A STOCHASTIC REVISED SAMPLED DATA
MODEL FOR EYE TRACKING MOVEMENTS
by
John D.
Forster
B.S.E. (Aerospace), The University of Michigan
(1966)
B.S.E. (Mathematics), The University of Michigan
(1966)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1968
Signature of Author
/epart ent of Aero rutics
Astrgdabtics
Jun&1 68
Certified by
sis
t
Y
I
Accepted by
Chairman, Departmental
Graduate Committee
and
ii
A STOCHASTIC REVISED SAMPLED DATA
MODEL FOR EYE TRACKING MOVEMENTS
by
John D.
Forster
Submitted to the Department of Aeronautics and Astro-
nautics on February 23, 1968, in partial fulfillment of the
requirements for the degree of Master of Science.
ABSTRACT
The sampled data model for eye tracking movements of
Young is revised to make the pursuit system continuous and
Target-synchronized and nonproportional to target rate.
synchronized sampler control logic are analyzed.
Frequency
distributions of latencies to target steps for non-synchronized sampling systems with stochastic intersampling intervals
Transient responses
are shown to be strictly non-increasing.
of the model are shown to agree with classes of observed eye
movement including steps, pulses, ramps, and step-ramps.
Four experiments are performed in which the occurrence of a
target step is synchronized to the occurrence of a saccade.
The results show responses corresponding to both synchronized
and non-synchronized sampling occurring in the eye movement
control system.
The sampler control logic in a sampled data
model for eye tracking movements, therefore, should have a
non-synchronized sampler which can be adapted in phase and
frequency depending upon the target movement.
Thesis Supervisor:
Title:
Laurence R. Young
Associate Professor of
Aeronautics and Astronautics
iii
ACKNOWLEDGMENTS
At the conclusion of this
study the author wishes to
thank most sincerely Prof. Laurence R. Young, his thesis
advisor, for his guidance in both the fields of eye move-
ment and control engineering, and his helpful criticism of
the manuscript.
The author wishes to thank his subjects for their time
and interest and for much assistance in preparing and carrying
out the experiments.
Miss Linda Merrifield also deserves
special thanks for tireless effort in preparing the manuscript.
The author acknowledges his research assistantship
supported in part by NASA grant NsG -
577, and the work of
the Computation Center as part of problem #M6037.
Finally the author wishes to express his deepest appreciation
to his wife Sue for long hours of patient assistance in preparing
the text.
iv
TABLE OF CONTENTS
Page No.
Chapter No.
CHAPTER
1
INTRODUCTION
1
CHAPTER
2
A STOCHASTIC REVISED SAMPLED DATA
MODEL
5
2.1
The Discrete Nature of Saccadic Eye
Movement
5
2.2
The Continuous Nature of Smooth
Pursuit Eye Movement
7
2.3
A Revised Sampled Data System
9
2.4
The Nature of Sampling
11
2.5
Intersample Distribution for Optimum
Unsynchronized Sampled Data Modeling
14
TRANSIENT RESPONSE OF THE REVISED MODEL
26
3.1
Step Response
26
3.2
Pulse Response
28
3.3
Ramp Response
33
3.4
Step-Ramp Response
36
3.5
Ramp-Step Response
39
EXPERIMENTAL PLAN, APPARATUS, AND
PROCEDURE
43
4.1
Saccade-Synchronized Data Reduction
43
4.2
The Saccade-Synchronized Inputs
44
4.3
Model Response to Saccade-Synchronized
47
CHAPTER
CHAPTER
3
4
Experiments
V
Page No.
Chapter No.
4.4
Apparatus and Procedures
48
4.5
Target Generation
48
4.6
Eye Position Measurement
50
4.7
Input Generation
51
4.8
Saccade-to-Step Delay Control
53
4.9
Eye Movement Recording
54
4.10
Procedure
55
4.11
Data Reduction
57
RESULTS
58
5.1
Distribution of Initial Saccadic
Response
59
5.2
Experiment One Returning Pulse
Synchronized
63
5.3
Experiment Two Stairway Pulse
Synchronized
66
5.4
Experiment Three - Ramp with
Synchronized Inward Step
69
5.5
Experiment Four - Ramp with
Synchronized Outward Step
72
5.6
Subject Interexperimental Results
72
CONCLUSIONS AND RECOMMENDATIONS
83
6.1
Conclusions
83
6.2
Recommendations for Further Study
85
CHAPTER
CHAPTER
5
6
87
REFERENCES
THE EXPERIMENTAL SYSTEM
91
A.1
The Digital System
92
A.2
The Analog System
97
APPENDIX
A
vi
Page No.
APPENDIX
B
EXPERIMENTAL DATA
102
APPENDIX
C
STOCHASTIC SAMPLED DATA SYSTEM
SIMULATION PROGRAMS
127
vii
LIST OF FIGURES
Figure No.
Page No.
2.1
A Revised Sampled Data Model
for Eye Tracking Movements
10
2.2
Definition of Symbols Showing
Inputs Occurring in Sampling
16
Instants T
c
2.3
Mathematical Descriptions of
Latency Histograms
20
2.4
Simulated Latency Histogram for
a Constant Sampling Interval
System
22
2.5
Simulated Latency Histogram for
a System with Sampling Intervals
Uniformly Distributed Between
0 and 200 msec.
23
2.6
Simulated Latency Histogram for
a System with Sampling Intervals
Uniformly Distributed Between
150 and 250 msec.
24
2.7
Simulated Latency Histogram for
a System with Sampling Intervals
Dual-Uniformly Distributed as
Described in Eq. 2.5
25
3.1
Step Input Model Variation as a
Function of Synchronization to
the Sampling Instants
27
3.2
Beeler's Average Latencies in
Response to the First Step of
Pulse Inputs
29
3.3
Beeler's Average Latencies in
Response to the Second Step of
Pulse Inputs
29
viii
Figure No.
Page No.
3.4
Forms of Response Predictable for
Pulse Inputs
31
3.5
Percent No Response to Returning
Pulse Input
32
3.6
Percent No Response to Stairway
Pulse Input
32
3.7
Robinson's 10 deg./sec. ramp
34
response
3.8
Step-Ramp Model Response as a
37
Function of Synchronization of
Inputs to Sampling Instants
3.9
Comparison of Regions of NoSaccade Step-Ramp
40
3.10
Ramp-Step Response
41
4.1
Experimental
Inputs
45
4.2
Average Latency Predicted to
Saccade-Synchronized Experiments
when Presented to Sampled Data
Models with different Sampler
Control Logic
49
4.3
Typical Eye Monitor Records
52
4.4
Typical Experimental Recording
56
5.1
Saccadic Latency Histograms
60
5.2
Experiment One -
64
5.3
Experiment One - Intersubject
Means and Model Predictions for
Two Sampler Control Logics
65
5.4
Experiment Two - All Subjects
67
5.5
Intersubject Means for Experiment
68
All Subjects
Two and Model Predictions for Two
Sampler Control Logics
5.6
Experiment Three - All Subjects
5.7
Experiment Three -
Intersui c
70
Me nq
71.J..
I
ix
Page No.
Figure No.
5.8
Experiment Four -
All Subjects
73
5.9
Experiment Four -
Intersubject Means
74
5.10
Subject CO -
5.11
Subject NVH -
All Experiments
77
5.12
Subject AVH -
All Experiments
78
5.13
Subject LN -
All Experiments
79
5.14
Subject SF -
All Experiments
80
5.15
Subject MK -
All Experiments
81
A.l
The Digital System Input List
A.2
Target Movement Circuit
99
A.3
Saccade Detector Circuit
99
A.4
Analog Control Panel Circuits
101
B.1-B.24
Experimental Data for All Subjects
to All Experiments
103-126
C.1
Simulation of Constant Sampling
Interval System
128
C.2
Simulation of System with Sampling
Intervals Uniformly Distributed
Between 0 and 200 msec.
129
C.3
Simulation of System with Sampling
Intervals Uniformly Distributed
Between 150 and 250 msec.
130
C.4
Simulation of System with Sampling
Intervals Dual-Uniformly Distributed
as Described in Eq. 2.5
131
C.5
Program Notes Applying to all ListingsLine References refer to Figure C.l
132
C.6
Specific Program Notes
133
All Experiments
Program and
for each Listing
76
93
CHAPTER 1
INTRODUCTION
In this thesis, the classes of outputs which arise from
varying the timing of an input in relation to the sampling
intervals are studied in a refined version of Young's sampled
data model for eye tracking movements
(23).
Target-synchronized
and non-synchronized sampler control logic for the model are
investigated by probabalistic analysis and simulation of a
non-synchronized system, and by four saccade-synchronized eye
movement experiments.
These
investigations reveal that both
types of sampler control logic
should play a role in a sampled
data model for eye tracking movements.
Saccadic eye movements were first distinguished from
smooth pursuit movements by Dodge
in 1903.
movement or saccade is a burst of muscle
A saccadic eye
force moving the eye
rapidly from one angular position in relation to the head, to
another.
The duration of a saccade is usually less than
.1
sec. during which the eye's rotation rate may reach 600 deg./sec.
for large saccades
(26).
The purpose of a saccade in eye
tracking movements is to correct position error between the
target and the eye.
The discrete nature of the saccadic eye movement control
2
system has been well established (1, 12, 13,
19, 20, 23).
Several discrete systems have been proposed, including preprogramed systems, saturating systems, digitally controlled
systems, and sampled data systems.
It is questionable whether
the minute differences between such systems allow differentiation between them in defining, from present research, the
exact nature of the eye movement control system.
at all, for example, could be equated to a
Any system
system pre-programed
to give the observed response to each input.
Furthermore for
inputs requiring only one sample, a target-synchronized sampled
data model need only chose stochastic synchronization times
to be exactly those of observed latencies minus a constant
time delay.
This thesis evaluates the assets and limitations
of a sampled data model including possible extentions to
include in model results,
sampler width.
sampler adaptation, and finite
This modeling does not show that such sampling
takes place in the actual saccadic eye movement control system.
The model does, however, give a simple analyzable means of
predicting saccadic eye movements based on target movement
only.
Pursuit eye movement consists of the smooth low velocity
eye movements which appear in eye tracking of target movements
with low velocity components.
do not exceed
30 deg./sec. and appear only when the
visually tracking a target.
is
Pursuit eye movements usually
subject is
The purpose of pursuit movement
to match eye angular velocity to that of the target in order
to prevent a build-up of error in eye position between possible
saccades.
3
The experiments of Rashbass
(14)
(12) and recently of Robinson
have lead to a change in the pursuit control system of
Young's
sampled data model to make it a continuous function of
target rate rather than a sampled function of error rate.
This revision is discussed in Chapter 2 of this thesis.
If unsynchronized sampling occurs in the eye movement
control system, observed latency distributions must be explainable as a function of the stochastic distribution of intersample
times.
A careful analysis and simulation of the non-synchronized
system at the end of Chapter 2 leads to the result that latency
distributions must be non-increasing except at the lowest
latency where they jump from zero to their maximum value.
Actual
latency distributions do increase, however, for approximately
the
first 50 msec. of possible latency.
Thus if unsynchronized
sampling occurs in the eye movement control system, the eye must
be able to shorten the sampling interval if a step input is
observed when the eye has not performed a saccade for
0.2 sec.
The transient response of the model is discussed in Chapter
3.
In general, the classes of eye movement predicted by varying
the timing of input to the first sample agree with observed
classes of eye movement.
If an input to the revised sampled data model occurs
immediately after a saccade, the
sample which caused that
saccade and the sample which will cause a response to the
input will be separated by only one sampling interval.
follows that the intersampling interval and the
It
sampler control
logic would be revealed by the distributions of response form
4
for inputs occurring at small constant times after a saccade.
Four such saccade-synchronized inputs were performed.
The
results show responses corresponding to both target-synchronized
and non-synchronized sampling with the predominant type of
control logic changing from experiment to experiment.
The sampler control
logic to model the results of these
experiments would be a free running non-synchronized sampler
which can be influenced in phase and frequency depending upon
the difficulty of observed target motion.
The trade-off
between difficulty and sampler influence, and the complete
extention of the model to finite width sampling are topics
for further research.
5
CHAPTER 2
A STOCHASTIC REVISED SAMPLED DATA MODEL
In this chapter, evidence is presented of the discrete
nature of saccadic eye tracking movements and the continuous
nature of smooth pursuit eye movements.
dence,
Based on this evi-
a revised sampled data model is presented and its
limitations discussed.
Target-synchronized and non-synchronized
forms of control logic for the sampler are weighed, and the
equation for the distribution of non-synchronized intersample
times for
2.1
fit of observed latencies is derived.
The Discrete Nature of Saccadic Eye Movement
A control system is discrete if it changes its output
based on new input information taken in only during very
short periods,
interspursed by periods of no revision of out-
put no matter how large the error may instantaneously become.
The most convincing demonstration of the discrete nature of
the saccadic eye movement control system is the response to
a target that steps
or less.
to one side and then returns in 0.2 sec.
If the eye responds, and it may not, it responds by
making a saccade approximately 0.2 sec. after the first step,
despite the fact that this movement is inappropriate since it
6
takes the eye away from the target.
after an additional
0.2 sec.
The eye then returns
The response predicted by a
continuous system with a pure delay would be a pulse of the
same duration as that of the target, delayed in time by an
amount equal to the reaction time.
A continuous system also
fails under any circumstance to predict no response.
of these responses have been shown by Westheimer
Young
(23) in 1962,
Beeler
(1) in 1965,
Evidence
(19) in 1954,
and by the results of
this thesis.
Further evidence of the discrete nature of saccadic eye
response is found in the results of open-loop and variable
feedback experiments.
In these experiments,
the effective
visual feedback is modified by the addition of an external
path from measured eye position to target position.
In the
open-loop experiment, the response to a target step is a staircase of equal amplitude saccades spaced approximately 0.2 sec.
apart.
The response to variable feedback also shows a refrac-
tory time of 0.2 sec. between saccadic responses.
These results
were found by Young (23) in 1962 and duplicated by Robinson
(14) in 1965.
Furthermore, the frequency response of the eye shows an
extraneous peak at about 2.5 cps.,
as would characterize a
discrete system with fundamental refractory interval of 0.2
sec.
This result was found by Young
(23),
who recorded subjects
tracking a continuous pseudo-random input consisting of a sum
of sine waves, and analyzed the response at each of the input
frequencies.
Young found good agreement with the results of
Fender and Nye and others.
For an explanation of frequency
7
response
in a discrete system, see Jury
(8).
The discrete nature of the saccadic eye movement system
also evidences itself in the response to predictive square
waves.
cps.,
Young studied subjects tracking a square wave of 0.4
He plotted
an input known to elicit predictive saccades.
the percent error in the size of the saccadic responses as a
function of the
time from actual target movement to the saccade.
Young found random error even when the target moved before
the already commanded saccade by as much as
120 msec.
result was also shown by Horrocks and Stark
(6).
This
In this
experiment, the eye was unable to modify an already commanded
saccade even though new information was available 0.12
before the onset of saccadic movement.
sec.
The system must be
discrete, then, since it cannot take in information over these
0.12
sec. intervals.
One discrete system which exhibits all the properties
described above is a sampled data system.
Young
(23) proposed
such a model of the saccadic eye movement control system in
which eye position error is sampled and used to command appropriate saccadic eye movements.
Young showed that this model
agrees well with mean saccadic eye movement responses.
2.2
Continuous Nature of Smooth Pursuit Eye Movement
Rashbass
(12) investigated the pursuit eye movement con-
trol system by presenting subjects with ramp inputs
velocity target movements),
(constant
and with step-ramp inputs
(constant
velocity movements preceded by a step movement in the opposite
direction).
Rashbass found that in response to both ramps
8
and step-ramps, smooth pursuit eye movement could occur before,
during, or after saccadic eye movement.
Thus he concluded
that the pursuit movement command system was independent of
the saccadic movement command system.
Since the occurrence
of smooth pursuit movement in the direction of the ramp before
a saccade in response to the step actually moved the eye away
from the target, Rashbass further concluded that the smooth
pursuit system was proportional to target rate only.
also noted that if the
Rashbass
step size in degrees is 0.15 to 0.2
times the ramp rate in degrees per second, the eye responded
with smooth pursuit motion containing no saccades.
*Robinson (14)
studied the smooth pursuit system using
sequences of the above described step-ramps that elicit no
saccades.
The responses showed that the pursuit system was
capable of making two distinct movements temporally spaced
by the same time interval as the input, for spacings as low
as 150,
100 and 75 msec.
Robinson also studied the pursuit
system under conditions of variable feedback by using a
differentiator to eliminate saccadic eye movements
feedback signal.
from the
Eye responses to these experiments were
always smooth and continuous even in the Tantalus-like chase
of positive feedback.
Under high
(-4 to -8) values of nega-
tive feedback, the pursuit system showed sinusoidal oscillations at a frequency of 2.9 - 3.3 cycles/sec.
These results
are in contrast to variable feedback around the saccadic
system which were also shown by Robinson to exhibit discrete
responses.
9
Robinson further showed that discrete changes in pursuit
velocity occur at saccadic responses in the same direction.
This finding helps to explain why Westheimer
(19) and Young
(23)
considered the possibility of pursuit movements occurring in
constant velocity segments between saccades since both their
experiments included saccadic responses
as the pursuit movements.
in the same direction
On the strength of these experiments,
Robinson concluded that the pursuit eye movement control system
was continuous rather than discrete in nature.
2.3
A Revised Sampled Data System
A revised sampled data model with a continuous, target
rate sensitive, pursuit loop has been developed by Van Houtte
and Forster
(4) and is shown in Fig. 2.1.
This model retains
the sampler of eye position error for the saccadic system
and thus preserves the excellent modeling of discrete saccadic
response of Young's original model.
proposed by Vossius
parameters.
A model of this type was
(17) but without any attempt to define
The continuous pursuit loop contains a delay and
a differentiator followed by a non-linearity and an integrator.
The input to the pursuit system is target position which is
differentiated, making the system proportional to target rate
only.
The pursuit non-linearity exhibits both saturation and
a cut-off level.
The saturation level of 25-30 deg/sec reflects
the actual maximum pursuit velocity of observed eye movement.
The cut-off level eliminates pursuit response to small target
steps which caused erroneous results in Young's sampled data
pursuit system.
(see Bleuze
(2) and Jury and Pavlidis
(9)).
Pursuit Control
Dynamics
Saccadic Control+Ey
Target
Position
Eye
Position
2
+
.ordr
-od
s 2+2
n
ws+W 2
n
(n
H
f
(T) = intersample time distribution
t
t2
= saccadic delay ( 100 msec. )
pursuit delay ( 134 msec. )
61 = foveal dead zone ( .30 )
62
= saturation limit
63 = cutoff limit ( 100
Dynamics of Westheimer (18)
wn = 120 rad./sec.
=
Figure 2.1
( 25 -
.7
A REVISED SAMPLED DATA MODEL FOR EYE TRACKING MOVEMENTS
0
30 0 /sec.)
/sec. )
11
The signal is then delayed before an integrator converts the
signal into position commands to the eye dynamics.
This model has the limitation of being a deterministic
model of a nondeterministic biological servomechanism.
The
choice of a deterministic model, however, has the advantage
of yielding a system that is simple, analyzable, and easily
simulated while retaining all principle characteristics of
eye tracking movements.
Moreover, by allowing random synchron-
ization of samples, a stochastic distribution of sampling
intervals, and a finite pulse width, the variation in model
response to the
same target motion closely resembles the
variation of eye movements actually observed to identical
target motions.
A
study of the nature of the sampler for
agreement with observed eye response forms the subject of
the following section.
2.4
The Nature of Sampling
In order to retain uniformity of analytic results, Young
made the
simplifying assumption that, "The synchronization of
the modulator must be set to coincide with the beginning of a
target motion, if the eye had made no saccadic jumps during
the previous 0.2 sec."*
mean the
sampler was
Beeler
(1) misinterpreted Young to
to remain closed except for the 0.2 sec.
immediately following a change in eye position error.
Zuber
the
(28) performed two experiments which suggest that
sampling instants are randomly distributed with respect
* Young
(23)
page 102
12
to the input.
In the first experiment Zuber presented sub-
jects with ramp-step-ramp inputs in which the magnitude and
direction of the ramps were random.
He
showed that the
size
of the saccade in response to the step was dependent upon the
ramp rate following the step.
For ramps moving in the same
direction as the step the saccade in response to the step
was enlarged, while for ramps in the opposite direction of
the step the saccade was smaller than the step.
This suggests
that some information, available only after the step, was used
in the determination of the size of the saccade.
This result
is consistent with a sample synchronized constant or stochastic
time after the step, or a sample unsynchronized
to the step,
but is not consistent with a sample synchronized instantaneously
after the step.
This fact is because the movement of the
target between the step and the sample would be included in
the calculation of the size of the saccade required for all
the former systems but not for the latter.
Zuber's second experiment consisted of step inputs followed
by periods during which the target was not displayed to the
subject.
Zuber argued that if the blank target period occurred
over a sampling instant, inflated error would result.
Zuber
allowed a 50 msec. blank period to occur over a range from
10 msec. to 200 msec. after the step, but observed only random oscillations in the error.
Thus the sampling must not
occur at a constant time after the input but still may be
stochastically synchronized or unsynchronized.
Experiments which may indicate a finite pulse width were
performed by Wheeless
(20) and Beeler
(1).
Wheeless presented
13
subjects with pulse-step stimuli consisting of a pulse in
one direction with the return step twice the size of the first
step, leaving a steady-state error in the opposite direction
from the initial pulse.
Wheeless noted that in cases in which
the eye did not respond to the pulse, the
latency in response
to the step was inflated by an average of
40 msec.
This
response indicates that on the average the pulse has not gone
completely unnoticed but has delayed the eye in response to
the step.
For a sampled data system to exhibit this response,
the samples would have to be of finite width with some samples
occurring during the step from one side to the other, and thus
containing both positive and negative error components which
cancel each other, resulting in a delay in response until the
next sample.
When these delays are averaged with all samples
which do not cross the positive to negative step, result is
an average delay increased by 40 msec. if the pulse width is
about 40 msec.
Complete interpretation of this experiment
must await further study, because, as Wheeless noted, subjects
showed inflated latencies to simple step inputs intermixed
with the pulse-steps, indicating hesitation in anticipation
of a pulse-step pair.
Further evidence of the possibility of a finite sample
width comes from Beeler
returning pulses
(1).
Beeler presented subjects with
(as described above) and with stairway pulses
(second step in the same direction as the first).
observed
(see Figs.
3.5 and 3.6)
Beeler
fewer abnormal responses
(single response to stairway pulse, no response to returning
pulse) in stairway pulses than in returning pulses when the
14
pulse width was less than 80 msec.
This suggests that the
eye differentiates in some way between the two and therefore
must have sampled over most of the input.
The meaning of
this experiment is also obscure since the eye may be acting
to minimize effort.
This criterion would imply the eye is
most inclined to not respond, next most inclined to make two
smaller saccades, and least inclined to make one large response.
Young noted the possibility of a finite sample width
in Young, Stark, and Zuber
(26).
Further work in this area
is necessary to establish the possibility of a finite width
sample.
Because of the high uncertainty of these results,
for the remainder of this thesis models with impulse sampling
will not be extended to finite width sampling.
2.5
Intersample Distribution for Optimum Unsynchronized
Sampled Data Modeling
If sampling intervals in the eye movement control system
are not changed by the occurrence of a target movement, observed
latency variations should be explainable on the basis of the
distribution of these sampling intervals.
This section derives
the equation for the required distribution of sampling instants
in an unsynchronized sampled data model which would nearly
produce observed latency distributions.
It is hoped that
some link will evidence itself between the model and some
control function within the eye movement system.
The following symbols will be used in the derivation:
L = latency predicted by the model
15
D = delay time from occurrence of the input to the
next occurrence of a sampling instant
(from this
definition, D is strictly non-negative)
t
= constant delay time as in Fig. 2.1
T = time between sampling instants
t = time
from last occurrence of sampling instant to
input occurrence
f
(x) = probability density function of the variable x
(any
of above variables)
Latency predicted by the model is the sum of the time
from the input to the next sampling instant plus the constant
delay t .
L = D + t
Since D is a random variable, L must also be a random variable
and their density functions must be related by:
[D + t ]
fL (L) = fD
The distribution of
latencies,
therefore, is determined by
the distribution of input-to-sample times translated by t 1
along the
times
time axis.
(fD (D))
This distribution of
input-to-sample
will be computed by assuming the input occurs
in an interval of size Tc'
the resulting conditional distri-
bution calculated, and then relieving the condition by
integrating the constant
of intersample times f
Tc
across
the entire distribution
(T).
If the input occurs within a sampling period of given
16
width Tc'
D is the difference between the given Tc and the
time t that the input occurs, as seen in Fig.
2.2.
Input
D
t
t -- o
c
Sampling
FIG.
2.2:
LI
cT
f tt
t1 I
f t
Definition of symbols showing inputs occurring
in sampling intervals Tc
D =
T
c
-t
given Tc,
a constant
From the definition of a probability density function:
b
P(a
! D < b/Tc)
=
f
(D/T C)
fD
dD
Eq.
a
but the left hand member may be written as:
P(a <
D
< b/T
)
=
P(a < Tc
-t
=
P(a -
<
=
P(Tc
Tc
-b
< t
< b/TC
-t
<
:!
Tc
b
-Tc /c
-a/Tc
2.1
17
T -a
ft
(t)
dt
f b
c
This integral is unconditional because of the assumption
that the occurrence of an input does not change the times
of occurrence of a sample, and thus t is independent of Tc'
Changing variables to D from the relation D =
Tc -t:
a
P(a < D
:
b/Tc )
ft (-Uc - D) (-dD)
=
b
b
f
=
(
-
dD
D)
a
by comparison with Eq.
fD
(D/Tc
)
=
2.1:
f
(1
-
Eq.
D)
2.2
This equation states that the probability density function
of D, given T=T c' is dependent only upon the probability
density function of t for the difference Tc -
D which is
equal to t.
From the definition of conditional density of a continuous
random variable:
f
(Y)
y0
f
fy
(Y/X
= XC
f
(X) dx
(see Papoulis
Thus'the conditional nature of Eq. 2.2 may be relieved by
integrating across all values of the conditioning variable
Tc'
that is:
(11))
18
00
f
fD (D )
t
(T
D)
-
fT
(T)
Eq.
dT
2.3
-00o
The function f
(T) must be found, then which makes this
integral, when translated forward through the time delay
ti, equal to observed distributions of latency.
If the occurrence of an input does not change the time
of a sample, then ft(t) may be reasonably assumed uniformly
distributed over the maximum intersample time Tmax that is:
0.
f(t)
0
ft
(T -
And:
f
(T)=0
i.e.
max
max
=
Then:
t
D)
otherwise
= 0
for
for
T>T
T -
D < 0
T
i.e.
< D
max
T cannot be greater than its maximum so that Eq.
2.3
becomes:
max
fD
(D)
jmax
/
f
(T)
dT for D
>
0
D
10
for D < 0
Eq.
2.4
This equation established the dependence upon intersample
time of latency distribution for the revised sampled data
model as calculated from fD
(D) by translating forward through
time delay ti, under the assumption that the input is uniformly
19
distributed over the maximum intersample time.
density function f
The probability
however, must be everywhere positive.
T(),
Thus as D increases, less and less positive area will be included in this integral.
Therefore f
D
(D) must be strictly
non-increasing under the assumption t uniformaly distributed
over Tmax, except at D = 0 where fD
D)
jumps from zero to
the total value of the integral:
T
fD
max
max
f
T
(T) dT
0
Fig. 2.3 shows possible mathematical descriptions of
observed latency distributions.
Fig. 2.3a shows the log
normal distribution used by Beeler
Rayleigh distribution.
(l).
Fig. 2.3b shows a
Fig. 2.3c shows the
form of a non-
increasing fL(L) which could be matched to the Rayleigh
distribution.
in Figs.
Actual histograms of step latencies appear
5.la -
f.
The result that fD
(D) is strictly non-increasing has
been verified by Monte Carlo simulation on the MIT timeshared
IBM 7094 computer using standard IBM random number generating
subroutines.
MAD language listings of the programs used and
program notes may be found in Appendix C.
this simulation are seen in Figs.
The results of
2.4 through 2.7.
All these
results were obtained under the assumption that the times
between inputs were equal to Tmax plus a time uniformly distributed between 0 and Tmax.
Each mark represents 5 occurrences
of latency in the interval noted in msec. at the left.
20
.Probability
2
k
f (x) = k e-s /2
x
=
a)
T
2T
T
2T
0
ln(x/T0 )
x
0
3T
0
S= 2
Log Normal Distribution
Probability
1
x
.
=
e
-x
/2a2
x
a
b)
2a
3a
Rayleigh Distribution
Probability
1 .
a
mE
a
c)
2a
3a
Non-increasing fit to Rayleigh Distribution
Figure 2.3
Mathematical Descriptions of Latency Histograms
21
Fig. 2.4 shows the histogram resulting from taking f
6(200 -
=
a constant sampling interval, and a time delay
T),
of 100 msec.
This histogram should be rectangular but exhibits
small variations due to use of a finite number
puter trials.
This effect is
histograms as well.
delay of 100 msec.
(T) = 100
1
for 150
(5000) of com-
seen in all other simulation
Fig. 2.5 shows the histogram resulting
(T) =
from taking f
fT
(T)
for 0
Fig. 2.6
<
T
T
, 200 msec. and a time
shows the results of taking
< 250 and a time delay of 100 msec.
Fig. 2.7 shows the result of a dual uniform distribution as
described in Eq. 2.5 with a time delay of 140 msec.
f
(T)
=
.01333
60
<
T
< 120
.0025
120
<
T
< 200
0
otherwise
Eq. 2.5
All these figures are closely predicted by Eq.
2.4, and
show the analytically predicted property of being strictly
non-increasing.
assumptions;
Similar results were obtained under the
(1) time between inputs
uniformaly distributed
over a time large with respect to the maximum intersample
time Tmax,
(2)
time between inputs a large constant time plus
a time uniformly distributed over the maximum intersample
time,
and
(3) inputs occur at large constant intervals.
Actual latency distributions, however, do increase for low
latencies.
Therefore, if free running sampling occurs in
the eye movement control system, the eye must sometimes be
able to shorten the sampling intervals when a step is observed.
This hypothesis is supported by the short intersample times
of the good fit to actual latencies seen in Fig. 2.7.
22
LATEiCY
100-
10
20
30
Ioqt
105- 110 1
110-
1151
115-
1201
120125130135-
1251
1301
1351
140l
1'm-
1hL51
145150155-
1501
155 1
1601
1q0-
1651
16517017q-
1701
1751
190I
1%F-
I P51
18519010520020 210215220225230235210245250255260265270275280285290-
1901
1951
2001
2101
2151
220!
22.51
2301
2351
?10 1
2451
250!
255 !
2601
2651
2701
275 1
280 1
2851
2901
29511
295-
30011
Slit
iii
II
Ill,
| IIIIIIII
||i
l i l I I'll
ili
| |I
it
I l II
||
2051
111111
I I
I II
lI11 'I I
'I'l
i
1I I!
II
II
Illi I I
Ill,
LATENCY
10
EX IT CALLEP. PM MAY BE TAKEN.
R? 8. 250+1.700
Figure 2.4
i IIl IIIl
1 II
i
lilt
20
30
Simulated Latency Histogram for a
Constant Sampling Interval System
40
23
I.
/ TF
in
Y
20
n0 - 1 or I I I
ins1101i5120125130135-
ihO-
lbSI I I
II
Th51501551501'-
150111
1951 11
1r 0I I
151 II
170? 1
174 IJI
1RP111
1511 1
190111
1951
2Oflf ,
20 I I I
2'011 1
2(51 1 1
220111
2? I I
230 1
235 1 1
2101 1 1
2451 1
Ifi
170175IPO-
1,9-inni05202052102'S22022523023.210245-
250 1 1 1
2502552"0-
2q51 II
2i0111
201 I
25-
270?1 II
i
i
i
i
i
II
Ifi
Ii
II
Il
If
II
1 I P i
115 11
12011!
125!? I
130
11
1.351 I I
1401 I11
40
30
i
i
i
l
i
i
i If
l
i
ii
i
ifi
i
II
II
II
lI
If
SII
II
I!
If
II
I
270- 25 I I
275- F P? I I I
2 0- 2R I 1 1
285- 2901
200- 2951
295- 300
LATE N C Y
Figure 2.5
10
20
30
Simulated Latency Histogram for a System with
Sampling Intervals Uniformly Distributed between
0 and 200 msec.
40
24
LATENCY
10
20
100-
10511111! liiimi
10n5-
11 l
l
i l
l
30
4n
11111i111111
l l i
l l
l
110- 1151111! 1111 I ill I
IIll!
115- 120111111111111111111
120- 1251111 1111111 liii 111,11111?
125- 1301iIm lllIllmllIll 1i1111
150- 13511i
i 1111 11111 11111
1i5- u4tnimmimmlllimmlfi
1201I1655150165175175-
15 111III Iiii 1111111111
170ll~lll
1q'0
111111 I I 11111111
lIlIllil 1IIIf
111111
1'55111111 I I 1 1111111111111
1701 1111ff 111111 If111f 1111
17q1111111
1111111
ff1! 1111
230! lIlfpfifIimI
I I 111
115255220200275-
20 If lllill 11111
111111
210 I 1 111 1 1 1 11111 tI l 111
275111111! IIIM1111111
205
111IIl II lIfii 1 111111111
230111111111I1111111
11
2602
0- 21ff
2 5 IIIIIi 11 I1 III
ff I 111111111iili
ii
I
IIII
26527011111
2 0 - 2I
5 1 1 1 1 1fillll~l
1 1 1 1 f 1 1 1lfi
1 1 II
f I 111111i
I I I I I I ! II
2953011 II fill,,,I
I I
I
22525 - 2901 111111111111111
301f q M1111111111111111f llil
1111
1111111
23 0- 2751111 11111
1 53002027523 0295-
2 011111111111111111
3051
ff111liilli 111l
275111111 11111
11
2*01111 111111111111
295111111111111
3onjjjjjjjjfj I ii
3on- 3or-mimlimmlli
30531031532032533033534 03 4 5-
31011 111111111
315i1l
11
3201111111
325101013
3301 1 1
33511111fl
3401 1 1
345 1 1 1
3 1;0
LATENCY
Figure 2.6
1020
30
Simulated Latency Histogram for a System with
Sampling Intervals Uniformly Distributed between
150 and 250 msec.
40
25
I-ATEMCY
140ihn1rn-
1
1 50
i rr.
1rt-
1
10
Iii
1i
ili
l ii
Iii
Sil
i10o- 1
nU5-1 70
170-
1 75
171801i5-
1 00
1
1
1flf-
1 05
_5-
2 On
1
ili
2P025;-
2 55
2
2 F5
2?F29F-
27027520252002?53003053103153?0330-
3 3q
335-
3 k0
LATE t'C Y
Figure 2.7
lii
Sil
lii
ii
illI
iii
30
40
ii
ii
ii,,i
liil,
t ill
ii
liii!
'iii,
iiii
iiii
iii
lii
litlll
ilt,
iiii
iii
iii
tilli
11
ii
i l it
iii
I. Il
ii
i
ii
It
Il
2 70
27 r
2 P0
2 8,5
2 90
295
3 00
3 05
3 10
1
*3
3 20
3 ?5
30
ii
iii
iii
Sil li
ili li
tt i
lii
li
Il I I
ii
lit
't li
?in
05
'0
210- 2 15
225- 2 20
2?2035- 2?
225- 230
?30- 2
2F;- 2 I,5
2
2 50
ii
it
200-
270275-
ii
ii
ii
it
it
li
li
li
Ii
20
ill
1
I
1
1
in
20
30
Simulated Latency Histogram for a System with
Sampling Intervals Dual-Uniformly Distributed
as Described in Eq. 2.5
40
26
CHAPTER 3
TRANSIENT RESPONSE OF THE REVISED MODEL
In this chapter the response of the revised sampled data
model for eye tracking movements presented in the last chapter
is analysed for each of six transient inputs.
For each input
the variation in types of response predicted by the model is
examined and the percentage occurrence compared to actual
response percentages.
3.1
Step Response
The distribution of latency predicted by the model for
a step input has already been discussed at length in the last
section of Chapter 2.
The synchronization diagrams of Fig. 3.1
show five different latencies obtainable from the revised
Young's model by varying the synchronization of input to
sampling instants.
The minimum latency obtainable is t
here taken to be 0.1 sec.
,
(Fig. 3.la) when the input occurs
immediately before a sampling instant.
Fig. 3.lc shows the
mean human latency of 0.2 sec. obtained from synchronizing
the input 0.1 sec. before a sampling instant, while Fig. 3.le
shows the maximum modelable latency of Tmax + t 1
obtainable
by synchronizing the input immediately after a sampling
27
Input
50 msec.
Sampling
i.
ti
=
Output
Fig. 3.lb
Fig. 3.la Latency = tj (minimum)
Input
p
.--
-j
100 -isec.
Latency = 50 + t
H-150 msec.
Sampling
FAt
1
output
Fig. 3.lc
Latency
=100
Fig. 3.1d
+ t
Latency = 150 + t1
Input
S--4
Samplinmr
max
Output
Fig. 3.le
Latency =
max + tj (mIaximrun)
Figure 3.1 Step Input Model Variation as a Function of Synchronization
to the Sampling Instants
28
instant, and before a maximum length sampling interval.
As seen in Chapter 2, the distribution of these latencies
is uniquely determined by choice of the distribution of
intersample times.
For the remainder of the inputs discussed,
saccadic responses elicited by sampled error exceeding the
dead zone limit will be understood to be distributed in the
same manner unless otherwise specified.
Even when tracking a small step the saccadic system
often performs inaccurately, and must follow the initial
saccade with a second to correct for the inaccuracy.
This
question of saccadic inaccuracy has not been investigated
at length, and therefore, very little can be said with con-
fidence.
Both overshoot and undershoot inaccuracies are
observed in eye movements.
One way of modeling these in-
accuracies would be to stochastically vary the shape of the
non-linearity in the saccadic system.
A line below the shown
45* line would produce undershoot, a line above would produce
overshoot.
This non-linearity may be a function of latency
as well as of error size.
3.2
Pulse Response
Beeler
(1) studied eye tracking movements in response
to both returning pulses and stairway pulses.
His results,
as shown in Figs. 3.2 and 3.3, agree with those of Westheimer
that, for pulse widths less than 0.2 sec.,
the eye responds
to the two target motions with two saccades, the first
averaging 200 msec. from the onset of target motion, the
second averaging at least 200 msec. from the first.
As seen
29
Latency(msec.)
250
Returnint Pulse -nd Stairway Pulse
200
150
100
50
.
(
Figure 3.2
100
150
2'00 250
3bO
350 460
450
50 550
660
Pulse Width(msec.)
Beeler's average latencies in response to the first step
of pulse inputs
Latpncy(msec.)
350300.
Returninse Pulse
250200-
-
N-
150
100.
504
50
100
150 260
250
3jO
350 460
450 50b
55'0
Pulse Width(risec.)
Figure 3.3
Beeler's average latencies in response to the second step
of pulse inputs
0
30
in Fig. 3.3, Beeler noted inflated average latency to the
second step of a returning pulse not evident in stairway
pulses, for pulse widths from 125-600 msec.
This finding
may have been due to the difference in predictability of
the two inputs arising from the use of only three target
positions, although recent experiments by Saslow (15)
suggests this was not the case.
Forms of response predicted
by the revised sampled data model are shown in Fig. 3.4.
For pulse widths
(W) less than or equal to 200 msec.,
the
revised sample data model with mean intersample time 200 msec.
predicts either abnormal response or two saccadic responses,
the first averaging 200 msec.,
the second averaging 400 msec.
For pulse widths greater than 200 msec.,
it predicts the
two saccades at average latencies of 200 msec. and W + 200
msec.
These predictions are true for both the returning
pulse and the stairway pulse since there is no dependence
of delay time upon past values of eye position error.
Thus
the revised sample data model agrees well with Beeler's
results for the stairway pulse but predicts slightly too
short latencies over the interval 125 < W < 600 for the
returning pulse.
The revised sampled data model also predicts the percent of inputs to which there will be abnormal response as
a function of pulse width.
This prediction arises because
response to the first step is dependent upon the occurrence
of a sampling instant within the pulse width.
But with a
mean intersample time of 200 msec. and the pulse uniformly
distributed over this interval, the probability of occurrence
31
Input
less than
Normal
Response
AK
200 msec.
Abnormal
Response
00
msec.
Thort Returning
Pulse
less than
200 msec.
Short Stairway
1K
-
200 msec.
Pulse
No
Abnormal
Long Returning
Pulse
Long Stairway
Pulse
Figure
3.4 Forms of Response Predictable for Pulse Inputs
Response
No
Abnormal
Response
32
of a sampling instant in time W is just W/200.
probability of no response is 1 -
(W/200).
Thus the
This linear
relationship compares well with the findings of Beeler
and Wheeless
(1)
(20) for returning pulses, as seen in Fig. 3.5.
*
Percent
+
....
100
yBee ler
Wheeless
Revised Model
.+
50.
00 450 500 550 600
250 300 350
Pulse Width(msec.)
Percent no response to returning pulse input
50 100 150 200
FIG. 3.5:
Beeler's results do not agree as well, however, for the case
of the stairway pulse, as seen in Fig. 3.6
Beeler
Per ent
100
50
-
Revised Model
50.:.
50 100 150 200 250300350 400450500550 600
Pulse Width(msec.)
FIG. 3.6:
Percent no response to stairway pulse input
This discrepancy has already been mentioned as a possible
indication of finite pulse width sampling.
Table 3.1 summarized the findings of this section on
the response of the revised sample data model to returning
pulse and stairway pulse inputs.
33
TABLE 3.1
INPUT
LATENCY
PERCENT ABNORMAL
RESPONSE
Returning Pulse
Slightly low
125 < W < 600
Excellent
Stairway Pulse
Excellent
Slightly high
below 80 msec.
3.3
Ramp Response
Another input which has been studied extensively is the
constant velocity or ramp input.
beginning
(0* to 5*)
ramp speed.
Rashbass
(12) studied the
of the ramp response as a function of
He reported the entrance of pursuit movement
into the response at approximately 150 msec. and a saccadic
response at about 200 msec.,
target motion.
both measured from the onset of
Rashbass also noted an increase in the size
of the saccadic response in direct proportion to the velocity
of the input.
Robinson
(14) reported three main forms of response to
a 10 deg/sec ramp and the percent of observation of each.
His results are redrawn in Fig. 3.7.
(59%
Robinson's most frequent
occurrence) response shows smooth pursuit movement
beginning at 125 msec.
(± 20 S.D.),
237 msec.
followed by an increase in smooth pur-
(± 30 S.D.),
a saccadic response at
suit velocity to greater than the target velocity in order
to reduce the error to zero, after which pursuit velocity
34
Eye Position(deg.)
6 -
5-
/
Target
59%
2-I
-- - - - ------- ---
31%
10%
1 -
-L
100
F-igure 3M7
200
400
300
Time (mse c.)
Robinson's 10 deg./sec. ramp tesponse
500
600
35
slackens to equal target velocity.
The remaining 41% of
response contain two saccades to reduce the error to zero.
Robinson observed that his data showed a lengthening of
saccadic latency over latencies observed in response to step
inputs.
Weighing Robinson's reported saccadic latencies by
his observed percentage of occurrences, the mean latency
resulting is 243 msec.
This displacement by about 40 msec.
of mean saccadic latency in response to a 10 deg/sec ramp
input compared with mean latencies to step inputs is substantiated by the experiments of this thesis.
Figs.
(see histograms,
5.la-f).
The revised sample data model predicts the entry of
pursuit motion invariable at 134 msec. due to the continuous
nature of the pursuit system.
mean of Robinson's data.
This latency is the weighted
The model also predicts one
saccadic
movement, proportional to the speed of the ramp, due to the
accumulation of error during the 134 msec. delay in pursuitmovement.
The magnitude and timing of the saccade are ran-
domly distributed depending on D.
Second saccades would be
predicted by the saccadic inaccuracy model or an equivalent
pursuit inaccuracy model.
The saccadic dead zone prevents
any sampled error from commanding movement unless it is greater
than 0.3*.
Thus the distribution of saccadic latencies is
displaced by the time required to exceed 0.3',
or 30 msec.
for a 10 deg/sec ramp, in good agreement with observed results.
The model does not, however, predict any velocity over-
shoot in pursuit motion, as observed by Robinson.
This suggests
36
the introduction of slightly underdamped dynamics into the
pursuit loop.
The other 40% of responses which show no velocity
overshoot, however, dictate dependence of these dynamics on
the saccadic system.
This area of saccadic augmentation of
pursuit movement requires further research before transfer
functions for it can be assigned.
Experiments 3 and 4 of this
thesis, for example, illustrate that previously initiated pursuit movement affects saccadic latency.
3.4
Step-Ramp Response
As previously reported, Rashbass
(12) showed the indepen-
dence of the pursuit and saccadic systems by presenting sub-
jects with step-ramp iAputs.
He observed smooth pursuit movement
before, at, and after saccadic movement in the responses.
did not report the percent occurrence of each response.
He
Rashbass
also observed that when the step size in degrees was 0.15-0.2
times the ramp rate in degrees per second, most responses contained no saccadic eye movement.
Fig. 3.8 shows three outputs obtainable from the revised
model for a 5 degree step -
10 degree/sec ramp combination by
assuming different synchronizations of input to sampling instants.
Fig. 3.8a shows the model output for an input-to-sample delay
of zero.
In this example, the pursuit movement enters the
response 34 msec. after the saccade.
Fig. 3.8b shows the
response for an input-to-sample delay of 34 msec.
represents pursuit movement at a saccade.
This response
Figs. 3.8c shows
response in which the pursuit movement begins before the
saccadic movement.
37
Input
&
.
Sampling
e
= 3
e
-
Output
Fig. 3.8a
Fig. 3.8b
D = 0
Input
D = 3i4msec.
T
5 deg.
k--5 sec.-....
Error
*
t
ii
I
I
Sanpling
Output
Fig 3.8c
Figure 3.8
D = 150msec.
Step-Ramp Model Response as a Function of Synchronization
of Input to Sampling Instants
38
The percent occurrence of these three types of output
may be estimated by assuming the distribution of D (inputto-sample delay) derived for the step at the end of Chapter 2,
and investigating the delay intervals in which each output is
predicted.
Taking the parameters of Fig. 2 and assuming pur-
suit movement unrecognizable until 30 msec. from its start,
pursuit motion after the saccade will occur in the interval
34
f
0 < D < 34 msec. or
D (D) dD probability.
pursuit motion at a saccade is predicted in the
34
< D <
64 msec. with
f
Similarly,
interval
64
fD (D) dD probability, and pursuit
34
motion before a saccade is predicted in the interval 64 < D < 200
200
msec. with
f64
(D) dD occurrence.
The estimated probability
of outputs with smooth pursuit movements at the saccade is
probably low due to ignoring the saccadic augmentation of
pursuit movement as discussed by Robinson
(14).
Further
investigation is needed in the area of saccadic augmentation
of pursuit movement to establish the complete effect of a
saccade on smooth pursuit movement.
Young's revised model also predicts a large number of
no-saccade responses to step-ramp inputs near the inputs to
which Robinson and Rashbass observed no saccadic response
experimentally.
As seen in Figs. 3.8a-c, once the pursuit
system begins following the target, predicted eye position
error remains constant until corrected by a saccadic eye
movement.
If, however, this constant eye position error is
within the ± 0.3*,
response.
the revised model predicts no saccadic
In equation form, the relationship necessary
between step size and ramp rate in order to elicit pure pursuit response is:
39
Ramp speed
Step size ± 0.30
134 msec.
This equation assumes that the foveal error is zero at the
initiation of the transient input.
The distribution of
saccades associated with random uniform distribution of
initial image on the fovea is described by Young in Young,
Stark, and Zuber
(26).
Fig. 3.9 shows that this prediction
compares favorably in the range below pursuit saturation
with observed results of Rashbass and Robinson.
Moreover,
Wheeless reported this result over wider ranges of
step-
ramp combinations.
The revised model does not, however, predict the
inflated pursuit latency noted by Robinson for this type
of input.
This indicates the possible presence of predic-
tion even when target motion is unknown and is another area
for future research.
3.5
Ramp-Step Response
Experimental observation shows that when the eye returns
to the original position after following a ramp, the eye
occasionally undershoots by 1-2 degrees, requiring another
saccade to bring the eye to the target as
shown in Fig. 3.10.
The revised model predicts this response, as did Young's
original model, when the continuation of the pursuit system
moves the eye further than the dead zone from the target,
after both the target return and the next sampling instant.
This continuation creates an error which must wait until
the next sampling instant to be corrected.
The model predicts
/
/
/
/
/
,20
Ramp
/
Rate
(deg./sec)
/
/
104
//
//
5.
/
//
/
/
/
/
/
/
/
/
0
//
//
Rashbass & Robinson
Ramp Rate = Step Size/.15 to .2
//
1/
Revised Sampled Data Model
_______
Ramp Rate = Step Size +
134 msec.
-I
-I--
1
Figure 3.9
2
3
4
Step Size (deg.)
5
6
Comparison of Regions of No-saccade Step-Ramps
.30
41
i
i
i
i
j
i
i
i
i
i
10
10
5
5
Target
(deg.)
0
0
-5 F
-5
-10
-10
00
0
0.8
0.4 0.8
a
10
10-
5
We*
0
(deg.)
-5-
------
-5
-10
-10
0
(a)
Figure 3.10
0.4 0.8
Time(sec.)
.
s c
(b)
Ramp-Step Response: (a) model; (b) experimental
42
continuation of pursuit tracking for 134 msec. following
the ramp termination.
For a 10 deg/sec ramp, if the sample
occurs in the last 30 of these 134 msec.,
be less than the dead zone limit.
the error will
Therefore, the model
predicts a second step if the sample occurs in the first
104
134 - 30 = 104 msec. or
D (D) dD probability. This
f
type of response would also be predicted by a saccadic inaccuracy model which undershoots the target position.
43
CHAPTER 4
EXPERIMENTAL PLAN, APPARATUS, AND PROCEDURES
In this chapter, a method of data reduction is proposed
which would yield predictable latency tendencies in a sampled
data model.
Four experiments are proposed to be reduced by
this method and the response of synchronized sampling and
random sampling sample data models
is discussed.
to these four experiments
The apparatus and procedures used in performing
these experiments are then presented.
Chapter 5 discusses
the observed results of six subjects to these experiments.
4.1
Saccade-Synchronized Data Reduction
From the preceding Chapter's analysis of transient responses,
it is evident that two sources of uncertainty contribute to the
determination of output in a non-synchronized sampled data model.
First, since the onset of target motion is independent of the
sampling instants it must be considered uniformly distributed
over the maximum intersampling interval.
Second, the inter-
sampling intervals are stochastically distributed themselves.
Since there is no output at the time of a sampling instant,
the only method of estimating the time of occurrence of a
sample is from observation of a saccade resulting from the
44
sample.
the
If a target input occurs immediately after a saccade,
sample which caused that saccade and the sample which
will cause a response to the current target motion are
ated by only one intersample time.
separ-
For this type of input
only one factor, the intersample times, contributes to the
uncertainty of response form.
If eye tracking were controlled
by a system such as the revised sampled data model, the dis-
tribution of intersampling intervals would be revealed by
the distribution of forms of response when the input occurs
at a constant time,
a saccade.
smaller than one
intersample time, after
Experiments to date which have involved inputs
near saccades have been reduced only by recording distributions
of latency from the beginning of target motion.
In order to
obtain a measure of synchronization of input to sampling
instants, responses must be grouped by constant saccade to
input time.
4.2
The Saccade-Synchronized Inputs
The experiments performed were to examine the nature of
sampling in the eye movement control system by grouping inputs
that occur at identical times
above.
after a saccade as described
In order to facilitate grouping inputs in this way, a
saccade detector was used to initiate a delay of controllable
length before the introduction of the second part of each
target motion.
The four experimental inputs used are illustrated in
Fig. 4.1.
Experiments 1 and 2 use a step of four degrees to
elicit the saccade which initiated the delayed target motion.
45
Target
-
-
Independent Variable
TS.1
Eye
Latency
Fig. 4.1a
Dependent Variable
Experiment One
Latency
Target
Eye
Fig. 4.1b Exoeriment Two
T
Fig. 4.1c
I-OWLatency
Experiment Three
Fatency
Fig. 4.1d
Ex-oeriment Four
Figure 4.1
Exoerimental Inputs
46
Experiments 3 and 4 used a ramp of 10 deg/sec to elicit the
saccade to which target motion is synchronized.
The target
motion introduced was a step in the opposite direction of
the
first saccade in Experiments 1 and 3, and a step in the
same direction as the first saccade in Experiments 2 and 4.
Thus Experiments 1 and 2 consisted of a returning pulse and
a stairway pulse respectively, in which the occurrence of
the second step was synchronized to the occurrence of a saccade
in response
to the first step.
Experiments
3 and 4 consisted
of a ramp into which was introduced, respectively, an inward
or outward step, synchronized to the occurrence of a saccade
in response to the initial ramp.
Due to the dependence of
these inputs, on the occurrence of a saccade, the pulse width
of any given input was indeterminable before that input was
presented.
The only dependent variable in Experiments 1 and 2 was
latency of response to the synchronized step.
the
Latencies to
first step were also recorded to assure normal non-predic-
tive tracking.
Initially the dependent variable of interest
in Experiment 3 was the form of response as seen in Fig. 3.8.
Since pursuit movement was previously initiated, however,
the effect of pursuit latency was lost and no results of this
kind were obtained.
Latency of response to the
step was recorded in Experiments
1 and 2.
synchronized
3 and 4 as in Experiments
Thus, the results of these four experiments represent
the effect on latency of recently occurred saccades.
47
4.3
Model Response to Saccade-Synchronized Experiments
The revised sampled data model predicts identical mean
latency variation to all four saccade-synchronized experiments.
In an unsynchronized sampling revised sampled data model, both
saccade-to-input time, TsI, and distribution of intersample
times affect predicted latency.
As the saccade-to-input delay
increases from zero to the expected time of occurrence of the
next sample, average latency decreases due to proportional
shortening of time from input to sample
(D).
As the saccade-
to-input delay increases near the mean time of occurrence of
a sample, average latency rises since a greater fraction of
responses must wait for the second sample after the saccade
to cause a response.
As input delay increases to near 200 msec.,
latency again decreases as all outputs must wait for the second
sample, and D
is decreasing for lengthening delay as
for short
delays.
If these experiments were presented to a
sampled data
model with synchronized sampling and time of synchronization
stochastically variable, mean latency would not be expected
to vary as a function of when the last saccade occurred, since
each target step sets off its own independent sample.
If this
system is to agree with observed pulse response, a further
constraint must be placed upon it limiting the minimum intersample time to about 200 msec.
constant delay of 100 msec.,
With this constraint and a
this system predicts high mean
latency when the input occurs during a saccade, decreasing
latency until saccade-to-input delay reaches 100 msec.
(for
200 msec. intersample time) and constant normal latency through
48
larger saccade-to-input delays.
Fig. 4.2 illustrates the variation of average latency
predicted by the revised sampled data model presented with
these inputs for two different unsynchronized
tributions and for synchronized sampling.
sampling dis-
Fig. 4.2a shows
latency for a sampling distribution of a delta function at
200 msec.,
that is,
a constant sampling interval system.
This system shows a sharp rise in latency at 100 msec. after
the
saccade due to the occurrence of the next sample always
100 msec. after the first saccade.
Fig.
4.2b shows average
latency for a revised sampled data model with sampling interval
uniformly distributed between 150 and 250 msec.
shows a slower rise in average latency over a
of delay times.
The
100 msec. band
important characteristics of these latencies
are the rise and fall of latency as T S
shows
This system
1
increases.
Fig.
4.2c
latency for synchronized sampling with minimum inter-
sample time 200 msec. as discussed above.
4.4
Apparatus and Procedures
The four experiments described were performed at the
Man-Vehicle Control Lab of the Massachusetts Institute of
Technology on six subjects.
The following sections describe
the apparatus used and the procedures followed in conducting
these experiments.
4.5
Target Generation
Subjects were seated 28.3 inches in front of an Electromec
model 565 10" x 12" oscilloscope.
A vertical line was gener-
ated on the oscilloscope by introducing a 100 kc sawtooth wave
49
a & b
NON-SYNCHRONIZED SAMPLITG
Latency(msec.)
300
-
200100 I
N
100
100
Fig. 4.2a.
f
200
T(msec.)
Constant Sampling Interval System
200
TS1 (msec.)
(1)
T
300+
200100
.01
.
1bo
200
100
T (msec.)
Fig. 4.2b
System with Sampling Intervals Uniformly
200
T5
(msec.)
Distributed between 150 and 250 msec.
C SYNCHRONIZED SANPLIUG
3001
Latency
(msec.)
2001
100.
100
200
Ts_(msec.)
Fig. 4.2c
Figure 4.2
Synchronized Sampling System with minimum intersample time of 200msec.
Average Latency Predicted to Saccade-Synchronized Experiments
when Presented to Sampled Data yodels with different Sampler
Control Logic
50
into the vertical input of the oscilloscope.
The line thus
displayed was adjusted to 3/4" high by 1/32" wide thus subtending a horizontal visual angle of .0625*.
Subjects were
allowed to adjust the intensity of the target to a comfortable
level which was then maintained throughout the experiments.
The target was moved horizontally by introducing voltage
signals generated by the lab's hybrid computer into the horizontal input of the oscilloscope.
The target moved along the
12" dimension to a maximum of ± 5 inches from center thereby
moving through ± 10*
of the subjects horizontal visual field.
The room was normally lighted and the oscilloscope had fine
graticule
inch
lines every 1/10"
(20).
(.2*)
and heavier lines every
Thus target motion relative
was easily detected.
to the oscilloscope
The P7 phosphor caused a faint after-
image but subjects reported no ambiguity in target position
at any time.
4.6
Eye Position Measurement
Subject eye position was measured using a Biosystem Inc.
GPl eye movement monitor.
This non-contact monitor uses the
differential reflection technique to produce a voltage proportional to eye position.
The monitor has
two photoresistors
mounted in a pair of glasses frames and centered in front of
the left and right scleral-iris junctions of the left eye.
The two photoresistors make up two legs of a wheatstone bridge
which may be balanced by adjusting the resistances of the
two other legs.
The sides of the bridge are introduced into
a differential amplifier with filtering of 60 cycle noise.
49
a & b
NON-SYNCHRONIZED SAMPLING
Latency(msec.)
I
-
200
-
100
-
M-
100
Fig. 4.2a
300
100
200
T
200
TS_(msec.)
r(msec.)
Constant Sampling Interval System
300+
200-
-W
100
.01
100
200
100
T (msec.)
Fig. 4.2b
System w Lth Sampling Intervals Uniformly
Distribu ted between 150 and 250 msec.
200
(msec.)
T
S-I
c SYNCHRONIZED SAMPLING
3001
Latency
(msec.)
2001
1004-
100
TSI
Synchronized Sampling System with minimum intersample time of 200msec.
Fig. 4.2c
Figure 4.2
200
(msec.)
Average Latency Predicted to Saccade-Synchronized Experiments
when Presented to Sampled Data yodels with different Sampler
Control Logic
50
into the vertical input of the oscilloscope.
The line thus
displayed was adjusted to 3/4" high by 1/32" wide thus subtending a horizontal visual angle of
.0625*.
Subjects were
allowed to adjust the intensity of the target to a comfortable
level which was then maintained throughout the experiments.
The target was moved horizontally by introducing voltage
signals generated by the lab's hybrid computer into the horizontal input of the oscilloscope.
12"
The target moved along the
dimension to a maximum of ± 5 inches from center thereby
moving through ± 10'
of the subjects horizontal visual
field.
The room was normally lighted and the oscilloscope had fine
graticule lines every 1/10"
inch
(2*).
(.2*)
and heavier lines every
Thus target motion relative to the oscilloscope
was easily detected.
The P7 phosphor caused a faint after-
image but subjects reported no ambiguity in target position
at any time.
4.6
Eye Position Measurement
Subject eye position was measured using a Biosystem Inc.
GPl eye movement monitor.
This non-contact monitor uses the
differential reflection technique to produce a voltage propor-
tional to eye position.
The monitor has two photoresistors
mounted in a pair of glasses frames and centered in front of
the left and right scleral-iris junctions of the left eye.
The two photoresistors make up two legs of a wheatstone bridge
which may be balanced by adjusting the resistances of the
two other legs.
The sides of the bridge are introduced into
a differential amplifier with filtering of 60 cycle noise.
51
Thus as the dark iris moves in front of the photoresistors,
the amplifier is biased positively or negatively in proportion to the size of the eye movement.
The resulting signal
is linear to ± 15* of horizontal eye motion with a noise level
of less than 1/4*.
The frequency response of the photoresistors was flat
to 10 C/S and then falls off at 6 db/octave.
responses invariably exceed this
Because saccadic
low frequency cutoff, records
of saccades were characterized by the photoresistors dynamics
For
rather than the dynamics of the subject's eye movements.
this reason the device was only valid for measuring the
of onset of a saccadic movement.
time
The predominance of the
same frequencies in every saccade, however, made the task
of detection of a saccade easier.
Typical records of eye
response to the four experiments, recorded using this monitor,
are seen in Fig. 4.3.
4.7
Input Generation
The M.I.T. Man-Vehicle Control Laboratory's GPS 290T
hybrid computer was used to control the horizontal movement
of the target.
A complete description of this computer and
the programs and circuits used appears in Appendix A.
An
experimental run consisted of 44 inputs containing 11 each
of the four experimental inputs.
The saccade-to-step delay
was varied from zero to 200 msec. in steps of 20 msec. among
the 11 inputs of the same type.
The input types and delays
were controlled by a 44 entry circular list stored in the
digital computer.
This list was initially chosen using a
52
.
10
5
0
-s
10
___
_
5 Target
(deg.)
t11F1T11i~
C
10
0
-5
L-.j
-I
10
10
10
5
(de
0
0
(deg.)
-5
-10
---------l
5
1-
-5
-1 Li
YVrIi4§4 ~I4zz~~r
I
Fig. 4.3a
I
I
I'
Fig. 4.3b
Experiment One
it I- 1~~%_TItLLit Ejj
It I--
I
10
10
7
~j{7f7f
5
- ---
5
Target
(deg.)
0
-5
F
-
-5
4d- Ti-
-10
-10
_
1 0
I I
||
LI A LA
I it~I_-1-4
|I\-\-
10
5
0
-5
Experiment Two
-
We
5
(deg.)
0
-5
2
-10
-1 L - t-I
Fig. 4.3c
Experiment Three
Figure 4.3
Fig. 4.3d
----
I
Experiment Four
Typical Eye Monitor Records
53
random number table and remained invariant throughout the
experiment.
Each list entry was a 12 bit computer word.
The digital program tested the three highest order bits to
set the input type and direction, then added 70008 to the
remaining 9 bits and used the result as
of the counter in the digital delay.
the initial value
The starting point in
the list was under the control of the experimenter and was
varied at his discretion from run to run.
When the computer
had generated 44 inputs and thus returned to the specified
starting point, the run was terminated.
The time of initia-
tion of each input was also controlled by the experimenter
through a switch on the computer console.
Time between inputs
was varied from about 2 sec. to about 5 sec. throughout each
The subjects reported complete inability to predict
run.
input beginning, saccade-to-step delay, or input form, throughout the experiment.
Saccade-to-Step Delay Control
4.8
In order to obtain exactly the saccade-to-step delay
intervals desired, a saccade detector was used to initiate
a digital delay which terminated in the introduction of a
40
step into the target motion.
The saccade detector con-
sisted of a pseudo-differentiator to estimate eye rate, which
was
input to a comparator.
sense
The comparator set a digital
line when the pseudo-differentiator exceeded a preset
threshold level just above the level of smooth pursuit movement.
Due to the low frequency cut-off of the photoresistors,
the best transfer function for the pseudo-differentiator was
54
found to be
S
S+25w
which was implemented using the circuitry
shown in Appendix A.
An input sign switching circuit, also
shown in Appendix A, was necessitated by the comparator's
characteristic of detecting threshold crossings in only one
direction, while the saccade to be detected changed direction
with the input.
The comparator was reset only at the beginning
of an input so that just the first saccade was detected.
After initiation of an input by the operator, the digital
program repeatedly tested the sense line
detecting comparator.
set by the saccade-
When this sense line was set, the pro-
gram began incrementing the preset counter once each msec.
When the counter reached zero, a control line was set which
introduced the 4* step into the input, in the direction preset
from the
three highest order bits of the current list entry.
After introducing the step, the computer waited 1 sec. and
then terminated the input by resetting the target position
to the center and setting the control lines and counter
for
the next input from the next list entry.
4.9
Eye Movement Recording
Initially data was recorded and analyzed digitally, however two factors unique to this system made this technique
inaccurate.
First, variability of time from actual saccade
to detection of the saccade ranged from 0 to 10 msec. due to
transmission delays, component variability, and variability
in eye monitor balance and sensitivity.
Second, low-quality
control pulses slightly contaminated the high quality analog
output signals causing variabilities of ± 10 msec. from commanded
55
to actual initiation of ramp movements.
For these reasons
the data reported was taken from the chart recordings made
of all responses.
The recordings were made at 20 mm/sec and
examined closely under a magnifier to an accuracy of ± 5 msec.
in all time measurements.
A
typical 4 channel recording is
seen in Fig. 4.4.
4.10
Procedure
Of the six subjects, four were male research assistants
in the Man-Vehicle Control Lab and two were female staff
members of M.I.T.
The subjects were instructed to fixate
with both eyes on the target line at all times.
All subjects
showed typical responses when given experience tracking common transient inputs.
In addition to this experience, no
experimental data was taken until the
subject reported feeling
familiar with tracking the actual experimental inputs.
Each subject was presented with at least 10 experimental
runs.
The runs were presented over the course of an approxi-
mately 3 hour experimental session broken by a long rest,
which usually included refreshments, halfway through and by
shorter, five to ten minute rests between experimental runs.
Each experimental run was preceded and followed by calibration of the eye movement monitor by instructing the subject
to look to the right and left edges of the oscilloscope screen
which subtended ± 12* of horizontal visual angle.
were encouraged to terminate a run if their eyes
or began to water uncomfortably.
Subjects
felt fatigued
Furthermore, eye position
was continuously monitored by watching the chart recorder and
56
i
Saccade
Detector
i
1
1
reset
detect
I.-
--
--
-
1-
10
5
Target
Position
(deg.)
0
-5
-10
777-
7
-7=
10
Wye
Position
(deg.)
5
0
-5
-10
Ware
Rate
S
s + 25
Experiment Three
Ts, = 120msec..
Figure 4.4
-
.
Experiment One
(opposite direction)
Ts I = 100msec.
used by switching circuit
Typical Experimental Recording
-
fl,
11,1 M11In
I.I. - , . M-IMMRN 111M
". ,
" 4 5 1- IM - I M M I
,
'I ,
M'.
I,
-
1--
57
the run terminated if excessive blinking or drifting was
noted.
3 minutes.
4.11
inputs lasted approximately
An experimental run of 44
A total of more than 3000 inputs were reduced.
Data Reduction
Excepting histograms, which. are self explanatory, data
was reduced to means and standard deviations of step latencies
observed as a function of time after a saccade.
Statistical
calculations were made from the raw data using a short special
purpose computer program written in compiler language for the
digital portion of the lab's computer facility.
The data
from each subject was quantized independently to take into
account differences in actual T S
of data taken.
1
observed and in the amount
Intersubject averaging, therefore, occasionally
required requantization to insure consistent saccade-to-step
delay within each group.
58
CHAPTER 5
RESULTS
This chapter reports the results of the four experiments
discussed in the preceeding chapter.
Histograms of saccadic
latency to the initial step and ramp portions are presented
to demonstrate normal non-predictive tracking and to indicate
tracking tendencies of each subject.
The results
are then
presented by experiment in the form of curves fit through
observed mean latencies.
Complete data including mean,
standard deviation, and curve fits through means are seen
in Appendix B for each subject in response to each experiment.
Intersubject differences are then discussed and compared to
the response of unsynchronized and synchronized revised
sampled data models.
At the end of the discussion of each
experiment, the mean and standard deviation of intersubject
mean latencies are presented and discussed.
remembered that this
It should be
intersubject averaging often covers
individual response characteristics and so must not be overemphasized.
The results are then regrouped by subject and
the interexperimental response of each subject is discussed.
59
5.1
Distribution of Initial Saccadic Responses
The first portion of each input was intended to elicit
a saccade to which a step would be synchronized.
done using a
This was
40 step or 10 deg/sec ramp input to either the
left or right.
The response to these initial inputs should
agree with other published results if the subjects are tracking
normally in the nonpredictive mode.
Histograms of saccadic
latency for each of the six subjects in response to the initial
step or ramp are seen in Figs.
5.1 a-f.
The histograms of
step latencies agree very well with those of Beeler
Young
(23),
and others, and thus indicate that all subjects
are tracking normally as desired.
bias
(1),
Most subjects showed a
in average latency for inputs going in one direction
over the other, sometimes by as much as 20 msec.
This
preference varied from subject to subject and was probably
due to inexact center position or undetected glare
background.
This effect accounts
oscillations
in data recorded in Appendix B,
for some of the small
due to the
predominance of left or right going inputs at some
to-step delay values.
in the
saccade-
Histograms of ramp saccadic latencies
agree with Robinson in so far as they show higher means and
larger deviations than the step latencies.
This effect is
modeled by the stochastic sampled data model as previously
discussed in Chapter 3.
The very low deviation of subject
NVH is probably a result of high motivation due to his knowledge of eye movement studies.
The secondary distribution
of subject AVH was made up almost exclusively of left going
10 deg./sec.
4 0 Step
201+
Ramp
15.
10.
a) Subject CO
5.
[111 111
150
200
250
1111
300
400
350
450
150
I
200
III1
250
2
I..
300
350
400
-I
450
Latency (msec.)
Latency (msec.)
OIA
C0
20
15+
10.
b) Subject AVH
5-
I 1L
150
200
250
iiI,~
300
I
350
III
Iii.1I
400
Latency (msec.)
Figure 5 .1
450
150
260
II a
250
300
350
Latency (msec.)
Saccadic Latency Histograms
400
450
30t
40 Step
10 deg./sec.
Ramp
20
15t
10
-
c) Subject NVH
5-
pep.
.
150
200
p
,
250
300
350
I
400
450
1111111
1 111 11 1
I
150
200
Latency (msec.)
11
1 1111111
I
II-
350
300
Latency (msec.)
250
400
450
400
450
20
15.
10
-
5.
-
I
150
d) Subject LN
II
200
250 300 350
Latency(msec.)
400
Figure 5.1(Continued)
450
150
11111
200
250
300
350
Latency(msec.)
Saccadic Latency Histograms
-
10 deg./sec.
4 0 Step
20-
Ramp
1510.
e) Subject MK
51
150
I1
-, ,
I
I
200
I1
II
II
I
250
300
350
Latency (msec.)
I
I
400
4'
450
150
200
250
III
I
350
400
III
I
Il
300
I
450
Latency (msec.)
Mn
201510f) Subject SF
54-
II
-1
150
I
200
111Ii1111
250
300
it
AL1IU
350
400
Latency(msec.)
Figure 5.1 (continued)
450
150
200
II I I
III
250
300
350
Latency (msec.)
Saccadic Latency Histograms
400
450
63
responses indicating his results may be atypical.
5.2
Experiment 1 ---
Synchronized Returning Pulse
Experiment 1 was a returning pulse in which the target
return was synchronized to the saccade
second
Fig. 5.2 shows plots of latency to the
first step.
the time from the
step as a function of TS_,
response to
in response to the
saccade in
the first step, to the occurrence of the second
target step.
Subjects show variation in latency characterized
by two portions, first decreasing latency for shorter TS
then little variation in latency.
1
,
In only two subjects has
mean latency decreased to the value of mean latency in response
to the initial step.
as TSI gets very
Since latency should decrease to normal
large, the effect of a saccade on latency
must continue even after 200 msec. in many cases.
In no
subject was there any significant tendency toward increasing
latency with increasing T S
sampled data model.
1
as predicted by the revised
This fact suggests synchronization of
sampling in response to this input, but with some delay to
account for above normal latencies.
Fig. 5.3
shows the average and standard deviation of
the intersubject means of Experiment 1 as a function of TS-I,
the saccade-to-step delay.
The predominant characteristic
is that of decreasing latency followed by a leveling off
above the value of initial step latency.
The two plots on
the same graph are the latencies predicted by the revised
sampled data model with sampling synchronized to the occurrence
of each step and minimum intersample time 200 msec.,
and the
64
Latency (msec.)
Subje cts
co
450
NVH
....-
AVH
o
400
9
-3
LN
-SF
MK
350
300
250
200
150
100
0
50
(s 1T0
1
TS-I(msec.)
Figure 5.2
Experiment One - All Subjects
2e
65
Latency (mse c.)
450
Non-synchronized Sampling
-
-
--
0
Synchronized Sampling
Mean and One Sigma of
Intersubject Means
4004-
0
350
-
300 -
0
0
0
0
0 0
250.
0 0
200 +
1504
10ool
0
Figure 5.3
100
TSI(msec.)
150
200
Experiment One - Intersubject Means and Model
Predictions for two Sampler Control Logics
66
prediction of the unsynchronized revised sampled data model
with sampling intervals uniformly distributed between 150
msec. and 250 msec.
The experimental averages follow the
synchronized sampling prediction but lie approximately 50 msec.
above it throughout.
For this experiment, then, the eye
delays sampling and synchronizes it to the input.
5.3
Experiment 2 ---
Synchronized Stairway Pulse
Experiment 2 consisted of a stairway pulse in which
the
second step was synchronized to the occurrence of a
saccade in response to the
first step..
Latencies observed
as a function of time from the first saccade are seen in
Fig. 5.4.
Variation of latency in this experiment was less
than that of Experiment 1.
T S-
The decrease in
latency for short
delays is observable in the responses of four subjects;
however, in Experiment 2 this decrease is from normal latencies
to slightly below normal values and occurs over a shorter
interval of T S
1
delays.
Furthermore all subjects exhibit
slight rises in latency as predicted by the unsynchronized
revised sampled data model, but most follow this rise with
non-varying, rather than decreasing latency.
In only two
subjects does this rise go above normal step latencies.
These results, then, show the effects of both synchronized
and unsynchronized sampling but with a larger unsynchronized
sampling effect than observed in Experiment 1.
Fig. 5.5 shows the mean and standard deviation of intersubject means observed in this experiment.
Plotted on the
same graph are the prediction of the revised sampled data
67
Latency(msec.)
450
Subject Line Symbols same as Figure 5.2
400
3504
3004
2504-
0-
0
200.
C3
0
0
1504
100..
I
6
I
56
1do
1 0
(msec.)
TS_
3
Figure 5.4
Experiment Two - All Subjects
2d0
68
Latency(msoc.)
4504
-ion-synchronized Sampling
-
-
0
4004
-Synchronized
Sampling
Mean and One Sigma of
Intersubject Means
3504
3004.
2504-
00
2004.
-0
0
0
0
1504
1 00...
a
T
Figure 5.5
5'0
a
T 6.
T 5 1I(msec.)
1'50
a
200
Intersubject Means for Experiment Two and
Model Predictions for Two Sampler Control Logics
69
model with synchronized sampling and with unsynchronized
sampling interval uniformly distributed between 150 msec.
and 250 msec.
This data follows the unsynchronized sampling
model prediction and thus indicates that in this experiment,
the eye exhibits response close to that of an unsynchronized
sampler.
5.4
Experiment 3 ---
Ramp with Synchronized Inward Step
Experiment 3 consisted of a 10 deg/sec ramp movement
into which was introduced a 4*
occurrence of the
step, synchronized to the
first saccade in response to the ramp and
in the opposite direction of the ramp movement.
Five curves
of observed latency in response to the introduced step are
seen in Fig. 5.6, as a function of T S 1 ,
input delay time.
the
saccade-to-
The sixth subject showed highly oscillatory
As Fig. 5.6
responses to which no meaningful fit could be made.
shows,
four subjects show slight decreases in latency for
short T S
1
values
other subject shows a rise in latency for low TSand decreasing latency for larger values.
TS_I,
The
and little or no variation for longer T S_.
At large values of
three subjects exhibit normal step latencies.
Experiment 1,
As in
these results indicate the effects of both
synchronized and unsynchronized sampling but with more emphasis
on synchronized sampling because of the lack of a rise in mean
latency.
Fig. 5.7
ment.
shows the intersubject averages for this experi-
Since all variation takes place within one
standard
deviation, little can be concluded from this result.
The
70
La
ncy(msec.)
450
Subject Line Symbols same as Figure 5.2
400-4-
350 +
300 +
0
20 4
K
200 +
150 +
100
0
4
I
0
1
50
100
150
T .r( se c. )
Figure 5.6
'Experiment Thre e - All Subje cts
200
71
Latency(msec.)
450 t
Mean and One Sigma of
Intersubject Means
400
-
350
+
300
+
250
+
0
0
0
0
0
0
0
0
0
0
200 +
150-
100+
I
p
0
1
10
I
1 .0
T3 _T (rse c.)
Figure 5.7
Experiment Three - Intersubject Means
I
20
72
fact that all means are above normal tracking latencies
indicates that, as might be expected from muscle force considerations, previously initiated pursuit motion in the
opposite direction of a saccade has an inflationary effect
on latency.
Experiment 4 ---
5.5
Ramp with Synchronized Outward Step
Experiment 4 consisted of a 10 deg/sec ramp into which
was introduced a 4'
the
step, synchronized to the occurrence of
first saccade in response to the ramp and in the
direction as the ramp.
Fig. 5.8
same
shows the curves of mean
latencies observed for this experiment.
Four subjects show
slight rises of latency while two show a decrease followed
by an increase in latency.
These
six rises indicate predomin-
ance of unsynchronized sampling but do not fit the model well.
Therefore,
little can be concluded about the nature of sampling
in this experiment.
Fig.
ment.
5.9 presents the intersubject means
for this experi-
As in Experiment 3, variations of latency are too small
and oscillatory to be meaningful.
All latencies, however, are
approximately as far below normal step latencies as Experiment
3 was above normal step latencies.
This indicates that the
effect on step latency of previously initiated pursuit movement
in the same direction is to decrease latency about as much as
pursuit movement in the opposite direction inflates latency.
5.6
Subject Interexperimental Results
Figs. 5.10, 5.11, 5.12, 5.13, 5.14, and 5.15 each show
73
Lat ncy(msec.)
4
450
Subject Line Symbols same as Figure 5.2
400 -L.
350
-
300
250 4-
200
-
\00---
150 -
0
0
-
100.
0'
Figure 5.8
I
50
i
1 (0
TS3 _(insec.)
Experiment Four
- All Subjects
I
1 '50
20'0
74
Latency (mse c.)
454
0
'ean
and One Sigma of
Intersubject Means
40C4
354-
304.
254.
2001-
0
0
150.
0
0
-
0
0
0
0
100 1.
0
5'
Ts
Figure 5.9
1
I
A
100
150
(msec.)
Experiment Four - Intersubject Means
6
200
75
the response of a different subject to the four experiments.
These figures show that actual mean step latencies in these
experiments were not identical as predicted by the revised
sampled data model.
Experiments 1 and 3 which required
reversal of eye movement direction elicited longer latencies
throughout than Experiments 2 and 4 which did not.
result agrees with the results of Beeler
This
(1) previously
1 and 2 which involved saccadic res-
discussed.
Experiments
ponse only,
showed larger variation of mean latency than
Experiments 3 and 4 which also involved pursuit movement.
Only one subject
(LN) showed a tendency toward increasing
latency in all experiments as predicted by the revised sampled
data model.
However, even these rises end in leveling off of
latency instead of again decreasing latency as predicted by
the model.
Four subjects show a point of minimum latency in Experiment
2 as do three subjects in Experiment 3 and two subjects in
Experiment 4.
All these minima occur between 60 and 80 msec.
after a saccade and indicate that a sampling instant may have
occurred immediately after the target step.
delay of 100 msec.,
intersample times
With a constant
this would indicate a predominance of
slightly higher than 160
to 180 msec.,
in
good agreement with intersample times for realistic model
results to other transient inputs as discussed in Chapter 3.
Other results which show no minima often show a transition
of some sort in the same region of TSI.
These transitions
might be attributable to saccadic suppression, but this does
not explain the rises of those showing minima.
76
Late ncy(msec.)
450
Experiment One
-
-
-
_-__-o
-
Experiment Two
Experiment Three
Experiment Four
400
350
300
250
200
00
150-
100
0
Figure 5.10
50
100
TS.1 (msec.)
150
Subject CO - All Experiments
200
77
Late cqy(msec.)
450
Experiment Line Symbols Same as Figure 5.10
400 -
350 -
300 -
250 -I
200
-
\
00
0
150
-
-- 00
100-
0
50
1 |
|
100
la
150
TS_
(msec.)
3
Figure 5.11
Subject IVH - All Experiments
260
78
Latency(msec.)
450
Efxeriment Line Symbol same as Figure 5.10
400
350
300
250 -
200
150
0
100
0
Figure 5.12
50
100
TSI(msec.)
150
Subject AVH - All Experiments
2b0
79
Latency(msec.)
450
Experiment Line Symbols same as Figure 5.10
-
400
350 -
300
250
200-
150
/
/
/
~
0
0
a
100
-
A
0
Figure 5.13
56
100
150
T _1 (msec.)
Subject LN - All Experiments
200
80
Late icy(msec.)
450.
400 4.
Experiment Line Symbols same as Figure 5.10
3504.
3004
2504.
-
200.L
-
-
/
0
150
101
I
0
1~
50
I
I
100
Ts..I(msec.)
Figure 5.14
Subject SF - All Experiments
p
150
200
81
Latengy(msec.)
450
Experiment Line Symbols same as Figure 5.10
400
350
300
250.
~
200
0
0
0
150t
I
0
p-
100
150
TSG(msec.)
Figure 5.15
Subject MK - All Experiments
200
82
The inability of either target-synchronized sampling
or unsynchronized sampling to explain the results of these
experiments indicates that both types of sampling play a
part in eye movement control.
One plausable system would
be an unsynchronized sampler which may be adapted to sample
less frequently when the eye detects difficult movements
required to follow the target.
Thus reversal of eye move-
ment direction as in Experiments 1 and 3, would show higher
latency and more synchronization effects as observed.
A
system of this sort would also explain the inflated latencies
observed by Wheeless
(see Chapter 2)
(20) to pulse-step combinations.
83
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1
Conclusions
The revised sampled data model has been shown to exhibit
responses which closely resemble eye tracking movements.
In
particular, classes of responses obtainable from the same input by varying the synchronization of input to sampling intervals
resemble actual classes of observed eye movement to identical
inputs.
The revised sampled data model is,
therefore, one
simple analyzable deterministic model which may be used to
predict classes of human eye tracking movements with remark-
able accuracy.
Predicted latency distributions to a single target step
movement for an unsynchronized sampled data model are strictly
non-increasing as shown at the end of Chapter 2.
distributions,
Actual latency
however, do increase over approximately the
50 msec. of possible latency.
first
Thus if unsynchronized sampling
occurs in the eye movement control system, the eye must be able
to adapt at least some of the samples to occur sooner when the
target step is observed.
When a target movement occurs immediately after a saccade,
the eye movement control system shows tendencies of both
84
target-synchronized and non-synchronized sampler control
logic.
The experiments requiring two movements in opposite
directions showed the decreasing then constant latencies
characteristic of target-synchronized sampling.
Most subjects'
latencies remained above normal throughout the entire range
of saccade-to-step delays used.
The experiments requiring two movements in the same
direction showed more of the decreasing, then increasing,
then decreasing latency tendencies characteristic of the nonsynchronized sampler.
Only in the experiment involving just
saccadic movement did these tendencies fit the unsynchronized
model to any degree.
This result indicates that pursuit move-
ment has some effect on sampler control logic.
The experiments involving previously initiated pursuit
movement show that saccadic latency to the introduced step
is shorter than normal if the step is in the same direction
as pursuit movement, and longer than normal if it is in the
opposite direction.
The best sampler control logic to model latency tendencies
observed in this study is a non-synchronized sampler which
could be adapted in phase and frequency depending upon the
difficulty of observed target movement.
Thus when a simple
step movement is observed, the eye could hurry the next sample
and show the observed response distributions which are best
modeled by short intersample times.
In a similar manner when
a complex movement is observed, a sample could be delayed and
brought into phase with the target movement.
This system
85
would explain observed results to pulse-steps and the wide
range of no-saccade step-ramps of Wheeless.
This system,
however, requires some continuous measure of target movement
difficulty and a description of sampling adaptation as a
function of this difficulty.
The best non-synchronized sampling system considered
in this thesis is the system with intersample
time distribution
uniformly distributed between 150 and 250 msec.
Although
this system predicts a trapazoidal step latency distribution
it retains the excellent pulse
model with mean
much of the
6.2
response of a sampled data
intersample time 200 msec. while matching
saccade-synchronized experimental results.
Recommendations for Further Study
1)
The saccade-synchronized experiments should be
extended to larger values of saccade-to-step time.
A step-
(step-ramp) experiment should be included in which the step-,
ramp is saccade-synchronized.
In the latter experiment,
reconstruction of responses in the manner of Robinson
(14)
should yield the responses predicted in Figure 3.8 of this
thesis.
2)
Further study should be made to
of assumptions on f D(D) and forms of f
find combinations
(T) in the analysis
of section 2.5 to exactly model observed latency distributions.
3)
Under the assumptions of section 2.5 of this thesis,
a polynomial fit to a distribution of intersample times could
be constructed to agree with observed step latencies at given
86
points on the decreasing portion.
The jump from zero to
the maximum of f D(D) could then be placed so that the integral over all values of f D(D) equals unity.
This function
would be an approximation to the distribution of intersample
times to agree with step latencies in a non-synchronized
sample data model.
4)
The changes in saccades due to pursuit movement
and the changes in pursuit movement due to saccades
(parti-
cularly the latter) need to be further investigated to
determine the intersystem control functions necessary in
the model.
5)
A complete investigation is in order of the phenomenon
observed by Beeler and substantiated in this thesis that
during a certain short period after an initial saccade the
eye can perform a saccade in the same direction as the initial
saccade but cannot perform a saccade in the opposite direction.
This tendency is probably due to muscle hysteresis nonlinearities
and viscoelastic elements in the eye.
87
REFERENCES
1.
Stochastic Processes in the Human Eye
Beeler, G. W.,
Movement Control System, PhD Thesis California Institute
of Technology, May 1965
2.
Bleuze, J. C.,
"A Sampled Data Model for Eye Tracking
Movements," M.
S. Research Project, University of California
Berkley, Department of E.
3.
Cook, G.,
E.,
August 1963
Stark, "The Human Eye, Movement, Mechanism,
and L.
Modeling and Model Testing,"
F.
J.
Seiler Research Lab
USAF Academy, Colorado, SRL-67-0005, June 1967
4.
Forster, J.
D.,
and N.
Tracking Movements,"
5.
Fuchs, A.
F.,
Van Houtte,
MIT Man-Vehicle Lab memo, March 28,
Horrocks, A.,
1967
"Saccadic and Smooth Pursuit Eye Movements
in the Monkey," J. Physiol.,
6.
"A Model for Eye
and L. Stark,
Vol. 191, 1967, pp. 609-631
"Experiments on Error as a
Function of Response Time in Horizontal Eye Movements,"
QPR 72,
7.
Res. Lab. Elec.,
Johnson, L. E.,
MIT, pp. 267-269, January 15, 1964
Human Eye Tracking of Aperiodic Target
Functions, Ph.D.,
Dissertation System Research Center
#37-B-63-8, Case Institute of Technology, Cleveland, Ohio
88
8.
Jury, E. I.,
Sampled Data Control Systems, 1958, New
York, Wiley
9.
Jury, E. I.,
and T. Pavlidis,
"Discussion of a Sampled
Data Model for Eye Tracking Movements'",
Second Inter-
national Congress of Interntl Federation of Automatic
Control, Basel, Switzerland, August 1963, Butterworths
Limited, London, P. 461
10.
Lanning, J.
H.,
and R. H.
Battin, Random Processes in
Automatic Control, 1956, New York, McGraw-Hill, Library
of Congress, Catalog Card #55-10410
11.
Papoulis, A.,
Probability Random Variables and Stochastic
Processes, 1965, McGraw-Hill, New York, Library of Congress
Catalog Card #64-22956
12.
Rashbass, C.,
"The Relationship Between Saccadic and
Smooth Tracking Eye Movements," J. Physiol., 159:326,
1961
13.
Robinson, D. A.,
"The Mechanics of Human Saccadic Eye
Movements," J. Physiol, 174:245-264, 1964
14.
15.
Robinson, D. A.,
"The Mechanics of Human Smooth Pursuit
Eye Movement,"
J. Physiol, 1965, 180, pp. 569-591
Saslow, M. G.,
"Latency for Saccadic Eye Movements,"
J. 0. S. A.,
pp. 1029-1033
Volume 57, Number 8, August 1967,
89
16.
Truxal, J.
G.,
Control Systems Synthesis, McGraw-Hill,
New York, 1955
17.
Vossius, G.,
"Der Kybernetishe Aspekt der Willkurbewegung,"
Progress in Biocybernetics, Vol. 2,
18.
19.
1965, P.
111-140
Westheimer, G.,
"Mechanism of Saccadic Eye Movements,"
Arch. Ophthal.,
New York 52,
Westheimer, G.,
"Eye Movement Responses to a Horizontally
Moving Visual Stimulus," A.
1954, P. 910
M.
A.
Arch. Ophthal. 52,
1954, pp. 932-943
20.
Wheeless, L. L.,
The Effects of Intensity on the Eye
Movement Control System, Ph.D. Thesis, University of
Rochester, 1965
21.
Wheeless, L. L.,
R.
M. Boynton, and G.
H.
Cohen, "Eye
Movement Responses to Step and Pulse-Step Stimuli,"
J.
22.
0.
S. A.,
Wilde, R.
W.,
Vol. 56 Number 7, July 1966
and J.
H. Westcott, "The Characteristics
of the Human Operator Engaged in a Tracking Task,"
Automatica I No. 1,
23.
Young, L.
R.,
Movements, S.
A
D.
1963
Sampled Data Model for Eye Tracking
Thesis, Massachusetts
Institute of
Technology, June 1962
24.
Young, L.
R.,
and L.
Stark, "Variable Feedback Experiments
Testing a Sampled Data Model for Eye Tracking Movements,"
90
24.
IEEE Transactions of the Professional Technical Group
on Human Factors in Electronics, Vol. HFE-4 Number 1,
September 1963
25.
Young, L. R.,
and L. Stark, "A Discrete Model for Eye
Tracking Movements, IEEE Transactions
on Military
Electronics, Vol. MIL-7 Number 2 and 3, April-July 1963
26.
Young, L.
R.,
B.
L.
Zuber, and L.
Stark, Visual and
Control Aspects of Saccadic Eye Movements, NASA,
CR-564, 1966
27.
Young, L.
R.,
J.
L. Meiry, and Y. T.
Li,
"Control Engineering
Approaches to Human Dynamic Space Orientation," Second
Symposium on the Role of the Vestibular Organs in Space
Exploration, NASA Ames Research Center, Moffett Field,
California, January 1966, NASA SP-115
28.
Zuber, B.
L.,
Physiological Control of Eye Movement in
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91
APPENDIX A
THE EXPERIMENTAL SYSTEM
The saccade synchronized experiments of this thesis were
performed using the Man-Vehicle Control Laboratory of the
Massachusetts Institute of Technology's GPS-290T hybrid computer.
The digital portion of this computer is a PDP-8, built
by the Digital Equipment. Corporation.
address,
This computer is a single
12 bit machine with 4096 word core memory and a cycle
time of 1.5 microseconds.
The analog portion consists of a
GPS-200T analog computer with amplifiers, integrators, multipliers,
comparators, and one-input two-output electronic
switches quite compatable with the digital portion since they
have a megacycle bandwidth.
Two-input one-output switches may
be constructed by patching integrators
as amplifiers and applying
switching signals to the mode control of the integrators.
The
computer has an analog control panel with individual integrator
mode controls, electronic switch controls, two clocks, NAND and
NOR gates, flip-flops, digital sense lines and control lines,
and program interrupt capability.
Only a small portion of these
computer capabilities were needed to perform the experiments.
This appendix should in no way be considered a complete descrip-
tion of the GPS-290T computer.
92
The hybrid system developed for the saccade-synchronized
experiments of this thesis generates the inputs for the four
experiments
(Section 4.2 & Figure 4.1) in the order specified
by a 4410 entry input list.
The digital portion sets the
switches which control input form, executes the variable time
delay, and performs counting functions.
The analog portion
generates the input voltage signals, detects saccades, and
records
the experimental variables.
In describing the system developed, a knowledge of basic
PDP-8 assembly language and a basic knowledge of analog circuitry are assumed.
In the digital portion, variable names
and statement labels are capitalized and followed by their
octal address in parentheses.
A.l
The Digital System
An assembly language listing of the complete digital
portion of the system developed is seen in Figure A.l together
with brief program notes.
is 200.
The starting address of this program
The three instructions preceeding 200 are used to
terminate an experimental run with the computer immediately
ready to start the next run.
The program must be started with
the location of entry into the input list set in the switch
registers.
The program immediately halts with this first
input location in the accumulator to allow a check of correct
entry.
When the CONTINUE key is pressed the computer stores
this value in INFROM(307),
initializes COUNT(306) which will
halt the run after 4410 inputs, and enters the main portion
at LOOP(205).
93
*175
017 6
0017
1777
200
0201
02' (
0203
020
6452
6402
7402
7200
7606
3307
1312
3306
0205
0206
0 20 7
0210
0211
0212
0213
0? 14
0215
0216
0217
0 220
022 1
0222
0223
022 A
0225
0226
0227
0230
0231
Q.232
6314
6322
6331
1307
1314
77
10
5216
1315
3307
1707
7510
6312
7004
7510
6321
OUT, CMR
HLT
CLA
LAS HLT
DCA INVP
FRf
lAD CM54;
DCA C0U N'T
LOOP, SCL03
SCL 0 4
S CL 05
TAD INFROM
TA0 CM374
SPA CLA
)CA
INF
SELECT INPUT
M
Et5f
/
3WI TCHES
RAL
7004
L
0316
AND
1311
TIALU
0233
331 1
023 -i
2307
V 235
6311
6 4 52
6 L'01
7604
7510
0CA DELAY
I sZ INFR M
SCL02
CMRP
7510
6324
DELAY
/SET
COUNTER
C777
C'70V0
/
INJCPEMEN T LIST LCA
If'ON
AI C
LAS
/
WAII
FOR SIGNAL
/
INITIATE
SPA
022 2
52 4aV
JMP
.- 2
02 43
4300
760 LA
7700
524A
6452
6402
6435
7700
5261
7604
7004
7700
5251
5205
JMI)S
NE
0246
0247
0250
0 251
0252
0253
0254
0255
0256
0257
0260
/
I NFRUM
TAD I
SPA
CCL03
7417
0001 1
0244
0245
sIAf<T
JMP 0+3
TAD C320
S PA
CCLO5
LSR
01
0236
0237
02 40
02Z I
/
LAS
SMA
CLA
JMP .- 2
C'MR
SLR
JIMP
CAC
CLA
PA S
/
T ESf
INPUT
SACCADE
UETECTPR
LAS
RAL
SMA CL A
JMP .- 6
JMP LUOP
FIGURE A.1
THE
DIGITAL
SYSFEM.1
-
PROGRAM
LISTING
94
0261
0262
0263
0264
0265
0266
0267
231 1
4270
63014
4300
2306
5205
5175
0270
0271
7344
0272
1270
3270
0274
6454
@275
@276
@277
64161
5670
5275
')
(
0300
03 A1
@302
@303
1313
33 10
2310
03041 4270
5700
@306
@307
0310
0 311
WA IT, 0
CLA CLL CMA
TAD WAI T
DCA WAIT
CLIF
SKIF
JMP I WAIT
JMP -- 2
ISZ
CM54-54
*1
/
WAIT ONE ANALOG FLAG
kETURN TO INSTRUCTION
/
DELAY ONr
/
CuNSTAi\jTS & SYMBOL
SEC.
USING
AHOVE CALL
WAIT
ROUTINE
END
24
/
FINISHED?
JMS WAIT
JMP I ONE
00
00 00
00 00
60 30
03111
74 04
0315
03 20
0316
07 77
0317
70 00
CM 1750
0313
INTJRODUCE STEP
/
KAML
ON E, 0
TAD CM1750
DCA END
COUNT, 0
IN FNOM, 0
END,
DELAY,0
t ," 00
0312
0313
DELAY PRESET' TIME
PAWSISZ DELAY /
JMS WAIT
/
CCL02
JMS ONE
/
ISZ COUNT
JMP LOOP
OUT
J"Vi
TABLE
f,.1750,-1750
74, -37 4
C320,320
C777,7/7
C7000,7000
C3
0314
CM3711
0312
COUNT
C320
C7000
C777
DELAY
END
I NFROM
LOOP
ONE
SUT
PAWS
W AI T
0306
0315
0317
0316
0311
0310
0307
0205
0300
0175
0261
0270
FIGURE A.1(CONTINUED)
THE DIGITAL
SYSTEM -
PROGRAM LISTING
95
* 32(
1633
(A322
2 32 1
A 322;
(A/77
M777
-- 537
2537
2323
5753
2 32/i
5753
1467
2346
1 /167
2727
3563
77 (13
7513
4657
6627
3467
1537
56-7
7753
1727
2633
6657
4513
2777
-563
A723
5657
0347
1777
? 350
P 351
2563
3-727
1467
7627
67 3
6513
2563
4753
4753
7537
32 5
2326
2327
2332
0331
0 332
V333
(A334
(A 335
0 336
(A 33 7
0 34 ()
2341
S342
(A3 zL_3
A 345
(352
2 354
(355
2 35.6
0 357
2 362
2 361
2362
2 363
(A364
365
0366
(,,367
037n
0 37 1
f 372
( 37 3
1633
7 537
1633
3777
1563
7657
6753
0537
2633
S727
5513
467
2467
2727
3563
77 03
7513
4 657
6627
3467
1537
56(7
7753
1727
3633
6657
4513
27 7 7
2563
* 7 (A3
5657
17 77
3727
v467
76M 7
67P3
6513
0633
3777
1563
7657
6753
0537
2633
2727
5513
4607
57 3
2467
F I G U E A. -I(
CONTfINOJUED)
IHE
DIGIiAL
SYSTEM
-
INPT
LIST
96
Each input generated starts at LOOP(205).
The program
first resets the control lines to be used to determine the
input, and tests INFROM(307) to see if the end of the list
has been reached or a value above the list has been accidentally
In either case,
initially specified.
the program resets this
pointer to the beginning of the input list by setting INFROM
(307)
to
The program then tests the three highest order
3208.
bits of the list entry whose address
is in INFROM(307),
the corresponding control line of any bit that is one.
clearing
Next
70008 is added to the remaining 9 bits and this value stored
in DELAY(311)
for later use as a counter.
Values of the last
9 bits corresponded to counters for delays of 0 to
With the analog flag set to occur at one
in steps of 20 msec.
msec. intervals
200 msec.
(as specified in Figure A.4),
these counters
are constructed by taking the twos complement negative of the
number of msec. to be delayed plus one expressed octally.
Counter values were placed on the input list at random.
The
program then puts the analog computer into initial condition
mode and prepares control line 2 to introduce the saccadesynchronized step.
Next, the program waits for switch register bit 0 to be
zero
(down),
delays one second, and waits for switch register
bit 0 to become one
These
instructions
(up),
at which time the input is initiated.
(240-246) give the experimenter control
over the initiation of an input, with a minimum time between
inputs of one second.
The instructions could easily be replaced
by a constant or random delay.
97
The program then puts the analog computer into compute
mode, thus introducing a step or ramp input to the subject.
Next the program continuously tests the sense line which is
set by the saccade detector.
When a saccade is detected, the
sense line is set allowing the program to go to PAWS(261)
where it delays the preset time by using the subroutine
WAIT(270) and the counter DELAY(311).
At the termination
of the delay, a step is introduced into the target motion
by clearing control line 2.
Finally the program delays one
second then tests COUNT(306) and goes accordingly to termination at OUT(175) or back for another input to LOOP(205).
Should the
saccade detector fail to detect a saccade,
the experimenter may return the program to LOOP(205) for the
next input by raising switch register bit 1.
In this case
the input will not be counted in the 4410 inputs per run.
This program may be easily altered to produce inputs of
known pulse width by changing SLR CAC at location 251 to NOP.
If this is done, the pulse width of an input will be exactly
the value of the saccade-to step delay of its corresponding
list entry.
Future more accurate systems should make possible digital
recording and digital data reduction routines to relieve the
burden of data reduction by hand.
Digital ensemble averaging,
however, has been found to conceal typical response character-
istics and therefore is not recommended.
A.2
The Analog System
Figure A.2 shows the analog circuit used to generate
98
target movement in the saccade-synchronized experiments of
this thesis.
Switches B,
trol the input form,
C,
and D are the switches that con-
Table A.l shows
the eight outputs obtain-
able from the eight different switch settings.
Also shown are
octal contents of the three highest order bits in the input
list to which each input corresponds.
Switch A introduces
the saccade-synchronized step.
Switch E is used to introduce.
initial steps, and integrator A
introduces ramps.
Figure A.3
shows
the circuit used for the
saccade detector.
The circuit for changing the sign of the input was necessary
because of the comparator's characteristic of detecting threshold crossings
in one direction only, while the
saccade to be
detected changed direction with the input direction.
The
s
s + 25 transfer function for the pseudo-differentiator was
chosen for its good results in conjunction with the
cutoff of the eye monitor used.
was
low frequency
The comparator threshold level
set just above the level of pursuit eye movement to minimize
delay in saccade detection.
Figure A.4 shows the circuits necessary on the analog
control panel to interface the analog and digital portions
of the experimental system.
99
All Gains One Unless Otherwise Specified
+1 v
ES B (Integrator used as electronic switch)
-10V
A
A FES
Po
ES C
A
II
ES E
Pot A - First Step Size
Pot B - Ramp Rate
Pot C - Second Step Size
to CRT
Target Movement Circuit
Figure A.2
I
Input Sign Switching Circuit
I
Comparator
Pseudo-Differentiator
5
or
tye
Monitor
>..
ES F
-Chart
Recorder
>
(integrator
used as
electronic
switch) S
Figure A.3
.
.25
a
e
C
Saccade Detector Circuit
-0Comp.
A
hreshold
s
100
Table A.1
Inputs Generated by List Entries
Three Highest
Order Bits
(oetal)
Input (deg.)
Description
0.-
0
Stairway Pulse
+5-to
the right
0 -
1
Ramp with
Outward Step
to the right
-5
2
--
Aeturning Pulse
to the left
0 --
-5 -_
Ramp with
Inward Step
to the left
0 -
-5 -
4.
50
Stairway Pulse
0-
to the left
-5-
Ramp with
Outward Step
to the left
06
0I
I
I
Returning Pulse
to the right
I
I
07
Ramp with
Inward Step
to the right
-5 a
U
101
CL 2 0
ES A
CLOCK -
050 1
050 1
CL 3
1rj~
E-'C B
0.C.
P 1
NAND
0. C.
0EMC F
NAND
I
INV
0ES C
ES D
CL 5
ES E
CONPUTE
L I
0
I.C.
L
Gated
Flip
-
Flop
Cl F
S.T.
INV
Figure A.4
Analog Control Panel Circuits
I. C.
COMPARATOR
A
102
APPENDIX B
EXPERIMENTAL DATA
Figures B.l - B.24 of this appendix present the results
of each subject in response to each experiment in the form
of means and standard deviations of step latency observed
as a function of time from the
of the step
(T S).
last saccade to the occurrence
The four experimental
inputs are described
in Section 4.2 of this thesis and are pictured in Figure 4.1.
Each graph also shows the curve fit to its means which represents
its data in the discussion of results in Chapter 5.
The data
for each graph were quantized independently to take into account
differences in amount and placement of data.
103
Latency (msec)
4501
400.
350-
300
0
2.50 t
E)
0
200
-1
150
4-
0~
IV
----
100 ..L
I
I
0
50
Figure B.1
1
I
100
150
Exp. One - Subject CO
200
(msec.)
104
Lat
cy(msec.)
4504
400-
-0-
-
350t
300 +
0
0
250+
0
200
-
150+
100+
0
0
Figure B. 2
a
50
i
100
TSI (mse c. )
Subject AVH - Exp. One
f
A
150
200
105
Latpncy (mse c.)
450+
400+
0
350+
300-
250
+
0
200 +
0
0
- C0
150
0
+
100 4-
a
6
m
50
I
100
TSI (msec.)
Figure B.-3
Exp. One - Subject NVH
a
1
200
106
Latqncy(msec.)
450 4-
400 -
350 -
300 .-
0
250 -
200 4-
150
-
100
iI
0
50
I
I
100
150
Ts
3 1 (msec.)
Figure B. 4
Exp. One - Subject LN
200
107
Lat ncy (msec.)
450
400
350 -I-
300
0
-
a
mmmmmmlr_
250 -
200 4-
150 +
100 --
I
0
Figure B.-5
-I
50
I
A
I
100
TS-1 (msec.)
150
200
Exp. One - Subject SF
b
108
Late cy(mse c.)
450
400 +
0
350 +
0
0
300t
250+
0
200+
150t
100-
a
i
0
50
a
100
TS
3
Figure B. 6
(msec.)
Exp. One - Subject MK
I
200
109
Late cy(msec.)
450-
K
400..
350+
300+
250-1-
150
10(.
a
0
Figure B.7
a
50
m
10
T 5 _ (msec.)
Exp.
Two - Subject CO
1.0
260
q
110
Latepcy(msec.)
450 -
400 -
350 -
300 -
250 -
200 +
00-
0
0
150 +
100 4-
I
0'
I
100
50
T _1 (msec.)
Figute B. 8
Exp. Two - Subject AVH
150
200
111
Lat ncy(msec.)
450
400
350 4-
300 +
250 4
200 4.
-M
150
100
-1
.
i
0
A
50
b
100
T..,(msec.)
Figure B. 9
Exp Two - Subject NVH
150
200
112
Lategcy(msec.)
450 -
400 -
350 +
300
250
200 +
150
S~~~
-
100 +
a
6
Figure B. 10
i
50
m
i
100
Ts.1 (msec.)
Exp. Two - Subject LN
150
I
200
113
Late cy(msec.)
4501
4004-
350
+
300 +
250-
G)
0
0
Welvi-
200-
GG
150+
0
1004
0
aw
i
100
TS_y (msec. )
Figure B.11
Exp.
Two - Subject SF
1 50
a
200
114
Late cy(msec.)
450
.
400 4-
350
300
250
-0
0
0
m
200 +
0
150 +
*AM
100-
a
0'
Figure B. 12
A
50
100
Tsi (msec.)
Exp. Two - Subject MK
150
a
200
115
Lateicy (mse c.)
p
400 4.
350 +
300 4
250 +
200 +
0
-
-
0
0
150 4.
100 -
a
IL
k
I
0
Figure B. 13
50
100
(msec.)
T _1
Exp. Three - Subject CO
150
200
116
Latepey (mse c.)
4504
400 4
350 -
300 -
0
0
Mom
250 +
200 -
150 -
100 -
a
0
50
TS
Figure B. 14
a
A
A
100
150
200
(msec.)
Exp. Three - Subject AVH
117
Latency(msec.)
450
j
400
-
350 -
300 t
250 't
- G
200 -
-
w
low
w
150
-
100
-
g
n. 0 0
0
G0
a
0
Figure B. 15
50
1
T _y (msec.)
Exp. Three - SubjectVH
-
150
200
0
118
Lat ncy (mse c.)
450
1
400 4
350 1
300
250 +
0
200 4
0
0
150 +
100 4
a
0
Figure B.16
50
1 60
TS-1 (msec.)
Exp. Three - Subject LN
1 50
200
119
Latency(nsec.)
450t
400 +
350 t
0
0
0
300 t
0
0
0
0
0
250 t
e
0
0
200 +
150 +
100 +
I
0
50
a
0
100
150
TS_1 (msec.)
Figure B. 17
Exp.
Three - Subject SF
------- 73
200
120
Latency(msec.)
450
400
350 +
0
300 -
0
0
0
250 -
0
0
200 4-
150 -
100 4-
I
0
100
50
Ts. 1 (msec.)
Figure B. 18
Exp. Three - Subject MK
150
200
121
Latency(msec.)
1
450
400 4-
350 -
300
250
+
200-
0
150-
000
0C
0
100+
a
0
100
56
T
Figure B. 19
A
(msec.)
Exp. Four - Subject CO
150
200
122
Latency(msec.)
1
450
400--
350 +
300-
250
-
200 +
0)
150 t
-
.
n.
~
0
A-
0
0
100+
s
0
0
50
Figure B.20
2
100
TS.I(msec.)
Exp. Four - Subject AVH
Mmm
150
200
123
Latency (inse c.)
4504
4004
350t
300 t
250+
200+
0-0
0
150 t
0
100+
a
0
2
a
50
100
TS.3
Figure B. 21
(msec.)
Exp. Four - Subject NVH
150
200
124
Lat ncy(msec.)
450
1
400 4-
350 +
300 +
250 +
200 -
0 .
150 -
-
G-
0
-
-
100 -
a
0
U
U
50
100
Tg_ (msec.)
Figure B.22
Exp. Four - Subject LN
I
U
150
200
125
Latecy (msec.)
450 -
400 4-
350
+
300-
250
+
2004
G
150 +
100+
I
0
I
I
50
10
T3 . 1 (msec.)
Figure B.23
Exp. Four - Subject SF
I
150
200
126
Latency(msec.)
450 1
400 4-
350
+
300 +
250 +
0
0
0
200 +
0
0
150 +
-
0
0
0
0
100 +
0
Figure B.24
a
50
0
100
Tsi (msec.)
Exp. Four - Subject MK
a
150
200
127
APPENDIX C
STOCHASTIC SAMPLED DATA SYSTEM SIMULATION PROGRAMS
Figures C.l -
C.4 of this appendix present MAD
(Michigan
Algorithm Decoder) listings of the programs used to generate
Figures 2.4 -
2.7 in Section 2.5 of this thesis.
Figure C.5
presents program notes that apply to all programs but with
line references to the listing of Figure C.l.
Figure C.6
presents individual program notes which apply to each specific
program.
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I P
Tr.".
00 '20
0 () 10
00'3 It
Y FOP
T14POUGT- L I;F-,
I F= (I + - )+IF
COT II
E
F0 P N=1, 1, N. r. 5
K~+0
J I +194
J= I+1j)I4
PR I !"T OrL I N7
V/TCTO V\l,11rT
CnPT I t''IPP I fIT n I I 117
PPI IT O1L It1
000490
0 1;0 0
00600
FORdA T '41 STOC K, J
HI STOP-=;S10, I 4, 1-, I 4, 'I
FOrl'AT R
F IIAT A
EXFCT
F IT. (0)
INTr1 T , K,.PN, I ! AM, J , I
I 'Tr (Y R M, IP HT, IF-
Crin OF
prnr-n,
I i.500+.600
Figure
.2
Simulation of System with Sampling Intervals
Jniformly Distributed Between 0 and 200 msec.
-
' (1
I)*e-
130
printf
I 130
nonty
o ll 0
00020
00030
0 00 4 0
FOPM/\T VARIAN-L7 IF
PI?'FrSION M(250)
0I.I F FOMJAT SICHAL
PrI T
VECTOP VALI'!S S I AL)$1fiRE/'Y
REAP FORMAT TAKEIN,IO
O'' FORMAT SI ONAL
PrI'T
R'An FORMAT TAK'il' ', K
VECTOR V\/''.IS TAKEIH= 18*,
q1=SFT'. ( I n)
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n0nq0
n orn
00' 7n
onoo
00090
00 1 n n
00110
00120
CONTI N1 E
I SAM=0
TLJPOUII L In,
M(I )=0
CO!TI UF
TI4ROIMM- I, I N Od,
I NPUT=250*r!'N0.
nolit 0
nor
00 19
00 200
LI IV7
L INC
I MPT
*
Ffr1 I=1, 1, 1 . 0.250
FOR I =1, 1., I Q. K
(Y)+250
I SAf1=150+100*R AVHO.
00210
002 20
00230
00241.0
00 250
00 2 F0
00270
FOR
RA=R/'O. (Y)
LINA
00130
Of0170
ind
.
(Y)+ I S'A
'NEVER
(I SAM- IPIT)
.L.0,
TRANSFER TO LI l.EC
N( ISAM- I UPHT+1 ) =( I S Ar- I NPIJT+1 )+1
I SAM= I SA'1- I NPUT
CONTI NIT
PR INT OL I NE FODMA T A
7HLAsTECY, 511, ?1O, 58, 21120, S8, 1130, SP, 2H4i*t
V'S A=nS10,
VILIMF FORMAT R
PIF'T
VFCT0'! VA .1'rS R= cl-(, 7H ------- , c'1 I ', 3 (~ . I9 t1')*
THRPouC LI YTF, FOR H=,5, I .0.250
LI I'P
00 2 80
00 290
00450
001.60
TIROtI(H LI NE -,
00 470
00t80
IF=M( 1+-1).+
rONT I NUF
I F=IF/5
.INE
00490
00500
rs' o
00r0
00530
00540
00550
00
0
00570
FOR N=1, 1, N. G. 5
F
K= I +99
L I
F
00580
n0osq
o nc)fno
3=1+104
PRINT ONLINE FO.MAT HISTOO,K,J
VECTOR VA LUES HI STOC=Si,4,1H-,IL4,'IF' (1I)*$
CONTINU
FOnMAT R
PrINT ONLINE
PRI NT OUL I NE FORMAT A
EXECUTE EXIT.(0)
I PrTECEP 1), KN, I SAM, J, I
I M TE FR M, I NPHIT, IF
ENO OF PPOGRAM
P 1.800+.683
Figure C.3
Simulation of System with Sampling Intervals
Uniformly Distributed Between 150 and 250 msec.
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TET
132
Line
10,20,580,590
Notes
Variable mode and format designation
30 -
80
Read in ID (used in initialization of
random number generator) and K (number
of trials)
90 -
170
Initialize random number generator,
ISAM, and M matrix
180 -
240
Main program loop - executes inputs and
generates samples until
total time
between samples exceeds time of input
190
Selects time of occurrence of inputs
210
Tests for total time between samples
exceeding input time
220
Increments member of M matrix corresponding to time from input to next
sample plus one (one added for easy
subscripting in printout)
230
Resets intersample time corresponding
to input at zero to avoid accumulation
of large numbers where only differences
are interesting
250 -
560
Print latency histogram resulting
500 -
510
Add the constant delay to form latency
from input to sample time
Figure C.5:
Program Notes Applying to All ListingsLine References refer to Figure C.l
133
Figure
Line
Notes
C.1
200
Sampling instants occur at 200
msec. intervals
C.2
200
Sampling intervals occur uniformly
distributed between 0 and 200 msec.
C.3
200
Sampling intervals occur uniformly
distributed between 150 & 250 msec.
C.4
200 -
Figure C.6:
240
This transformation carries values
of DR (uniformly distributed between
0 and 1) that are less than .8 into
intersample times uniformly distributed between 60 and 120 msec., and
values of DR greater than or equal
to .8 into intersample times uniformly
distributed between 120 and 200 msec.
Specific Program Notes for each Listing