CIE TC2-49 Draft 4.1
July 22, 2008
Measurement of Effective Intensity of Flashing Lights
Prepared by
TC2-49 Photometry of Flashing Lights
Chairman: Yoshi Ohno (USA)
Members:
Andersen (USA), Austin (USA), Berkhout (USA), Couzin (USA), Ellis (USA), Eppeldauer
(USA), Fryc (Hungary), Gibbs (UK), Goodman (UK), Hengstberger (South Africa), King
(USA),
Rennilson (USA),
Sagawa (Japan),
Schmidt-Clausen (Germany),
Sauter
(Germany), Tutt (UK), Vienot (France), Webb (USA). Rattunde† (Germany) – updated
May 2007
TR:
Produce a technical report on CIE recommendation for measurement of effective intensity
of flashing lights.
–1–
Table of Contents
1.
SCOPE .......................................................................................................................3
2.
INTRODUCTION.........................................................................................................3
3.
TERMINOLOGY..........................................................................................................3
4.
DETERMINATION OF EFFECTIVE INTENSITY .........................................................5
5.
6.
4.1
Recommendation...................................................................................................5
4.2
Rationale for the recommendation .........................................................................6
4.3
Limitations of the recommended method ...............................................................7
4.4
Repetition rate of flash ...........................................................................................8
PHYSICAL MEASUREMENT OF EFFECTIVE INTENSITY ........................................8
5.1
Digital method........................................................................................................8
5.2
Analog method.......................................................................................................9
Relationship with other methods................................................................................10
Appendix A. Historical overview of effective intensity .......................................................12
Appendix B Analysis of the 1986 U.S. Coast Guard paper ..............................................17
–2–
1.
SCOPE
The objective of this report is to give the CIE recommendation on the measurement of
effective intensity of flashing lights used for signaling applications.
The report
recommends one method to determine effective intensity for standardization purposes.
This report also provides guidance on physical measurements of effective intensity based
on the recommended method, for flashing lights using any types of light sources including
xenon flash tubes, light-emitting diodes (LEDs), and rotating beacons, that produce pulse
widths in the range from micro seconds to several seconds. This report does not cover
specific measurement requirements for signaling light products.
2. INTRODUCTION
Flashing lights are widely used in many
signaling applications in aviation, marine, and
land transportation. Flashing lights, such as
aircraft anticollision lights, marine aids-tonavigation lights, obstruction lights, and
emergency vehicle warning lights, are specified
for effective intensity (cd). These lights need to
be physically measured to ensure that they
meet specifications. Several different formulae
have been used to determine effective intensity
in the past. When these formulae are applied
to a given flash, their results often disagree,
and standardization for one method has long
been desired. The purpose of this technical
report is to recommend one method for
standardization purposes. This technical report
also provides information on physical
measurements of effective intensity, dealing
with flashing lights with pulse widths in the
range from micro seconds to several seconds.
Xenon flash sources are commonly used, but
recently, LEDs are increasingly used for
signaling sources. Some examples of the
waveform of flashing light sources are shown
in Fig. 1.
3. TERMINOLOGY
Figure 1. Examples of waveform of
flashing lights – xenon flash with a long
duration (upper), with a short duration
(center), and an LED flashing light
(lower).
The terminology in this document follows the
definitions given in reference [1,2]. The important terms used in this document including
quantities and units relevant to flashing light are listed below. Some of the terms of
quantities and units are not found in any previous publication, and definitions are given for
the first time in this document.
–3–
Flashing light
Rhythmic light in which every appearance of light (flash) is of the same duration, and,
except possibly for rhythms with rapid rates of flashing, the total duration of light in a
period is clearly shorter than the total duration of darkness. [1]
Flash (of light)
A pulse of light, the intensity of which starts from zero, reaches to a peak, and falls to zero
or negligible amount. Multiple flashes consisting of individual flashes that are separated
no more than 0.2 s can be regarded as one flash when calculating effective intensity. A
flash of light that does not fall to zero (e.g., mixed with steady light) is not covered in this
document.
Flash duration
In this document, “flash duration” is used in the meaning of the duration in which all the
flash waveform necessary for determining effective intensity of the flash is included.
Note: Some flashing lights have a long onset or decay time and it is difficult to precisely
determine their durations. Other specific terms such as “effective flash duration” and “total
flash duration” are used with specific definitions [2]. Similarly, “effective duration” is often
used as the duration of a part of the flash that is effective to determine the effective
intensity based on the Blondel-Rey equation.
Luminous energy (Quantity of light [1])
Quantity symbol: Q, Qv
Unit: lumen second (lm·s)
Time integral of the luminous fluxFv(t) over a given duration Δt
Q=
$
#t
(1)
"v dt
Luminous exposure (at a point of a surface, for a given duration)
Quantity symbol: H, Hv
Unit: lux second (lx·s = lm·s·m-2)
Quotient of luminous energy dQv incident on an element of the surface containing the point
over the given duration, by the area dA of that element. [1]
Hv =
dQv
=
dA
#
"t
E v dt
(2)
The luminous exposure of a flash having instantaneous illuminance Ev(t) over the flash
duration T is given by
Hv =
"
T
0
E v (t)dt
Time-integrated luminous intensity (of a source, in a given direction)
Quantity symbol: J, Jv
Unit: candela⋅second (cd·s = lm·s·sr-1)
–4–
(3)
Quotient of the luminous energy dQv leaving the source and propagated in the element of
solid angle dW containing the given direction, by the element of solid angle.
Jv =
dQv
=
d"
$
#t
I v dt
(4)
Integrated luminous intensity Jv of a flash from a source, in a given direction, having
instantaneous luminous intensity Iv(t) over the flash duration T is given by
Jv =
"
T
0
I v (t)dt
(5)
Effective intensity (of a flashing light)
Quantity symbol: Ieff
Unit: candela (cd)
Luminous intensity of a fixed (steady) light, of the same relative spectral distribution as the
flashing light, which would have the same luminous range (or visual range in aviation
terminology) as the flashing light under identical conditions of observation [1]. See Section
4 for prescribed formula.
Time-integrated luminance (in a given direction, at a given point of a real or imaginary
surface)
Quantity symbol: B, Bv
Unit: candela·second per square meter (cd·s·m-2)
Time integral of luminance Lv(t) over a given duration Δt.
Bv =
#
"t
Lv (t)dt
(6)
Visual time constant
Quantity symbol: a
Unit: second
The response time of human visual perception in foveal vision at achromatic threshold.
Although there is no precisely defined value for the visual time-constant, a value of 0.2
seconds is commonly used in effective intensity models for a dark-adapted observer. More
importantly perhaps, the value of a is sometimes chosen to ensure the ‘best fit’ of a model
to visual data.
4. DETERMINATION OF EFFECTIVE INTENSITY
4.1
Recommendation
This recommendation is based on the Modified Allard method [3]. The effective intensity is
determined as below.
Given that i(t) is the instantaneous luminous intensity of a flash, the effective intensity is
determined by the peak of the following convolution:
–5–
i (t ) = I (t ) * q (t )
where q (t ) =
a
(a + t ) 2
and a = 0.2 s
(7)
The flash starts at t = 0 . The effective intensity Ie is
given as the peak value of i(t) . The q(t) is the
visual impulse response function as shown in Fig. 3
plotted with
! that of the original Allard method.
!
The convolution can be obtained easily by
calculating sum-products of the two functions, I (t)
and the reversed q(t) function, as q(t) is moved
along relative to I (t) , as
N
Figure 2. Schematic of Modified
Allard method.
!
! i(t ) =
(8)
I (tk ) "!q(t j # tk )
j
!
k =0
where, I(t) is sampled at t0(=0), t1, t2, …., tN over
the entire flash duration.
$
!
Figure 3. The visual impulse
4.2 Rationale for the recommendation
response function in the original Allard
The historical overview of the three formulae for effective
intensity is provided in Appendix
and the Modified Allard Method
A. In summary, Blondel-Rey [4] (or Blondel-Rey-Douglas [5]) equation has been most
widely used and it is known to be accurate for rectangular pulses [6]. The treatment for
non-rectangular pulses, however, is complex, requiring iterative computation, and is not
mathematically coherent. The Form Factor method was developed as a practical method
to measure effective intensity of non-rectangular pulses, allowing simple calculation from
the peak and the integral of the waveform. This method, however, was found to fail for a
train of pulses [7,2] and other specific forms of pulse. The Allard method [8] was not well
known and not widely used but recommended for use for trains of pulses [7]. A method
that performs accurately for all forms of pulses (including trains of pulses) and that can be
easily applied has been desired.
The following basic desiderata for recommended effective Intensity formula are
considered:
1) The formula should agree with the Blondel-Rey (and the Form Factor method) for
rectangular flashes.
2) The formula should agree with published data for trains of flashes.
3) The formula should not be demonstrably tricked by any potential complex form flashes.
4) The formula should allow for simple measurement techniques.
5) The formula should agree with published visual observation data for studied nonrectangular flash forms.
Blondel-Rey-Douglas [5] does not meet criteria 4 as described above, and also is
problematic for criteria 3 and 2: the iterative solution does not produce a result for a certain
form of pulse. It is also not recommended for train of pulses [7, 9]. The Form Factor
method does not meet criteria 2, as identified experimentally [10] as well as
–6–
computationally [3]. It is also problematic for criteria 3: the results are tricked by pulses
with very narrow peak superimposed on a broad pulse. The Allard method does not meet
criteria 1 as computationally shown [3]: the results deviate from Blondel-Rey by about
25 % for pulse duration from 0.2 to 1 s. But, it was recommended for train of pulses [7]
(criteria 2), mathematically coherent for any forms of pulses (criteria 3), and the
convolution can be achieved electronically easily (criteria 4). The Modified Allard method
was developed to eliminate the problem for criteria 1 of the Allard method, thus it satisfies
all the five criteria except that more experimental evaluation was desired for criteria 5. The
US Coast Guard paper [10] reported visual experiments on trains of pulses, the results of
which agreed extremely well with the calculation results by the Modified Allard method,
and has been taken as experimental validation. The details of the analysis on Ref. [10]
are described in Appendix B.
To summarize important points of the Modified Allard method,
1) It is mathematically equivalent to the Blondel-Rey (and Form Factor) equation for
rectangular pulses.
2) It works accurately for train of pulses as validated by the visual experimental data [10]
as well as by computational analysis [3].
3) There are no known forms of pulse of any duration for which the method produces
anomalous results.
4) The method can be realized by single readout analog circuit, without requiring
waveform recording and calculation by computer (see section 5.2)
While further experimental results for various other pulse waveforms are desirable,
Modified Allard method is considered to perform satisfactorily for all forms of pulses and it
also provides practicality for realizing portable ‘flash’ photometers.
4.3 Limitations of the recommended method
The Modified Allard method is made equivalent to the Blondel-Rey equation for
rectangular pulses. Therefore its application conditions are considered the same as those
for Blondel-Rey equation:
•
•
•
•
•
threshold of detection
white light
dark background
foveal vision
angular size should be visually zero.
These conditions apply also for all the three conventional methods described above. No
details on spectra of illumination and angular size of stimuli on Blondel-Rey equation are
available. It is reported that the value of the Blondel-Rey constant a varies depending on
these conditions [11]. Therefore, the users should be alerted that perceived effective
intensity in real applications, where the viewing conditions deviate from above, can deviate
significantly from what is predicted by the calculated effective intensity. For example, it is
reported that the constant a varies from 0.15 (yellow, white) to red (0.25) for chromatic
threshold [11].
Thus, the effective intensity formula recommended in this document will not be applicable
to a supra-threshold condition, in peripheral vision condition, nor when lights are observed
with a significantly bright background or with many other lights in the background.
–7–
4.4
Repetition rate of flash
The effective intensity is normally determined
(calculated) from one flash among the repeated
flashes of lights to be tested, assuming that the
frequency of repetition is 1 Hz or less. If pulses
repeat at a significantly higher frequency, the
effective intensity is considered to increase.
Whilst such an effect of the frequency of
flashing lights on effective intensity is not well
understood, we recommend the following.
If the repetition period of a flashing light is less
than 1 s (repetition frequency higher than 1 Hz),
the number of flashes included within a 1 s
window should be used to calculate effective
intensity. For example, two flashes if the period
is 0.7 s, three flashes if the period is 0.4 s,
should be used as the input for the calculation.
The above recommendation, in turn, can be
interpreted that the effective intensity for any
shape of pulse at any frequency can be
measured by sampling the flashing lights for the
1 s window.
Figure 4. Example of flashing lights with
different frequencies.
Figure 4 shows such an example. The upper
figure shows the case of 1 Hz or less, center figure 1.25 Hz, lower figure 2.5 Hz.
Assuming each flash has same physical intensity (10 cd•s), the calculated effective
intensity for these three flashes are: 46 cd (upper), 47 cd (middle), 53 cd (lower figure),
respectively.
5. PHYSICAL MEASUREMENT OF EFFECTIVE INTENSITY
The effective intensity of flashing lights as defined in the section above can be physically
measured using two approaches: digital method and analog method. The impulse
response function q(t) is close to an exponential function, thus the convoluted i(t) can be
obtained by an analog low-pass filter circuit.
5.1 Digital
! method
The
waveform
of
instantaneous
luminous intensity I (t) (cd) is measured
at small time intervals, digitized,
recorded, and the effective intensity is
calculated according to Eqs. 7 and 8.
Figure 5 !shows a schematic of an
effective intensity photometer using this
approach. The detector signal is first
converted to voltage with a high-speed
!
Figure 5. An example of effective intensity
photometer using digital method.
–8–
pre-amplifier (current-to-voltage converter), digitized, and recorded into the computer.
Then, effective intensity (and other photometric quantities) can be calculated based on
their definitions.
In this method, care must be taken so that the
instantaneous flash signal at its peak is not
saturated at the current-to-voltage converter,
and also that the sampling interval is small
enough to measure the pulse shape
accurately when pulses are very short. It is
also important that the preamplifier response
time is adequate to faithfully follow the flash
profile.
5.2 Analog method
The impulse response function for Modified
Allard method can be approximated by using
two or more exponential functions. Below is
an approximation using two exponential
functions:
t
Figure 6. The visual impulse response
function approximated by the two
exponential functions.
t
w #
w #
q(t ) " 1 e a1 + 2 e a 2 ,
a1
a2
(9)
where
w1 w2 1
+
" ,
a1 a2 a
!
w1 + w2 " 1, a = 0.2 s,
and
q(t ) = 0 , when t < 0 .
!One of the solutions for optimization for
smallest
error
is
a1=0.093,
Figure 7. Measurement error with the
two exponential function model.
a2=0.519,
!
! w1=0.363, w2=.562.
With these parameters,
the results agree with the exact formula to
within 1.2 % for any duration less than 1 s of
rectangular pulses.
The approximated
visual impulse response function is shown
in Fig.6, and the error (%) in measured
effective intensity using this model, as a
function of pulse duration, is shown in Fig.
7.
This approximation using two
exponential function is considered accurate
enough for practical measurements.
This approximation given in eq. (9) can be
realized by combining two electronic lowpass filter circuits, added at the prescribed
ratios. Figure 8 shows an example of such
–9–
Figure 8. An example of a configuration
of an effective intensity photometer using
the analog method.
a circuit to realize a photometer to measure effective intensity based on the Modified
Allard method, where the capacitors and resistors are chosen so that
C1 R1 = a1,
and
w1 = k "
C2 R2 = a2
R1 " R5
R "R
, w2 = k " 2 5
R3
R4
(10)
(11)
where k is the calibration factor.
!
6. Relationship with other methods
If only single rectangular pulses (not trains of pulses) are measured, the Blondel-Rey and
Form Factor methods will produce the same results as the effective intensity
recommended by this document. This is often the case with flashing lights using LEDs.
If only flashing lights composed of a very short single pulse (less than a few milli-seconds)
repeated at frequency of ~1 Hz or less (e.g., flashing lights using xenon strobe), the
Blondel-Rey, Form Factor, and Allard methods will produce the same results as the
effective intensity recommended by this document. In this case, the effective intensity can
be measured as the time-integrated luminous intensity (cd·s) divided by 0.2.
The results for various forms of non-rectangular pulses vary between different methods.
The difference depends on the pulse shape and duration. Comparison of the Blondel-Rey,
the Form Factor, and the Allard methods for several different forms of single pulse are
reported in Ref. 7, which shows the differences of ~30 % at most for these examples. The
results by Modified Allard method lie between the values of the Blondel-Rey equation and
the Form Factor method in most cases. Similar comparisons including the Modified Allard
method are available in Ref. 3, showing similar magnitude of differences. However, the
differences can be much larger for more complicated forms of pulse such as modulated
pulse (e.g., from discharge lamps) and for trains of multiple pulses.
References
1. CIE International Lighting Vocabulary, CIE Publication No.17.4 (1987).
2. CIE Publication 105, Spectroradiometry of pulsed optical radiation sources (1993).
3. Y. Ohno and D. Couzin, Modified Allard Method for Effective Intensity of Flashing
Lights, Proc., CIE Symposium’02, Veszprem, Hungary, CIE x025:2003, 23-28 (2003).
4. Blondel A. et Rey J., Sur la perception des lumiéres brèves à la limite de leur portée,
Journal de Physique, Vol CLIII, p.54 (1911).
5. Douglas, C.A., Computation of the effective intensity of flashing lights, Illuminating
Engineering, N.Y. Vol. LII.No 12, pp.641-646 (1957).
6. Schmidt-Clausen, H. J., Über das Wahrnehmen verschiedenartiger Lichtimpulse bei
veränderlichen Umfeldleuchtdichten (Concerning the perception of various light flashes
with varying surrounding luminances), Darmstadt Dissertation D17, Darmstadt
University of Technology (1968).
7. IALA, Recommendations on the determination of the luminous intensity of a marine
aid-to-navigation light, (1977).
– 10 –
8. Allard E., “Mémoire sur l’intensité et la portée des phares”, 62-73, Imprimerie
Nationale, Paris (1876).
9. IALA, Recommendations for the calculation of effective intensity of a rhythmic light,
IALA Bulletin, 1981/2, 27 (1981).
10. M. B. Mandler and J. R. Thacker, A Method of Calculating The Effective Intensity of
Multiple-Flick Flashtube Signals, U.S. Coast Guard Publication CG-D-13-86 (1986).
11. H.J. Schmidt-Clausen, The influence of the angular size, adaptation luminance, pulse
shape, and light colour on the Blondel-Rey constant a, The Perception and Appllication
of Flashing Lights, Proc., Intn. Symposium held at Imperial College, London, April
1971, Adam Hilger Ltd, London (1971).
– 11 –
Appendix A. Historical overview of effective intensity
Several different methods were proposed and/or used to calculate effective intensity of
flashing lights. To understand these methods, technical summaries of the important
methods proposed in the past are overviewed in this section.
Allard proposed in 1876 [A1] that the visual sensation i(t) in the eyes for flashing light with
instantaneous intensity I(t) is given by
di(t) I(t) " i(t)
=
dt
a
(A.1)
This differential equation, as depicted in Fig. A.1,
indicates an exponential decay of i(t) with time constant
a, and is solved as a mathematical convolution of I(t)
with a visual impulse function q(t) as given by
i(t) = I(t) *q(t);
1 "t
q(t) = e a
a
(A.2)
The effective intensity Ie is given as the maximum value
of i(t). a (=0.2 s) is the visual time constant (later known
as the Blondel-Rey constant). With q(t) being an
exponential decay function, this convolution can be
achieved electronically by a simple R-C low-pass filter
circuit as shown in Fig. A.2. This method did not prevail
probably due to lack of publicity and difficulty of
calculation in the past.
Figure A.1. Schematic of Allard
method.
R
I(t)
C
i(t)
Figure A.2. R-C filter circuit to
achieve the convolution.
In 1911, based on visual experiments for threshold detection of flashing lights, BlondelRey proposed that the effective intensity Ieff of flashing lights is described by the equation
I eff =
"
t2
t1
I (t)dt
a + (t2 - t1 )
,
(A.3)
where I(t) is the instantaneous luminous intensity of the flash, (t2-t1) is the duration of the
flash, and a is a visual time constant, 0.2 s, known as the Blondel-Rey constant [A.2]. The
numerator of the equation
is the time-integral of I(t), which is given in the unit of cd·s. This
!
equation was developed for rectangular pulses, for achromatic, foveal, and threshold
conditions. It gained wide acceptance, and was confirmed to be accurate for rectangular
pulses by many other studies.
This equation was straightforward for rectangular pulses, but they soon faced a question
as to how t1 and t2 should be determined for non-rectangular pulses rising and diminishing
slowly. Such waveform was common for rotating beacons. Blondel and Rey later proposed
that, for any pulse waveforms, t1 and t2 should be determined in such a way that
Ieff =I(t1)=I(t2)
(A.4)
is satisfied in Eq. (A.3), resulting in an integral equation,
!
t2
t1
( I (t ) " I eff )dt = a I eff .
– 12 –
(A.5)
This equation, as depicted in Fig. A.3, can be solved
only by iterative computation. This must have been a
difficulty until the advent of computers in 1950s.
In 1957, Douglas proved that the condition given in
Eq. (A.5) is achieved when Ieff is maximized [A.3]. He
also proposed that, for a train of pulses as shown in
Fig. A.4, the effective intensity Ieff is determined by
I eff =
"
ta
t1
t2
I (t )dt + " I (t )dt
tb
Figure A.3. Solution for the
Blondel-Rey equation for a
non-rectangular pulse.
(A.6)
a + (t 2 ! t1 )
and I eff = I (t1 ) = I (t 2 )
This formula was accepted in a recommendation in the
USA in 1964 [A.4], referred to as the Blondel-ReyDouglas method. While this method provided a solution
for non-rectangular and multiple pulses, it requires
iterative computation.
The method also requires
measuring the waveform of the pulse and needs a
computer to obtain results, so some disadvantages on
practicality.
Figure A.4. An example of a
train of two pulses for BlodelRay-Douglas solution.
In 1968, Schmidt-Clausen introduced a concept of Form Factor, and proposed a method
that simplified the calculation of effective intensity for non-rectangular pulses [A.5]. The
effective intensity Ieff of a flash pulse I(t) is given by
I max
=
;
a
1+
F "T
Ieff
F=
#
T
0
I(t)dt
(A.7)
I max "T
where F is called Form Factor, and Imax is the maximum
of the instantaneous effective intensity I(t). This
equation can be transformed into a form
I eff =
!
"
T
0
I (t)dt
a + #T
where #T =
"
T
0
I (t)dt
I max
Figure A5. Schematic of the
= F $T
(A.8)
Form Factor method.
which gives an interpretation that this method is an extension of the Blondel-Rey equation
with a new way of determining the duration of the flash. Figure A.5 illustrates the concept
of this method. The effective intensity is determined by the time integral and the
instantaneous maximum of the flash pulse, both of which can be directly measured with a
detector and analog circuitry. For short pulses the measurement of Ieff does not
necessarily require the pulse waveform, which is a practical advantage of this method over
Blondel-Rey-Douglas. Theoretically, the method has a problem with pulses having a very
narrow high peak. The Form Factor method is used in some applications [A.6].
In 1977, the International Association of Lighthouse Authorities (IALA) published a
recommendation [A.7], in which they investigated the three methods (Blondel-ReyDouglas, Form Factor, and Allard) on different waveforms of pulses, and concluded that all
the three methods are recommended, except that only Allard method is recommended for
– 13 –
trains of pulse. For general cases, this IALA recommendation left users to select any of
the three methods, though it was desired that one agreed method be used universally for
all forms of pulses in all applications.
Following the IALA recommendation with lack of experimental data, U.S. Coast Guard
conducted vision experiments in 1986, on detection threshold for a train of short pulses at
different intervals (50 ms to 200 ms) and different number of pulses (1 to 15 pulses) [A.8].
The experimental results revealed that Allard method overestimates the effective intensity
for train of pulses by up to 25 %, which was considered a problem in spite of IALA
recommendation in 1977. This paper proposed an empirical formula to calculate effective
intensity.
In 2002, Ohno and Couzin conducted
computational analyses to compare the
three methods for calculated effective
intensity values for ten different
waveforms of pulses [A.9]. Figure A.6
shows the results for a train of four
pulses at varied intervals. The curve of
relative effective intensity for a train of
pulses, as its interval increases to 1 s,
should merge to the curve for a single
flash. Figure A.6 shows that the Form
Factor curve never merges to the single
flash curve, and the Blondel-ReyDouglas curve goes too low. The Allard
method curve merges to the single flash
curve at around Δt = 2 s (pulse interval
~0.7 s), which seems very reasonable.
Figure A.6. Comparison of the different
methods for a train of four pulses. The
curves show relative effective intensity per J
(cd·s) of a train of pulses as a function of
The Allard method did not indicate any
duration of the train.
problems with other forms of pulses also,
except that it gives effective intensity
values for rectangular pulses higher than Blondel-Rey-Douglas by 20 to 25 % at 0.2 s to
0.5 s pulse widths. This is consistent with the results of the Coast Guard results [A.8]. To
correct this problem of Allard method, Ohno and Couzin [A.9] modified the Allard formula
as
i (t ) = I (t ) * q (t )
a
;t !0
(a + t ) 2
q (t ) = 0 ; t < 0
where q (t ) =
(A.9)
The effective intensity value is determined as the peak value of i(t) . Eq. (A.9) is perfectly
equivalent to the Blondel-Rey equation for rectangular pulses. Note that a similar
modification of Allard method was presented already in 1960 [A.10] and the problem of
Allard method was already addressed then.
!
The results of the 1986 Coat Guard paper were compared with the effective intensity
values calculated by the four methods – Blondel-Rey-Douglas, Form Factor, Allard, and
– 14 –
Modified Allard. One of the results is
shown in Fig. A7, where the pulse interval
is 71 ms (14 Hz), with the number of
pulses being 1,3,5,7,9,11. See Appendix
B for the details of all other results, which
are similar to this. The results of the US
Coast Guard paper for trains of multiple
pulses verified that
• Allard method overestimates the
effective intensity (by up to ~25 %).
• Blondel-Rey-Douglas underestimates
the results (by up to ~25 %).
• Form Factor method overestimates
the results by unacceptable
magnitude.
• Modified Allard results agree most
closely with the experimental results.
Figure A.7. One of the experimental
results in the 1986 US Coast Guard
paper, compared with the results by the
four methods.
Modified Allard method also agreed well
with the experimental data on multiple pulses reported in another reference [A.11].
References
A.1. Allard E., “Mémoire sur l’intensité et la portée des phares”, 62-73, Imprimerie
Nationale, Paris (1876)
A.2. Blondel A. et Rey J., Sur la perception des lumiéres brèves à la limite de leur portée,
Journal de Physique, Vol CLIII, 3 July 1911, p.54
A.3 Douglas, C.A., Computation of the effective intensity of flashing lights, Illuminating
Engineering, N.Y. Vol. LII.No 12 December 1957, pp.641-646
A.4 IES Guide for Calculating the Effective Intensity of Flashing Signal Lights,
Illuminating Engineering, November 1964, pp. 747-753 (1964)
A.5 Schmidt-Clausen, H. J., Über das Wahrnehmen verschiedenartiger Lichtimpulse bei
veränderlichen Umfeldleuchtdichten, Concerning the perception of various light
flashes with varying surrounding luminances, Darmstadt Dissertation D17, Darmstadt
University of Technology, 1968.
A.6 ECE Regulation No. 65, Uniform Provisions Concerning the Approval of Special
warning Lights for Motor Vehicles
A.7 IALA, Recommendations on the determination of the luminous intensity of a marine
aid-to-navigation light, December 1977.
A.8 M. B. Mandler and J. R. Thacker, A Method of Calculating The Effective Intensity of
Multiple-Flick Flashtube Signals, U.S. Coast Guard Publication CG-D-13-86 (1986).
A.9 Y. Ohno and D. Couzin, Modified Allard Method for Effective Intensity of Flashing
Lights, Proc., CIE Symposium’02, Veszprem, Hungary, CIE x025:2003, 23-28
(2003).
A.10 Paper 5-4-8 Vision inertia as applied to the observation of navigation lights, USSR,
Sixth International Technical Conference on Lighthouses and Other Aids to
Navigation, published by U.S. Coast Guard (1960).
– 15 –
A.11 Ikeda & Fujii (1966), Diphasic nature of the visual response as inferred from
the summation index of n flashes, JOSA, vol. 56, no. 8, pp. 1129-113..
– 16 –
Appendix B Analysis of the 1986 U.S. Coast Guard paper
1. Summary of the paper
The paper [B.1] describes the results of comprehensive experiments conducted on
detection of a train of pulses at different intervals and different number of pulses. Figure
B.1 shows an example of pulses (called “signal” in the paper). The interval of each pulses
is expressed by “Flick frequency” [Hz]. Different number of pulses are presented at each
different frequency, and intensity for threshold detection was measured.
Figure B.1. Examples of trains of pulses used in the experiments.
Flash stimulus (signal) was presented as a point source guided with four neighboring
fixation points. Flash source was white “xenon tube”, and computer controlled, and
measured with a calibrated PMT. Duration of each pulse is ~70 µs. The flash intensity was
computer-controlled linked with observer responses to determine the intensity for a ”79%
probability of detection”. Four observers participated in the experiments, and were dark
adapted for at least 20 minutes. See the paper for further details of experimental set up
and conditions.
Table below shows all the flash signal conditions used in the experiment. Flash duration is
the time from the first flick to the last flick.
– 17 –
Threshold is defined as the illuminance of the signal that could be detected 79 % of the
time. Peak illuminance is used as the measure of threshold. The measured threshold
illuminances were normalized as the ratio to that of one flash. The effective intensity is
obtained as reciprocal of the relative threshold illuminance.
The results from the paper are shown in Figure B.2 below. The black dots and lines show
results of this experiment, and white circles are the calculated results for Allard method.
– 18 –
Figure B.2. Results of the experiments, from the paper.
Points made in this paper
• IALA recognized that, of three existing methods (Allard, Schmidt-Clausen, BlondelRey-Douglas), only Allard method is appropriate for multiple-flick flashes (IALA 1977).
However, the accuracy of Allard method was lacking in experimental confirmation.
• Allard method involves lengthy computer calculations of the explicit solutions of a
differential equation and was not practical (This is no longer true).
• From the results of their experiments, it was clear that the Allard method
overestimates the effective intensity of the multiple-flick signals. Allard method is not
recommended. (Ohno predicted the same results in 2002 [B.2].)
• The paper proposes a formula for effective intensity of multiple-flick signals based on
the fitting of the empirical results in Fig. B2.
2. Comparison with the four existing methods
The effective intensities of all the “multiple-flick” pulses used in this paper were calculated
using the four methods (Allard, Blondel-Rey-Douglas, Form Factor, and Modified Allard)
and compared. The figures B.3 show the calculation results.
– 19 –
Figure B.3. Comparison of measured effective intensities (labeled “CG paper”) and
those calculated by the four different methods (Allard, Blondel-Rey-Douglas, Form
Factor, Modified Allard).
– 20 –
It is shown that, the curves of the Coast Guard experiments mostly overlap with the curves
of Modified Allard results (with slight diviiation only in 17 Hz). These results provide good
experimental validation for the Modified Allard method.
It is also shown that calculation by Allard method overestimates (by up to ~25 %, e.g., 20
Hz) and Blondel-Rey method underestimates effective intensity (by up to ~25 %, e.g., 5
Hz), and that Form-Factor method overestimates it by an unacceptable magnitude.
Calculation of Allard (or Modified Allard) method is no longer difficult. Results are given by
the peak value of convolution, which can be programmed easily. Effective intensity meter
can be constructed with fairly simple analog electronic circuit [B.3].
References
B.1. M. B. Mandler and J. R. Thacker, A Method of Calculating The Effective Intensity of
Multiple-Flick Flashtube Signals, U.S. Coast Guard Publication CG-D-13-86 (1986).
B.2. Y. Ohno and D. Couzin, Modified Allard Method for Effective Intensity of Flashing
Lights , Proc. CIE Symposium’02, Veszprem, Hungary, CIE x025:2003, 23-28 (2003).
B.3. Y. Ohno, Physical Measurement of Flashing Lights - Now and Then, Proc. CIE
Symposium '02, Veszprem, Hungary, CIE x025:2003, 31-36 (2003).
– 21 –