THE EFFECTS OF THE APPARENT SIZE
OF AFTERIMAGES IN STUDIES
OF EMMERT'S LAW

 

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This is to certify that the

thesis entitled
The Effects of the Apparent Size

of Afterimages in Studies of
Emmert's Law

presented by
Frederick N. Dyer

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Psychology

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Michigan State
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The University of Alberta

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ABSTRACT

THE EFFECTS OF THE APPARENT SIZE OF AFTERIMAGES
IN STUDIES OF EMMERT'S LAW

by Frederick N. Dyer

Emmert's law states that the projected size of afterimages (A15)
is directly proportional to the projection distance. Many studies of the
projected size of A13 have found near-projected A15 to be larger than the
prediction of Emmert's law and far-projected A15 to be smaller. This
suggests that the eye has greater magnification with distant fixation than
near but this is contrary to the accepted belief that a small magnification
at near occurs. However, greater magnification with distant fixation would
also explain a number of perceptual anomalies such as "overconstancy" and
greater visual acuity at a distance than up close. The problem of the
study was to account for the deviations from Emmert's law that often occur.
This was approached by carefully measuring the projected size of Ale and
by investigating the "apparent size" of A18 at different projection dist-
ances.

Each of 12 83 formed and measured AIs with four different methods:
1. The traditional outlining method where E adjusted calipers around
the AI until S reported that the points touch its extremities.
2. An accurate coincidence method used on one previous study which
did not indicate deviations from Emmert's law where a figure of the same
shape as the Al was moved forward or backward until it just coincided with
the AI. Distance of the figure was the dependent variable in this method.

3. A new coincidence method where an outline figure was adjusted in

Frederick N. Dyer

size at a fixed distance until it coincided with the AI.
4. A method where the "apparent size" of Ala was assessed. 8 observed
the AI, noted its size and then compared it to the space between caliper
points. S was required to make a successive comparison of the size of the
AI and the comparison stimulus instead of the simultaneous comparison re-
quested in the three other methods. Previous studies of the apparent size
of Ala which used large projection distances had shown that apparent size
was less than the size predicted by Emmert‘s law. Two formation distances
and three or five projection distances were used for each method.

Both coincidence methods gave results nearly coincident with Emmert's
law. This indicated little magnification change in the eye for different

' and greater visual acuity

fixation distances and leaves "overconstancy'
at a distance unexplained. For the apparent size method, near-projected

AIs were 35% greater than the prediction of Emmert's law and far-projected
AIs were found to be slightly smaller than this prediction. The traditional
outlining method gave results intermediate to the apparent size and coinci-
dence methods with AIs about 15% larger at near projection distances than

at far.

The study indicated that the outlining method is in part an apparent
size measurement method where successive comparisons of AI size and compari-
son stimulus size occur. Deviations from Emmert's law in previous studies
are thus artifacts of the measurement method.

An explanation of this interaction of apparent size of Ala with

projection distance was presented which was based on the tendency of the

eyes to deviate toward an intermediate rest position during the shift in

Frederick N. Dyer

attention from the comparison stimulus to the AI. This shift in fixation
results in different metrics being used for the successive size judgments
with the AI being magnified relative to the comparison stimulus for projec»
tion distances (and comparison stimuli) nearer than the intermediate rest
position and minified relative to comparison stimuli beyond this inter-

mediate position.

THE EFFECTS OF THE APPARENT SIZE OF AFTERIMAGES

IN STUDIES OF EMMERT'S LAW

By

Frederick N. Dyer

A THESIS
Submitted to

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

DOCTOR OF PHILOSOPHY
Department of Psychology

1968

ACKNOWLEDGMENTS

I wish to thank Dr. Terrence Allen, Dr. Paul Bakan, Dr. Richard
Hart, and Dr. John Hunter for their many suggestions for setting up and
running the experiment. I am particularly grateful to Dr. Allen for
his willingness to supervise the project as well as for the critical
insights that kept it solidly on course. I am also grateful to Dr.
Matthew Alpern at the University of Michigan and Dr. Francis Young of
Washington State University who generpusly supplied me with information
regarding physiological optics, basic visual processes, and afterimage
measurement. I would also like to thank my friends, particularly Jerry
Gillmore, who provided me with hours of pilot afterimage data and, more
importantly, with useful criticism of the measurement apparatus and
procedure. Finally, I wish to thank my wife, Jean, who contributed to

the success of the project at every level.

ii

Chapter I:
Chapter II:
Chapter III:
Chapter IV:

Chapter V:

TABLE OF CONTENTS

The Problem

Review of Literature

Method

Results

Discussion

iii

Page

18
30

49

Table I:

Table II:

Table III:

Table IV:

LIST OF TABLES

Analysis of Variance

Significance Tests of Differences for
Coincidence Methods

Significance Tests of Differences for
Apparent Size and Calipers Methods

Correlations Between Pairs of Measurement
Methods at Each Projection Distance

iv

Page

31

35

36

39

Figure 1:

Figure 2:
Figure 3:

Figure 4:
Figure 5:
Figure 6:

Figure 7:

Figure 8:
Figure 9:
Figure 10:

Figure 11:

LIST OF FIGURES

Pattern and Size Used for Both Afterimage
Forming Stimuli

Distances to Projection Target Centers
Taper Coincidence Target

Afterimage Measurements for the Different
Methods & Projection Distances

Afterimage Measurements for Different
Formation Distances & Methods

Afterimage Measurements for Different
Methods by Males and Females

Afterimage Msmts. at lst and 2nd Sessions
for 50 cm. Formation First and 200 cm.
Formation First Groups

Individual Data for Males who Formed Afterimages
at 50 cm. During lst Session

Individual Data for Females who Formed
Afterimages at 50 cm. During lst Session

Individual Data for Males who Formed After-
images at 200 cm. During lst Session

Individual Data for Females who Formed
Afterimages at 200 cm. During lst Session

Page

20
22

25

32

41

43

44

65

66

67

68

LIST OF APPENDICES

Page

Appendix A: Data for Individual Subjects 64

vi

CHAPTER I: THE PROBLEM

Emmert's (1881) law for afterimages deals with their size when they
are projected at different distances and states that afterimage size in-
creases in direct proportion to the distance. Some controversey has
arisen regarding whether Emmert's law refers to the physical projection
distance or to the apparent projection distance (Boring, 1940; Young,
1951; Edwards, 1950). It is now generally accepted that Emmert was
referring to the physical distance since his own experiments involved
the measured distance to the projection screen. This controversy was
probably stimulated by different results in many afterimage measurement
studies from the strict proportionality of afterimage size to projection
distance that Emmert's law predicts. The more typical finding has been
that afterimages are reliably measured to be somewhat larger than Emmert's
prediction at near projection distances and equal to or smaller than
Emmert's law would predict at far projection distances. Studies demon—
strating this typical deviation from Emmert's law will be discussed in
detail in the next chapter.

No one has satisfactorily explained these systematic deviations
from Emmertls law. A likely explanation would be that the Optical
magnification of the eye changes with different viewing distances.
Greater magnification of the eye at a distance than up close would be
required to produce this typical finding of smaller afterimages with
distant projection than with close projection.

Such a change in magnification with fixation change could provide
an explanation for a number of other poorly explained phenomena of

_ 1 _

_ 2 _

visual perception. These are ”overconstancy", where distant objects
areoverestimated in size, greater visual acuity at a distance than

at near, the unexpected appearance of figural aftereffects when inspec-
tion and test figures presented at different distances from the eye but
of equal visual angle are used, and a finding of a higher Critical-
flicker-frequency for an 80-inch-distant one-inch diameter stimulus
than for a 40-inch—distant, 8-inch diameter stimulus both of which,
presumably, should be stimulating the same retinal area. Howevem3 the
science of physiological Optics predicts a slight magnification at
near, not the magnification at far described above (Helmholtz, 1866;
Pascal, 1952), and one recent afterimage measurement study (Onizawa,
1954, Series B) gave data that would support this traditional view.
IJnlike the typical afterimage.measurement method which involves outlin-
ing of the afterimage with some device such as calipers or a beam com-
pass, Onizawa's method in Series B of his experiment involved an outline
target of fixed size and the same shape as the afterimage. This target
was moved away from the observer until it was reported to exactly coin-
cide with the afterimage.“ The distance of the coincidence target was
the dependent variable in this method. Other support for the traditional
physiological optics interpretation of the eye's magnification was pro-
vided by a study where photographs of the images on the retina were
obtained (Heinemann, 1961). These studies will also be described in
more detail in Chapter II.

The basic problem of the dissertation was to determine which, if

_ 3 _
either, of the afterimage measurement methods is a valid measurement of
the Optical magnification of the eye at different distances of fixation.
In addition, an explanation of the difference in results obtained by the
two afterimage measurement methods was sought. It was felt that such an
explanation could have considerable relevance for the perceptual anomalies
of overconstancy, etc., as well as the afterimage measurement findings.
There is some possibility that this involves the magnification and

minifications of apparent size that can occur which are known as macrop-

 

sia and micrOpsia, respectively (McCready, 1965). These apparent size
changes occur primarily with alterations of the oculomotor adjustments
of the eyes during Object perception. They also apply to afterimages
(e.g., Urist, 1959).

In the next chapter the afterimage measurement studies which
have produced the two discrepant results are reviewed, along with
other perceptual phenomena which could share an optical explanation
(or perhaps some other explanation) with the typical deviations from
Emmert's law that have repeatedly been found. In addition, material
relevant to the Optical explanation and to an apparent size eXplanation

Of these deviations is presented.

CHAPTER II: REVIEW OF LITERATURE

Included in this chapter is a review Of (1) the relevant studies
of afterimage measurement, (2) possibly related perceptual anomalies,
(3) studies Of the Optical magnification of the eye, and (4) apparent
size findings relevant to afterimage size. In addition, a hypothesis
is developed tO explain how apparent size could enter into what, at
first sight, appear to be physical measurements of afterimages and
specific experimental hypotheses derived from this hypothesis are pre-

sented.

Afterimage Measurement Studies

Prolonged fixation of a visual stimulus and even very brief
presentations of a bright stimulus can lead to a distinct afterimage
of the stimulus which can be seen for as much as several minutes after
actual viewing of the stimulus ends (Brindley, 1963). These afterimages
take two different forms, positive afterimages, which maintain the
brightness relations of the initial stimulus, generally occur initially
and are then followed by negative afterimages where these brightness
relations are reversed. Both types are accounted for in a recent theory
which states that the receptors in the retina which are exposed to a
bright stimulus maintain continued "noisy" activity after external
stimulation ceases (Barlow and Sparrock, 1964). Once formed, these
afterimages do not change in size or position on the retina and thus
provide a unique means of determining the relative magnification of
the eye at different fixation distances. Since Emmert's law specifies
that the afterimage will project sizes directly proportional to distance,

- 4 -

- 5 -
it implies that no change in magnification occurs with different fixa-
tion distances.

Even before Emmert's study (1881), research was conducted which
actually tested a more sophisticated hypothesis than the direct relation-
ship between afterimage projection distance and afterimage size that
Emmert proposed. In 1857 Bahr tested and apparently confirmed the
prediction of Helmholtz (1866) Of a two or three percent magnification
of the eye with accommodation of the eye for very close distances. The
report of this dissertation by Helmholtz (1866) did not specify any of
Bahr's procedures, but only the positive results of the study. This is
unfortunate since his procedure must have been quite sophisticated to
indicate such small deviations from strict proportionality of afterimage
size to projection distance.

Emmert's own article (1881) was largely theoretical but his
small amount Of data did not lead him to conclude that any deviation
from straight prOportionality was occurring. Questionable support for
Emmert's law has been derived from several studies typified by the
study of Norris (1934) which reported no data but simply stated that no
deviation from Emmert's law was found greater than that which could be
accounted for by the measurement error.

When quantitative results are presented, however, the more
typical finding is about a 10 percent larger afterimage at close pro—
jection than at far. This is shown in a summary of the results of three
afterimage measurement studies which were reported by Carr (1935) and

which are reproduced below. A study by Schmulling gave the following:

- 6 _

Distance in cm. 35 50 100 150

Size in cm. 3.87 5.25 10.33 15.3
Ratio .110 .105 .103 .102 (p. 366).

The following is from a study by Kluver:

Distance in cm. 12.5 25 50 ‘100 200
Size in cm. 1.40 2.55 5.18 9.94 20.2
Ratio .112 .102 .103 .099 .101 (p. 366).

Carr himself extended the results of the above to greater distances and

part Of his data follows:

Distance in feet 4 6 8 10 20 25 30
Size in inches 3.08 4.38 5.88 7.33 14.17 16.26 19.03
Ratio .77 .73 .74 .71 .65 .63 (p. 366).

NO discussion Of procedures was given by Carr (1935) but it is
fairly safe to assume that the afterimage was formed from a near stimulus
and then projected at the various distances where it was outlined with
calipers. It can be seen in all these results that the nearer projec-
tion distance led to the largest afterimage in angular measurement.

Another similar study that supported these findings Of Kluver,
Schmulling, and Carr was Series A of the experiment of Onizawa (1954).
Afterimages were formed of a circle five cm. in diameter located 60 cm.
from the eye, then projected at 30, 120, and 180 cm. and measured with
calipers. Measured size was found to be eight percent larger at the
30 cm. projection distance than at the 120 and 180 cm. distances which
were nearly identical in angular size.

The same finding appeared in four out of five subjects in a
study by Young (1948). Afterimages formed of a one-inch square at
30.5 cm. from the eye were projected and outlined with boresight lamps.

For these four subjects afterimages were measured to be about seven

_ 7 _

percent larger at a meter than at three meters. Beyond three meters
these subjects showed another increase in afterimage size, but for the
shorter distances the results are closely parallel to the studies
mentioned above.

Larger measured afterimages at near than far projection distances
suggest that the near outlining instruments are being relatively mini-
fied, i.e., reduced in size and thus require greater separation to span
the afterimage than would be required to span the afterimage if they
were not minified or were instead magnified. This interpretation of
the magnification of the eye is contrary to the interpretation of
physiological optics, however (Helmholtz, 1924; Pascal, 1952; McCready,
1963). During visual accommodation the front surface of the crystalline
lens Of the eye moves forward a small amount and this increases the
distance from the center of magnification to the retina. This results
in the image on the retina being slightly expanded in the same way that
an image formed by a lens on a sheet of paper is enlarged as the lens
is moved a greater distance from the paper. The effect Of this small
magnification change on afterimage size would be in the Opposite
direction from the typical deviations from Emmert's law.

If such relative magnification at a distance were the case, it could
account for the data of a very different afterimage measurement study
done by Ohwaki (1955). This also involved outlining measurements Of
afterimages but the afterimages were formed at different distances
(50, 75, 150, and 200 cm.) and were all projected at the same distance

(100 cm.). All forming stimuli were four degrees 34 minutes in height

- 3 -

and Emmert's law would predict a measured afterimage Of eight cm. at,
the 100 cm. projection distance for all. Instead, the average for five
very similar subjects were 7.86, 8.01, 8.44, and 8.70 cm. for the 50,
75, 150, and 200 cm. formation distances, respectively. Minification
at near and magnification at far could also produce this result.

Both types Of afterimage measurement experiment led to deviations

from Emmert's law Of about 10 percent from far to near.

Related Perceptual Anbmalies

Not only does this Optical explanation work well for these two
different types of afterimage measurement studies, but it also could
account for several other.important perceptual anomalies. These are
overconstancy, greater visual acuity at far than near distances, figural
aftereffects when inspection and test figures are of the same visual
angle but are at different distances, and a greater critical flicker'
frequency for a distant stimulus than a near one of equal visual angle.

Overconstancy refers to a highly reliable finding that the size
of objects at’a distance is overestimated relative to the size of Objects
at near (Wohlwill, 1963; Epstein, Park and Casey, 1961). It is called
overconstancy since it is as if the constancy process that permits us to
recognize an Object as the same object when it is moved away, is over-
working.

One excellent study in which the phenomenon of overconstancy
appeared was done by Heineman, Tulving, and Nachmias (1959). They re-

quired subjects to match a near target subtending a visual angle of one

_ 9 -

degree with a variable target presented at a greater distance, with
the match to be made on the basis of visual angle. On the average,
subjects chose a .8 degree target to match the near one degree standard
indicating that the distant target appeared larger than it was. The
order of magnitude is similar to that Of the afterimage studies and
relative magnification at far could also account for these findings.
Also congruent with this explanation are studies which have
indicated greater visual acuity at far than at near distances. Freeman
(1932) found acuity at 300 cm. to be 63 percent greater than at 30 cm.
Luckiesh and Moss (1933) found a 17 percent increase in acuity at 280
cm. over 120 cm. Giese (1946) found acuity measured at the reciprocal
visual angle to increase from .95 at 20 cm. to 1.63 at 100 cm., almost
100 percent. McCready (1963) performed more careful experiments using
Optical means to vary the accommodation distance of acuity targets and
also found small but significant improvements in acuity with increased
distance on the order of 6 to 10 percent for the two subjects in the
study. McCready accepted the traditional physiological Optics interpre-
tation of the eye's magnification at different fixation distances. He
considers these results to be related to the minifications and magnifica-
tions of apparent size that result from changes in the oculomotor adjust-
ments of accommodation and convergence. He admitted that this is
"empty" magnification similar to the enlargement Of a photo with no
increase in the detail of the photo occurring. It is not clear how such
empty magnification could account for these results.

Ganz (1966) has recently shown the importance of an interaction

_ 10 -

between the afterimage of the inspection figure and the test figure in
the figural aftereffect. One figural aftereffect involves concentric
circles. If the circular inspection figure is smaller than the test
figure (also a circle), the afterimage of the inspection circle repells
the real contours Of the test figure causing it to appear larger than an
equal-sized comparison figure which did not have inspection figure con-
tours inside it. If the circular inspection figure is larger than the
circular test figure the test figure is made to appear smaller by a
similar repulsion Of the real image by the afterimage according to this
explanation of Ganz. Using this figural aftereffect, Sutherland (1954)
found with a circle of four inches in diameter at 57.6 inches from the
eye as the inspection figure, and with a 10 inch diameter circle 144
inches away from the;eye as the test figure, that the test figure was
seen to be expanded. Conversely, when the inspection figure was the
distant 10 inch diameter circle and the inspection figure was the nearer
four inch diameter circle, the test figure appeared to be contracted.
Thus in both instances the distant figure behaved as if it were larger
on the retina than the close one although both subtend the same visual
angle at the eye. Story (1962) replicated this finding but found that
it did not occur with monocular vision, with small circles, or with
disks instead of outlines of circles. This finding by Sutherland also
suggests that minification of the eye takes place with near viewing and/
or magnification of the eye takes place with far viewing.

Spigel (1964) compared the critical flicker frequency (CFF) for a

_ 11 _

luminous one-inch diameter circle located 80 inches from the eye with the
CFF for a k-inch diameter circle at 40 inches. He also determined the
CFF for the one-inch diameter circle at 40 inches. CFFs for the three

target-distance combinations were as follows:

l-inch diameter stimulus at 40 inches 31.3
l-inch diameter stimulus at 80 inches 30.5
k—inch diameter stimulus at 40 inches 27.6

All differences were reported to be significant. The latter two stimuli
would subtend the same visual angle but the results suggest that the one-
inch diameter stimulus at 80 inches is timulating more retinal area than
the k-inch diameter stimulus at 40 inches. This finding would also
follow if minification took place at near relative to far.

If an optical magnification change with fixation distance does
not account for the above anomalies then they may share some central
mechanism that increases the "gain" of the visual system during distant
fixation relative to near fixation. The same mechanism could perhaps
account for the typical afterimage measurement deviations from Emmert's
law. However, prior to accepting such a central explanation it is import"
ant to consider the evidence against the simpler peripheral explanation

that magnification is relatively greater at a distance.

Evidence Contrary to an Optical Explanation Of these Anomalies

Although greater magnification for far fixation relative to near
fixation could account for all of the above anomalies of perception and
afterimage data, systematic studies such as those of Helmholtz and Bahr
have not found such magnification changes. Another check of this eXplanau

tion (Heinemann, 1961) was.made in an att‘npt to account

- 12 _

Heinemann used a technique where the retinal images of targets were
actually photographed. The targets used were of a constant visual angle
of four degrees and were presented at 25 and 100 cm. The actual size of
the retinal images was determined by relating them to prominent blood
vessels on the retina. Results for the single subject indicated that

the retinal image was very slightly larger for the target presented at

25 cm. This supports the traditional interpretation of Optical magnifica-
tion of the eye and not a minification at near and magnification at far
which would be required if overconstancy were an optical phenomenon.

In a recent afterimage measurement study, Onizawa (1954) compared
the classical measurement technique where the extremities Of an afterimage
are outlined with beam compass points, calipers, boresight lights or some
other device, with a new technique where a coincidence figure of the same
shape as the afterimage and of a fixed size was moved toward or away from
the subject until he reported that it just matched the afterimage in size.
In this new method the distance of the target was the dependent variable.

With the calipers outlining method in Series A of Onizawa's experi-
ment he found the typical afterimage data where near projected afterimages
are larger than those projected at a distance. In Series B with the
coincidence figure measurement method the distances of the coincidence
target indicated a very slight magnification Of the eye for near projec-
tion, i.e., the data supported the traditional magnification interpreta-
tion of physiological optics.

Onizawa found the variation in responses to be 3 to 5 times

greater with the outlining technique than with the coincidence technique

_ 13 _

of Series B and concluded that the latter method was preferable for
measuring afterimages. He does not recognize, or at least does not
account for the statistically significant differences between the out-
lining measurements and Emmert's law that occurred for the outlining
measurements. Perhaps the most striking difference between the outlining
method and the coincidence method was the variable distance of the target
in the latter. It might be argued that the increased saliency of distance

with the coincidence technique produced these different results.

An Apparent Size Explanation of the Afterimage Data

The results of Series A and Series B of the Onizawa study suggest
that either optical changes of two types can occur in the eye, or, as is
more likely, the perceptual processes involved in outlining measurements
and in coincidence measurements are different. It is probable that
coincidence measurement involves a unitary viewing of the afterimage and
the coincidence target. Outlining with calipers or some other device,
on the other hand, may be a dual measurement process with the outlining
device and the afterimage being viewed at least somewhat independently
and successively. Outlining measurements would thus fit the criteria
for apparent size measurements where an object's size is remembered and
compared to the size of another object.

The apparent size of afterimages has been investigated for far
projection distances (Price, 1961; Hastorf and Kennedy, 1957; Crookes,
1959). In these studies afterimages and real objects have been presented
on projection screens, (not at the same time), with the objects constructed

to be the same shape as the afterimages and to the size that Emmert's lav

_ 14 _

would predict for the afterimage at the distance of the projection screen.
Comparison objects at a different distance were then adjusted until they
appeared to be the same size as these afterimages and objects. All
studies found the apparent size of the afterimages to be less than the
apparent size of the real objects.

If apparent size of the afterimages were entering into the out-
lining measurement method, this would account for the small afterimages
at a distance that are typically found. No one has reported data for
the apparent size of afterimages when they are projected closer than five
feet. If they should be found to appear larger than what Emmert's law
would predict at close distances then the typical results for the calipers
outlining technique at close distances could also be accounted for by
apparent size influencing these measurements.

At least three factors argue for an apparent size explanation of
the typical results of the calipers outlining technique. One is that
the making of outlining measurements of afterimages with calipers is
difficult for the subject and could lead to what may be an easier succes-
sive assessment of first the afterimage size then the size of the space
between caliper points.

A second factor is that large changes in apparent size of objects
can take place when normal convergence and accommodation positions for
these objects are altered. Leibowitz and Moore (1966) found the per-
ceived size of distant objects to be reduced several-fold by viewing
them with accommodation and convergence levels corresponding to near

distances. Lie (1965) altered only convergence during perception of a

- 15 -

repeating pattern and found changes in apparent size of similar magnitude.
These apparent size changes are not confined to real Objects. Three studies
(Gregory, Wallace, and Campbell, 1959; Taylor, 1941; Urist, 1959) have
shown that convergence in particular produces large changes in the appa-
rent size of afterimages, even when they are observed in complete darkness.

The third factor that argues for apparent size influencing outlin-
ing afterimage measurements is that the oculomotor adjustments that are
responsible for the apparent size changes can take place during afterimage
perception without altering either the fusion or blurredness of an after-
image. If the afterimage—forming stimulus is fused and in focus when the
afterimage is formed no adjustment of the eyes can separate or blur it
(Zajac, 1960).

Greater convergence than normal for Objects leads to the objects
appearing smaller than normal. Underconvergence leads to large apparent
size. To produce large appearing afterimages at near and small appearing
afterimages at far in this successive measurement hypothesis, one would
expect convergence to be at a position farther than the near projection
screen when the afterimage size is assessed and to be at a closer position
than the far projection screen when the size of the afterimage projected
at that distance is assessed. It is known that in the absence of a visual
stimulus, accommodation tends to adopt an intermediate distance and con-
vergence is known to adopt a position conforming to that of accommodation
(Alpern, 1962). This position is about one meter from the eye. If, when

the afterimage size was assessed in this hypothesized "successive" process

_ 16 _

the eyes drifted away from the projection screen toward this intermediate
position only to return to the distance of the "real" caliper points when
their spacing is assessed both Of the above convergence relationships
would be met.

The well-done Ohwaki (1955) study would require a slightly different
explanation than this assumption of an intermediate convergence rest
position. In this study afterimages were all projected at the same distance
(100 cm.) after being formed at 50, 75, 150, and 200 cm. The afterimages
formed at the closer distances were smaller than those formed farther away.
This could be explained if convergence were enroute from the formation dis~
tance to the projection distance when the afterimage size was assessed
and at the 100 cm. projection distance when the space between the caliper
points was assessed. This would lead to too great convergence when the
afterimage was assessed with the distances closer than 100 cm. and too
little convergence when the afterimage was assessed for the formation
distances greater than 100 cm. Small afterimages would again accompany
overconvergence and large afterimages would again accompany under-conver-
gence, in this explanation.

The main purpose of this study was to test this apparent size
explanation for the afterimage data. Unfortunately, this apparent size
explanation does not account for the other perceptual anomalies which were
so parsimoniously explained by the hypothesis of greater retinal image
magnification at far than at near. In fact, the cogency of the optical
explanation creates a need for additional evidence that this magnification

change with fixation distance change does not occur, along with the need

_ 17 _

to test the alternative apparent size explanation for the afterimage data.
To meet both needs the experiment described in the next chapter was designed.

It tests the following specific hypotheses.

Hypotheses

 

1. The apparent size of afterimages is greater than Emmert's law would
predict for projected size at near projection distances and is less than
this figure at far projection distances.

2. The apparent size of afterimages influences measurements made with
calipers or other outlining devices and these measurements have the same
relationship to Emmert's law as described in Hypothesis 1 for the apparent
size measurements.

3. When apparent size is eliminated from afterimage measurements these
measurements deviate little or none from the predictions of Emmert's law.
4. The saliency of distance in Onizawa's moving coincidence target
measurement method does not account for its accuracy and small deviation
from Emmert's law, but the same result will be obtained using a coincidence
target where distance is held constant.

5. When apparent size is eliminated from afterimage measurements, for-
mation distance will have little or no effect on afterimage size with
forming stimuli of equal angle for the different distances.

6. The apparent size of afterimages which are formed at close formation
distances will be less than the apparent size of afterimages formed from

stimuli of equal visual angle but at greater distances.

CHAPTER III: METHOD

The following experiment was conducted to test the hypotheses pre-
sented in Chapter II. It was basically a methodological experiment with

each subject measuring afterimages with four different measurement methods.

Design

Method 1. This represented the "classical" outlining technique and
involved calipers which were adjusted by the experimenter around an
afterimage at the projection screen until the subject reported that they
just touched the top and bottom of the afterimage.

Method 2. This method was based on the coincidence technique used by
Onizawa (1954) in Series B of his experiment. A figure of similar shape
as the afterimage was presented on a movable projection screen and the
experimenter moved it closer to or farther away from the subject on an
optical bench until the subject reported that it coincided in height with
the afterimage.

Method 3. This was also similar to the Onizawa coincidence technique,
except that the target was fixed in distance instead of size and its size
was adjusted by the experimenter at this fixed distance until the subject
reported that it coincided in height with the afterimage.

Method 4. This involved the apparent size of afterimages. Calipers were
used in this method but they were not presented around the afterimage as
in Method 1. Instead they were presented to the right of an area where
the afterimage was observed and were kept in motion so that the subject

could not directly compare afterimage and caliper points but instead first

18»

- 19 _

looked at the afterimage then remembering its size instructed the experi-
menter to adjust the calipers until they appeared to span the afterimage.
Perhaps for the first time in any afterimage measurement experi-
ment, this experiment combined multiple formation distances (as in
OHWaki's study) with the more common multiple projection distances. All
24 combinations of the four measurement methods described above, two
formation distances of 50 and 200 cm. and three projection distances of
25, 100, and 400 cm. were presented to each subject. In addition, eight
other measurements were made using the two caliper measurement methods
(1 and 4) at 50 and 200 cm. projection distances after formation at both
50 and 200 cm. Pilot work had indicated that only these two techniques
showed sufficient deviation from the predictions of Emmert's law to pro-
vide sufficient information to warrant the additional measurements at
these distances. Each subject thus formed and measured 32 afterimages.
Each afterimage was measured a number of times during the approximately

three minutes that it lasted.

Apparatus

The two stimuli which were used to form afterimages were both out-
lines of the right half of a square (See Fig. 1). A small dot was located
at what would be the center of the square and was the point which the sub-
jects fixated during formation of the afterimage. At the 50 cm. formation
distance the figure was four centimeters high and the outline was three
mm. wide. The stimulus used at the 200 cm. formation distance was 16 cm.

high and.the outline was 1.2 cm. wide. Both stimuli subtended the same

 

 

 

J” T“

20 I 33"

 

   

2,300 ft. — L.

 

 

 

AFT ERIMAGE FORMING STIMULI

FIGURE I. PATTERN AND SIZE FOR BOTH

_ 21 _

visual angle of four degrees 34 minutes. The figures were outlined in
black tape on translucent material and transilluminated. Brightness of
both figures was 2,300 ft. L.

These forming-stimuli were presented at eye level and were located
on a long platform which was grooved at the 50 and 200 cm. distances to
accurately locate the stimuli and the light source. The distance from
the stimulus was measured to the entrance-pupil of the eye which is located
three mm. behind the front surface of the cornea. A wooden rod 47.7 cm.
long was placed against the center of the 50 cm. forming-stimulus and a
headrest and chinrest were adjusted until the rod just brushed lightly
against the closed eyelid of the subject. Figure 2 shows the distances
to the various targets which result from the establishment of this 50 cm.
distance.

Since the close 25 cm. projection target was located 25 cm. from
the 50 cm. target along the perpendicular bisector of the line joining the
eyes, the actual distance of this projection target would be 25.122 cm.
considering a large 7 cm. interpupillary distance. This .5 percent error
is very small relative to the differences being investigated and for
practical purposes is disregarded.

Three tracks in the form of optical benches were aligned and
centered at 25, 100, and 400 cm. and the projection targets were placed
on these tracks. Centimeter scales were glued to the tops of these tracks
so that distances of the moving slide which carried the coincidence target
for Method 2 could be easily determined. For the other measurement technin

que the slide with its appropriate projection target was clamped on these

 

 

 

 

i
99.94011.
50cm.
U 50 C"l.
A Reference
Dis'once
25c
2:1. '2 CHI.
.
7cm.
lnterpupfllary
Distance

 

350

399.89cnm

Cm.

 

l9‘r.9|cm.

 

 

 

150cm.

 

 

505m.
/Reference

Dismnce

 

 

Figure 2. Distances to proiection torqet centers.

_ 23 -

tracks at the 25, 100, and 400 cm. distances.

The projection target for the outlining technique (Method 1) was a
blank sheet of grey posterboard with a fixation point centered on it at
eye level. The same projection target was used for the apparent size
measurements (Method 4). For this method, however, fixation points were
located somewhat to the left of center to allow more room on the projection
screens to move the calipers up and down at a location to the right of the
area where the afterimage was projected. At the 50 and 200 cm. projection
distances, which were also the afterimage formation distances, the projec-
tion screens were not clamped to tracks but were inserted into the forming-
stimulus holder. This was either already located at the proper distance
during formation of the afterimage or was moved there after afterimage
formation if projection was at the other distance.

Two sets of calipers were used for the two calipers measurement
techniques. One which opened to 21 cm. was used for the 25, 50, 100, and
200 cm. projection distances. A large calipers was constructed of the same
general shape as the smaller calipers to measure afterimages at the 400 cm.
distance. This calipers could easily open to twice the 32 cm. height
which Emmert's law would predict for afterimages at this distance.

The three coincidence targets for the second measurement technique
were of the same proportions as the forming stimuli but were the left
halves instead of the right halves of squares. At the 25 cm. projection
distance this was a 2 cm. target with outlines 1.5 mm. wide. At the 100

cm. this was an eight cm. target with six mm. outlines and at 400 cm.,

it was 32 cm. high with 2.4 cm. outlines. A fixation pninr corresponding

_ 24 _

to the one on the forming-stimuli was located on each of these targets.
This fixation point was viewed after an afterimage was formed and the
target was then positioned by the experimenter at a distance from the
subject where the afterimage and coincidence target were reported to be
the same height. At this point, the combined figure of afterimage and
coincidence target looked like a completed square. Since the coincidence
target was located alongside the afterimage a vernier type of measurement
was involved. This was found in pilot work to be more accurate than
having a coincidence target which overlapped with the afterimage. This
may have been because the contours of a real image interact to a great
extent with afterimage contours, pushing each other around, so to speak.

A similar vernier principle was used in the third measurement
technique. At the 25 cm. projection distance this consisted of two 1.5
mm. bands which formed a taper that varied from 1.5 cm. apart at one end
to 2.6 cm. apart at the other end with the 1.1 cm. difference taking place
over a length of 38 cm. This taper was exposed in a slot, 1 cm. wide
which was bordered on the right by a blank grey projection field which
the afterimage was viewed against (See Fig. 3). The afterimage thus
butted up against the exposed pair of lines in a similar manner to the
way the coincidence target and afterimage met in the second measurement
method described above. The experimenter slid this taper along until
the subject reported that the height of the afterimage just coincided
with the height of the bands.

A similar target was used at the 100 cm. distance. The taper

/ Afteriioge as it appeared with

/ comparison stimulus too large

 

\ .
/
/

/

 

 

l
”Ll

 

 

l... \‘
I'm (
Fixation
Point

 

 

 

 

 

Movable slide

 

 

 

 

 

 

Figure 3. Taper coincidence target,

_ 26 -

ranged from 7 cm. to 9 cm. and took place over 71 cm. The width of

these bands was 6 millimeters corresponding to the width of the fixed
size figure in Method 2. At the 400 cm. distance a different measurement
method was used although similar in principle since the distance remained
fixed while the target changed in size. An adjustable figure similar to
that used in the second method was constructed from cardboard which could
be varied in height from 25 cm. to 38 cm. This was held alongside of the
afterimage projection area and adjusted by the experimenter until it
coincided in height with the afterimage. A taper target was not used at
this distance because the large size posed difficulties of construction

and adjustment.

Procedure

Twelve subjects, six men and six women ranging in age from 17 to
24 were used in the study. Visual acuity, with correction if necessary,
was excellent in both eyes and this was the only criterion used in their
selection. Subjects were all undergraduate college students, fewtof
which had any previous experience in psychology experiments. They were
paid 4 dollars for approximately three hours of data collection time.

The 32 afterimages were measured by the subject in two one and
one-half hour sessions on two separate days. All 16 at one session were
formed at one of the two formation distances and the initial formation
distance was alternated among subjects, three of each sex starting with
the 50 cm. forming distance and the others with the 200 cm. distance.

Presentation of the 16 was random for each session.

_ 27 _

At the first session, subjects were introduced to the apparatus,
the distance of the headrest was adjusted, and instructions and practice
given with each of the afterimage measurement techniques. Then when a
subject stated that he understood how to make the different measurements
and his afterimage measurements indicated this to be so, the regular
experiment was begun.

To form each afterimage, subjects placed their heads in the head
and chin rest and fixated the fixation point on the forming-stimulus.
This was then illuminated for 20 seconds after which the forming-stimulus
was removed and the appropriate projection target was presented at the
apprOpriate distance. Measurements of this afterimage then began imme-
diately and continuedfor three minutes or more unless the afterimage faded
prior to this time. The time of each measurement from the end of stimula-
tion was recorded. This was done to control for the shrinkage in after-
image size over time that occurred with most subjects. Young (1948) also
reported such a decline in afterimage size with time. His procedure con—
trolled for this by taking a single measurement at a fixed time after the
afterimage was formed. The present method of obtaining several measure—
ments and keeping track of the elapsed time provided much more data, with
instances of as many as a dozen measurements per afterimage for some
subjects.

As soon as one afterimage was faded to the point where further
measurements could not be made, a new afterimage was formed, projected,

and measured. After ten such formations and measurements, the vision of

_ 23 _

the subject was tested on the Banach & Lamb Orthorater. Acuity of the
eyes together and singly was determined at both far and near. Lateral
and vertical phorias were also determined at the two distances. In addi-
tion, color vision and depth perception were also tested. Half of these
vision tests were made at one session and half at the next since they
provided a welcome break for both subject and experimenter. Following
the vision testing the final six afterimages of the session were formed
and measured.

In all four measurement methods the measuring device was initially
positioned larger on the first measurement of an afterimage followed by
the device being positioned smaller, than large and small positionings
were alternated until the afterimage was no longer measurable. The cali—
pers measurement techniques, in particular, were highly influenced by the
initial separation of the points.

Very early afterimage measurements were often considerably larger
than succeeding ones. This, no doubt, resulted from the enlarged fuzzy
appearance of afterimages after they were first formed which was noted by
several subjects and probably observed by all. In addition, very late
afterimage measurements in the sequence were often much smaller or much
larger than the others in the sequence. For these two reasons measurements
earlier than one minute after formation and later than three minutes after
formation were not included in the main results.

Since the scalloping that resulted from alternating the initial

position of the measuring device for a measurement was quite pronouned with

_ 29 _

some measurement techniques, it was essential that an even number of
measurements be used in computing the mean for the series of measurements
of a single afterimage. If there were an odd number of measurements be—
tween one and three minutes the following procedure was used. If there
were seven or nine measurements the measurement closest in time to either
1 or 3 minutes was eliminated and the mean calculated with six or eight
measurements respectively. If there were three or five measurements bet-
ween one and three minutes, the closest measurement to one and three
minutes which was not previously included was included to make four or
six measurements.

This fixed procedure of averaging all measurements over a fixed
time period should have eliminated any bias produced by diminution of the
size of the afterimage over time. For most subjects this diminution was
considerably smaller than the unsystematic variation and very little
variance reduction would have been derived from covarying Observation

time, a procedure that had been initially considered.

CHAPTER IV: RESULTS

The order of presentation of the results is determined by their
relevance to (1) the questions regarding the apparent size of afterimages
at different projection distances and the influence of this apparent size
on typical afterimage measurements made with calipers or compass points,
and to (2) the question of whether magnification changes take place in
the eye for different fixation distances which could account for the
perceptual anomalies of overconstancy, changes in visual acuity at diffe—
rent distances, etc. The remaining findings of sex differences, practice
effects, and individual differences follow. These latter results are only

tangentially relevant to the above theoretical questions.

 

gpapges in Afterimage Size with Projection Distance for Different
Measurement Methods

The analysis of variance of afterimage measurements for the three
common projection distances indicated that the main effects of measure—
ment method and projection distance and the interaction of these two
variables accounted for more than 70 percent of the total variation (see
Table 1 for the analysis of variance). F-ratios for method, projection
distance, and their interaction were 40.7, 84.5, and 69.5, respectively.

These are the main findings of the dissertation and are illustrated
in Fig. 4. In this figure the mean visual angle of the comparison stimulus
required to match the subjects' afterimages is plotted at the 25, 100, and
400 cm. projection distances for all four measurement methods and also at
the 50 and 200 cm. projection distances for the calipers and apparent-size

measurement methods.
- 30 _

_ 31 _

 

TABLE 1; Analysis of Variance

Source of Variance Sum of Mean
Squares df Square F

Between Subjects VT
A (Sex) .031432 1 .031432 6.31*
B (Order of Formation Dist) .003275 1 .003275 0.66
AB .008613 1 .008613 1.73
Subjects Within Groups .039900 8 .004988
Within Subjects
C(Formation Distance) .007644 1 .007644 2.16
A0 .004464 1 .004464 1.26
BC .000082 1 .000082 0.02
ABC .000842 1 .000842 0.23
C x subj. w. groups .028347 8 .004545
D (Projection Distance) .510245 2 .255122 84.52**
AD .006193 2 .003097 1.02
BD .012978 2 .006489 2.15
ABD .009321 2 .004661 1.54
D x subj. w. groups .048297 16 .003018
CD .009880 2 .004940 3.88*
ACD .000358 2 .000179 0.14
BCD .004894 2 .002447 1.92
ABCD .000513 2 .000256 0.20
CD'x subj. w. groups .020365 16 .001273 '
E (Measurement Method) .655440 3 .218480 40.75**
AE .018565 3 .006189 1.15
BE .005180 3 .001727 0.32
ABE .007752 3 .002584 0.48
E x subj. w. groups .128686 24 .005362
CE .012343 3 .004114 1.63
ACE .017080 3 .005693 2.25
BCE .004205 3 .001402 0.55
ABCE .003895 3 .001298 0.51
CE x subj. w. groups .060669 24 .002528
DE .738578 6 .123096 69.48**
ADE .011346 6 .001891 1.07
BDE .017234 6 .002872 1.62
ABDE .020120 6 .003353 1.89
DE x subj. w. groups .085035 48 .001772
CDE .013194 6 .002199 2.34*
ACDE .004666 6 .000778 0.83
BCDE .030470 6 .005078 5.41**
ABCDE .004686 6 .000781 0.83
CDE x subj. w. groups .045041 48 .000938
TOTAL 2.631350 287 *Significant at .05 level

**Significant at .001 level

VISUAL ANGLE

OF
OF COMPARISON STIMULUS

TANGENT

o—A—O Apparent sixe method
._____. Outlining method
D-———~——U IsI coincidence method

.IIO .. .____._. 2nd coincidence method
.IOO -
.090 n 0

    
 

 

 

.080 _. ~32

dire of formation stimulus

 

.070 1 l I i I
25 50 I00 200 400
PROJFCTION DISTANCE ( CM.)

Figure 4. Afterimage measurements For the different
methods and projection distances.

_33_

The ordinate in Fig. 4 and in all following plots of the data re-
presents the tangent of the visual angle of the matching target. For the
apparent size, calipers, and taper measurement methods thisiwas obtained by
dividing the size of the space between the caliper points or between the
outer edges of the tapered lines by the fixed distance of the particular
projection screen being used: 25, 50, 100, 200, or 400 cm. For the
other measurement method with the movable slide, the tangent of the visual
angle was obtained by dividing the 2, 8, or 32 cm. target height by the
distance that it was positioned from the subject when it matched the
afterimage in size.

The tangent of the visual angle of the formation stimulus was
.0800 for both the 50 and 200 cm. stimuli. (The .0800 figure obtained
by dividing the distance of the target into the size of the target under—
estimates the actual visual angle, which would be obtained exactly by
determining the arctangent of .0400 and doubling it. The tangent of
the actual visual angle is thus .08017, a negligible difference.)

Emmert's law predicts that all of the data would fall on the horizontal

line representing this .0800 tangent.

Findiqgs with the Coincidence Measurement Method. The line representing
the .0800 tangent of the visual angle of the forming-stimuli is also

presented in Fig. 4. It can be seen that only slight deviations from it
did, in fact, occur for the slide and taper coincidence measurement methods.
This corresponds to a similar finding by Onizawa (1954) for the slide

technique.

_ 34 _

T-tests were calculated to determine whether the deviations from
Emmert's law at each projection distance are significant, and also to
test whether the measurements by the two coincidence methods differ from
each other. These are presented in Table II.

The small (average 1%, maximum 3%), but significant positive
differences between some projection distance measurements with these
coincidence techniques and the .0800 figure that Emmert's law predicts
can probably be accounted for by the enlargement of the afterimage as a
result of diffraction, spherical abberation, and the small tremor movements
of the eye. These factors would combine to produce slightly blurred after"
images which thus would be slightly larger and would require slightly
larger targets to match them than the targets that formed them.

The absence of significant differences at the extreme projection
distances for the two coincidence measurement techniques would support
Hypothesis 4 that it was not the saliency of distance in the slide techni-
que that accounted for the Onizawa (1954) findings but something related

to the coincidence measurement process.

Results of the Apparent Size Measurement Method. Very large deviations
from Emmert's law were found with the apparent size measurement method.

It will be recalled that this method involved calipers presented somewhat
away from the portion of the projection screen where the afterimage was
viewed and kept in motion to prevent any attempt at coincidence measure-
ment. The afterimage projected at 25 cm. was found to be 38 percent larger

than the afterimage projected at 400 cm. In the first row of Table III

TABLE

II:

Significance Tests of Differences

_ 35 _

for Coincidence Methods

 

PROJECTION DISTANCE

 

 

 

 

 

25 cm. 100 cm. 400 cm.
Slide & .0800 t=.60 t=6.8 t=2.2
p<.001 p<.05
Taper & .0800 t-3.3 t-2.5 t-O.9
p<.05 p<.05
Slide & Taper t=1.1 t-3.9 t-1.3
p<.001

 

 

 

 

 

TABLE III:

_ 36 _

Significance Tests of

Differences for Apparent Size and Calipers Methods

 

PROJECTION DISTANCE

 

 

 

 

 

25 em. 50 cm. 100 cm. 200 cm. 400 cm.
Apparent size t=11.8 t=11.4 t-5.7 t-0.2 t-1.2
& .0800 p<.001 p<.001 p<.001
Calipers & t-10.6 t-3.7 t-4.3 tsO.2 t-4.3
.0800 p<.001 p<.001 p<.001 p<.001
Apparent Size t=7.8 t-8.2 t-3.9 t=0.01 tsl.4
& Calipers p<.001 p<.001 p<.001

 

 

 

 

 

 

 

_ 37 _

are presented the results of t—tests for the differences between the appa-
rent size measurements and the .0800 prediction of Emmert's law for the five
projection distances. The measurement at 400 cm. is not significantly less
than the prediction of Emmert's law but it does correspond to similar find»
ings by Crookes (1959), Hastorf and Kennedy (1957), and Price (1961) of a
smaller apparent size than the size predicted by Emmert's law for after-

images projected at a considerable distance.

Results for the Calipers Measurement Method. The "classical" measurement
method, where calipers were held around the afterimage and adjusted until
the points were reported by the subject to just touch the extremities of
the afterimage, also provided large deviations from the .0800 prediction
of Emmert's law although the deviations were not as great as for the
apparent size measurement method except at the 400 cm. projection distance.
Afterimages projected at 25 cm. were found to be about 15 percent larger
than the 400 cm. projected afterimages. The difference is in the general
range of the typical findings of other studies (Carr, 1935, etc.) where
afterimages were found to be larger at near projection distances than at
far projection distances, when measured with calipers or with a beam com-
pass.

The second and third rows of Table III present the results of t-tests
for the differences between these measurements and the .0800 prediction of
Emmert's law and between these measurements and the apparent size measure-
ments, respectively. For the 25, 50, and 100 cm. projection distances the

"classical" calipers measurements are significantly less than the apparent

-38-‘

size measurements and significantly greater than the value predicted by
Emmert's law. Apparent size and calipers measurements were nearly iden-
tical at the 200 cm. projection distance and neither differed significantly

from the value predicted by Emmert's law at that distance.

Relation Between Calipers and Apparent SizewMeasurements. The fact that
the calipers measurements are in between the apparent size measurements
and the predictions of Emmert's law at 25, SO, and 100 cm., are nearly
identical with this prediction at 200 cm. and are not significantly
different at 400 cm. suggests that the calipers measurements are compromises
between apparent size measurements and coincidence measurements (relative
to the apparent size and calipers measurements coincidence measurements
were all nearly equal to the .0800 figure predicted by Emmert). The
direct relation between the magnitudes of the measurements for apparent
size and calipers methods at the different distances (except for the neg-
ligible difference between the SO and 100 cm. projection distance for

the calipers technique) also supports such an interpretation. This
direct relation was also generally the case for the data of individual
subjects.

In addition, subjects who gave large apparent size measurements
also tended to give large calipers measurements. In Table IV are pre-
sented correlations for the four different measurement techniques with
separate correlations computed for each projection distance. The highest
average correlations across subjects were between the apparent size and

calipers measurements. (The high correlation between the calipers

TABLE IV:

of Measurement

_ 39 -

Correlations;Between Pairs

Methods at Each Projection Distance (N=12)

 

 

 

 

 

 

*fProjectionv App. Size App. Size .App. Size Calipers Calipers Slide
Distance & Calipers & Slide & Taper G Slide & Taper & Taper
25 .55 —.30 .29 .32 .75 .56
100 .52 .14 -.05 .15 .00 .09
400 .56 -.32 -.04 -.07 .13 .32
Average .54 -.16 .07 .13 .29 .32

 

 

 

 

 

 

 

 

_ 4o _

measurement technique and the taper measurement method at 25 cm. did not

occur at the other distances and may be spurious.)

Factors Related to the Magnification Change Hypothesis

The results obtained with the two coincidence techniques have al-
ready been reported. Relatively little deviation from Emmert's law for
these techniques was found at any distance. The standard deviation of
the slide coincidence technique was .0022. That of the taper coincidence
measurement technique.was .0014. These compare to .0151 for the apparent
size measurement method and .0063 for the calipers techniques. These
much smaller variances with the coincidence techniques argue strongly for
their superiority in providing an indication of the eye's magnification
with different fixation distances over the calipers technique. Further
evidence for the validity of the coincidence methods is provided by the
lack of correlation between apparent size measurements and the coincidence
method measurements at all measurement distances. If the coincidence
measurements are biased, it at least is not by the same factor related to
the apparent size measurements that biases the calipers measurements.

With respect to this theoretical question of magnification change,
it is also important to note that the main effect of formation distance
was not significant. Figure.5 shows the barely significant interaction
of this variable with the variables of method of measurement and projection
distance. The slight differences that did occur are for the calipers and
apparent size techniques and then primarily at only the 100 cm. projection

distance. These measurements were found to be less with the 200 cm.

TANGENT OF VISUAL ANGLE

OF COMPARISON STIMULUS

   
   
  

 

 

 

 

-—-G>— Apparent size method
HO .4... Outlining method
' "“ Ist Coincidence method
o\ - 2nd Coincidence method
\
\ 50cm. Formation
.ICO -— -- —— _ 200cm. Formation
——4
.090—1
. 8
0 0“1
I
.080...
.070 J J 1 ' L 4

 

 

25 50 IOO 200 400

PROJECTION DISTANCE (C M.)

Figure 5. Afterimage measurements for different formation
distances and methods.

_ 42 _

formation distance than with the 50 cm. formation distance. This finding
is not relevant to the magnification change hypothesis, but it is of con-
siderable interest since it is opposite to the results of the Ohwaki
study (1955) where afterimages formed at 200 cm. were larger than those
formed at 50 cm. when both were projected at 100 cm.

For the low-variance coincidence measurement techniques the forma~
tion distances produce negligible differences in measured size. The mean
for the 50 cm. formation distance for the two coincidence methods was
.08088 for the 200 cm. formation distance the mean for the two coincidence

methods was .08093.

Sex Differences, Practice EffectsL and Individual Differences

Sex Differences. One other main effect was significant. Males were
found to give largerafterimage measurements than females. Figure 6 shows
the interaction of‘measurement method and projection distance with a further
breakdown based on sex. It can be seen that very little difference bet-
ween the sexes occurred with the slide and taper coincidence techniques
and that this difference was greatest for the apparent size measurements.
Practice Effects. No significant difference appeared for a main effect
that consisted of two levels of a variable based on whether the 50 cm.
formation stimulus was presented at the first session or whether the 200
cm. formation stimulus was presented first. (This was variable "B" in
the Analysis of Variance table.) A highly significant interaction with
this variable was found, however. This interaction is illustrated in

Figure 7. It is the "formation distance at the first session" by forma-

bmbgv

TANGENT OF VISUAL ANGLE
COMPARISON STIMULUS

OF

———O——-— Apparent size method

 

_...__.__ Outlining method
____.c3___ Ist Coincidence method
+— 2nd Coincidence method
‘. ITO —« .
MALES
————— FEMALES
. I00 -+
.090 —‘
.680 -*

 

 

 

‘ ‘ §‘~‘
air-r" '- "4 __ ‘ “a
g“.-
080—
O

 

.070 L

 

25 50 100 260 150
PROJECTION DISTANCE (C.M.)

Figure 6. Afterimage measurements for different methods
by males and females. '

-—O—— Apparent size method
. Oil..;r:eil d

.tt0_€ .110- —O- U ”m3 ' ‘0

.43...

Ist Coincidence method

2nd Coincidence method

._...--—-

.090.“ .090

 

 

 

n
.080 \r . .080 $5”—

 

 

 

 

--- .9

I
.. _ I
3: IST SESSION 2ND SLSSION ; I
“it . i 1 1 a t t 1 #L :5 I
g: 25 50 too 200 400 25 50 I00 200 400 C. I
5,9,: AFTERIMAGES i'ORMED AT 5r Em. C: I

.........4 C2 ‘
.IIO 5 J

.090—1

 

 

.080 "

 

 

 

 

 

 

 

2ND SESSION IST SESSION
1 1 L L 1 l J l
25 . 50 too 200 400 25 50 I00 200 400

AFTERIMAGES FORMED AT 200 C. M.

Figure 7. Afterimage msmts. at Ist and 2nd session for

50cm. formation first and 200cm. formation
first arouos.

_ 45 _

In the upper left hand corner of Figure 7 is presented the graph for the
group receiving the 50 cm. formation stimulus at their first session and
the graph depicts the data for this first session. Directly below this
is the graph of data for the same group but for the 200 cm. formation
stimulus which this group received at the second session. The right hand
curves are for the group that received the 200 cm. formation stimulus
distance first and top and bottom are again the 50 and 200 cm. formation
distances, respectively. The diagonals of the figure thus represent the
first experimental session from upper left to lower right, and the second
experimental session from lower left to upper right.

Despite representing different formation distances the data of the
two figures of the second session diagonal were quite similar, and except
for less overestimation and underestimation of the apparent size measure-
ments for the extreme projection distances did not differ basically from
the overall means of the method by projection distance interaction (Figure
4). The first session diagonal, on the other hand, shows the greater
overestimation and underestimation of these extreme projection distances
that occurred. The effect of practice in the first session is to bring
the apparent size measurements of the second session closer to Emmert's
law. The first session diagonal also showed a large difference between
measurements for the two formation distances. The apparent size measure-
ment at the 100 cm. projection distance was found to be greatly overestimated
when the afterimage was formed at 50 cm., but was estimated to be very much

smaller when the formation stimulus was at 200 cm. Overestimation also

appeared for the calipers data at the 100 cm. prnjecrinn distance For the

_ 46 _

50 cm. formation stimulus. Practice in session one again may have
accounted for these 100 cm. projection distance differences not occurring
in session two.

Individugl Differences. Although the general pattern of the group means
was followed by most subjects in the experiment, there was still wide
variation in their results, particularly for the apparent size measure-
ments. Individual data appear in Figures 8 through 11 of Appendix A.
Figure 8 represents males in the group that received the 50 cm. formation
stimulus first. Figure 10 and Figure 11 present data for males and fe-
males of the groups that received the 200 cm. formation stimulus at the
first session. The curves plotted for an individual are the method by
projection distance interactions and each point represents the mean of
the observations for the two formation distances.

One difference from the overall means that appeared for K.L. and
S.M. (Figure 9) and for J.S. (Figure 10) was a smaller apparent size
method measurement for the 25 cm. projection distance than for the 50 cm.
projection distance. For K.L. a similar relation appeared for the calipers
measurements. For this subject, at least, this initial lower measurement
value does not appear to be a chance occurrence.

Other differences appeared in the slope of the curve representing
apparent size measurements when plotted against projection distance.
These ranged from very steep (M.B., Fig. 11) to fairly flat (J.S., Fig.
10). Individual differences also appeared in the lateral displacement of

these apparent size curves. D.S. (Fig. 10) and S.M. (Fig. 9) have these

_ 47 -

curves displaced to the right with only the 400 cm. projection distance
measurement approaching the .0800 value predictedtby Emmert's law. Others
(C.T., Fig. 11; M.M., Fig. 11) cross the .0800 line at the 100 cm. projec-
tion distance or earlier.

The calipers measurements also reflected individual differences.
This variation generally occurred along a dimension ranging from nearly
exact correspondence to Emmert's law (J.R., Fig. 10; M.B., Fig. 11), to
nearly identical measurements for calipers as those for the apparent size
method (K.L., Fig. 9).

Individual differences in measurements with the slide and taper
measurement methods are negligible and may reflect errors in location of
the headrest for the subject or changes in the way in which his head was
positioned in the headrest, as much as they reflect basic differences in
some factor such as visual function of these individuals. This may be an
indictment of the experimental apparatus and procedure but it is only
meant as a restatement of the fact that the differences over distance with
these measurement methods were very small. It will be argued in the next
chapter that these small differences imply that for almost all size and
distance perception research purposes, Emmert's law may be accepted as
valid along with.its corollary that the magnification changes of the eye
for different fixation distances are negligible.

Correlations of Measurements with Observer Characertistics

Other data on the subjects was obtained beside the afterimage measure-

ments. Correlations were computed between visual acuity, visual phoria,

spherical correction of glasses (0 if none were worn), depth perception and

_ 43 _

age of subjects and their afterimage measurements for the various measure-
ment methods at the different projection distances. With five borderline
exceptions, none of the 96 resulting correlations were greater than the
.50 required for statistical significance at the .05 level with an n of
12. Some patterns of correlations were suggestive, however. Exophoria,
the tendency for the eyes to diverge, was somewhat associated with large
afterimages at the 25 cm. projection distancetand conversely, exophoria's
Opposite, esophoria, was slightly associated with small afterimages at
this projection distance. At the 400 cm. projection distance these re-
lationships appeared to be somewhat opposite to those at the 25 cm. pro-
jection distance. Exophoria tended to go with small afterimages and
esophoria with large afterimages.

Age despite its restricted range of 17 to 24, seemed to show a
pattern with the 400 cm. projection distance measurements, also. For the
slide and taper coincidence measurements methods it produced barely
significant positive correlations, for the apparent size and calipers
measurement methods, nearly significant negative correlations were found.
This latter finding supported an observation from pilot work that the older
the subject, thermore he underestimated the distant afterimage with the
apparent size measurement technique. These age differences are confounded
with the number of years of close work attendant to college work and prob-
ably with many other factors. Specific investigations of variables such
as phoria and age with larger ranges of variation and larger numbers of
subjects are required before any conclusion can be drawn regarding their
effects. Experimental manipulation of the phorias with prisms and lenses
might be a better investigative procedure than correlational studies of

this variable.

CHAPTER V: DISCUSSION

The main results and conclusions of this study can be summarized
in three statements. (1) The apparent size of afterimages is greater than
the value predicted by Emmert's law with close projection distances and
equal to or less than this value for distant projected afterimages. (2)
This apparent size enters into the classical calipers measurement method
causing the large deviations from Emmert's law that have been found in
previous studies. (3) The traditional interpretation of little or no
change in the magnification of the eye at different fixation distances is
supported, since measurement techniques utilizing coincidence targets do
not show deviations from Emmert's law nor do afterimages formed at diffe-
rent distances with constant visual angle stimuli show any differences in
size. Each of these statements is discussed in this chapter plus other
findings related to the effect of formation distance on the apparent size
of afterimages, sex differences, and practice effects. Finally important
implications of the study are presented and further research needs in the

area are outlined.

The Interaction of Apparent Size with Distance

Group means and also data from individual subjects clearly indicated
that the-apparent size of afterimages decreased with the distance of pro-
jection as was specified in Hypothesis 1. This interaction was predicted
prior to the experiment, with the prediction based on the facts of the
large changes of apparent size that occur with oculomotor change, and the
absence of a fixation stimulus during the viewing of afterimages. The
explanation derived for the interaction was that the subject first observed

- 49 _

_ 50 _

either the caliper point-spacing or the afterimage size, then at a slightly
later time, observed the other. It was assumed that this period of time
between the successive judgments allowed the eyes to assume slightly
different fixation positions for each judgment. Close fixation has long
been known to make things appear smaller and, conversely, far fixation
makes things appear larger. To predict an interaction of apparent size
with projection distance where afterimages are judged larger at near than
at far, required that for close projection distances the afterimage por-
tion of the successive size judgments be made with fixation at a greater
distance than fixation during the judgment of the size of the caliper
point spacing. Conversely, with far projection distances the afterimage
size had to be assessed with closer fixation than occurred during the
assessment of the spacing of the caliper points. A more detailed account
of this explanation is presented in Chapter II.

The resting position of accommodation and convergence is at a
somewhat intermediate position (Alpern, 1962) and the assumption was made
in this explanation that the lack of a fixation stimulus during afterimage
viewing allowed the eyes to move toward this fixation rest position. This
assumption of fixation drift plus the assumption of successive measurements
provided the necessary mechanism for the interaction. Admittedly, it was
the need for this interaction to provide an explanation of the calipers
data that led to the aboNe derivation. However, at least some support is
derived for this explanation of the interaction, by the fact that the
interaction of apparent size with projection distance did occur. In

addition, one subject spontaneously reported that his eyes drifted during

- 51 _

apparent size measurements.

This study did not conclusively indicate that the apparent size of
afterimages projected at a large distance (400 cm.) are smaller than
Emmert's law would predict which was part of Hypbthesis 1. However, this
had already been shown by several other studies (Price, 1961; Hastorf and
Kennedy, 1957; Crookes, 1959) where distant projection of the afterimages

occurred.

The Influence of Afterimage Apparent Size on Calipers Measurements

Although the cause of the interaction of apparent size with distance
of afterimage projection cannot be completely specified in this study. The
high correlation of apparent size measurements and calipers measurements
for the 5 projection distances strongly supports Hypothesis 2 that the
typical deviations from Emmert's law in the studies of Carr (1935),
Onizawa (1954), etc., result from the calipers measurements being in some
part apparent size measurements. Individual data, as well as group means,
supported this position. Even when the afterimages did not show the pattern
of largest size at near and smallest at far, there were two instances (K.L.,
Fig. 9; H.H., Fig. 10) where the five measurements for calipers and appa—
rent size correlated perfectly. Further support for this is derived from
the significant moderate correlation across subjects for these two_techni-
ques.

Exactly how apparent size enters into the calipers measurements
cannot be specified until the mechanism for the apparent size changes with

projection distance is known. The fixation resting point hypothesis states

_ 52 _

that it results when the subject, knowingly or unknowingly, does not make
a simultaneous comparison of afterimage and caliper points, but instead
allows a little time and oculomotor change to intervene through successive
judgments of their sizes. The reported difficulty of observing the small
calipers points in these measurements might account for subjects giving
such successive judgments rather than judgments of the simultaneous coin-

cidence of points and afterimages.

The Maggification of the Eye at Different Fixation Distances

An explanation of the typical afterimage size finding (large after-
images at near projection distances and smaller afterimages at far projec-
tion distances) based on changes of the eye's magnification with the diffe-
rent fixation distances was very attractive. Such an explanation would not
only account for the different sized afterimages, but also accounted for
several other important perceptual anomalies, such as increased visual
acuity at a distance over near, "overconstancy", figural aftereffects with
stimuli of constant visual angle at different distances, etc. In providing
an apparent size explanation of the typical afterimage finding, the study
also cast doubt on this optical explanation for the other anomalies. Fur-
ther, stronger evidence against a magnification change explanation of these
anomalies was provided by the near coincidence to Emmert's law with the
Onizawa—type slide coincidence technique and with another coincidence
technique that differed from the Onizawa technique in that it-used a pro-
jection screen at a fixed distance with a target that varied in size. Thus

the data support Hypothesis 3 which stated that when apparent size is

_ 53 -

eliminated Emmert's law will hold, and the absence of differences between
coincidence methods supported Hypothesis 4. Finally the absence of diffe-
rences in afterimage size when afterimages were formed at different dist—
ances supported Hypothesis 5 and indicated that the magnification of the
eye does not differ for the fixation distances of 50 and 200 cm.

Since there was relatively little difference between the overall
means for the slide and taper techniques at the three projection distances,
it is probably safest to conclude only that both methods indicate little
if any change in the magnification of the eye at different distances of
fixation. The Onizawa-type slide technique did result in slightly smaller
afterimage measurements at the close projection distances than at the more
distant ones which is what the traditional physiological optics explanation
would predict would happen. On the other hand, the group means for the
taper technique were nearly identical at the three distances and this
suggests that Emmert's law is true as originally formulated. The group
means for the two techniques did not differ among themselves by much more
than two percent and data for individual Subjects generally did not show
much greater differences. An investigation with trained subjects might
eliminate the differences between these two coincidence.techniques and
more closely illustrate actual magnification changes of the eye. The
present study shows that such deviations are very small, much smaller than

would be required to explain "overconstancy”, for example.

The Failure of Afterimage Size to Vary with Formation Distance

Although the typical finding of large afterimages at near projection

- 54 -

distances and small afterimages at far projection distances seems to be
well accounted for by the assumption that successive apparent size judg-
ments enter the caliper measurements, the Ohwaki (1955) finding of smaller
afterimages with closer formation distances was not replicated in this study
and Hypothesis 6 derived from Ohwaki's results was not supported. As men-
tioned in the last section, the differences with the coincidence measure-
ment techniques for the 50 and 200 cm. formation stimuli ware‘negligible.
The slight differences that did appear actually cancelled each other in-
stead of favoring larger or smaller afterimages at one formation distance*
or the other. Differences with the calipers and apparent size measurement
methods were somewhat larger, but only at 100 cm. for the apparent size
method were they significant. .HoweVer, they were in the opposite relation
to formation distance from the findings of the Ohwaki study when she_used
this same projection distance with the 50 and 200 cm. formation distances.
It is not clear why the Ohwaki finding was not obtained, although
many differences existed between the present study and Ohwaki's. In her
study the forming stimuli were red cardboard squares viewed under normal
room illumination. The brightness of these squares was not given but it
may have» been as much as two orders of magnitude less than the 2,300 ft.-L.
stimulus brightness of the present study. Because of this the afterimages
must have been of much shorter duration than afterimages in the present
study. This may account for the fact that she made only one measurement
per afterimage. A check of first afterimage measurement data in the pre—
sent study was made to see if a different pattern was present than for the

means of all observations between one and three minutes. Little difference

_ 55 -

was found between the two with the 50 cm. formation distance again provid-
ing the largest afterimages (.0908 vs. .0899).

One important difference between the studies that may have existed
is an absence of a fixation point on the projection screen in the Ohwaki
study. She simply stated that the afterimage was "projected on the centre
of a gray screen." An absence of a fixation point might have allowed the
subjects to continue fixating at the distance of the formation stimulus
when they were projecting the afterimage and assessing it for size. If
this afterimage size assessment were then followed by a compass point
spacing assessment at the actual projection distance, the relation of
oculomotor adjustments would be such as to predict small afterimages with
near formation and large afterimages with far formation. In the present
study the presence of fixation points on the projection targets may have
resulted in the eyes being at nearly the same distance for both ends of
the successive judgment measurement process for this 100 cm. projection
distance. If elimination of the fixation point on projection screens with
the present apparatus and procedure were to produce the relationship between
formation stimulus distance and afterimage size that Ohwaki obtained, it

would give additional support to the successive judgment hypothesis.

Possible Explanations of Sex and Other Differences

The differences between apparent size and calipers measurements for
males and females were quite large, particularly at the closer projection
distances. To account for this the fixation—resting-point hypothesis would

predict that the fixation-resting—point is more distant for males than

_ 56 _

females. Male eyes would thus be fixated at a greater distance when the
afterimage size was assessed and thus the apparent size metric would be
greater and the afterimage would look larger. One might account for such
a difference in fixation rest position on the basis of greater participa-
tion by males than females in athletics and other activities that involve
viewing at a distance.

However, individual differences, including the sex differences,
might not reflect different fixation-resting-points, even if the fixation
resting position explanation does apply. Instead, they could reflect
differences in the amount that the eyes are allowed to drift away from the
projection screen toward this rest position. Another possibility is that
equal changes of fixation distance produce different changes in apparent
size for different observers. Several investigators have shown that large
changes in apparent size result from oculomotor changes (Hermans, 1954;
Leibowitz and Moore, 1966; Lie, 1965), but little is known about individual
variations in these apparent size changes.

In the first session there was found to be a greater overestimation
of the apparent size measurements at 25 cm. and a greater underestimatidn
of these measurements at 400 cm. than occurred in the second session. In
terms of the successive judgment explanation, this would probably mean that
subjects allowed their eyes to move closer to the fixation-resting—point
during assessment of the size of the afterimage in the first session than
in the second. The increase in familiarity with the distances of projection
in the second session might account for this since they could allow more

accurate fixation at these distances. Another possible explanation is that

_ 57 _

the time between the successive judgments decreased fromithe first session
to the second and the reduced time prevented as much drift from the projec-
tion screen toward the fixation-resting-point in the second session as
occurred in the first.

In the first session it was also found that the apparent size
measurement at the 100 cm. projection distance was greatly overestimated
for the 50 cm. formation distance but was estimated to be nearly 20 percent
smaller for the 200 cm. formation distance. To account for this in terms
of different oculomotor adjustments in successive size judgments would
require the eyes to be adopting a rest position beyond the 100 cm. projec-
tion screen when the afterimage was formed at 50 cm. and to be adopting a
rest position closer than the 100 cm. projection screen when the afterimage
was formed at 200 cm. It could be argued that the 20 second fixation at‘
one distance during afterimage formation might cause the eyes to seek a
different fixation position to rest the eye muscles. If formation were
close this new position might be expected to be far. If formation were far,
then this new position might be closer than formation. This seem plausible,
but it did not happen in the Ohwaki study where the assumption required to
explain small afterimages with mean formation was that no oculomotor change
took place after formation of the afterimage. No satisfactory explanation
of the contradictory results of this study and the Ohwaki study seems pos-

sible at this time.

Important Implications and Future Research Needs
This final section reviews and discusses some implications of the

presenL study. Perhaps the most important is the explanation the results

_ 58 _

provide of contradictory findings in past studies of Emmert's law. This
explanation is that the apparent size of afterimages has often entered in-
to outlining afterimage measurements, and the more that the data of some
study deviated from Emmert's law in the typical direction, the greater

this influence of apparent size was. When data were in accord with Emmert's
law in a study or indicated somewhat smaller afterimages at near projection
than at far projection, then the measurements were probably bona fide
coincidences between the measurement device and the afterimage and actually
reflected magnification of the eye at the different projection distances.

The study suggests that coincidence methods are sufficiently accur-
ate to assess individual differences in magnification of the eye with
different formation distances. A well-trained subject could probably
demonstrate magnification changes of less than one percent. Because such
changes are very small their measurement would probably be of little
psychological importance but might be invaluable to physiologists and
ophthalmologists for studying the structure of the eye, or changes in its
structure during the development of refractive errors. The study indicates
that the traditional outlining methods of afterimage measurement would not
be appropriate for such research.

The study indicated sex differences and other interesting individual
differences in the measurement of the apparent size of afterimages, and
further investigation of these differences would surely prove enlightening.
These differences were also reflected in the outlining measurements but
apparent size measurements are more apt to get at these individual diffe-

rences and the outlining measurement method should probably be avoided for

_ 59 _

these quite different purposes, also.

In agreeing with-other research (Heinemann, 1961) indicating that
the perceptual anomalies such as overconstancy are not the result of
optical magnification, the study supported the view that some central
magnification process occurs, instead. The process appears to be very
general, applying to the apparent size of objects, visual acuity, flicker
perception, figural aftereffects, and probably other perceptual phenomena,
and thus must be classed as one of the most important perceptual processes.
One approach to the study of this process would be to look at these'anoma-
lies and at the apparent size of afterimages in the same_subjects and
determine if_a relation exists between the phenomena.

There is an immediate need to test the present fixation-rest-posi—
tion explanation of the apparent size changes with distance that were
found to occur. Photographic or other objective means for observing the
position of the eyes during apparent size measurements should indicate if
the size changes are related to changes in convergence of the eyes. If the
drift in fixation were. confined to visual accommodation this might be re-
flected in changes in the size of the pupil which would be expected to in-
crease as the accommodation distance increased. Another approach to this
question could involve manipulation of convergence and accommodation with
prisms and lenses and observe the effect of this on the apparent size of
afterimages.

One assumption in the fixation-rest-position explanation was that
the afterimage of a fused stimulus did not constitute a fixation stimulus.

A parallel assumption to this is that an afterimage formed while the

_ 6O -

stimulus is not fused would lead to disparate afterimages in the two eyes
that gppld,serve as a stimulus for fixation change. No adjustment of the
eyes could fuse these afterimages and one could imagine the eyes becoming
maximally converged or diverged (depending on the initial disparity) in an
attempt to fuse them. Apparently no one has tested this possibility. An
objective means of monitoring eye movements would be useful in this re-
search, also.

These would appear to be the major implications of the present
study and the more obvious avenues for research that could follow it in
this relatively neglected area of study that falls somewhere between
sensory psychology and the more cognitive or conscious aspects of percep-

tion.

_ 61 -
REFERENCES

Alpern, M. Movements of the eyes. Part 1 in Davson, H. (Ed.)
The Eye. Vol. 3, New York, Academic Press, 1962.

Barlow, H.B. and Sparrock, J.M.B. The role of afterimages in dark
adaptation. Science, 1964, 144, 1309-1314.‘,

Boring, E.G. Size constancy and Emmert's law. Amer. J. Psychol.,
1940, 53, 293-295.

Brindley, G.S. Afterimages. Scientific American, 1963, 209, 84—93.
Carr, H.A. An Introduction to Space Perception, 1935.

Crookes, T.C. The apparent size of afterimages. Amer. J. Psychol.,
1959, 72, 547-553.

Edwards, W. Emmert's law and Euclid's optics. Amer. J. Psychol.,
1950, 63, 607-612.

Emmert, E. Grossenverhaltnisse der nachbilder. Klin. Monatsbl. f.
Augenheilkunde, 1881, 19, 443-450.

Epstein, W., Park, J. and Casey, A.. The current status of the size-
distance hypothesis. Psychol. Bull., 1961, 58, 491—514.

Freeman, E. Anomalies of visual acuity in relation to stimulus distance.
Jo Gite SOC. Amara, 1932’ 22, 2854-2920

Ganz, L. Is the figural aftereffect an aftereffect? A review of its
intensity, onset, decay, and transfer characteristics. Psychol.
Bull., 1966, 66, 151-165.

Giese, W.J. The interrelationship of visual acuity at different
distances. J. Applied Psychol., 1946, 30, 91-106.

Gregory, R.L., Wallace, J.G., and Campbell, F.W. Changes in the size
and shape of visual afterimages observed in complete darkness
during changes of position in-space. Qpart. J. Exp. Psychol.,
1959, 11, 54-55.

Hastorf, A.H. and Kennedy, J.L.v Emmert's law and size constancy.
Amer. J. Psychol., 1957, 70, 114-116.

Heinemann, E.G.,.Tulving, E. and Nachmias, J. The effect of oculomotor
adjustments on apparent size. Amer. J. Psychol., 1959, 72, 32-45.

- 62 -

Heinemann, E.G. Photographic Measurement of the retinal image.
Amer. J. Psychol., 1961, 74, 440—445.

Helmholtz, H. Handbuch der Physiologischen Optik. Vol. 1. Verlag
von Leopold Voss, 1866. - ' ' .

Hermans, T.C. The relationship of convergence and elevation changes
to judgments of size. J. Exp. Psychol., 1954, 48, 204-208.

Leibowitz, H. and Moore, D. Role of changes in accommodation and conver-
gence in the perception of size. J. Opt. Soc. Amer., 1966, 56,
1120-1123.

Lie, I. Convergence as a cue to perceived size and distance. Scand. J.
Psychol., 1956, 6, 109-116.

Lukiesh, M. and Moss, F.K. The dependence of visual acuity upon stimulus
distance. J. Opt. Soc. Amer., 1933, 23, 25-29.

McCready, D.W. "Visual Acuity under Conditions that Induce Size Illusions"
Ph. D. Dissertation, Univ. of Mich., 1963.

McCready, D.W. Size-distance perception and accommodation-convergence
micropsia--—a critique. Vision Research, 1965, 5, 189-206.

Norris, 0.0. The nature of distance vision. J. Exp. Psychol., 1934, 17,
462—476.

 

Ohwaki, S. On the factors determining accommodation:' research on size
constancy phenomenon. Tohoku Psychologica Folia, 1955, 14,
147—158.

Onizawa, T. Research on the size of the projected afterimage. Part I.
On the method of measurement. Tohoku Psychologica Folia, 1954,
14, 75-78. -

Pascal, J.I. Effect of accommodation on the retinal image. Brit. J.
Ophtha1., 1952, 36, 676-687.

Price, G.R. On Emmert's law of apparent sizes. Psychol. Record.,
1961, 11, 145-151.

Spigel, I.M. Size constancy and critical flicker frequency. Amer. J.
Psychol., 1964, 77, 496—471. '

_ 63 -
Story, A.W. Has apparent size been tested as a factor in figural
aftereffects? ,Qpart. J. Exp. Psychol., 1961, 13, 204-208.

Sutherland, N.S. Figural after-effects, retinal size, and apparent
size. Quart. J. Exp. Psychol., 1954, 6, 35-44.

Taylor, F.V. Changes in size of the afterimage induced in total
darkness. J. Exp. Psycholp, 1941, 29, 75-80.

Urist, M.J. Afterimages and ocular muscle proprioception. AMA
Arch. Ophth., 1959, 61, 230—232.

 

Woholwill, J.F. "Overconstancy" in space perception. In Lipsitt, L.P.
and Spiker, C.C. (Eds.) Advances in Child Develppment and
Behavior. Vol. I. Academic Press, New York, 1963.

Young, F.A. The projection of afterimages and Emmert's law. J. Gen.
Psychol., 1948, 39, 161-166.

Young, F.A. Concerning, Emmert's law. Amer. J. Ppychol., 1951, 64,
124-128.

 

Zajac, J.L. Spatial localization of afterimages. Amer. J. Psychol.,
1960, 73, 505—522.

 

APPENDIX A

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-64-

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