LAs IN

4:.

AAA

HOLDS

ES

HR

 

. L ..
. . L .
L
L .. . .
. . L. L . L7.
. L fl.
r . L . . . L
i
. L.. ‘11..
L
. L n V r .
L n.
w L . _ L. .
. . L
. .L . . .
.. . . .
. ... ... L. L. . .
.. .L. L.
... .. .
. L.. L. .L . L
L .. L .
L L.. .
.. . . 7
L .. L L
L. -. . . . . u
.. L L . LLL. .
L ~
I . .n .. .
L . . L L
.L . .
‘ .
.. L L
_ .L
..-o. y.» -_. L
L ..L. .. .L ..

 

L

. . .15....

 

L....rvL..._L.(...oL..

 

.L...L..c.31: ...:..:..L.

 

 
 

u

L..) 1 1.: ::.:;..L ... :3 _L. . 2

 

3.. L.. a r t: 3113.: ti. .11...— r L. .2» >_

  

 

. Fh?
. L .45]. L

88

.Dégt

Thesis-‘ for . :9"

ST

2:. _9L 3 .L.

 

~ :1

.723...

I
Q

. A

MIGHEGAN
BB

.2. . _....

 

..

[ANTS 7

UGLAS HALL:

‘WTLL

9;?

..:: L:

 

I

 

                          

      

    

 

 

 

 

. L
LL .
L
L....
_. .
. .
v: ..
_
.
1
'L .1: . .L.
_ L L. i... .
. ¢ . imamvbvr 3
. 2” .ngun 3.8.x
. . . n1. . . aka... A
L.
. #44,...
. . Writ...”
. . ul‘ (3
. ‘ ...
L L.
0 A.
. _...
u.
.
.
. u
L
.I .L L ¢ fl... V
.(__L . _LL .. 3.7L LL. 3. ._ L..L.... .9... .L..¢.-_...r...L .

 
 

 

$13. .. .Lr .. 1

 

o:::.|.:-.I

 

This is to certify that the

thesis entitled

VISIBILITY T'T"‘_"3:3.'-.KTLDS

TC“
.A. '3.‘

ELASHE G Llsgrs
presented by

Douglas Hall Williams

has been accepted towards fulfillment
of the requirements for

1331.1). degree in 9337610101737

 

 

Mam

Major professor

LW/
“:‘L  . L Ll

 

 

ABSTRACT

VISIBILITY THRESHOLDS FOR FLASHING LIGHTS

BY

Douglas Hall Williams

Absolute foveal thresholds were determined for lights
flashing with pulse lengths of .01, .025, .05, .07, .l, .14,
.2, .4, and 1.6 seconds, and null periods of .025, .05, .l,
.4, and 3.2 seconds. The method of limits was used with
three human subjects. It was concluded that neither the
Blondel-Rey equation nor subsequent modifications of it ade-
quately described the threshold of lights flashing with a
null period of less than approximately one second. A modifi-
cation of the Blondel-Rey equation was offered which de—
scribed the data. It adds only one new term, the null period
of the flashing light. The new equation is

.2n

 

§__= .2 + n + t
E t
o
where

E = Threshold illumination for the flashing light
E0 = Threshold illumination for a steady light
n = Null period
t = Pulse length

This equation can be used for any pulse length or null period,

whether the light appears to flash or not.

VISIBILITY THRESHOLDS FOR FLASHING LIGHTS

BY

Douglas Hall Williams

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Psychology

1971

ACKNOWLEDGMENTS

To my long-suffering committee, and especially my

Chairman, T. M. Allen, thanks are due.

All my friends, professors, and even the
tudes of undergraduates had some part in the
research, even though it may not show on the
only hope is that we are all immortalized in

by the results of it.

ii

faceless multi-
creation of this
surface. My

some small way

PLEASE NOTE:

Some Pages have indistinct
print. Filmed as received.

UNIVERSITY MICROFILMS

 

 

L7

 

TABLE OF CONTENTS

Page

LIST OF TABLES . . . . . . . . . . . . . . . . . . . .
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . vi
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . 1
II. LITERATURE . . . . . . . . . . . . . . . . . . . . 3
III. METHOD . . . . . . . . . . . . . . . . . . . . . . 19
A. FACILITY DESCRIPTION . . . . . . . . . . . . . 19

B. CONTROL EQUIPMENT . . . . . . . . . . . . . . 19

C. STIMULUS GENERATION EQUIPMENT . . . . . . . . 20

D. STIMULUS GENERATION . . . . . . . . . . . . . 20

E. STIMULUS PRESENTATION . . . . . . . . . . . . 22

F. DIMENSIONS AND VISUAL ANGLES . . . . . . . . . 26

G. PULSE PARAMETERS . . . . . . . . . . . . . . . 27

H. RATIONALE FOR SELECTED PULSE PARAMETERS . . . 28

I. PHOTOMETRY . . . . . . . . . . . . . . . . . . 30

J. EXPERIMENTAL DESIGN . . . . . . . . . . . . . 31

IV. PROCEDURE . . . . . . . . . . . . . . . . . . . . 32
V. RESULTS . . . . . . . . . . . . . . . . . . . . . 36
VI. DISCUSSION . . . . . . . . . . . . . . . . . . . . 45

A. ANALYSIS OF VARIANCE RESULTS . . . . . . . . . 45

Subjects . . . . . . . . . . . . . . . . .45
Null Periods . . . . . . . . . . . . . . . 45
Pulse Length . . . . . . . . . . . . . . . 47
Subjects x Null Period Interaction . . . . 47

thH
0

iii

5.
6.
7.
B.
VII. CONCLUSIONS

APPENDIX . . . . .

LIST OF REFERENCES

GRAPHICAL RESULTS.

iv

Subjects x Pulse Length Interaction

Null Period x Pulse Length Interaction
Subjects x Pulse Length x Null Period
Interaction

48
48

48
49

56

57

60

l.

2.

3.

LIST OF TABLES

Visual Angles . . .

Pulse Parameters .

Analysis of Variance

13.

Al
A2

A3

LIST OF FIGURES

Contrast Thresholds, from Clark and Blackwell .
Overview of Relevant Laws . . . . . . . . . . .
Plan of Experimental Room . . . . . . . . . . .
Equipment Block Diagram . . . . . . . . . . .

Detail of Mounting of Glow Tubes and Filters on
Stimulus Board . . . . . . . . . . . . . . . .

Wavelength vs Energy for R-ll3l Tube . . . . .
Dimensions of Stimulus Board (inches) . . . . .

Experimenter Actions . . . . . . . . . . . . .

Results for Subject 1. Average of Two Replications..
Results for Subject 2. Average of Two Replications..

Results for Subject 3. Average of Two Replications..

Grand Average Over all Three Subjects, and Two
Replications. Various Theoretical Curves also
Shown O O O O O O O O O O O O O O O O O O O 0 0

The Curves of the Data from Figure 12, with Curves

Produced by the Williams-Allen Formula Described
in the Text . . . . . . . . . . . . . . . . . .

Calibration Flash Data for Subject 1

Calibration Flash Data for Subject 2

Calibration Flash Data for Subject 3

vi

Page

16
21

21

23
24
24

34

42

53

57
58

59

I. INTRODUCTION

 

Flashing lights have been studied by many investigators
over the years. From these studies have come several useful
laws and rules of thumb concerning the response of the human
visual system to intermittent stimulation. As an upper bound
of this area, Talbot's Law is well accepted as a description
of the behavior of lights above CFF. For flashes with a dura-
tion less than .1 seconds, the Bunsen-Roscoe Law (also called
Bloch's Law when the visual system is being considered as a
whole) is applied. For flashes of longer duration, the
Blondel-Rey equation is commonly accepted. Sometimes Hamp-
ton's modification of Blondel and Rey's equation is used.

For longer flashes, (durations of more than a second or so)
the steady threshold is thought to apply.

Exactly where one of these laws fades into another is not
always clear. Often any differences in predictions between
different equations are small and of no practical signifi~
cance, and any given practical question can often be answered
by a quick experiment. But it is of great importance to
engineers designing visual warning systems to know what the
response of the human element of the system will be. It
would be much easier to specify with a single relation than
with a collection of laws and equations, each with an ill-

‘ defined range of applicability.

2

The purpose of this paper will be to review the litera-
ture concerned with the derivation and practical application
of these several laws. Other experiments which tend to show
the inadequacy of all these laws in certain areas will be
reviewed. Finally, data will be collected over the whole
range and a model will be offered which should be of some use

to engineers designing flashing light systems.

II . LITERATURE

 

The primary orientation of this paper will be to derive
a relation which would be useful in an applied setting. How-
ever, in order to do this most efficiently, it is necessary
to examine the theoretical foundations of the laws which are
currently used.

Bloch's Law applies to flashes with a duration less than
.1 seconds. For such flashes, it has been found that
I x t = Constant. For longer flashes, the law necessarily
breaks down, since a long flash has the same visibility as a
steady light. One of the most commonly used formulations is
that of Blondel and Rey. In 1912, it was of importance to
know something about the human eye so that an optimum flash
duration and intensity could be selected for lighthouse
flashes. Blondel and Rey's approach was to determine the
brightness of a flashing light which would appear as bright
as a steady light of known intensity. Subjects adjusted the
single test flash to apparent equality with a long control
flash of known candle power. In this way, the relative visi-
bility of the stimuli could be determined. Three seconds
were left between presentations of test flashes, as Blondel
and Rey assumed that this would allow any effects of one
flash to die out before the next was presented. They found
that their data were described by an equation which they

wrote :

 

E___ a + t
E ’ t
o
where

E = Threshold illumination for a flashing light
E0 = Threshold illumination for a steady light
t = Length of the flash, in seconds
a = an empirical constant, .21

Several studies have been done since 1912 which have
usually more or less supported Blondel and Rey's findings.

In 1938, Neeland, Laufer and Schaub set up airway beacons on
buildings 8.3 and 2.9 miles from observers. The observers
matched the apparent intensity of the flashing beacons with
an adjustable steady light from a remote projector. Despite
several methodological difficulties, they obtained fair
agreement with the Blondel-Rey equation.

In lighthouse use, interest is in comparison of signals
somewhat above threshold, when the signal has "adequate" con-
spicuity. Toulmin-Smith and Green (1933) used a device simi-
lar to Blondel and Rey's to derive an equation for luminances
greater than those used by them. Single pulses of different
lengths (.05 to .5 seconds) with one second between succes-

sive flashes were used. The data were described by the

equation
E§_= 1.1 t
I .15 + t
where
t = duration of the flash (seconds)
I = Intensity of a steady light for threshold
Ie = Intensity of a flashing light for threshold

("apparent intensity")

5

This equation gives a ratio of the intensity of a flash—
ing light to that of a steady light of equal visibility.
Such an equation is in inverse form to that of Blondel and
Rey, who gave the ratio of thresholds. This form is slightly
more convenient to use.

Hampton, in 1934, objected to Toulmin-Smith and Green's
formulation on the grounds that their equation led to the
prediction that for very long flashes, the flashing light
would appear brighter than the steady light. Using.their
data, he derived an equation which was of the same form as
Blondel and Rey's, but with an additional parameter, Ec'
This was defined as the "minimum illumination required for
adequate conspicuity." His equation fit their data as well

as their formula had.

H

 

.2-
I

 

where

Apparent intensity

Intensity for threshold of a steady light
time of flash, in seconds
Conspicuity

Wt+k4 H
II II II

c
Note that except for the inversion due to statement in
terms of equivalent intensities, his equation is that of

Blondel and Rey with their constant "a" replaced by

0255 ’81 . .
(' E ) . Ec could be set at any value of conspicuity the

C

 

user felt was necessary for his application. Using a value

for "useful" brightness of EC = .425, his equation reduces to
t
+

Hampton's paper seems to be nearly the last word for this
kind of study. One can find papers and practical applica-
tions using these equations and the value of .l to .2 for the
constant "a" right up until the present day. (Projector,
1957; Douglas, 1957).

With a very different application in mind, A series of
widely quoted studies was performed by Gerathewohl (1951,
1952, 1953, 1954). He was interested in the conspicuity of
supra-threshold flashing lights, similar to what would be
encountered on a radarscope or control panel. His method
consisted of placing a subject in front of a lighted screen
on which were flashed signals of different luminances, colors,
flash rates, and positions. The subject also had an auditory
task. He responded to both tasks using footpedals and levers.
The dependent variable in all studies was reaction time. He
found that the response time decreased with increasing con-
trast, increasing flash frequency, and longer flash duration.
His recommendation was that the most conspicuous signal would
be three flashes per second when the signal was at least
twice as bright as the background (1954).

However, in two similar studies, Dean (1962) was unable
to duplicate these results with similar reaction time data.

He hypothesized that flash rate might not be a determinant

of signal conspicuity when apparent brightness had been
adjusted by the Blondel-Rey formulas.

Gerathewohl's method suffered from problems reviewed in
detail in Williams (1966). These problems included use of
a cumulative clock, so that missed stimuli resulted in 15
seconds being added to the total reaction time, and failure
to correct the stimulus brightnesses by using the Blondel-Rey
equation. In general, the studies may provide data of some
use in specific situations similar to those of the study,
when reaction time is of importance; but the failure of Dean
(1966) to replicate Gerathewohl's results make even this
somewhat doubtful. Where reaction time can be definitely
correlated with some variable of interest, methods similar to
Gerathewohl's could be used; but even then, only the rankings
of the various stimuli would be dependable, since it is al-
most certain that in a situation where more stimuli were
available, or more distractions entered in, the reaction
times themselves would change radically. Also, Gerathewohl
was using supra-threshold stimuli, which made sense given the
applications (radarscopes and panels) to which he was putting
the data. One should, however, exercise caution in applying
these results to the threshold situation.

In 1959, Clark and Blackwell studied thresholds of single
and double pulses in the fovea. They used a temporal forced-
choice procedure, with seven observers. Data on contrast

thresholds were plotted on log-log axes, as shown in Figure l.

I11

 

‘ A

 

inure 1.

' I
-2 -1
LOG DURATIC“ (SE

Contrast thresholds,
Blackvell, (195"?) ,

U)

CCFJD

from

)

Clark

and

Curves were fit by eye, and no mathematical relation
was derived to describe them; but an interesting result is
clear; between about .2 and about .075 seconds, a short pla-
teau appears. This is a consistent finding for all back-
ground luminances. The break on this kind of plot from a
downward-sloping line to a horizontal one is well—known and
accepted and in fact a pulse length of .1 seconds is known as
being of "critical duration" due to this effect; (Long, 1951)
but the "bump" had not been found before.

In explanation for the failunaof other investigators to
find such a discontinuity, Clark and Blackwell point out that
few other investigators took as many points in the region in
question, nor as reliable ones (250-1000 observations per
point). So there is little question that the plateau is a
real effect. Unfortunately it is not easily explained.

Clark and Blackwell do not consider it too important, ex-
plaining that
“The interval of approximately .1 second

appears to be a critical one for the visual

system; it corresponds to the frequency of the

alpha waves over the visual cortex and to the

light frequency which produces a number of

unusual visual effects . . . " (Clark and

Blackwell, p. 2)
And it is, in fact, a very small effect, amounting to a frac-
tion of a log contrast unit. For the purposes of practical
application, we would be happy with predictions as accurate
as a smooth curve ignoring this "bump."

Schmidt-Clausen (1967) exhaustively investigated the

effects of five variables on the foveal threshold of short

10

photic pulses. The variables were color, visual angle, back-
ground luminance, pulse shape, and exposure time. A total
of more than 30,000 individual measurements were made on two
subjects, and the data were extensively plotted and analyzed.
Schmidt-Clausen compares all his variables with the func-
tion Lu = f(t), where Lu = threshold luminance and t = length
of flash. For example, the results for different pulse shapes
are presented as a family of curves of Lu = f(t), one for each
pulse shape. Often, the Blondel-Rey relation is plotted on
the same graph for comparison. Often also, in the text, a
calculation of the "constant" a_in the Blondel-Rey equation
is presented. It turns out not to be very constant; in fact
it varies from .1 to 1.45 seconds as a function of background
luminance, visual angle, pulse shape, and color.
Schmidt-Clausen's procedure was to present single short
flashes foveally, apparently using the method of adjustment
(though the exact procedure in regard to the responses is not
stated). His flashes were a minimum of five seconds apart,
(somewhat longer than the three seconds used by Blondel and
Rey) and were apparently presented at the experimenters' con-
venience, without S knowing one was coming. There seems to
be little or no effect due to the procedural differences,
since in cases which are most similar to Blondel and Rey's
experiment, nearly exact agreement is obtained with their
equations. Schmidt-Clausen shows that the shape of the
Blondel-Rey curves changes very little over all the variables

investigated, except for color; he expressed his results in

ll

terms of a modification of the equation

Ls _ f(d)+t

Ls0° t
where

Ls = Threshold luminance

st = Threshold luminance for a long pulse
f(a) for the pulse shapes, surround luminance, and visual
angle were given in the report. Note that here again, the
equation is of the same form as that of Blondel and Rey.

It should be pointed out that the graphs he presents do
not seem to have been derived from a mathematical curve fit
of the data, although he doesn't say. Rather it appears that
the shape was derived from the Blondel Rey equation, and the
constant "a" varied, or the curves raised and lowered to
provide a fit.

The discontinuity which Clark and Blackwell (1959) found
with similar presentations of single flashes does not show in
any of Schmidt-Clausen's graphs. He was apparently not aware
of the findings of Clark and Blackwell, and even though he
plots several data points well within the region in which one
would expect to find the irregularity, no such effects can be
seen in the graphs which he presents. However, the graphs
are a little difficult to read in the region in question, and
it is possible that the very small effect could be obscured.

In general, Schmidt-Clausen's results seem to support,
with some modifications, the results of Blondel and Rey, and

Bloch. The effects of the wave-shape, color, background

12

luminance, and visual angle can be calculated using formulas
developed by Schmidt-Clausen. However, the caution which
applies to use of the Blondel-Rey equation applies to his
study also: it was based on single flashes, several seconds
apart. It is clear that flashes, even if not perceived, can
affect the threshold of subsequent flashes (Clark, 1959).

In common with the other studies reviewed so far, null
period (or frequency) is not considered. One cannot expect
one study to consider all possible variables; but it should
be pointed out that all of Schmidt-Clausen's results might be
changed if a train of pulses were studied, instead of the
single pulses.

One other law deals with intermittent photic stimulation
and needs to be discussed here. It does not, however, deal
with discriminable flashes. Talbot's Law applies only to
lights which are intermittent, but appear fused to a contin-
uous light. Ideally, any mathematical relation which deals
with intermittent photic pulses should reduce to Talbot's
Law above fusion.

Graham (1965) states the Talbot Law as
t

_1
Lm—EIOLdt

where

Lm = the luminance of a steady light which matches
the time-varying luminance

L = the instantaneous luminance of the time-varying
field

t = the period of a single cycle of the varying field

13

For the case of square pulses, which is what the Blondel—
Rey and Bloch laws deal with, we may express the Talbot Law

as

where

Equivalent intensity

Intensity of the pulse
Pulse length
d - Null period

rrd'HH
p rh m
II

Notice that the null period of the pulse is a necessary
factor in Talbot's Law. None of the previously mentioned
laws have taken null period of the pulse into account. Hence,
using any of these other laws, one would calculate that a
train of .1 second pulses with .05 seconds of null period
between them would be exactly as visible as a train of .1
second pulses of the same luminance with 1 second of null
period between them. But if null period enters into determi-
nations of the threshold above CFF, as Talbot's Law states it
must, it is reasonable to think that it might enter in, to
some degree, below CFF.

All the formulas reviewed, again excepting Talbot's Law,
which would currently be applied to a continuous light with a
null period of, say, .1 second duration every second would
predict that it would be seen at exactly the same luminance
as a continuous flash. As far as the author can determine,

no studies have been done on the threshold of this sort of

14

pulse. It is certainly an area worthy of investigation, if

for no other reason than to validate any mathematical gener-
alizations over the entire range of possible pulse-length—-

null period variations.

As was noted above, all the equations describing inter-
mittent photic pulses, except Talbot's Law, fail to take into
account the dark time of the pulse. Dark time is almost
certainly an important variable which needs to be incorporated
into an equation relating pulse characteristics and thresh—
old. One of the major drawbacks seems to be lack of an
adequate way of representing data taken at different fre-
quencies. If one assumes frequency is an important variable,
one must draw a separate graph for each frequency, and the
result quickly becomes confusing (Erdmann, 1962). Hence,
null period or frequency of the flashes tends to be ignored,
and graphs are presented (Grahan, 1965; Schmidt-Clausen,
1967) showing threshold plotted against length of pulse, re-
gardless of the time between pulses.

Distinction should be made here between several experi-
mental procedures which are used. One can hold null period
constant, and vary pulse length. This yields data for
various pulse lengths of approximately the same frequency.
(For exactly the same frequency, the null period would need
to be varied so that pulse length + null period = constant.)
Here, both pulse length and null period vary; but a pulse
length-null period plot is typically not used. One can also

study various dependent variables. The present study, like

15

many others, will study absolute thresholds (no background
luminance). It is possible to do a similar study using a
comparison flash which is varied to appear the same as the
test flash. Or, the luminances may all be held constant and
the frequency necessary for fusion of the flashing light may
be studied. Which of these is chosen depends upon the
purpose for which the study is being done.

This paper will not be the last word in any of these
areas. However, a way of looking at all the threshold stud-
ies simultaneously will be offered. When such laws as
Bloch's, Talbot's, and the Blondel-Rey relation are all seen
to be related and flow into one another, the necessity for
more studies of for different studies can be quickly seen.
Also, the border between the predictions of two equations can
be seen, and often this is an area on which a great deal of
effort should be spent, since the rates of change of the
threshold function are higher here.

Figure 2 is a representation which is a partial solution
to problems of plotting these equations. It is a plot with
null period on a log scale on one axis, and log pulse length
on the other axis. Note that for certain combinations of

light and dark time (near the origin) Talbot's Law will apply,

light time

and threshold Will be a function of dark time

. The exact

 

point where Talbot's Law ceases being applicable is not
easily discovered from the literature. The Ferry-Porter Law
(Garham, 1965) can be used to estimate CFF but according to

Graham, applying that law at threshold luminance is suspect.

16

$44 9

BLCC‘LI' S L.".' 1'

1.0 .

.\\'\\\\

 
     
     
 

O \ o o 0
. .. O . . . 0 o . I o .. . ‘ a. . ..o o.
. . . . o . . . O Q . . . 0. . 0.... ..
f" o . ° 0 ° . 0 O . . .0
g3) . O. . . . O .0. O .0. .. . O .... . ...C
a
:13. . . .. O . .. . . O. :Q‘..... .. -
\J o ' o O . . . . . I .' z
13 ‘ °. ‘ . . , ° . ' - o
('14 .‘o . ' ° ' 0 . '0. ' ' H
C’) .1. . o . . . . ... . . o o I. : .. [—4
a
V o . . . . o . . .. . ¢
q CFF , -. .-.-. - g
L: BOUNDARY - . . - .1. G
M ’3ED BY FERRY- . - t2
{1" _- - ‘ ‘0 <3
a. .“HRT31 LAn - 0
H
#3 H
:3 H

"C?

o
O
|-‘

 

       

O

BLL'V‘iD‘SL- 3‘. BY

1‘ 3‘

141;“; r J

FLAT REGIC”.

FLASTTIT‘TG

LIT-1T

TRRESWQLD EQUALS
STEADY LIGHT

Vfiv-‘-
h'l'
_.Iss

FizurC Z. CvcrvifW of relfvnnt laws.
arcs indicates unfnovn roclons.

WC "1." -.-.
L..)' \LU o

S tinnl 0d

17

As dark time increases so that the intermittency is below
CFF, Bloch's Law is said to hold. This would imply that the
entire surface below a pulse length of .1 seconds (critical
duration) is a plane, sloping upward from a minimum thresh-
old at .1 seconds pulse length. Blondel and Rey's equation
would substitute a slight curve for the flashes near .1
second, and raise the level of the plane slightly, the
greatest difference occurring for the slower flashes.

Both Blondel and Rey and Bloch neglect to mention null
period. One could either assume that their derived relations
apply for only the null periods they used in their experi—
ments, or that they apply for any null period. The latter
assumption is commonly made.

Above a certain length of flash (which is not too clearly
defined), the steady threshold is said to apply to intermit-
tent sources. Data here are rather sparse. "Flashing light"
studies are usually motivated by some applied problem (such
as lighthouses or roadway flashers) and usually no one is
able to provide the large amounts of energy that such a long
flash requires in a practical field flasher. Hence, almost
no research is done on flashes of lengths greater than one
second, and the author knows of no research whatsoever on the
threshold of flashes with long pulse lengths and short null
periods. A threshold value the same as for a steady source,
or higher, would not be surprising. If it were lower, none

of the present equations would handle it.

18

The purpose of the present study was to investigate the
entire range of flash length and null periods between them.
For simplicity, absolute foveal thresholds of white square-

wave pulses were obtained in a completely dark room.

III. METHOD

A. FACILITY DESCRIPTION

The experiment was run in the MSU psychology research
building in a room 40 feet long by 8 feet wide. The walls
and floor were black, as was the ceiling, except for light
fixtures inset into it and covered with white plastic. The
room was totally light-tight, it being impossible for the
experimenter to see any stray light after one hour dark
adaptation.

At one end of the room was the stimulus board (described
in detail later). Twenty feet from the stimulus board, the
S sat in an ordinary chair. Ss were free to move around in
the chair and shift their bodies but were asked to fixate the
red fixation light during experimental trials. Any failure
on their part to do so resulted in a rather drastic drop in

thresholds, and any such trials were discarded.

B. CONTROL EQUIPMENT

Behind the S, and separated from him by a flat black
plywood partition was the control and monitoring equipment.
This consisted of a console from which the light time, dark
time, and brightness of the light pulses could be controlled.
Two power supplies (low and high voltage) were incorporated
in the console, along with a dim red panel illumination and
a writing surface. An oscilloscope provided a means of

monitoring the outgoing pulses to the glow tube. The

19

20
overhead illumination could be controlled from a wall switch

near the console. (See Figure 3 for a plan of the room.)

C. STIMULUS GENERATION EQUIPMENT

Figure 4 is a system block diagram of the stimulus gener—
ation system. The duration of the pulses and null periods
provided to the glow tubes could be regulated by means of a
specially-constructed solid-state pulse generator. The two
variables could be set independently on two lO-turn potentio-
meters, which had been calibrated using the calibrated sweep
of a Tektronix oscilloscope. Null periods from less than .01
seconds to more than three seconds, and pulse lengths from
less than .01 to more than three seconds could be obtained.

A special setting resulted in a continuous pulse.

D. STIMULUS GENERATION

A control for the brightness of the stimulii was provided
on the control console. The control was accomplished by de-
creasing the current fed to the glow-tubes, by changing the
bias on a tube in the constant current circuit. The poten-
tiometer shaft was geared to a mechanical counter so that a
given position of the control could be read precisely. All
data were recorded in terms of the arbitrary numbers, and
converted to photometric units later. This brightness control
was only used for the slight adjustments in brightness neces-
sary to apply the limits method to determining the thresholds.
Primary reduction of the high light output of the glow-tubes

was provided by a set of neutral density filters, a diaphragm,

21

 

A.

Stimulus board Bafflc
Raffle Subject

 

 

 

 

 

Control console ‘/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fizure 3. Plan of synerimontal room.
PUISG length LUIL periOd Brifihtness
control control control
L ' J 3 GI, ow
‘ 7 tubes
Pulse; Glow tube #3
generator fl . . .
river Circuit C3
1 1.“ Constant, Cscilloscone
2 volt DC voltaze monitor
power supply sunnLv

 

 

 

I

Ficurc 4. Louinmant block diacrnm.

22

and an Opaque plastic diffusion screen. (See Figure 5.)
Glow tubes were Sylvania R-ll3l-C units, with a spectral
distribution of output shown in Figure 6. Rise time and fall
times of these units is negligible--in the fractions of a
microsecond range.

Light output values for the stimuli were obtained using
a Prichard spectra photometer. Each of the four aperatures
were calibrated for the full range of the brightness control.
Each of the aperatures differed in the brightness range it
covered, so that a large range of brightnesses could be
presented without disturbing the stimulus board to change
filters. As near as was possible, the filters were set So
that the dimmest panel control positions for the brightest
aperature was nearly equal to the brightest panel control
position for the second brightest aperature; etc. When pulse-
length-null period combinations were found for which thresh-
olds could not be determined with any of the four available
aperatures, a note was made and when enough of these accumu-
lated, a filter change was made to bring one of the stimuli

to a point where a threshold could be taken.

E. STIMULUS PRESENTATION
The stimulus board and associated components had to
accomplish several objectives:
1) presentation of the stimuli at constant locations
2) provision for some method of keeping the S's point

of regard at a constant position when no stimulus was present.

23

 

 

 

 

 

 

 

 

 

 

 

1.... _(. rm. L. CL Tx .. C. v... C _ Wm... L. (H... o _. (y (1.)» . .. vi. 3.

u:LC~L toéhfZZEt CHUumgm

f(fLLm
wrwmswewa

 

 

 

oju mamna

f

mL(uawm

(C(LLU OCH

CLQC£

 

 

 

 

 

uzwmwo

ESSquU

 

 

 

 

I“.

7.. a

7 r .
" ‘)
1'

r 3“ ‘
[.
bx (-1 5
1;:
; 14.”) ‘
l .* ‘
T v
40")"11 11.11.? :2]. 7211')
:i 1. "V“L’i ' T. ”1“” "a“ 11, ~_
L .1
f 2"— ’1
L .1 "-"I .
A- ’;
3 /‘-
11"
f n 3 a
'l -+
:l 1: II
" I
'I II
' l
’1?
71:.
LELH C)_1

 

24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T‘x- ~ 4". -..
7 . grlj‘Tflt".')L_>'L\) 9

mln?

~11. . 1
13.)..15

25

This would also help prevent empty-field myopia.

3) elimination of all glare from shiny objects between
the S and the stimulus.

4) prevention of all stray light from the back and
sides of the glow tubes from reaching the S's eye.

In order to accomplish 1), four glow tubes were mounted
on the stimulus board three inches from the central fixation
light, as shown in Figure 7. Each glow tube and filter set
was mounted on a rail and could be adjusted so as to line up
the light beam from the tube with the aperture in the board.
(See Figure 5.) The stimulus board was mounted two feet off
the floor on two adjustable stands, painted flat black.

Condition 2) was provided for by a dim red fixation
light. It was mounted in the center of the board. The light
was an NEéz neon bulb operated from the llO-volt supply thru
a lOO-Kohm resistor. The bulb was pushed into a l/4-inch
hole, and covered with a hemispherical red plastic filter.

3) was accomplished by removing all possible items which
could reflect light, and thereby confuse the S. Some non-
removable features of the room were found to reflect, and
these were treated in various ways: metal fixtures in the
floor were painted flat black; shelves along the side of the
room were covered with black matte paper. A baffle 18 inches
high was placed on the floor approximately five feet in front
of the stimulus board to prevent reflections from the black

vinyl floor.

26

4) was eliminated as a problem by enclosing the back and
sides of the stimulus board in wood and covering the cradks
with black tape; in addition, each glow tube was enclosed in
a black cardboard tube. In this way, the light generated by
each tube could be kept within the area directly behind the

individual stimulus aperature.

F. DIMENSIONS AND VISUAL ANGLES

Table 1 gives the calculated visual angles at the Ss eye
of various important features. The dimensions of interest
are the size of the stimulus aperature and the distance of

the stimulus from the fixation point.

TABLE 1

VISUAL ANGLES

 

Item Calculated Visual Angle

 

Fixation light . . . . . . . . . 4'
Fixation light to any

stimulus light . . . . . . . . 45'
Stimulus aperatures:
TOp . . . . . . . . . . . 2'
Bottom . . . . . . . . . 2-1/2'
Left . . . . . . . . . . . 3-1/2'
Right . . . . . . . . . . 3'

 

The other critical dimension is the distance between the
fixation light and any stimulus light. Subjects would pre-
sumably have the fixation light centrally fixated during

trials when the stimulus was dimmer than threshold; it is

27

therefore necessary that the stimuli be on the fovea during
this time. It is generally accepted that the fovea is 2° in
extent, with the central fovea being half this size or less
(Graham, 1965). In any case, the 45' used in the present
study between the fixation light and any stimulus assures
foveal thresholds. After a stimulus was defected on descent-
ing trials, it would of course be centrally fixated by the S,

as he was instructed to do so.

G. PULSE PARAMETERS

The number of thresholds needed in any area of the pulse
length-null period threshold curve varied according to the
expected rate-of-change of shape of the surface in that
area. For instance, for very long flashes, there is little
difference in thresholds for flashes of 1.0 seconds duration
and flashes of 1.2 seconds duration. Hence, thresholds could
be spaced widely apart and still reflect an accurate picture
of the surface. For shorter flashes, say, durations of
around .1 seconds, a much smaller change in the length of the
pulse duration (or null period) has a great effect on the
threshold. Here, thresholds were spaced as closely together
as necessary until an accurate picture of the surface could
be obtained. The pulse durations and null periods used are

shown in Table 2.

28

TABLE 2

PULSE PARAMETERS

 

 

Pulse Length (Seconds) Null Period (Seconds)

.01 .025
.025 .05
.05 .l
.07 .4
.l 3.2
.14
.2
.4

1.6

 

H. RATIONALE FOR SELECTED PULSE PARAMETERS

The values of the light pulse and null period duration
were selected carefully to maximize information obtained from
each combination. Each pulse length was paired with each
null period, giving a total of 45 data points on the surface.
The reasons for selecting each combination are given below.

1. Light pulses .01, .025 and .05; null period .025 and
.05 seconds.

 

These combinations give a stimulus which is above CFF
or is nearly so. In other words, the sensation is that of a
continuous light. For these stimuli, Talbot's Law should
predict the brightness necessary for threshold. They are
included so that the position of the part of the surface rep-

resenting Talbot's Law may be plotted. The threshold for

29

these points should be higher than the steady threshold by
an amount proportional to the PCP.
2. Light pulse of .07 thru .4 seconds, all null periods.

These were included as an investigation of the
"bump" shown by Clark and Blackwell. Their study used "long"
null periods, and the series of points at a null period of
3.2 seconds serves as a partial replication of their experi-
ment. However, the shorter null periods were also run with
these critical light pulse lengths to see what the behavior
of the "bump" is over different frequencies.

3. Pulse length of 1.6 seconds, all nu11_periods.

This series was included because a pulse of that
length can be effectively a steady light. Most null periods
have little or no effect on the threshold when the light pulse
is this long, so these five points can all be considered as
checks on each other. It is extremely important that the
steady threshold be accurately determined since the calcula-
tion of the theoretical points in the Talbot's Law and
Bloch's Law region depend on the determination of the steady
threshold and since the actual thresholds are compared with
these calculated values. Hence, it is felt that including
five points with the expectation that the thresholds will be
nearly the same for all of them is not excessive.

4. Pulse length of less than .1 seconds and null period
of .l or longer.

 

 

This group was included to verify and locate the

Bloch's Law region. As with the Talbot's Law region, the

30
theoretical points in this area can be calculated from the
steady threshold. However, it is worthwhile checking Bloch's
Law over several short null periods, since it was derived for
long null periods only.

The spacing of the points on the surface was also chosen
carefully. A previous study (Williams, 1966) used frequency
and PCF as parameters of the flashes. On a logarithmic null
period-pulse length plot this resulted in the data points
being arranged in concentric arcs, and made the results dif-
ficult to interpret. For the present study, the points were
purposely picked in terms of pulse length and null period.

In addition, they were spaced in terms of a standard interval
on the log scale. This interval is equal to the distance
between .1 and .14 seconds. Starting with .025 seconds, the
distance to .05 is 2 units; from .05 to .07 is one unit; from
.1 to .14 is of course one unit; etc. This scheme allows
several computational simplifications on the computer, and

makes plotting results easier.

I . PHOTOMETRY

All brightness readings were taken with a Prichard
Spectra-Photometer model 1970 Number 299. It was calibrated
in terms of footcandles by use of an N.B.S. calibrated
standard lamp. All readings were taken 10 feet from the
stimulus board, in line with the subject's eye. The glow
tubes were set for a long pulse length and the average of

several flashes taken as the brightness of the stimulus.

31

J. EXPERIMENTAL DESIGN

The experiment was set up as a 9 by 5 factorial design,
with two replications. Each of the nine pulse lengths was
ordered randomly within each of the five null periods, and
the null periods were ordered randomly within a replication.
Randomization was accomplished by writing each of the five
null periods on a card and each of the nine pulse periods
on another set of cards. Each day, before the subject came
in, one card was drawn (without replacement) from the "null
period" deck. The number on the card drawn determined the
null period for that day. The "pulse length" deck was then
shuffled, and the order of the cards recorded on the data
sheets. To guide the experimenter, and eliminate errors made
in the dark, the dial settings for the pulse generator were
also written on the data sheet at this time.

Each session consisted, then, of nine pulse lengths
paired with one null period. Ten thresholds were taken for
each pulse length-null period combination, for each replica-
tion. A total of three replications were performed, but the
data of the first was not used, in order to allow practice
and learning effects to subside. The data points, then, are

based on twenty thresholds, ten taken on each of two occasions.

IV. PROCEDURE

 

Subjects were paid to participate. They were referred
to the experimenter by a student work-study office, and their
inclusion in the experiment was contingent on their passing
the eye test and being willing to participate in the experi-
ment for its full duration.

Each subject was checked for visual acuity with a pro-
jected acuity chart, to assure they had 20:20 vision, or had
been corrected to that standard.

Subjects were given a practice session of one or two
hours duration which included the eye test, administrative
details, and a brief explanation of the purpose of the ex—
periment. After a short period of dark adaptation, thresh-
olds for two or three different points were taken. These
thresholds gave the subject an idea of the nature of the
experiment and allowed any practice effects to dissipate.
After this session, the subject was asked if he was still
interested in participating, and if so, an appointment was
made for another session. The threshold data from the prac-
tice session was not used.

Sessions after the practice session were a minimum of two
hours in duration. This included approximately 15 minutes for
dark adaption. A session shorter than two hours was felt to
be inefficient due to the necessity for dark adaptation;

times longer than 2-1/2 - 3 hours were found in a pilot study

to be fatiguing to the subject.
32

33

An attempt was made to schedule the majority of the ses-
sions at night so as to minimize effects of walking into the
experiment directly from bright sunlight. Occasionally day-
time sessions had to be scheduled, and in these cases 85 were
asked to wear dark glasses when outside, before the session.

Each session was sprinkled with rest periods at the dis-
cretion of the E or 8. During a rest period a subject could
stretch, move around, or close his eyes, as desired. He was
not allowed to leave the room, smoke, or drink coffee or soda.

After a subject was dark adapted and had fixated the red
light and stated his readiness to proceed, a stimulus was
presented. Since the experimenter had little or no idea where
the threshold would be for a particular combination of pulse
length and null period, a guess was made as to which apera-
ture should be used. Then the experimenter operated accord-
ing to the flow chart shown in Figure 8.

A typical smooth-running sequence would consist of pick-

ing the correct aperature, then:

E: "Starting bright" (turns stimulus light on, and slowly
starts decreasing its brightness).

S: "I don't see it.“

E: (Writes number corresponding to position of brightness

control, resets know to a low value, then says. . . .)
"Starting dim."

S: "I see it."

E: (Writes number, resets brightness knob to some high value,
then says. . . .)
"Starting bright."

The exchange would continue until 10 thresholds (a thresh-

old is one ascending and descending pair) had been done. Then

34

 

]

1 8 IA r

 

 

 

P‘—

l

v

q. H " “fy"' T‘
‘.).‘1 1. 1.1:»

TZJ".I "‘..T n tracts
.‘J _ I- L .-

. ‘ I.-. ‘o-or‘r”!
S‘s]? ’.3.~..I':*".L '
11 CAL"? 171””?
‘5‘ .-_‘ u." (i '., .:~-:.

 

 

I PRES “‘7'? STIT'ULUS

L S [‘ITJUL US

8

4

“FT

'6

 

 

 

 

 

 

 

u')
“I,
H Pd
U)

P:

*l ..
-1

Ox)

 

T N Y ”’9

14‘ »-,.-...T ‘F
IE. .- 7“. ,.~..I.¢_,.J.:.

Cu‘ifi’L 7331)? ’33:;le POSITION O: Rigs.

-.\

 

 

 

     

Y vs

8‘ FE "“~T“l".“€'g‘.‘ ‘3 7. 1‘s.
. A. O? I. n
S\ 3’ f" If TI 37,-“ 3‘? Y E. 3‘-

 

 

 

 

 

 

(w

 

 

 

 

 

 

 

 

 

 

 

 

"I "‘7“
1411..
F ‘- 117‘: "
..TI 1.x:
"‘fi-‘I‘ \\ “95“.“
wr '. Lt '
til-p
m c ”ELI 2“?
K32: \ P‘F “AI-‘1‘ '1'
PW." “I:
H"
Y 1.
ALT
7;;3?

 

 

35

a rest period would be called while E set a new pulse-
length--null period combination on the console.

Each of the three replications included 10 thresholds for
each pulse length-null period combination. The first entire
replication was completed but not used in the data analysis,
in order to allow practice and learning effects to subside.

In case a brighter or dimmer aperature was needed than
was available on the stimulus board, the threshold determina-
tion for that data point was postponed until a filter change
could be made. Photometric readings were taken after each
such change, and at bi-weekly intervals throughout the
experiment.

Data sheets were specially prepared, listing the date,
time, subject, and other pertinent data. Above each column
of data was the pulse length and null period which was being
used, along with the appropriate control settings.

When all thresholds for one combination for one subject
had been completed, the data sheet was taken to the Olivetti-
Underwood Programa desk computer and the means and standard
deviations were calculated. Any data which had an unusually

high variance were re-determined at the next session.

V. RESULTS

The major results are shown in Figures 9, 10, and 11.
Each graph is the data for one subject. The two replica-
tions for each subject have been averaged. Figure 12 is a
graph of the same results averaged over both replications and
all three subjects.

In all of these graphs, the amount of illumination at the
subject's eye is plotted on the vertical axis and the pulse
length in seconds is plotted on the horizontal axis. The
curves are identified by different kinds of lines with longer
dashes for longer null periods. Each graph has five curves,
one for each null period. Figures 9 - 11 are presented to
show how the subjects differed; most of the discussion will
center around the over-all average graph, Figure 12. In gen-
eral, the perturbations and deviations from the expected
curves which are found in the individual subject graphs dis-
appear when they are averaged together. This is to be ex-
pected, for the laws which the curves are being compared to
(Talbot's, Bloch's, etc.) are derived based on averages of
large numbers of thresholds. No individual subject in only
20 thresholds could be expected to conform exactly to these
laws.

In the Appendix, one graph for each subject will be found
which shows how this threshold for the calibration standard

flash varies from day to day. The dotted curves are for the

36

subject's eye

at the

-8

10

‘f
:1.

footcandles

Thrc shol d ,

100

LA
13

43

N
O

(EDI—4
ON O

@000

37

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

"’ULL ”27.11115
3.7
ll - — - —
.1. _—
\ '.1 — n — — — — _
nq-- -- - - - - ---
t\ \ o ..
.OQCCIOOCOUCOOIODOO.....
\ \
:7 X *>: \
‘ ~
I ‘ \ '\‘§;
L‘ 3' =
\
Ca. ~ \ V:
x \ '\
‘3. \ \
2‘. \k \
‘ W.
.0. “ ~ \
Q. .\ \
I. ‘
...'0 Q
:~~ \
a ‘1..‘:0:0‘0000“ ooooooo-ol cocoa-cocoa... '
/ "‘" ’4‘ "I - -~ -~—-v -‘ —<‘ 'fl. J
30...} .CT' J E .. 5.: l'.‘ .811: LIJ '
j
'I
I
E
i
l
l
l
.025 .05 .97 .1 .14 .2 .4 1.”
TULS: LTH'ETH, SECC 33
Zimurc 9. . H1 ts c.0r suvj'ct 1. JV? r9?
of tIIo replicat c: s.

38

 

 

 

 

 

 

 

, .3

 

\_ ‘\\_ .1 _.__._._._.__._

x
L..)

Ava
, J .

 

\

\ .02.5.IOOOOOOIOIOOOOCOC.

ct's

10

1.“ ' r.‘
w

L1
(3“

795‘.

.t t1

'3
L

C

A 10')

V?

('2

footcandlo.
1-4
O
Io

Threshold,

 

 

 

 

 

 

 

 

 

 

 

"SCI" 8 s‘

 

 

 

 

 

 

- _. _H-_ _.___.JL

 

 

 

 

 

 

 

 

 

 

7"- IT 1‘“ T .‘ ’I‘I'T‘" cant" ‘1‘
14).! g.) I 1.1. , ’ATJ‘ 4)
3.~- ‘r‘ .C h N
l Llr‘ 1’1. .4'9'11tr‘ L03:- 0111)]: nt 9. [\‘(7 r,“ h
,- O
I two TCO1108t191C.

a
l

10-“ 9t ti;
1.5

0

Ir
-L
1‘0

1

Idles

ootca

f

rcshold,

Q1

'13

O

39

 

 

 

 

 

 

 

 

 

n:-———--—---—
‘1.»

. ,. , ._‘ ._ _. Y.‘ '_
J g 4-.
. [I — - —— - —
g 1 — — — — — — —

n?§."'00005 cannon-0-.

 

 

 

 

 

A

.I//

iv];

 

;; Z/
7,7
,3

h--.---—--

--.°N5. ....‘--~°'°“

'l

".1711

vv

 

 

‘- STE;

ECT'S

.IOLD

 

 

 

 

 

 

 

 

 

 

 

 

 

 

f.-‘:i-jjII-.3:c 1 l .

of two replicati

L

3
subject 3.

(I. ‘2 ,l}.

1

"r' ‘I'f': M”T f‘ “(1.“!
1 .' .‘. .‘ x

.1. --c . «J .4~ .

I)

40

first calibration flash threshold of the day (at the start
of the session), the solid curves for the last one of the
session. Various small bumps and valleys appear in the
average of these curves, and in general, these were minor and
of no consequence. Where major changes in the threshold ap-
peared, the cause was investigated and usually found to be
due to subject fatigue, forgetting to wear sunglasses on a
bright day, etc. Figure 12 is the key result graph of the
experiment. For this reason, the comparison curves
(Blondel-Rey, Bloch's Law, etc.) have been plotted here for
quick comparison.

The straight lines in the left side of the graph, slant-
ing downward at a 45° angle represent the predictions of
Bloch's Law, Ixt = constant. One line has been drawn for
each null period curve so that one may see how each compares
with the reciprocity prediction.

The curves for .025 and .05 seconds null periods seem to
break from the Bloch's Law line at shorter pulse lengths and
slope toward the steady light threshold more quickly. Sub—
jects were asked what these lights looked like, and almost
unanimous agreement was shown that for these two null periods,
with pulse lengths longer than .07 or .1 seconds the stimuli
appeared fused. This varied some from subject to subject;
but the reason for the shape of the curves is clear; when the
stimuli became fused, the threshold is governed by Talbot's
Law, and hence their shape will differ from the other curves,

where the stimuli weren't fused.

41

The Blondel-Rey curve has been plotted near to the 3.2
second null period curve, to compare the fit of the data to
that law. Up to about .1 seconds, the fit is excellent. As
expected, between .1 and about .3 seconds, the data depart
from the prediction of the law and rejoin it at about .4
seconds, for a good fit out to the longest pulse length used
in this experiment.

All of the curves (except the .025 and .05 null period)
show irregularities in the vicinity of .l-.2 seconds. This
is slight for the 3.2 null period, extending only from .1 to
about .3 seconds. For the .4 null period it is more exten-
sive, starting at about .05 pulse length and extending to
about .2. For the .1 null period it also starts around .05
pulse length and extends to about .2 seconds. This irreg-
ularity suggests that the "bump" Clark and Blackwell found
does indeed exist for different null periods than they used;
and is in fact more pronounced than the curves they showed.

The clearest finding of the study is seen by examining
the null period curves of Figure 12. If Blondel and Rey's
relation were completely correct, all the curves would fall
on top of the 3.2 null period one: Obviously, they haven't
and in fact, they have sorted themselves out in order of de-
creasing null period, with no overlaps except in the area of
1.0 seconds for the three most similar null periods.

The general shape of the curves, however, is similar to
that predicted by Blondel and Rey, except for the "bump"

region noted above. But in general this is to be expected,

H
O

ksco

ox

,z.

42

 

 

 

 

 

 
 
  

_TTT '1'.""\ 4‘“{"
.'.th L‘IIJ151‘V-‘JJ

 

 

 

   

.O__I-- ---- -- - --—-

 

 

 

09:]...O................

a.»

 

 

 

 

 

 

 

 

 

BLOFDEL-REY as.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.14 .2

 

.025 .05 .07 .17

:ijuro 12. Grand Averaéo over all three subjects,
‘ a, . 1" O H a - '7 O C

one tho raplicrtions. various theoretical curves
also shown.

43

since the curves should match Bloch's Law (asymptotic to
Blondel and Rey's for pulse lengths less than .1) and must
at some point level off, implying that lengthening the pulse
will not lower the threshold (steady level).

The raw data were punched onto cards, and an analysis of
variance was carried out on the CDC 3600 computer. The re-
sults are shown in Table 3.

Note that the replications effect is not significant,
indicating that practice was not a significant factor; for
each subject, the first replication was not different from
the second. All other main effects are significant. The
"remaining error" consists of the sum of interactions between
replications and all other effects.

The graphs and AOV table will be discussed and related to

each other in detail in the discussion section, which follows.

44

 

 

mom nm.noahv Hmuoe

mn.m «mm dddeNll Honum mchHmEmm

mcofluom Hasz x

mooo.ov en.w mm.~m vm on.mmo~ mcumsmq mmasm x muomnbsm

mooo.ov mm.mm on.am~ mm wm.vnmm mcpmcmq cmasm x coauwm Hasz

mooo.ov mH.mm em.mmm CH mm.mamm mnpmcmq mmasm x muomflnsm

mooo.ov vh.mmm hm.omwm m mh.nvvma mcumcmq mmasm

mooo.ov mm.aw mm.amm w mm.~mmm mcoflumm Hasz x muocnbsm

mooo.ov Hm.wmm wv.amma v vn.mmom mcofluwm Hasz

mooo.ov mm.vom mo.mmo~ N mo.mmaq mnemmgsm

mmo.o mm.m mm.wm a mm.¢m macaumoflammm

oaMMMWMMMbmHWo oeumflumum_m mumsvm com: Eocmmnm mmumsqm mocmHHm> mo condom
If... 3......
mumaflxoumma

 

modem¢> m0 mHmMA¢Zd

m mqmdfi

VI. DISCUSSION

 

A. ANALYSIS OF VARIANCE RESULTS

The analysis of variance Table, Table 3, gives an over-
view of the general outcome of the experiment. Each
significant factor will be discussed in turn.

1. Subjects

This significant F merely indicates that subjects

differ in their average threshold, in the over-all sensitiv-
ity of their eyes. Subject 1 seems to be the most sensitive,
subject 2 the least.

2. Null Periods

 

This significant factor is a primary finding of the
experiment, and is in fact the main phenomenon which was being
investigated. Other investigators have implicitly assumed that
null periods other than those which they used in their experi-
ments would give the same results. Blondel and Rey, and
Toulmin-Smith and Green used a long null period in the orig-
inal studies, but their equations have no stated limiting
values on null period. Reviewers who have applied the formu-
las to general cases have made no statement that the formulas
should be used with caution. (Projector, 1957; Graham, 1964).
Douglas (1957) applies his integral form of the Blondel-Rey
equation to flashes with null periods of .l and .01 seconds.

He also states:

45

46

"When the dark period is between .01 and .1
second, the effective intensity will lie
between that of a single flash and that of
the group. The behavior during the transi-
tion is not known.“ (Douglas, p. 644)

and:
"If the (dark) periods . . . are of the order
of .1 second or more, it is believed that the
individual flashes will be seen. Therefore,
the effective intensity should be computed on
the basis of a single flash." (£2id.)

The significant effect of the null period shows on all
the subjects' graphs, Figures 9 - 11. It is most clearly
shown on Figure 12, the over-all averages. The null periods
themselves out in order, with the longest (3.2 seconds be-
tween flashes) being the least visible, and the shortest
(.025 seconds between flashes) being the most visible. At
very long pulse lengths (1.6 seconds) null period makes
little difference in the threshold.

If the difference in threshold for differing null periods
was significant but very small, one would tend to dismiss it
as experimental error, or perhaps a real but not useful
effect. But the difference shown in thresholds in Figure 12
amounts to as much as one full log unit. We will examine
these differences in detail.

The 3.2 second null period can be considered a baseline,
since this is closest to the long null periods used by Blondel
and Rey, and others. The .4 null period curve has a slightly
lower threshold, with the .1 null period below that. About

half a log unit has been covered at this point. The flashes

are still distinctly separate (the fastest is still only 10

47

per second, not above CFF). The longer flashes are like
steady lights for all null periods, which was expected. The
shape of the three curves is very similar.

The .05 and .025 second null periods fall below the .l,
and account for the rest of the threshold differences between
the longest and shortest null periods. The shapes of the
curves for these are slightly different from the others.
Subject reports provide the answer as to why: for pulse
lengths of 0.1 sec. or longer, these flashes generally ap-
peared to be either a steady light or a light with a slight
rippling or fluttering effect superimposed on it, especially
for the .025 second null period. Hence, we would not expect
these null periods to have effects much different from a
steady light. At shorter pulse lengths, the lights again
appear to flash, and hence the threshold begins to rise.
Since the length of these flashes is shorter than the crit—
ical duration (.1 sec.), the slope of the rise is determined
by Bloch's Law, IXt=C.

3. Pulse Length

 

It was anticipated that this factor would be signif-
icant; every study ever performed in this area has shown a
significant effect of pulse length. The irregularities which
appeared between .07 and .2 seconds will be discussed later.
4. Subject x Null Period Interaction
This significant interaction indicates that subjects
responded differently to some null periods. The reason for

it is clear in examining the individual subjects' graphs,

48
Figures 9 - ll. Subject 2's curves separate in order accord-
ing to null period, subject l's do not except for the 3.2
and .4 null periods, and subject 3's curves run close to-
gether except for the 3.2 null period. Without a large num-
ber of subjects with which to explore these different re-
sponses more fully, no conclusions can be made about this
interaction.
5. Subjects x Pulse Length Interaction
This interaction would not seem to be particularly
meaningful. It merely states that some subjects reacted dif-
ferently to some pulse lengths. Given the different over-all
levels of sensitivity of the different 55 eyes, and the
slight differences in the nature of the "bump" in the area
of .07 to .2 second pulse lengths, it is not surprising to
see a significant interaction here.
6. Null Period x Pulse Length Interaction
This significant interaction indicates that the null
period curves are not parallel. Obviously they cannot be if
they are all to converge at long pulse lengths.
7. Subjects x Pulse Length x Null Period Interaction
This second-order interaction means subjects are dif-
ferentially affected by combinations of pulse length and null
periods. Figures 9 - 11 show this effect; but the effect is
small; the general shape of the curves is the same for all

subjects.

49
B. GRAPHICAL RESULTS

Each subject's data is presented in Figures 9 - 11.

Since the two replications were not significantly different
from each other, they have been averaged together for these
three graphs.

Subject 1, whose results are shown in Figure 9, shows a
very low threshold over—all, but no abnormalities in the
shapes of the curves. The 3.2 second null period line starts
by following the Bloch's Law slope at the shortest pulse
length used and continued to do so until the critical dura-
tion is reached. At this point a break occurs, similar to
that shown by Clark and Blackwell. The curve then levels
off near the steady threshold level. The .4 second null
period performs similarly, except for a slightly high thresh-
old at .05 seconds. This is most likely caused by some ran-
dom fluctuation in the subject's sensitivity, as none of the
other subjects Show this particular abnormality. The .4
second null period curve also shows the expected "bump" near
.14 seconds.

The rest of the curves are similar to the one for the 3.2
second null period, though below it (lower threshold). All
of them (except .025 null period) show some irregularity be-
tween .05 and .2 seconds pulse length, before leveling off
at the steady light level. The .025 second null period curve
does not show this irregularity, but this is probably because
the flash appears to the subject to be steady, with this

combination of null periods and pulse lengths. Subject 2 has

50

a higher over—all threshold than the other two, but in all
other respects his curves are similar to those of subject 1.

Subject 3 is slightly different. The 3.2 second null
period curve resembles that of the other subjects, but the
curves for the .4, .l and .05 second null periods are closer
together than for the other subjects. At pulse lengths longer
than the critical duration, all the curves (except the 3.2
second null period) clump together with a slope near zero.

The shapes of the curves, however, are very similar to those
of the other 83. It appears that this subject reacts differ-
ently than the other Ss to changes in null period. However,
the general trend is the same; the longer null periods are
more difficult to see, the shorter ones easier. And again,
the irregularities in the area of .07-.2 seconds pulse length
appear.

Figure 12 is a composite graph, consisting of the average
of the data which went to make up Figures 9 - 11. Hence indi-
vidual subject idiosyncrasies have (hopefully) been averaged
out. Since this is the easiest figure to work with, Bloch's
Law, the Blondel-Rey relation, and a predicted steady level
have been plotted here for convenience. The predicted steady
level was derived by taking the average threshold obtained for
each subject each day on the calibration flashes at the start
and end of the session. This level (since the calibration
flash was above CFF, and had a 50% PCF) was twice what the
threshold would have been for a steady light. This over-all

average value, for three subjects, was divided by 2. The

51

value obtained should be a good estimate of the threshold
which would have been obtained for these subjects if a steady
light had actually been used. (A steady stimulus was not
used in order not to overheat the glow tubes.) Note that the
steady line value is quite close to the points for a 1.6
second pulse for all null periods except the 3.2 second null
period. These two independent determinations of a steady
light threshold (calibration flash and 1.6 second flash)
should agree rather closely.

The 3.2 second null period curve is probably too high,
that is, the subjects didn't see these lights as easily as
expected. This is probably an artifact caused by the diffi-
culty in seeing a very brief flash in an uncertain location a
long time (3.2 seconds) after the previous flash.

The Blondel-Rey Law was derived based on flashes separated
by several seconds. It is reasonable, then, that the Blondel-
Rey curve would plot near the 3.2 second null period line.
This is the line labeled "Blondel-Rey“ in Figure 12. Note
that the experimental curve follows it very closely up to the
critical curation, 0.1 sec. At this point, the experimental
data tumble down irregularly, down to a pulse length of about
.4 seconds, where it again closely follows the Blondel-Rey
curve out to the longest flash used in this experiment. The
curves for the null periods 0.4 and 0.1 seconds have a very
similar shape, but at a lower threshold. The only departures
from the smooth curve are in the area between .07 and .2 sec-

onds pulse length, the same area where Clark and Blackwell

found a similar bump.

52

So, one could characterize the data as agreeing with
the established laws where they are applicable (below criti-
cal duration and with long null periods). But the findings
of this study also would have to cause revision of part of
the established laws. In the case of a flash with a null
period of less than .5 seconds or so, and a flash of duration
less than .4 seconds or so, none of the old laws (Bloch's,
Blondel-Rey, or Talbot's) will apply with complete accuracy.

As far as can be seen from the data of this experiment,
the irregularities in the curves between .07 and .2 seconds
pulse length have no simple mathematical description. Further
definition of the area by a very fine-grained study of those
pulse lengths might determine a more accurate shape for the
curve, and from this, perhaps a simple formula could be de-
rived. It will not be attempted in this paper.

However, the variation due to the changein null period
seems amenable to a mathematical treatment. Various curves
were plotted in an attempt to fit the data of the experiment.
It was found that when "a" is decreased the fit becomes better
for the curves obtained with the shorter null periods. The
modification of the Blondel-Rey Law becomes obvious, then; for
null periods shorter than about 1.0 seconds, the constant "a"
must be changed for a good prediction of threshold to be made.

Dr. T. M. Allen, working with the author on the basis of

these data, has derived an equation which not only fits the

-9, .
10 " at the subject's eye

‘7

80
70
<30
50
40

3O

29

10

(J\ NCO

\J1

Tz>

53

 

 

 

 

 

 

 

 

 

5
0:.0I000000000000.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.025 .05 .07 .1 .14 .2 .4 1.6

PUL-E LEfoTv, swnr*ns

0.)»-

’-

1.; .. .—...- r7"

J} arc 13. In: curves 0: the detr frcn Finure 12,
{’7‘ ‘fi -.-"7' . x A,” .2 /-. 1 1- I .' o '
”.lt .. 01.1» ”f? I»: .‘(J-.1_h,(4 ,3, t 10. ”1L1_3_35~.s-[~.11_or1 foyjuLa
croscribrd in the tort.

54

data of this study, but also fits the data of other studies,
such as those of Schuil, and accurately describes the behavior
of the threshold for flashes from above CFF down to steady
lights. Essentially, it incorporates Bloch's Law, Talbot's
Law, and the Blondel-Rey equation; and in addition it ade-
quately describes areas which none of these laws handle.

The equation simply replaces "a" in the original Blondel-
Rey equation with the quantity

a

n max

n+a
max

a:

where
n = null period
a = the Blondel-Rey constant, 0.2 sec.
max

substituting, we have

 

with n and t short, this reduces to approximately Talbot's

Law,

n + t
t O

 

With n long and t more than .1 seconds, we have approxi—
mately
+ t
t
which is the Blondel-Rey equation. With n long and t<.l

seconds, we have approximately Bloch's Law.

55

In Figure 13, the curves for this equation are plotted
along with the data of the present experiment. The fit,
while not perfect, is certainly close enough to be useful,
and is far better than any of the other equations discussed.
Further research with more subjects would be necessary to

refine the equation or reject it in favor of a better one.

VII. CONCLUSIONS

 

It can be concluded that the Blondel-Rey equation and
subsequent modifications of it are inadequate to handle
predictions of the threshold of lights flashing with a null
period of less than approximately one second. However, the
Blondel-Rey equation can be modified simply by changing "a"
depending on the null period. The new equation is

.2n

 

§__= .2 + n + t
E t
o
where

E = threshold illumination for the flashing light
E0 = threshold illumination for a steady light
n = null period
t = pulse length

This equation can be used for any pulse length or null period,
whether the light appears to flash or not. Although further
data would be needed for a precise test of this equation, it
is likely to be useful in practical settings due to its

simplicity.

56

APPENDIX

57

P

 

 

aka w.uocm£5w 649

O
1
pm

-
00
o

..
_...-..

C

ID

.C.
s. .V

mtawsmouoow

 

T.
2.
CM
«HI.

«.5

37 0??

data

fin
F”, ..

an fl

3 ,

O
1 o
- 1
AF.“
t
n. C
A.“ a...
o .. I
C .3
n5, .5
.l u
”I. S

‘J

' ject's (:yo

SUD

at the

_9
10 ‘

-r
l
«5

~ 3

0
Q\

4

 

58

 

ILAILIILJ

 

l L l
5 10 15
STSCIC“S
Fiturn A-E. C:-ibrrticn flash data for
subj Pct 2 .

59

 

 

 

C...
11
i
l
n...
'1
‘
Ill—L
‘
A
l
b u p p — p b L .
flu no ,0 In. 04
o o o o o

. J 1
0......0 m.ucc.r£:m cob u... . CH M mufocmcuoom ...o~0......m....u.-..w
Nb..-

—.-.vf'§
_')

1'5--.

F" """v‘"
::‘ ‘_IJ'_:"-

u .3
_... . .0
.l U.
.31. S

LIST OF REFERENCES

LIST OF REFERENCES

Blondel, A., and Rey, J. “The Perception of Lights of Short
Durations at their Range Limits." Trans. Illum.
Engn. Soc., 1912, 7,p. 626.

 

 

Clark, W. C., and Blackwell, H. R. "Relations Between Visi-
bility Thresholds for Single and Double Pulses."
Willow Run Laboratories Research Report, 1959.

 

Dean, R. F. "Conspicuity of Steady and Flashing Lights at Low
Levels of Brightness." AM. J. Psych., 17, 1962, p.386.

 

Douglas, C. A. "Computation of the Effective Intensity of
Flashing Lights." Illum. Engn., 1957, 52,#12, p. 641.

 

Erdmann, R. L. "Brightness Discriminations with Constant
Duration Intermittent Flashes." J. Exp. Psy., 1962,
63, p. 353.

Graham, C. H. Vision and Visual Perception. New York: John
Wiley and Sons, 1965.

 

Gerathewohl, S. J. "Conspicuity of Steady and Flashing Light
Signals, I." USAF School of Aviation Medicine,
April, 1951.

 

. “Conspicuity of Flashing and Steady Light Signals,
II." USAF School of Aviation Medicine, January, 1952.

. "Conspicuity of Flashing and Steady Light Signals,
III. Variation of Contrast.“ J. Opt. Soc. Am., 43,
1953, p. 567.

 

. "Conspicuity of Flashing Light Signals. Effects
of Variation Among Frequency, Duration, and Contrast
of the Signals.“ USAF School of Aviation Medicine,
June, 1954.

 

Hampton, W. M. "The Fixed Light Equivalent of Flashing
Lights." Illum. Engn. (London), 27, 1934, p. 48.

 

Long, G. E. "Effect of Duration of Onset and Cessation of
Light Flashes on the Intensity Time Relation in the
Peripheral Retina." JOSA, 41, 1941, p. 743.

60

61

Projector, T. H. “Efficiency of Flashing Lights." Illum.
Engn., 53, 1957, p. 600.

Schmidt-Clausen, H. J. "Uber das Wahrnehmen Verschieden-
martiger Licht-impulse bei varanderlichen
Umfeldleuchtdichten." Darmstadt Technical University,
1967.

 

Schuil, A. E. "The Fixed Light Equivalent of Flashing
Lights Having Constant Duration." Trans. Illum. Engn.
Soc. (London) 5, 1940, p. 117.

 

Spencer, J. A. "A Report of the Literature Published on
Flashing Lights." Applied Optics Section, Imperial
College, London, 1964.

 

Toulman-Smith, A. K., and Green, H. N. "The Fixed Equivalent
of Flashing Lights.“ Illum. Engn. (London) XXVII,
1933, p. 305.

 

Williams, D. H. "The Threshold Detectability of Slowly
Flashing Lights." Unpublished MA Thesis, Michigan
State University, 1966.

"The Perception and Application of Flashing Lights." Inter-
national Symposium, 19-22 April, Imperial College,
London. Adam Hilger., Ltd., London, 1971.

 

 

 

M

\ .

—1—_-

  

|||||||||||||||||||||||||||||||

WWWmlW"WWW"IWIWIM‘

 

“:2. ”5"“ -. ~ A ' “

/;°&m& -m a...