
predict the relative visual effectiveness of
these lights. Using several different flashing
light conditions in which three-pulse flashes
were presented with different dark intervals
between pulses, applying the Blondel–Rey14
formulation as recommended by Douglas38
and by the IES39 appears to be more
appropriate for estimating the relative effectiveness of multiple-pulse flashing lights, for
the range of pulse intervals used in the present
study.
The use of different response measures in
Experiment 1 of the present study, and the
very different steady-burning light intensities
found to provide equivalence according to
each of those criteria, serve to emphasise
several important limitations of the effective
intensity concept. It should be recalled that as
initially defined by Blondel and Rey,14 the
effective intensity was used to determine the
relative visibility of lights when viewed at
threshold conditions, when the light is barely
visible, such as at very long range viewing
distances. It could be argued that flashing
lights used in many aviation applications
such as obstruction lighting or runway end
identification lights are, by design, meant to
be seen well above threshold, more similar
to the conditions employed in the present
experiments. At least one authority19 has
pointed out that although effective intensity
values are not applicable to suprathreshold
viewing conditions, there is presently no
alternative to this formulation, and on this
basis it recommends using effective intensity
to evaluate signal lights even when viewed
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above threshold conditions. The relative
effectiveness seems to be characterised reasonably by the effective intensity concept,
provided the issue of multiple-pulse flashes of
light is handled appropriately.
Although the absolute values of the
equivalent steady-burning intensity data for
overall visibility in the present study were
more closely predicted when the value of the
constant a in the Blondel–Rey–Douglas formulation38,39 (equation (1)) was modified,
the present results alone do not justify a
recommendation to use a value of a different
from 0.2. This is because previously reported
values of a have ranged from 0.08 to 0.35,24
and Projector16 stated that the inherent
imprecision of effective or equivalent intensity judgments limits the precision of specifying the value of a in such formulations.
Projector’s statement16 is certainly consistent
with the level of noise found in the data for
the present study as well. This historical
imprecision, as well as that of the present
study, reinforces the inertia associated with
the widespread historical use of 0.2 for the
value of a in the effective intensity formulation in equation (1).14,38,39 Future studies
should investigate using performance-based
response measures such as reaction times or
search times in an effort to increase precision
for effective intensity as a more meaningful
concept for specification of flashing light
signals.
Funding
The present study was sponsored by the U.S.
Federal Aviation Administration (FAA)
under
contract
2010-G-013.
Donald
Gallagher and Robert Bassey served as
FAA project managers.
Acknowledgments
The authors gratefully acknowledge N.
Narendran from the Lighting Research
Center (LRC) at Rensselaer Polytechnic
Institute for his advice and guidance of this
study as principal investigator for Rensselaer’s
contract with the FAA. Terence Klein and
Anna Lok from the LRC also made important
technical contributions to this study.
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