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Stochastic Control in Eye Movement Tracking 
 
 By 
 
 r -* 
 
 Shean Wang i 
 t- + 
 
 RESEARCH PROJECT 
 
 Submitted in partial satisfaction of the requirements for the degree of 
 
 MASTER OF SCIENCE 
 
 in 
 Electrical Engineering and Computer Sciences 
 
 in the 
 GRADUATE DIVISION 
 
 of the 
 UNIVERSITY OF CALIFORNIA, BERKELEY 
 
 Approved: 
 
 Lawrence Stark, Research Adf/i so r Edwin R. Lewis, Research Advisor 
 
T7 
 
 INTRODUCTI^II 1 
 
 sxp3T.i::.::T r j: JIIOD 3 
 
 033EHVA-TIOU ?^Ci: OJHZ EXP2S1MEIITAL RZ3UL23. 6 
 
 DISCUSSION 9 
 
 POSSIBLE ?U2URE Din2CO?lCi; 24 
 
 SUI'2>iASY 26 
 
 RZFSREKCI 28 
 
 PIGUHSS 29-72 
 
range of fr-jcuer.cy , the eye can even anticipate the 
 target. This leads numerous models of a predictor for 
 the eye movement systen. Consequently, an effort is made 
 to compare the experimental results of this report with 
 those of existing proposed models. 
 II. The pursuit and saccadic movements of eyes. 
 
 Many established experiments have shown that the afferent 
 signals are continuous but the efferent signals are 
 either continuous or discrete or both. Thus the 
 respective eye movement can be pursuit, saccadic, or both 
 pursuit and saccadic. Therefore, questions are raised 
 about the discrete nature of eye movements. Where does 
 the discrete nature come from? How does it work? As of 
 now, there is no physiological explanation. However, from 
 the engineering point of view, there can be numerous 
 possibilities. The most satisfactory model is a 
 stochastic sample-data control system with a uniformly 
 distributed inter-sampling time. This system v/ill be 
 reviewed in this reoort. 
 

 . -i. . :---. _ ;-. 
 
 The experimental procedure for the measurement of horizontal 
 eye movements has been well established and therefore only a 
 brief description v.-ill be presented here. 
 
 In a dark room, the subject v;as asked to fixate on a light 
 spot which, is controlled by a target notion generator. A 
 small beam of infra-rad light was directed to the left eye 
 ball, and its reflection was collected by a pair of 
 photocells aimed at the iris-scleral border as shown in 
 Figure 3a. 2ye positions could be detected by the difference 
 in output of these two photocells. Then an operational 
 amplifier was used to amplify the difference and send it to 
 a Sanborn recorder. In order to minimize the interference 
 introduced by motion, the subject leaned his forehead 
 against =i fir b?.r ?.nd bit on a piece of dinLal iia^ression 
 wax as shown in Figure 3t>. 
 
 Experimental data were collected from three subjects. Three 
 different kinds of stimuli were presented: regular square 
 wave, irregular square wave (or staircase wave), and ramp 
 input. The latency of response to each stimulus could be 
 defined in three different ways as shown in Figure 4a, 4b, 
 and 4-c. However, in Figure 4-c, it was very hard to decide to 
 which particular input the eye did respond. The time required 
 for eye to respond upon a stimulus (reaction time) was about 
 150 msec, therefore, the tine larger than but closest to 
 150 msec was choosen. 
 
 For each experimental run, a histogram of latency of 
 response was generated. The binwidth was 25 msec, and the 
 middle point of each bin was used as the latency within its 
 
+ 12 msec range (see Figure 5 to Figure 11). The average 
 and standard, deviation of latency were computed by IBM 6A-00 
 for each experimental run of both square wave and staircase 
 wave stimuli. A set of experimental data v;as collected from 
 the same subject with the sane stimulus by changing the 
 frequency alone. The frequencies used are listed in Table 1 
 (see next page). For each set of square wave and staircase 
 wave experimental runs, the inedian(H), average(Av), mode(Hd), 
 and standard deviation(s) of latency were ploted vs. 
 frequency as shown in Figure 5 to Figure 10. In the ramp 
 input case, only median vs. frequency was ploted. 
 
Set I. Regular square v/ave input! 
 
 1. 
 
 2. 
 
 3. 
 4. 
 
 5. 
 6. 
 
 7. 
 
 8. 
 
 9. 
 10. 
 
 0.1 Hz. 
 0.3 Hz. 
 0.5 Hz. 
 0.9 Hz. 
 1.1 Hz. 
 1.3 Hz. 
 1.5 Hz. 
 1.7 Hz. 
 1.9 Hz. 
 2.3 Hz. 
 
 Set II_. Irregular square 
 
 v/ave inputs: 
 
 1. 
 
 
 
 .150 Hz, 
 
 
 
 .235 
 
 Hz, 
 
 
 
 .488 
 
 Hz 
 
 2. 
 
 
 
 .255 Hz, 
 
 
 
 .488 
 
 Hz, 
 
 
 
 .785 
 
 Hz 
 
 3. 
 
 
 
 .488 Hz, 
 
 
 
 .785 
 
 Hz, 
 
 1 
 
 .230 
 
 Hz 
 
 4. 
 
 
 
 .785 Hz, 
 
 1 
 
 .230 
 
 Hz, 
 
 1 
 
 .480 
 
 Hz 
 
 5. 
 
 1 
 
 .230 Hz, 
 
 1 
 
 .480 
 
 Hz, 
 
 1 
 
 .710 
 
 Hz 
 
 6. 
 
 1 
 
 .480 Hz, 
 
 1 
 
 .710 
 
 Hz, 
 
 1 
 
 .950 
 
 Hz 
 
 7. 
 
 1 
 
 .710 Hz, 
 
 1 
 
 .950 
 
 Hz, 
 
 2 
 
 .210 
 
 Hz 
 
 8. 
 
 1 
 
 .950 Hz, 
 
 2 
 
 .210 
 
 Hz, 
 
 2 
 
 .450 
 
 Hz 
 
 9. 
 
 2 
 
 .210 Hz, 
 
 2 
 
 .450 
 
 Kz, 
 
 2 
 
 .730 
 
 Hz 
 
 10. 
 
 2 
 
 .450 Hz, 
 
 2 
 
 .730 
 
 Hz, 
 
 3 
 
 .010 
 
 Hz 
 
 Set III. Samp 
 
 inputs: 
 
 
 
 
 
 
 
 1. 
 
 2 
 
 /sec. 
 
 
 
 
 
 
 
 2. 
 
 1 
 
 /sec. 
 
 
 
 
 
 
 
 3. 
 
 
 
 .7/sec. 
 
 
 
 
 
 
 
 4. 
 
 
 
 o?'j /sec. 
 
 5. 
 
 
 
 ,5/sec. 
 
 
 
 
 
 
 
 6. 
 
 0.33/sec. 
 
 7. 
 
 O.l33/sec. 
 
 8. 
 
 1 
 
 6/sec. 
 
 
 
 
 
 
 
 Table 1 . 
 
'T ;1 
 
 -lj_. 
 
 (A) Regular square v;ave inputs: 
 
 The results from subject C (Figure 5) and subject W ( 
 Figure 7) give similar conclusior. for the values of the 
 median, the average, and the mode of the latency 
 distribution curve. They shov; that these three values are 
 all frequency dependent. But at the meantime, subject C 
 and subject S shov/ a similarity in the curve of the 
 standard deviation of latency distribution vs. frequency. 
 That is, the standard deviation of the latency 
 distribution is also frequency dependent. 
 
 For the latency distribution curve, 
 Let M = median 
 Av = average 
 lid = mode 
 
 s = standard deviation 
 then the above similarities can be summarized as follows: 
 
 (1) 0^ frequency <O. 5 Hz. 
 
 a. M, Av, Hd are all decreasing as frequency 
 increasing. 
 
 b. s is increasing as frequency increasing. 
 
 (2) 0.5 Hz.^ frequency < 1.5 Hz. 
 
 a. M, Av, and Md are within + 25 msec range. 
 
 b. s is decreasing as frequency increasing. 
 (5) frequency>1.5 Hz. 
 
 M, Av, Ivd, and s are increasing as frequency 
 increasing. 
 
 Therefore the distribution of latency is shifted as 
 frequency is changed. The distribution starts at the large 
 time l-.g region, then shifts to the tine lead region. As 
 
frequency continue 3 J ;o increase, it shifts back tov:ards 
 the time region. Subject 3 (Figure 8) yields a set of 
 different results for ~~:ic.n, average, and node. These 
 three values are all betv;een 100 nsec and 175 msec. The 
 distribution curves do not have any obvious shift as 
 frequency changed. 
 
 
 The standard deviation curve from subject W shows that the 
 value varies betv;een +_ 35 msec to + 88 "sec, and it is 
 frequency independent. 
 
 Despite the differences among the above discussed three 
 subjects, they do have seme similarities. When frequency 
 was increased, the number of abnormal responses of all 
 three subjects would increase, and their distribution 
 curves all were normal form. 
 
 ( r- +- Q n -r"/->or*^N T.TOTr^ i f TJ*-? i~n*-*\s\ Q 4- 
 V^-; v_-^ ^ ->._ ~ ..^Vt-y x - J-j-j* ^ %_; ow 
 
 Figure 10) : 
 
 The median, average, mode, and standard deviation of the 
 latency distribution are not all frequency dependent. The 
 values of median, average, and mode varied within the range 
 of 150 msec to 250 msec. But the shape of the latency 
 distribution curve seems to be frequency dependent. As 
 frequency increases the distribution curve tends to change 
 its shape from a nor~al distribution to a square form 
 distribution. This change can be observed by comparing 
 Figure Sa to 8c Figure 9a to 9c, and Figure 10a to 10c. 
 
 (C) Ramp inputs (Figure 11): 
 
 (1) The speed of target 0.33/sec: 
 Latency decreased as speed increased. 
 
 (2) 0.53/sec the speed of target 0.83/sec: 
 
 As speed increased, the latency of response to the 
 continuous portion increased (Figure 11), and the 
 
8 
 
 latency of response to the discontinuous portion 
 decreased (Figure 11). 
 O) Tiie speed of the target O.G5/3ec: 
 
 Latency of response decreased as speed decreased. 
 The latency of response to the discontinuous portion 
 is much less than the latency of response to the 
 continuous portion as shown in Figure 11d. 
 
In this report, the discussion was divided as tv/o parts: one 
 emphasises the pattern recognition associated with the eye 
 movement, the other one concentrates on the discrete nature 
 of eye movement. In either case, different models were 
 discussed. Comparison was made between models or between 
 those models and my experimental results. 
 
 There were three models discussed in the pattern recognition 
 phenomenon, namely, Dallos and Jones' model, Susie's model 
 Cyr and Fender's model. In the discrete phenomenon, 
 Forster's model was reviewed, and Latour's experimental 
 results were mentioned. 
 
 (A) Pattern Recognition 
 
 (1) Dallos and Jones' model: 
 
 From the above presentation, it is obvious that the 
 distribution of latency is very much dependent upon both 
 the wave form and the frequency of the stimulus. In 
 fact, this is the property that led Dallos and Jones'" 
 to theorize about the "acquisition of learning". From 
 their theor;/, a model is proposed. Three properties 
 of this model are worth discussing, namely, learning 
 speed, prediction, rnd detection. 
 
 (a) Learning Speed 
 
 By examining the first few cycles of tracking responses 
 to sinusoidal and square wave inputs (Figure 12), Dallos 
 and Jones believed that the rate of learning was 
 considerably greater for continuous than for discontinuous 
 input with the same frequency. But from my experimental 
 
observation (see previous section and Figure lid), the 
 response of the ramp tracking shov/ed that it is not so. 
 When "both continuous and discontinuous changes were presented 
 in a repetitive manner, namely the ramp stimulus, the rate 
 of learning in the discontinuous portion was faster than that 
 of continuous portion (Figure 11d), thus contradicted their 
 conclusion. Therefore, the correlation, if any, between the 
 rate of learning and the continuity of stimuli remains still 
 a question. 
 
 (b) Predictor 
 
 For each input stimulus, an output Bode plot v;as ploted. 
 Then the corresponding closed-loop transfer function was 
 obtained by curve fitting. Basing on the assumption of 
 linearity and unit feedback, the corresponding open-loop 
 transfer function for each stimulus can be computed froa 
 its closed-loop trancf c-r function. 
 
 Let G I) (ov/)= closed-loop transfer function for sinusoidal 
 
 input . 
 G(jw) = closed-loop transfer function for random 
 
 input . 
 gr>(d w )= open-loop transfer function for sinusoidal 
 
 input . 
 g(jv;) = open-loop transfer function for random 
 
 input . 
 
 then gp(jv/) and g(j'.;) can be computed from the following 
 equations: 
 
 E 
 G p (jw)= 
 
11 
 
 By cor.parins the tv;o open-loop transfer functions, G 
 
 and gCo'w), a hypothetical predictor transfer function P(jw) 
 
 was defined as follov;s: 
 
 Since this predictor v:as derived aia thematic ally, its 
 validity should be examined by various ways. 
 
 Firstly, hov; reliable is this predictor? According to Dallos 
 and Jones, the predictor should give a phase lead starting 
 fron 100 decrees increasing to 250 degrees as frequency 
 increased iron 0.5 cps to 2.5 cps. In our experiment, the 
 subject S was presented with square wave stimuli (as shown 
 in Figure 6d). The frequency distribution of latency for the 
 subject showed that the existence of prediction is question- 
 able. As frequency changed, there was no significant shifts 
 in the dlslrlouljion curve. ( The latency of the response fall 
 into the interval of 100 msec and 1pO msec) It therefore 
 implied that the response of subject S failed to predict 
 any of the stinuli within the applied range of the frequency 
 of the square wave. 
 
 Secondly, under a specific frequency, what kind of distri- 
 bution curve of latency would the predictor have? Because 
 by examining this curve, I believe that the efficiency of 
 the predictor could be obtained. A sharp and narrow curve 
 (eg. a nornal distribution) could represent an effective 
 predictor. On the other hand, a flat and wider curve (like 
 rectangular shape) could mean a weaker one. The efficiency 
 of the proposed predictor was not discussed. 
 
 Thirdly, since learning was an unconventional process, it 
 should not be inconceivable that the predictor ni.-ht not be 
 
12 
 
 physically reclined. Hut from a physiological point of vie;;, 
 it would be an interesting and meaningful thins to know the 
 possible mechanism or location of the predictor. But Dallos 
 and Jones made no attemp to suggest it. 
 
 (c) Detector 
 
 Since the operation of the predictor depended upon the 
 
 wave forn of stimulus, there should be another element, 
 
 namely, detector, which could exhibit the predictor under 
 
 periodic stimuli and could inhibit it under aperiodic 
 
 stimuli. A simple detector was suggested by Dallos and 
 
 Jones. The detector included a memory unit M with a finite 
 
 decay time, and a comparator D (Figure 12). The comparator 
 
 would continuously compare the output signal from the 
 
 memory unit and the present error signal. If the two signals 
 
 were dislike, then the error signal would bypass the predictor 
 
 ^ *>* -I- r^ i 
 
 stimuli. If the tv/o signal v;ere alike, then the error 
 information would be channelled through the predictor. 
 
 Based on this model, Dallos and Jones tried to explain the 
 frequency response of square wave stimuli. There were three 
 cases: 
 
 1. For low frequency stimuli: 
 
 Since the nemori sable information for a square wave 
 appeared to be the time duration betv;een the transitions, 
 therefore, when the time duration was longer than the 
 memory trace, then no information could be stored, 
 consequently, no learning process could proceed. 
 
 2. For high frequency stimuli: 
 
 Since the target motion was too fast, even with a 
 periodic input, the error signal could not be a periodic 
 one. 3o learning failed. 
 
 3. For intermediate frequency G : ;:.auli: 
 
 A steady state tracking could well be established. The 
 
amplitude of distortion in eye motion was not significant. 
 V.'ithin this range of frequency, there was almost complete 
 synchronism between input and output, therefore, the 
 memory trace could not be continuously reinforced. Since 
 the memory trace was assumed to decay with time, then 
 after some period of tine, the loss of synchronism should 
 be expected. Dallos and Jones observed that in the steady 
 state tracking, the average time duration for good tracking 
 period was approximately 5 to 7 seconds. Following those 
 good tracking periods, there were a few cycles without 
 compensation. 
 
 From the above explanation of the square wave response, it 
 seemed to me that there were some points open for argument: 
 (a) It is questionable, that whether the large value of 
 latency during a high frequency target tracking was 
 cauccd by the aperiodic error signal or noo. If we 
 took eye muscle into consideration, it should be easy 
 to demonstrate that the eye could not move as fast as 
 one wished to. Suppose a subject was asked to count 
 repeatedly "one, two, one, two, one, ", and simult- 
 aneously, the subject's eye moved back and forth 
 between two points in front of him, the counting of 
 number and the movement of the eye were synchronized. 
 If the counting started at a low frequency, the eye 
 could keep the synchronisation very well. If the speed 
 of counting was increased, the eye gradually become 
 unable to follow. The back and forth movement of the 
 eye would get worse and worse as the speed of counting 
 increased. In this demonstration, the brain knew the 
 speed and the exact positions of the two fixation points, 
 The speed c.nd position were not known by "learning" but 
 by "given", the failure of the eye showed that there 
 
14- 
 
 was a speed, lir.itc.tior. for the eye. It should not be 
 confused with the arbitrary eye movement, namely, the eye 
 was asked to cove bad: and forth between left and right 
 without specific position to fixate. In this case, because 
 no accuracy was required, the eye could respond faster than 
 in the former case. 
 
 In the case of eye tracking movement , the speed of the 
 eye and the positions for fixation v;ere not given. If the 
 eye could "learn", as suggested by many models, it should 
 be expected that the response would not be better than 
 the "given" case. Thus the bad tracking response of a 
 high frequency square wave stimulus could be caused simply 
 by the limitation of the eye muscle movement. I was one of 
 the subjects. According to my own experience, at high 
 frequency.' tracking, I could "feel" or "sense" the frequency 
 of the target, over. v.'hcr. my eye failocl to follov. 7 it. 
 Therefore, it seemed to me that the "learning behavior" 
 should belong to the brain, not to the eye. Thus when the 
 target frequency was high, and the eye failed to track 
 properly, the brain still could "learn" the frequency of 
 the target, if the target motion was periodic. 
 
 (b) There were many mechanical models for the muscle. No 
 
 matter which one was the best, at least they implied that 
 the muscle possessed mechanical properties. Therefore, it 
 would be proper to assume that there was a nature frequency 
 for the eye muscle mechanism. If the frequency of the 
 target motion was close to the natural frequency of the 
 eye muscle mechanism, then a resonance phenomenon might 
 happen. This was probably the reason for the good tracking 
 responses for the intermediate frequency stimuli. 
 
The above argument was just induced, from ''common cense" and 
 "experimental feclir .j" , no strong evidence or experimental 
 results supported it. However, it seemed to me that using 
 mechanical (or mathematical) model of physiological 
 properties to approach the eye tracking s-stem might be more 
 realistic and practical than a pure mathematical derivation 
 or curve fitting. 
 
 (2) Sugie's model: 
 
 A different approach to the stud;/ of the "predictive control" 
 of the eye movement v;as carried out by Sugie. After studying 
 the response to regular square v:ave inputs, he proposed a 
 mathematical model of estimation based on stochastic optimal 
 control concept (Figure 14- and Figure 15). The variable to 
 be estimated was the period of the target notion, and the 
 statistical parameter was the variance of the estimated 
 period. 
 
 Four assumptions were made, (i) The estimation depended 
 upon the target frequency and the number of target cycles, 
 (ii) The estimated period of the target motion was accom- 
 panied v;ith some stochastic randomness caused by the 
 uncertainty of human memory, (iii) The mean of the estim- 
 ated period coincided with the period of the target motion, 
 because the probability function had no reason to be 
 biased, (iv) The variance of the estimated period should 
 depend on the target frequency and the number of target 
 cycles (Figure 15). A brief reason for the last assum- 
 ption Y/as worth mentioning: 
 
 (a) The dependence of the variance upon target frequency: 
 As Dallos and Jones suggested, for a square wave 
 input, the useful information could be obtained only 
 twice a cycle. V/hen frequency was low, the memory 
 dec.'.y would cauce uncertain information, therefore, 
 the variance of the estimated r>eriod could be assumed 
 
16 
 
 large. However, when the tnrget frequency was very high, 
 the sample data phenomenon was taking into account. 
 Accourding to L. R. Young and L. Stark-"*, the sampling 
 period was 250 msec. Therefore, when the input period 
 became compatible with the sampling period, the change 
 of the target position could not be sensed very 
 accurately. Consequently, the variance of the estimated 
 period could be assumed large. Thus the variance should 
 have its minimum value at the intermediate input 
 frequency range. 
 
 (b) The dependence of the variance upon the number of cycles 
 of target motion: 
 
 As more information became available, the variance of the 
 estimated period should be decreased. Consequently, the 
 variance of estimated period should be a inonotonically 
 decreasing function of the number of cycles. 
 
 For simplification, he assumed a rectangular probability 
 density function (Figure 18), that is, 
 
 / i 
 probability density 
 
 2 
 
 = otherwise 
 
 a 
 
 The estimation was assumed to optimise a "performance index". 
 This performance index PI was defined as a mean-squared value 
 of the length of time by which a stimulus preceded or laged 
 behind a response. 
 
 ( 91 O Cy' + "kri-r.-*- ~ X ' 
 
 p-r , +.<- . fl-f- 4. TT Ot)o 
 
 .r X = I w LLUJt ' 
 
 2y< 
 
 where x = constant reaction time without prediction. 
 
 t = ontinr.1 reaction tine. 
 opt 
 
The response of this r.odel (7i~ure 1?) rave a .3000. suggestion 
 for the possible range of the mode an'l average for the 
 distribution of latency. But it failed to jive a desired 
 distribution curve. 
 
 As Dallos ar.d Jones, Sugie assumed the memory decayed as the 
 only explanation for the low frequency square wave response. 
 However, he had a different explanation for the higher 
 frequency response. He considered the discrete nature of the 
 saccadic eye movement which, I believe, was more realistic 
 than the explanation given by Dallos and Jonse. 
 
 Sugie assumed that the variance also depended upon the cycle 
 number of the target notion, that is, the variance was a 
 nonotonically decreasing function of cycle nunber, independent 
 of target frequency. Statistically, it should be true. But 
 practically, it would be doubltful. When conducting experiments 
 cf a longer time duration, the eye night be fatigue, which 
 could give unreliable responses. Therefore the variance could 
 be larger as sore experimental runs were recorded. 2n the 
 derivation of his model, Sugie assumed the number of cycles 
 of the target motion to be infinite. Since the data he used 
 was fron several other models, therefore the cycle numbers 
 would not necessary be equal nor infinite. It seemed to me 
 that the dependence of the variance upon the cycle number was 
 not a proper assumption. 
 
 Another interesting assumption worth mentioning was concerning 
 the unbiased probability density function. A rectangular 
 function was assumed for simplification. But Sugie did not 
 suggest any other suitable functions. Whether a normal 
 distribution function could give a desirable distribution 
 curve for latency or not was worth to know. 
 
18 
 
 (3) Cyr and Fender's model: 
 
 After a number of predictive models (lender and ITye, 1961; 
 Young and Stark, 1963 i Hobinson, 1955) for the eye tracking 
 system were proposed, the existence of the predictive ability 
 of the eye movement was challenged by Cyr and Fender. Based 
 on the study of human eye movement in two dimensional 
 tracking task, Cyr and Fender found that the system was 
 non-linear. Therefore, a transfer function could, be derived 
 for the oculomotor system. Thus it should not be possible to 
 predict the response to one class of target motion by linear 
 
 combinations of the responses to other classes of stimuli 
 
 /\ 
 
 (as in the Dallos and Jon model ) Consequently, the 
 computation of a minimum phase lag (Dallos and Jones, 1963^; 
 Young and Stark, 1963 ) should not be possible. Accordingly, 
 the latency was only a simple delay which depended on the class 
 of target motion. 
 
 Since all of my experimental results of this report were from 
 one dimensional eye tracking movement, therefore no comparision 
 between Cyr and Fender's results and mine could be carried out. 
 However, there was a point which might be worth mentioning. 
 In the one-dimensional eye tracking movement, the ability to 
 predict was based not only on the frequency of the stimulus, 
 but also on the shape of the target motion. In other words, the 
 eye could predict, if the stimulus was of periodic form with 
 a intermediate frequency. Thus for disproving the predictive 
 two-dimensional input with a intermediate frequency should be 
 used. But Cyr and Fender only used two kinds of stimuli, one 
 was random signal, the other one was a sum of four small 
 sinusoids in both vertical and horizontal directions. Therefore, 
 no periodical input was used by Cyr and Fender. Consequently, 
 their conclusion was not strong enough. 
 
(B) Sirro^o ITature Of .77 e Movement 
 
 The discrete nature of the saccadic eye movement control is 
 well established. Since the introduction of the sample-data 
 model by Youn;~ and Stark, the analysis of this discrete 
 nature has developed numerous refined models (see reference 
 6, 7, 8). There are three different types of sample-data 
 systems. A model has either target-synchronized or target- 
 asynchronized properties. A target-synchronized system is 
 c ock-asynchronized. But a target-asynchronized system can 
 be either clock-synchronized or clock-asynchronized. These 
 definitions for the three types of sample-data systems are 
 summarised in Table 2. 
 
 desk- 
 
 clock- 
 
 targe t- 
 
 STnchronlzed 
 
 impossible 
 
 possible 
 
 target- 
 
 asynchronized 
 
 possible 
 
 possible 
 
 Table 2 
 
20 
 
 (1 ) Latour's experimental results: 
 
 In the early studies of horizontal eye movement by Latour 
 
 q 
 and Bouraan , the frequency distribution of reaction time 
 
 for both short run ( Figure 24- ) and long; run ( Figure 25 ) 
 were obtained. Latour noticed that, in short sessions the 
 reaction time distribution was multimodal, such that: 
 
 t = ka 
 where t = reaction time 
 
 = most frequent t value 
 ** ' 2 j 3j ~ - ~ 
 
 a = 20 to 40 msec. 
 
 In longer sessions, this phenomenon faded out* But the 
 distribution of the "difference between the reaction time 
 and its succeeding movements" showed a similar frequency 
 distribution curve. 
 
 Let *t = t n - t n+1 
 where t = reaction time at the nth reaction 
 
 t n+ -p reaction time at the (n+1 )th reaction 
 
 At = difference between the reaction time and 
 its succeeding movement. 
 
 then the distribution of *t ( Figure 26 ) could be represented 
 
 t = T - 
 where ^ = some positive value 
 
 By comparing the frequency distribution of reaction time t 
 and the frequency distribution of the At ( Figure 26 ), Latour 
 concluded that there was a continuous decrease in the " most 
 
21 
 
 frequent reaction tiae " , follov.od by a relatively fact 
 increase of within a period of about 20 seconds ( Figure 
 27 ). In other words, for a long session tracking, the eye 
 could graduatly shorten its reaction tine then rapidly 
 drift back to the starting value of reaction tine. This 
 cycle could be continued as the experiment went on. 
 
 Latour's experimental results and observations could be in 
 the discussion of the following .burster's model. 
 
 (2) ii'orsber's stochastic sample-data model: 
 
 n 
 The studies by Lang' showed that the model for the discrete 
 
 nature of the eye movement was more satisfactory if it was 
 
 o 
 
 randomly sampled. Forster reexanined the three possible 
 types of interosample time distribution function ( see Table 
 2, page 19 ) with his revised sample data model ( Figure 19 ). 
 
 Started from target asynchronized system, he assumed that: 
 
 L = t 1 + D 
 
 where L = latency 
 
 D = dealy time from occurrence of the input to 
 the next occurrence of a sampling instant 
 (-from this definition D should be strictly 
 non-negative ). 
 
 t* = constant delay time, as in Figure 20. 
 f v (x) - probability density function of the variable 
 
 3C 
 
 x ( any of the above variables ). 
 
 Since D was a random variable, L should also be a random 
 variable, thus the density function would be related by: 
 
 = fy( a 
 
22 
 
 .based on the assumptions that: 
 
 (a) the input occurcd in as interval f , 
 
 (b) the time between inputs were greater than f , the 
 
 DloLjC 
 
 maximum value of f_ , 
 
 C 
 
 (c) the input v/as uniformly distributed 
 Forster derived out f. 
 
 '!) 
 
 /fmax 
 
 i) 
 
 clt , for Di 
 
 ' max J i) 
 for D*. 
 
 Since fy(-U) was a non-increasing function, thus it should 
 give a non- increasing latency histogram ( Figure 21 ). But 
 the actual latency distribution increased for low latencies. 
 Therefore, Forster suggested that for asynchronized sample, 
 the eye sometimes was able to shorten the sampling intervals, 
 when a step v/as observed. This hypothesis could be supported 
 if the function v/as as follev/ed: 
 
 0.0133 60 <T <120 
 
 0.0025 120 < tr$200 
 
 . c otherwise 
 
 The corresponding simulation latency histogram from this 
 function v/as showen in figure 22. After comparing the 
 simulations and the experimental results, Jforster showed 
 that the eye control system had characteristics of both 
 target-synchronized and target-asynchronized. Lat the best 
 sampler logic should be non-synchonized with a sample T which 
 was composed by a constant T plus a noise n, i.e. 
 
 T = T Q + n . 
 
 examining u'orster's model by iiatour's conclusion and my 
 experimental results, two points should discussed: 
 
(.&) The sar.pler logic of Forstcr's model v;as unifornly 
 
 distributed in the interval of 150 to 250 mseconds. when 
 the period of a square v:ave stimulus was compatible with 
 the sampling interval . then the change of target position 
 could not be accurately sensed or sometimes even missed 
 ( Figure 25 ). Thus as increased percentage of abnormal 
 responses should be expected as the frequency of the input 
 increased. Conversely, for a low frequency stimulus, the 
 period of the input was much larger than the interval of 
 sampler, thus a small value of percentage of abnormal 
 response was able to be obtained. According to ray 
 experimental results shov/en in Figure 5 to Figure 7 the 
 above was confirmed. 
 
 (b) In the assumption of Forster's model, the latency was 
 defined as: 
 
 L = D + t 1 
 
 where t. v;as constant delay time, and D was the time interval 
 between the occurence of input and the occurance of the 
 next sampling instant ( Figure 20 ). It should be obvious 
 that latency L was proportional to the value of D. However, 
 considering Latour's difference phenomenon, the mode of the 
 latency distribution curve tend to decrease as the time for 
 experimental run increased ( Figure 27 ). It seemed to me 
 that the decrease of the mode of latency should imply the 
 decrease of latency. Thus the value of D should also be 
 decreaseing. The decreasing of D could only be achieved by 
 shortening the sampling period. If this was true, then the 
 eye could sense the change of target position more 
 accurately. Thus, for a highfrequency stimulus, the 
 percentage of abnormal response duringa long session run 
 could be reduced, oirice all of my experimental runs were 
 
24- 
 
 POSSIBLE FUTURE SI33CTIOH 
 
 Based on the review and examination of those models 
 disscused in the above section, some possible future experi- 
 ments could be conducted: 
 
 (1) For a furthur understanding of "learning behavior" and 
 "learning speed", a detailed comparison of the difference 
 between the response of continuous stimuli and disconti- 
 nuous stimuli could be done. Therefore, more experiments 
 could be carried out in this direction. 
 
 (2) As far as learning behavior as concerned, the two- 
 dimensional eye tracking movement should be tacken into 
 account. Cyr and Fender only used two types of stimuli: 
 one was a random signal, the other one was a sum of small 
 sinusoids in both vertical and horizontal direction* 
 Since the one dimensional eye tracking system shov/ed that 
 the latency distribution curve v/as both input freqxiency 
 and input shape dependent, and furthur more, it was 
 believed that in some models a periodic input with proper 
 frequency could be predicted by the eye, thus a two- 
 dimensional periodic input should be used in order to make 
 a comparison with the one dimensional results. A simple 
 two-dimensional stimulus could be made by a square wave 
 movement in both vertical and horizontal direction. The 
 response of this input might bring some information such 
 as whether or not the latency distribution curve would 
 shift to some phase lead region as the input frequency 
 varied to a certain range. Ho matter what kind of results 
 could be obtained, it should be halpful for the furthur 
 analysis of the "learning behavior". 
 
 (3) The oversimplification of Sugie's probability density 
 
function failed to give a proper latency distribution 
 curve. Since the latency distribution curve was similar 
 to normal distribution, therefore, a probability density 
 function similar to normal distribution might be reasonable 
 to try. 
 
 (4-) Longer session experimental runs could be carried out. 
 The results could be used for the following purpose: 
 
 (a) Re-exanine Latour's difference phenomenon. 
 
 (b) Re-check Dallos and Jones' memory decay phenomenon, 
 especially the periodic forgetness in a steady state 
 tracking movement. 
 
 (c) Whether the percentage of abnormal response would be 
 decreased or not, as suggested in the discussion of 
 this report. 
 
 (d) It might be useful for a furthur study of Forster's 
 sample-data model. 
 
26 
 
 SUMMARY 
 
 One dimensional eye tracking movement was measured. Following 
 types of stimili were presented, namely, regular square wave, 
 irregular square wave ( or staircase wave ), and ramp input. 
 The results showed that latency distribution curve was 
 frequency dependent. For square wave, the curve similar to a 
 normal distribution shifted back and forth between the time 
 lag region and the tine lead region. For staircase wave, the 
 cruve changed its shape from a normal distribution to a 
 regutangular distribution as frequency increased. The response 
 of ramp inputs showed that when both continuous and disconti- 
 nuous motion were involved, the discontinuous portion was 
 faster than the continuous portion. 
 
 Based on our experimental results, the strong and weak points 
 of scnc proposed mcdolc v;crc discussed, 
 
 (1) Dallos and Jones' model: 
 
 (a) Strong point: It could explain the response for square 
 wave stimili^ 
 
 (b) Weak point: 
 
 i. The dependence of learning speed on the continuity 
 of input v/as questionable. 
 
 ii. The predictor v/as purely derived out from curve 
 fitting and matheinatic equations. There was no 
 simulation results. The efficiency of the 
 predictor was discussed. The existance of this 
 predictor was doubtful. 
 
 (2) Sugie's model: 
 
 (a) Strong point: 
 
 For square wave stimuli, the model could give a good 
 suggestion of the possible ran~e of the mode and the 
 average of the latency distribution curve, 
 
 (b) Weak point: 
 
27 
 
 i. The dependence of variance of latency distribu- 
 tion upon the cycle number of the target motion 
 v/as questionable. 
 ii Oversimplification of the probability density 
 
 function. 
 
 iii. Failed to predict the shape of latency 
 distribution curve. 
 
 (3) Cyr and Fender's model: 
 
 This model v;as not discussed here. It was only a reference 
 to show a different point view. However, it could be safe 
 to say that the two-dimensional tracking was a good 
 approach. But the type of stimuli should be one which v;as 
 coniprable to the one-diinensional tracking. 
 
 (4) Latour's difference phenomenon was reviewed here. This 
 phenomenon implied G. decreased reaction time as tho 
 experimental runs get longer. 
 
 (5) Forster's sampl-data was also reviewed. This target- 
 asynchronized model could explain the dependence of "the 
 percentage of abnormal response " upon the stimulus 
 frequency. But the experieraental results possessed both 
 target-synchronized and target-asynchronized properties. 
 
 Based on the discussion, some possible future directions were 
 suggested. These directions included longer session 
 experimental runs, two-dimensional tracking measurements, 
 comparison between continuous and discontinuous stimuli, 
 verification of Sugie's model, and relationship between eye 
 muscle mechanism and eye tracking movement. 
 
28 
 
 REFERENCE 
 
 1. D. J. Dallos, and R. V/. Jones, "Learning Behavior of The 
 Eye Fixation Control System", IEEE Trans, on Automatic 
 control, vol. AC-3, pp. 218-22?, July 1563. 
 
 2. N. Sugie, "A Model of Predictive Control in Visual Target 
 Tracking". IEEE Trans, on System, Men, and Cybernetics, 
 vol. 3MC-1, no. 1, Jan. 1971. pp. 2-7. 
 
 J>. G. J. 3t-Cyr and D. H. Fender, " Nonlinearities of The 
 Human Oculomotor System Time Delay". Vision Res. vol. 9, 
 pp. 14-91-1503. Pergamon Press 1959. 
 
 4-. L. Stark, G. Vossius, and L. R. Young, IEEE, Trans, on 
 Human Factor in Electronics HFE-5, pp. 52-57. 1962. 
 
 5. L. R. Young, and L. Stark, IEEE Trans, on Human Factors 
 in Electronics, IIFE-4-, pp. 32-51. 1963. 
 
 6. L. Stark, "Neurological Control System, Studies in 
 Eiocngincering" . Plenum Press, Nev/ York, pp. 240-24 7 !-, 
 351-357. 1953. 
 
 7. G. V. r . Lang, " Representation of The Human Operator As A 
 Sampled- Data System", PhD Thesis, University of London, 
 
 1967. 
 
 8. 3. M. Forster, 2. M. Thesis Report MIT-6S-2, Man Veliical 
 Laboratory, Center for Space Research, HIT, Cambridge, 
 Mass., 1968. 
 
 9. P. L. Latour, and M, A. Bouman, "A Non-analog Time Component 
 in Eye Pursuit Movement". Proc. MIT Symposium, 1959. 
 
 10. P. L. Latour, "The Eye and Its Tinirng" . 1961. 
 
29 
 
 Muscle 
 
 Afferent 
 
 Si en 
 
 Efferent 
 Signals 
 
 Visual 
 Corte:: 
 17, 13, 19 
 
 Afferent Signals : continuous. 
 
 Efferent Signals : continuous and discret 
 
 Fig. 1 
 
sampler 
 
 target 
 position 
 
 eye 
 detector 
 
 controller 
 and plant 
 
 eye 
 
 position 
 
 Fig. 2 
 
iris 
 
 > solera 
 
 nhotocell 
 
 subtraction 
 
 moving li^ht spot 
 (target) 
 
 oscilloscope; 
 
 . 3a. 
 
 Fir:, ob . 
 
(a) 
 
 Signal 
 
 Normal 
 Response 
 
 (b) 
 
 Abnormal 
 Response 
 
 (c) 
 
 n 
 
 v 
 
 L=min. (L i >150insec. ) , 1=1 
 
 Signal 
 
 1 
 
 1 
 
 
 
 1 
 
 i 
 
 1 
 
 1 
 
 
 
 1 
 
 1 
 
 
 
 Response 
 
33 
 
 0.1 or 3. 
 
 of occurer.ce. 
 
 M: . : ;ns. 
 
 -. 277.15ns. s: 75.75 
 
 - 
 
 
 5 
 
 
 
 2 
 
 
 
 - 
 
 1' 
 
 
 I 
 
 
 
 200 2 35 ; -' : .')0 
 
 us 
 
 2 . 0.3 cr: s . 
 
 of occurenc . 
 51 
 4- 
 3 
 
 M: 14-Oras. Hd: 14-Or.s. 
 Av: 135.56ms. s: 33.82 
 
 50 
 
 100 
 
 150 
 
 200 
 
 ms 
 
 3. 0.5 ~ps 
 
 fr Of OCC. 
 
 M: 100:as. Md: 100ms. 
 Av: 77.71ms. s: 63.04- 
 
 5- 
 
 
 
 
 
 '- 
 
 4. 
 
 -. ' 
 
 
 
 
 
 
 
 
 
 
 1 
 
 ML , 
 
 
 INI 
 
 
 
 
 
 
 
 
 , . I , . . I 
 
 ~i5o so 50 
 
 
 
 5 
 
 
 
 100 150 200 ms 
 
 4. 0.7 cvs. 
 
 ;,'-of occ . 
 
 M: -10ms. Md: -130.-80,-70,-30,0,30,50n3 
 Av: -7.5ms. s: 91. 06 
 
 3 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 
 
 
 
 - 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 | j 
 
 
 
 
 50 Q 
 
 50 
 
 100 200 500 4-00 n 
 
 ms 
 
 5. 0.9 cps. 
 
 2 of occ. 
 
 M: -60ns. Md: -70, -60ms. 
 Av: -4-9. 60ms. s: 52.56 
 
 
 c 
 
 " 
 
 
 
 
 s 
 
 
 
 
 
 
 
 4- 
 
 
 
 
 
 
 
 
 
 
 
 
 2- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 "' 
 
 \ I 
 
 
 
 
 
 
 
 
 
 
 
 ! . 
 
 1 
 
 
 1CO. 50 
 
 
 50 100 1GO 
 
 Predictable square '..av/o; Sub; ^'j; 
 
1.1 c-os. 
 
 .IS . 
 
 Av: 9.43ns. s: 57.39 
 
 
 ox ucc; . 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 1- 
 
 j 
 
 
 
 
 
 
 
 
 
 
 100 
 
 50 50 100 130 ms 
 
 7. 1.3 cps. 
 
 
 II: 50ns. Md: -10,30ms. 
 
 ': Of OCC . 
 
 
 Av: 37.04nis. s: 48.89 
 
 6 
 
 
 
 
 
 
 
 5- 
 
 
 
 
 
 
 
 
 3- 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 1 
 
 I 
 
 
 
 
 
 
 
 
 i 
 
 
 50 
 
 
 6 50 100 150 ms 
 
 3. 1.5 cps. 
 
 
 M: 70ms. Md: 50ins. 
 
 V of occ. 
 
 
 Av: 63.6833. s: 40ms. 
 
 8 
 
 
 
 
 
 n 
 
 7 
 
 
 
 
 
 
 G 
 
 
 
 
 
 
 
 5' 
 
 
 
 
 
 
 
 
 4 
 
 . 
 
 
 
 
 
 
 
 3 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 1 
 
 j 
 
 
 
 
 
 
 
 
 
 
 
 
 50 "100 150 ms 
 
 9. 1.75 cps. 
 
 
 
 M: 90ms. Md: 100ms. 
 
 
 of occ. 
 
 
 
 Av: 85. 00ms. s: 53.49 
 
 12 
 
 
 
 
 
 11 
 
 
 
 
 
 10 
 
 
 
 
 
 
 9 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 7 
 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 
 5" 
 
 
 
 i 
 
 
 
 I 
 
 ^> 
 
 
 
 
 
 
 
 
 3' 
 
 
 
 
 
 
 
 
 
 2 
 
 1 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 ; i : 1 
 
 
 | 
 
 f i 
 
 , J_ 
 
35 
 
 ^- . 
 
 . 
 s: 59. 80" .-!-5as. 
 
 or occ. 
 
 11 
 
 
 
 
 
 10- 
 
 
 
 
 
 9 
 
 8- 
 
 
 
 
 
 7 
 
 6- 
 
 
 
 
 
 t 
 
 5' 
 
 
 
 
 
 
 
 4-- 
 
 
 
 
 
 
 
 3" 
 
 
 
 
 
 
 
 2" 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 
 j 
 
 
 X 
 
 50 
 
 100 150 200 250 300 ms 
 
 
 \ M. vs. freo. 
 \ Average x K 
 
 \ Mode Q D 
 
 >00 
 
 \ 
 
 ^ 
 
 Median * 
 
 0.1 0.3 0.5 
 
 Hz 
 
 80 
 70 
 
 60 
 50 
 
 Standard deviation 
 
 
 X1 O.'j 
 
 0.5 
 
 0.7 
 
 0.9 1 
 
 1 1.3 1.5 1. 75 2 
 
 Figure 5c 
 
. 
 
 36 
 ( res . ; 
 
 : : 
 
 . ' . . 
 
 2 - 
 
 of occ;. 
 
 . 
 
 50 
 
 100 
 
 150 
 
 200 
 
 ms 
 
 2. 0.3 cjs. (res. 
 
 6 
 
 of occ 
 
 I-:-. 113ns. Md 125ras, 
 Av.: 153.3; : 
 i : +55.21 
 
 50 
 
 0.5 cps. 
 
 i' Of OCC. 
 
 8 
 6 -f 
 
 100 
 
 (res. 22) 
 
 150 
 
 200 
 
 ms 
 
 M: 125ms. Md: 150ms. 
 Av. : 73.8ms. 
 SOJDV: -120.79 
 
 200 150 100 50 50 100 150 200 250 
 
 ins 
 
 14 - 
 
 12 ' 
 10 * 
 
 8 
 6 ' 
 
 0.9 cps. (res. 32) 
 
 ~ of occ. 
 
 II: 100ms. Md 100ns. 
 Av.: 103.67 
 S'IDV: 157.45 
 
 50 100 150 200 2=0 300 350 
 
 ms 
 
 (a) 
 
 ig. 6. Predictable squaro v.'uve. Subject: 3iiiro. 
 
37 
 
 1.1 Tr ~. 
 
 f occ. 
 20' 
 18 
 
 12 
 
 1C 
 
 8 
 
 6 
 
 . 
 
 Av.: 133. 
 ST. 
 
 
 
 50 
 
 100 
 
 150 
 
 200 
 
 6. 1. 
 
 5 Hz. (res. 51) 
 
 M: 125ns. I-id: 150ms 
 
 
 ' o-P ,^ AV ' : IpO.OmS. 
 
 ,r 01 occ. orr7w . zo co 
 
 16 
 
 
 * -X J 
 
 14-' 
 
 
 
 
 
 12 
 
 
 
 
 
 10 
 
 
 
 
 
 8- 
 
 
 
 
 
 6 
 
 
 
 
 
 2 ' 
 
 
 
 
 
 
 C-/-1 xl/- 
 
 /^/^.x^ ^^ r s\ 
 
 50 
 
 150 
 
 250 
 
 7. 1.5 Hz. (res. 65) 
 # cf occ. 
 
 M: 150ns. lid: 150ms. 
 Av.: 136.11ns. 
 
 
 MJV : pu. / i 
 
 22 
 
 
 
 20 
 18 
 
 
 
 
 16 
 14 
 
 
 
 
 12 
 10' 
 
 
 
 
 
 8 
 6 
 4-' 
 
 
 
 
 
 2 
 
 
 
 
 
 
 "" 1 ; [ 
 
 50 100 150 200 
 
 ins 
 
 iS. 6b. 
 
1.7 
 
 (resp. 
 
 M: 12>-.i. . : as, 
 
 Av. : 1 . . ".c; . 
 
 
 ,, <j^. wwv-- * 
 
 STW: - . ! 
 
 14 
 
 
 
 
 12 
 
 
 
 
 
 10 
 
 
 
 
 
 
 8 
 6' 
 
 
 
 
 
 
 4-' 
 
 
 
 
 
 
 2 ' 
 
 | 
 
 
 
 
 ! I i 
 
 
 50 
 
 100 150 200 250 350 ms 
 
 9. 1.9 Hz. (resp. 46, abnormal 33) M: 162.5ns. Kd: 150ns, 
 
 1C 1 
 
 8 
 
 of occ. 
 
 
 
 ^ i v i s * ' '*-' x^^ * 
 
 STDV: I 65.23 
 
 6' 
 
 
 
 
 
 
 
 '' I 
 2' 
 
 1 
 
 
 
 
 
 1C 
 
 
 50 100 150 200 250 ms 
 
 10. 2.3 Hz. (resp. 29, abnormal 4-8) 
 
 M: 125ms. I-ld: 150~3, 
 Av.: 113.96ms. 
 
 10 
 
 # of occ. 
 
 ** V > .1 Nu/ ^/ 'w/i-H I/ * 
 
 STDV: I 73.39 
 
 8 
 
 - 
 
 
 
 6 
 
 
 
 
 
 2 
 
 i I 
 
 
 
 
 . ! 
 
 -50 6 56 100 
 
 150 200 250 300 ns 
 
 11. 2.5 Hz. (resp. 52, abnormal 80) 
 $ of occ. 
 
 M: 100ms. Md: 100ms. 
 Av.: 126.08ms. 
 STDV: I 77.30 
 
 10 
 
 
 
 
 8 
 
 
 
 
 
 6' 
 
 ) 
 
 
 
 
 
 
 4- ' 
 
 
 
 
 
 
 
 
 
 2" 
 
 
 
 
 
 
 
 ; 
 
 i , t 
 
 
 50 
 
 100 
 
 150 200 250 300 m: 
 
 Fi-% 6c. 
 
39 
 
 
 175 
 
 150 
 125 
 100 
 
 
 Average X- 
 I-Iode Q- 
 i'ledian * 
 
 D.I 0.3 0.5 0.9 1.1 1.3 1-5 1.7 1.9 2.3 2.5 Hz 
 
 Standard deviation 
 
 0.1 0.3 0.5 0.9 1.1 1.3 1.5 1.7 1.9 2.3 2.5 
 
 Hz 
 
 Vir;. 3d. 
 
1. . :is. (resp. 5) 
 
 2. 0.5 Hz. (resp. 16) 
 
 
 of occ. 
 
 or occ. 
 
 
 5 
 
 
 4' 
 
 4 
 
 
 3 
 
 3 
 
 
 2 
 
 2 
 
 I ! 
 
 1 
 
 1 
 
 i 
 
 
 1 i 
 
 100 200 as 
 
 ( , I 
 
 100 200 ras 
 
 M: 200ns. Md: 2?0ms. M: 100mc. Md: 100ms. 
 
 ;-.v: 132.5ns. s: 68.46 Av: 105.5zas. s: 46.8 
 
 c 
 
 3. 0.5 Hz. (resp. 22) 4. 0.? Hz. (resp. 25) 
 
 
 of occ. 
 
 -/? of occ . 
 
 
 7- 
 
 
 6" 
 
 6- 
 
 
 5' 
 
 5- 
 
 
 4 
 
 4- 
 
 
 3 
 
 3- 
 
 
 0+ 2- 
 
 I 
 
 in i | i 1 
 
 I 
 
 f i ' i r- 
 
 1 I 
 
 -50 50 100 ns 
 
 -150 -50 o 50 100 i 
 
 M: 50ms. Md: 100ns. M: -25ms. Md: -50ms. 
 
 Av: 51.2ms. s: 76.9 AV: -2ns. s: 74.9 
 
 5. 0.? Hz. (resp. 30) 
 
 
 ; of occ. M: -25nis. Md: Oas. 
 
 10- 
 
 Av: -22ns. s: 59- r -is. 
 
 9- 
 
 
 Q 
 
 
 
 
 
 7 
 
 
 6" 
 
 
 5 
 
 
 
 4- 
 
 
 3 : 
 
 
 2- 
 
 1 
 
 1; 
 
 
 
 100 ;:o o 50 100 ns 
 
 (a) 
 
 ?iS. 7: Prodictable sour.ro v;ave. Subjsct;: S. 
 
6. 1.1 Hz. (resp. 34) 
 
 M: Ons. Md: Cms. 
 
 10 
 
 of occ. 
 
 s : GO .-.v : 
 
 9 
 
 
 
 
 8- 
 
 
 
 
 7 
 
 
 
 
 6 
 
 
 
 
 
 5- 
 
 
 
 
 
 4- 
 
 
 
 
 
 3 
 
 
 
 
 
 2- 
 
 
 
 
 
 1 
 
 
 
 
 
 
 -100 -50 ( 
 
 ) 50 100 200 300 ms 
 
 7. 1.3 Hz. (resp. 50) 
 
 20 
 
 18- 
 
 16 
 
 12 
 10 
 
 8 
 
 6- 
 
 4 
 
 2 
 
 of occ . 
 
 -50 o 50 100 
 
 200 
 
 M: Oms. Md: Oms. 
 s: 48.5 Av: 18ras, 
 
 300 
 
 ms 
 
 8. 1 
 
 10- 
 
 9 
 
 5 Hz. (resp. 46) 
 of occ. 
 
 M: 25ms. Md: 25ms. 
 s: 68.8 Av: 14.6:23, 
 
 c 
 
 7 
 
 
 
 
 
 
 6' 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 ." 
 
 
 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 
 ! 
 
 - 
 
 
 
 
 
 
 
 
 
 
 1 
 
 * 
 
 
 
 
 
 
 
 
 
 
 i i 
 
 
 
 
 
 
 
 
 } 
 
 
 
 I . ! . 
 
 
 s\ r- r\ 
 
 c 
 
 r\ r\ c.r\ ir\r\ onr\ znn m 
 
42 
 
 
 "I r ' " ( -p. - 
 
 i r 
 
 ' : 3. 're 
 
 sp . 4-6 
 
 
 of occ. 
 
 
 ~f .~>"C 
 
 - ^ # 
 
 
 25 
 
 
 
 
 , 
 
 _ _ 9 
 
 
 24 
 
 
 
 ^s 
 
 
 22- 
 
 
 
 21 
 
 
 
 
 
 
 
 20 
 
 
 
 19 
 
 
 
 
 
 
 
 
 18 
 
 
 
 17 
 
 
 
 
 
 
 
 16 
 
 
 
 15 
 
 
 
 
 
 
 
 14 
 
 
 
 13 
 
 - 
 
 
 
 
 
 
 12 
 
 
 
 11 
 
 
 
 
 
 
 
 
 10 
 
 
 
 9 
 
 - 
 
 
 
 
 
 
 8 
 
 
 
 7 
 
 
 6- 
 
 
 
 5 
 
 - 
 
 
 
 
 3 
 
 
 4 
 
 
 
 
 
 2- 
 
 
 
 1 
 
 1 
 
 
 " , i 
 
 1 , ' I , 
 
 
 50 100 1= 
 
 ~C 
 ?0 ms 
 
 1 
 
 DO 200 300 as 
 
 
 M: 75ms. i:i: 
 
 100ms. 
 
 H: 100ms. ] 
 
 Id: 100ms. 
 
 200 
 150- 
 
 msec. 
 
 
 T- T r>^ 
 
 
 ^i ^>/-\ 
 
 \x_ 
 
 
 IMUU.I 
 p^ r* ~ ' ci r\ ' 
 
 
 100 
 
 > ^ 
 
 
 D -0,1'iea. 
 
 /r^ x^AVe] 
 
 cm 
 
 50 
 
 ^^/^""^ 
 
 x/ / / \^- X 
 
 N-^,^ r ^ i ^'3ta3 
 
 CS.QQ X X 
 
 idard 
 
 
 \.7 
 
 QQ ,> r "^--- :3 
 
 
 
 
 0.1 0.3 3-5 \v 
 
 ^Kl.1 1.3 1. 
 
 5 1.75 2 
 
 Hz. 
 
 -50- 
 
 or 
 
 
 
 
 Pig. 7c. 
 
-;. j.1J, 0.257, 0.468 Hz.' 
 
 resp.: f . ' . -'id: 
 abnor::'il: 2. 
 
 
 \J 
 
 J. VJO 
 
 ** 
 
 
 
 
 V: - ','.^3 
 
 20 
 
 
 
 
 
 
 
 
 
 18 
 
 
 
 
 
 
 
 
 
 16 
 
 
 
 
 
 
 
 
 
 12 
 
 
 
 
 
 
 
 
 
 10 
 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 
 t 
 
 4 
 
 
 
 
 
 
 
 
 
 2 ' 
 
 
 
 
 
 
 
 
 
 I 
 
 
 50 
 
 150 
 
 250 350 450 550 650 ms 
 
 2. 0.235, 0.488, 0.785 Hz. resp.: 90. M: 150ms. Kd: 150ms. 
 Av.: 167.70ns. 
 # of OGC - STDV: - 52.48. 
 
 30' 
 
 
 
 
 
 
 
 
 28 ' 
 
 
 
 
 
 
 
 
 
 26 ^ 
 
 
 
 
 
 
 
 
 
 24 
 
 
 
 
 
 
 
 
 
 .-. 2 - - 
 
 
 
 
 
 
 
 
 20- 
 
 
 
 
 
 
 
 
 
 18' 
 
 
 
 
 
 
 
 
 
 16- 
 
 
 
 
 
 
 
 
 
 14- 
 
 
 
 
 
 
 
 
 
 12- 
 
 
 
 
 
 
 
 
 
 10- 
 
 
 
 
 
 
 
 
 
 8- 
 
 
 
 
 
 
 
 
 
 6- 
 
 
 
 
 
 
 
 
 
 4- 
 
 
 
 
 
 
 
 
 
 2 
 
 - 
 
 
 
 
 
 
 
 \ 
 
 50 
 
 1CO 
 
 150 200 250 300 350 ms 
 
 Fiq, 8: Unpredictable 3P\;r.rc wave. Subject: G. 
 
44 
 
 
 
 . , . >, ,23 Hz. 
 of occ. 
 
 . : ' . 
 
 : . Av. : 179. 1m 
 DV: - . . 
 
 20 
 
 
 
 
 
 
 
 
 16 
 
 
 
 
 14 
 
 
 
 
 
 12 ' 
 
 
 
 
 
 10 
 
 
 
 
 
 
 
 8' 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 4' 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 ' 100 150 200 250 300 ms 
 
 4. 0.73?, 1.23, 1.43 Hz. 
 
 # of occ. 
 
 24i 
 22 
 
 20' 
 
 15- 
 
 14 
 12 
 
 10" 
 8-- 
 
 6' 
 
 4" 
 
 2 
 
 resp.: 
 
 K: 175ns. Kd: 150ns 
 Av.: 199.32ms. 
 STDV: I 73.4. 
 c 
 
 100 . 150 200 250 300 350 400 450 500 ns 
 
 5. 1.23, 1<48, 1.71 Hz. 
 # of occ. 
 
 resp.: 45. 
 abnormal : 7 . 
 
 I-I: 200ms. I-Id: 
 Av.: 2Q7.95ms. 
 STDV: - 66.2. 
 
 14- 
 
 
 
 
 12- 
 
 
 
 
 10- 
 
 
 
 
 
 8- 
 
 
 
 
 
 
 r. 
 
 
 
 
 
 
 4- 
 
 
 
 
 
 
 2 
 
 
 
 i 
 
 ! 
 
 1 . 
 
 
 
 
 150 200 250 500 550 400 
 
**? 
 
 6. 1.43, 1.71, 
 
 
 r- 
 
 
 
 'I l\ 
 
 t 
 
 M: . L: 125ms. 
 
 
 STDV: -133.5. 
 
 
 
 
 
 
 
 
 
 4 
 
 
 
 
 2 
 
 I 
 
 i 
 , I 
 
 ns 
 
 
 1C - 5CO OC 700 
 
 7. 1.71, 1.95, 2.21 . 
 ,7 of occ. 
 
 4i 
 
 res:..: 21. M: 15Cms. KG: ICO, 
 
 abnormal: 10^. 125, 
 
 150ms. 
 Av.: 159.52ms. 
 
 STDV: - 65.98 
 
 50 
 
 1 150 2: 250 300 
 
 ns 
 
 8. 1.95, 2.21, 2.45 Hz. resp.: 26. 
 
 M: 125ns. 
 
 
 _y ^j> # n ' fOt "V . : IO >--'-" a 
 
 //- '-'-i- ^ -^ -^ T~ o<~7 ^>^v 
 
 oxijv : -o/.Oi 
 
 4- 
 
 
 
 
 
 
 
 3- 
 
 
 
 
 
 
 
 2. 
 1- 
 
 
 
 
 
 L 
 
 
 
 
 1 
 
 
 56 100 15 200 250 5C 
 
 350 as 
 
 9. 
 
 P 
 
 , <- 
 
 res?.: 19. M: 175ms. 
 
 7- 
 
 # of occ. 
 
 
 ctijxiui; JCLX; ^o^> ^i.v.: o.^ ;..:.. 
 
 SJDV: 1 48.' . 
 
 6' 
 
 
 
 
 5- 
 
 
 
 
 
 
 >^ - 
 2- 
 
 
 
 
 
 
 1- 
 
 
 i 
 
 
 r 
 
 
 
 
 __ 1^Oi --> ,-.,-> OC^O Xr^~' 
 
 ' '. oC. 
 
4-3 
 
 10. 2.4-5, 2.73, 5.0" 
 
 3 r 
 
 2 
 1 4- 
 
 occ, 
 
 recr>. : 1 " . 
 
 : 
 
 
 150 
 
 250 
 
 M: 
 . : 
 : - 
 
 300 ms 
 
 200 
 150 
 
 100 
 
 msec 
 
 i 
 
 Average X- 
 
 ;-:ed- *- 
 
 Ilodel a- 
 
 }' 
 
 \. .../: 
 
 \ ** 
 
 -v V 
 
 , \ 
 
 Standard 
 
 . o.evi-.oion 
 
 
 123^4 
 
 567 
 
 -i of 
 
 10 order 
 exrjer. 
 
 1: 0.15, 0.235, 0.-':-33, Us. 
 
 2; : 0.235, 0.4SG, 0.735, Hz. 
 
 3: 0.4-88, 0.785, 1.230, Hz. 
 
 4-: 0.735, 1.230, 1.4-80, Hz. 
 
 5: 1.230, 1.4-30, 1.710, Hz. 
 
 6: 1.4-SC, 1.?10, 1.950, Hz. 
 
 7: 1.710, 1.9?0, 2.210, Hz. 
 
 3: 1.950, 2.210, 2.4-^0, Hz. 
 
 9: 2.210, 2.450, 2.750, Hz. 
 
 10: 2.4-50, 2.730, 3.010, Hz. 
 
 Pis. 8d. 
 
4-7 
 
 . . , 
 
 ccc. 
 
 28 
 
 26 
 
 24 
 22 
 
 20 
 18 
 16 
 14 
 12 
 10" 
 
 8 
 6 
 4 
 
 2 
 
 : 10. 
 
 -100 
 
 (UN -I ro-v,-. 
 
 
 . : . 
 
 - .7 
 
 50 100 150 200 250 500 $50 400 
 
 ms 
 
 2. 0.235, 0.433, 0.755 Hz. 
 if- of occ. 
 
 2? 
 261 
 
 24 
 
 22 
 
 20 
 
 16 
 
 12 
 
 8 
 
 6- 
 
 resp.: 67. M: 150ras. Md: 1,50ns. 
 
 abnormal: 3. Av.: 161.15ns. 
 
 SO?L>Y: - 54.67. 
 
 50 100 150 200 250 300 350 400 
 
 ms . 
 
 Unpredictable ccuare ucve. out;' : ^o. 
 
 17 -i rr 
 - J. ,. 
 

 
 ab. : : . 
 
 26 
 24 
 22 
 20 
 
 16 
 
 14 
 
 12- 
 
 10 
 
 8 
 
 6 
 ^ 
 
 o 
 
 f OCC. 
 
 100 1. D 
 
 
 . 
 
 A.V. : .3. 
 
 STBV: - 
 
 ms 
 
 0.755, 1.23' 
 
 rr OT uCC. 
 
 r~ s~\ s\ r~ % 
 
 ^j o 50 
 
 Hz. 
 
 resp. : 77. 
 abnormal: 32. 
 
 150 250 
 
 450 
 
 M: 200ms. Md: 200ns 
 Av.: 2Q2ias. 
 
 20 
 18 
 
 
 
 
 
 16 
 14 
 
 
 
 
 c 
 
 12 
 
 
 
 
 
 
 10 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 4- 
 
 2; 
 
 
 
 
 
 
 I , i , , , ' , 
 
 ns 
 
 5. i.::33, 1.430, 1.7"<0 Hz. 
 
 ;' ol occ. 
 10 
 
 resp.: 52. 
 
 M: 225ns. Md: 2503S. 
 Av.: 211.G7r.s. 
 STDV: i 53.99 
 
 4 
 
 2 
 
 
 
 
 
 i ! 
 
 i 
 
 
 100 2-JO 500 
 
 400 
 
 500 
 
 600 
 
 ns 
 
49 
 
 . 1.710, 
 
 Hz 
 
 res . : i . 
 
 abnor:"-!: 1 
 
 100 
 
 300 
 
 M: 2, ;. lid: ?. r -Cns. 
 Av. : 
 
 
 u.u uu^; 
 
 3TLV: - ' 
 
 14 
 
 
 
 12 
 
 
 
 
 10 
 
 
 i 
 
 
 8 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 
 4- 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 . ! I 
 
 
 i 
 
 ins 
 
 7. 1.710, 1.950, 2.210 Hz. 
 
 # of occ. 
 10 
 
 res-.: 41. M: 250ms. Md: 250ms, 
 abnormal: 209. Av.: 220.38ns. 
 
 SOJDV: i 128.58. 
 
 8 
 
 
 6 
 
 
 
 
 
 
 2 
 
 
 
 
 
 ) I 
 
 
 
 
 I 
 
 1 I ! 
 
 
 50 
 
 150 
 
 250 350 
 
 4-50 
 
 550 
 
 ins, 
 
 8. 1.950, 2.210, 2.450 Hz. 
 
 # Ox OCC, 
 
 resp.: 13. 
 abnormal: 58. 
 
 M: 225ms. Md: 200, 
 
 250ns . 
 
 Av.: 234.62ns. 
 STDV: - 66.57. 
 
 4 
 
 
 2 
 
 i 
 
 
 
 
 
 I I 
 
 I 
 
 i 
 
 
 
 
 
 
 = 100 
 
 200 
 
 300 
 
 400 
 
 ms 
 
 9. 2.210, 2.450, 2.730 Hz. 
 # of occ. 
 
 resp.: 23. M: 200ms. Md: 150ns 
 
 6 ' 
 2 ' 
 
 1 i 
 
 ' ! ! 
 
 STBV: --124 
 
 . ! ! LJ , 
 
 
 ' 
 
 
 .M.vs. freq. 
 
 300 
 
 500 
 
 ins 
 
 Average x x 
 
 "Median - 
 
 '.ode a - G 
 
 deviation 
 
50 
 
 1. 
 
 
 
 
 24 
 
 * 
 /N 
 
 TL ' 0-217 
 ' ccc. 
 
 - . . : . . : 
 -2". 1: ' . ". : 1^ . "1ns. 
 : - 7.6v. 
 
 22 
 
 - 
 
 
 20 
 
 
 
 13 
 
 - 
 
 
 16 
 
 
 
 
 12 
 
 
 
 
 
 10 
 8- 
 
 
 
 
 
 6 
 
 
 
 
 
 2- 
 
 ; i 
 
 
 
 i ! , , 
 
 50 
 
 100 
 
 150 
 
 200 
 
 250 
 
 300 
 
 ns 
 
 2. /\ : 0.3--6 PIz. i 3. 
 XL: 0.217 Hz. - 3. 
 
 # of occ. 
 
 8 
 
 6 
 
 resp.:36. 
 
 M: 150ms. Md: 150ms. 
 S^DV: - 69.06! 
 
 -175 
 
 -100 
 
 
 
 100 
 
 200 
 
 300 ms 
 
 3. A : 0. r -55 Hz. 
 : 0.3S'i- Hz. 
 
 16 
 14 
 12" 
 10 
 
 6' 
 4. 
 
 21 
 
 of occ. 
 
 resp.: 43. H: 150ns. I'd: 150ns. 
 abnormal: 30. Av.: 156.97mc. 
 
 STDV: - 32.42. 
 
 30 
 
 100 
 
 Fig. 10.: Unpredictable sif-nv.-.l. Subj-co: './ang. 
 
: - 
 
 J\ : . 
 
 . : 23 . 
 
 - . - _ . 
 
 Av . : ' 
 
 '. : - . , 
 
 
 
 \ 
 14 
 
 12 
 
 10 
 
 8- 
 6 
 
 occ. 
 
 5',} 100 15D 2 ::'.: '-' ' ' 350 4CT 4-^0 $00 
 
 ns 
 
 5 . A : . 3 
 
 n : 0.217 
 
 # of occ. 
 
 8-- 
 
 6 
 4 
 p 
 
 rasp.: 32. 
 ?rr.al: 4. 
 
 M: 150ns. Hd: 150ms, 
 Av. : ,06ms. 
 
 STDV: I 62. -3. 
 
 100 
 
 150 
 
 260 250 
 
 300 
 
 350 ns 
 
 6. A : 0-5?G Hz. 
 : 0.217 :-:z. 
 
 + - 
 
 .: 60. M: 150ras. Md: l5Cas, 
 
 abnoriaals 11. Av.: "\y\. 2an. 
 
 3TDV: *70.7*. 
 
 
 y o 
 
 I OCC . 
 
 12' 
 
 
 
 
 10' 
 
 
 
 
 B- 
 
 
 
 
 
 & 
 
 
 
 
 
 
 2' 
 
 i 
 
 I 
 
 
 
 i i ; i __] 
 
 
 
 100 200 300 400 500 ms 
 
 Fi-r. Ob. 
 
52 
 
 200 
 
 150 
 
 100 - 
 50 
 
 msec 
 
 tandard deviation 
 
 order of 
 experiments. 
 
 Pig. 10c. 
 
55 
 
 ?v;o 1:3 ' .ular -;ave: 
 
 a * 
 b. 
 
 ?,:;-: edr;ej 
 Dro ' edge: 
 
 1 
 
 7-* o <? A **^ c* r\ 
 
 -lo-' * 1 . 
 
 r.odir-.r.: M . 
 
 nedian: M,. 
 
 1. 2 /S9C. ?"po a. 
 Tots.1 rospcnsa: 
 
 : Of OCC. 
 
 ' 
 
 
 h 
 
 
 
 
 
 
 2 
 
 
 
 .Ml 
 
 
 
 -^0 100 -15Q 200 2^0 LIS 
 
 - 
 
 isir.rj edro: M.,: 200ms 
 
 DroDir.r ed^e: ;,: 1->Cc.s. 
 c. 
 
 r. 
 
 
 
 
 /r 
 
 
 
 6- 
 
 
 
 
 
 /. - 
 
 t 
 
 4 
 i i- i 
 
 I 
 
 2- 
 
 . nif 
 
 
 50 100 200 n 
 
 s . 50 100 1 JO 200 250 rr 
 
 ri;3. 11: P.o.-p fimc-'cior.. Subject;: '/anj; 
 
54- 
 
 o O C /~"~ -1 ^ v '.' . ", ' ' ' <~ ' ?f^-r- . 17,fy,~ 
 
 ,i , ci / -. ^ , - J i '-.> -lo ,;L/.^O. 
 
 6- 
 
 ;/- WJ. UU<^. 
 
 * 
 
 V 
 
 < 
 
 
 2- ? 
 
 
 
 
 M 
 
 
 
 
 1_ j i f 
 
 5 ~ 1 00 1 ; 
 
 , i -i -i 
 200 250 300 ri 
 
 o 
 
 5. 1 /sec. 
 
 # 01 occ, 
 
 o 
 
 5' 
 
 5 
 
 2- 
 1- 
 
 I 
 1 
 
 ^ i r r r 
 
 ! 
 
 1C 
 
 1^0 '2ho 2^0 500 350 4-00 as 
 
 " C 
 
 b. 
 
 -,, 
 
 3:\:s. i-'i : 575^-s M,: 170:::s. 
 
 2-f 
 
 1 " 
 
 . . . r ; . 
 
 f . - r 
 
 T J 1 
 
 1C 
 
 o' Mo 
 
 '200 
 
 25'0 . 3C50 3^0 40b- 4-50 r.s 
 
 
 
 '# of occ] 
 
 ,rpo 
 
 a*~>-r\r* T> "* 'I^Q -^"~i ^ T* ^*'^ r 7 ^r-^ 
 cXllC D i'ii. Z 1 ^ ' / yiilO * 1\ t J'~> / y UiS 
 
 M d : 175~:3. 
 
 5 " 
 
 
 j 
 
 i 
 
 1 ' 
 
 M, , 
 
 I 
 I 
 
 . 1 I 1- 
 
 
 icto 150 200 250 500 350 4-00 
 
55 
 
 6. 0.5 /sec. 
 
 fypo a. H t : 175-:'. :r : 275ns. M : 175ms. 
 
 d' 
 
 
 # of occ. 
 
 2 
 
 4 
 
 
 1 ' 
 
 I 
 
 1 
 
 
 1 , . _ - I 
 
 
 100 i::"- 300 ^-00 5 - :.o 600 ms 
 
 7. 0.33 /sec. C"pe a. H t : 2; Ons. II: 225ns, 
 
 of occ. 
 
 
 . 
 
 , t__t__*_. ]_..., . . * I . 14 i J i- i i f ( - L. i | 
 
 ibo 150 200 250 300 350 
 
 350 ms 
 
 3. 0.133 /sec. Type a. I-Ir 250r s s. H,,: 600ns. H: 225ms, 
 
 I ~ O- OCC . 
 
 100 
 
 200 300 
 
 1 
 
 500 600 
 
 ms 
 
 9. 1.G /ssc. Type a. I-L: 175ms. M p : ?00ms. II^: 150ms. 
 
 i< r l 2 
 
 if 
 11 
 
 or occ 
 
 I ' 
 
 I L L il 
 
 --J- --.*- ( l-~l I > i . 
 
 100 150 200 250 
 
 ms 
 
 Pic;. 11c. 
 
56 
 
 600 - 
 550 
 
 500 
 
 450 
 400 
 350 -- 
 
 300 -' 
 250 - 
 
 200 - 
 
 150 
 
 msec. 
 
 
 07T53 0.5 0133 
 0.33 0.7 1 
 
 Total response: 
 
 -1-! CT- T- -. -T^-^ . 
 
 Drop in:; edge: 
 
 1.6 
 
 /sec 
 
 Fir. 11 d. 
 
57 
 
 Sinusoid: 
 Latencies (i 
 
 20C 
 
 10( 
 
 0.5 1.0 1.5 2.0 
 
 freq. 
 
 Square wave 
 Latencies (ms) 
 
 50Q 
 
 200 
 
 100 
 
 100 
 
 .5/1.0 1.5 2.0 
 
 -- o 
 
 - e- 
 
 or..v. st 
 c;-clo 1 
 cycle 2 
 cycle 3 
 
 Fir;. 12 
 
c(t) 
 
 r(t) = target motion 
 c(t) = eye motion 
 1-1= memory unit 
 D= comparator 
 P(ov;)= predictor 
 g(jw)= plant 
 
 FiS.13 
 
59 
 
 TJ 
 
 V 
 
 ( 
 
 'H W 
 
 O OT 
 M OJ 
 
 c o 
 
 O i-i 
 O Pi 
 
 t, 
 
 0) 
 
 c 
 
 
 
 o 
 
 ! o 
 u 
 
 Q) 
 
 (X 
 
 OO 
 
 10 
 
 -p 
 
 g 
 
 0> 
 
 fH 
 
 O 
 -P 
 
 <o 
 
 f 
 O 
 O 
 
 
 o, 
 rt 
 
60 
 
 estimation 
 
 rr^p;:ro f 
 pred.v ;. 
 control 
 prc 
 
 yes 
 
 'ictive 
 control 
 
 uiiprodictive 
 control 
 
 Decision ileclianisra 
 
61 
 
 -1 
 pr 
 
 2 
 
 (b) Variance of probability density functions s (f , N) 
 
 VI -t " 1^ f~t /-N 
 
 s*<^' N) 
 
 frecuenc;/ (Hz) 
 
 16 
 
62 
 
 L 
 
 
 
 
 
 
 
 -X 
 
 X 
 
 la 
 
 
 lead 
 
 y 1 ?? x 
 
 Time 
 
 b. 
 
 la.-: 
 
 f req . 
 
 x 
 
 lead 
 
 
 c. 
 
 1 free . 
 
 -X 
 
 la- 
 
 x 
 
 lead 
 
 x : ror.otion tine, 
 y f : variance. 
 
Probability 
 density 
 
 
 
 'opt 
 
 Lead 
 
 Lag 
 
 when 
 
 'opt 
 
 X 
 
 t 
 
 = mean of probability density function 
 
 = reaction time without prediction 
 = 0, target changes position 
 
 Probability densitj/ function of predicted reaction time. 
 
 Pig. 18 
 
o 
 
 
 
 c r o 
 
 o v 
 
 rl W 
 
 -t: X 
 
 8 1 
 M*J . 
 
 o 
 n 
 
 
 
 
 1 
 
 
 
 v\ 
 
 
 
 r^ 
 
 in \ 
 
 
 3 
 
 CM O 
 
 * 
 
 fr 
 
 
 to CN r: 
 
 W 
 
 o 
 
 O 
 
 r: j 
 
 5/3 
 
 "O 
 
 e 
 
 ^ 
 
 -P rH ., 
 
 3 i. $?; 
 
 rj 
 
 CN 
 
 * * ^ 
 
 1 
 
 f 
 
 H ^ g 
 
 .Q 
 
 CN 
 
 n 
 
 H -U O o W 
 
 ' -H G d > 
 
 * / 
 
 e . -H w o 
 
 O 
 
 o -H <y \ s 
 
 jjs 
 
 ft 
 
 H rH si . 
 P 4J 13 O 
 
 . - . / 
 
 v^^> 
 
 nj U-i w rrj 
 
 i 
 
 ^ H H M 
 
 1"^" 
 
 3 O ^ j< 
 
 1 
 
 P -P o u 
 
 "" " ~"> 
 
 d 3 <4H CM r-~ 2 
 
 rH 
 
 W O O rH 2 
 
 H| W 
 
 4J 
 
 J) 
 1 
 
 II II W || II 
 O M 
 
 
 O 
 
 N -H C >< 
 
 - 
 
 pJn 
 
 E 3 U> pq 
 RJ 
 
 c 
 Q S 
 
 
 -p 
 
 W 
 1 
 
 \ > 
 
 w ^ 
 6 
 
 i 
 
 i \; 
 
 
 to 
 
 
 i' 
 
 < 7* 
 
 1 
 
 r p-i 
 
 
 : 
 
 
 
 
 Q 
 
 f| 
 
 o o *d 
 
 S 
 
 
 M 'd r-l 
 
 1 ^^ 
 
 IN 
 
 >-i O 
 
 -P ^ 
 
 V <o 
 
 N O . 
 
 o s 
 
 -Xr- 
 
 1 
 
 _ 
 
 H w <y M 
 
 ^w 
 
 
 
 W ^ WO 
 
 . I 
 
 
 
 en - D - 
 
 i 
 
 rH 
 
 
 WO . (J 
 
 I 
 
 i 
 
 O 
 
 
 HO** w 
 
 f 
 
 ^ j i'~~i v 
 
 -c / 
 
 / H 
 
 j 1 w 
 
 w ^ QJ E} 
 
 . -H >i O 
 P (3 >i N < 
 
 n 
 
 *- / 
 
 -H j 
 
 O N 
 
 
 0> rH T3 
 rH TJ (1) rt 
 
 Gi 13(1) 
 O 'O 
 
 y" 
 
 1 . J o -i- 
 
 1 eO -H 4J 
 
 /. nJ 
 
 W T3 -H rH 
 
 W 
 
 M (tf p nj 
 
 j 
 
 U (0 tt 
 
 
 c: <d 3 o 
 
 
 H in a, w 
 
 c 
 
 II II II II 
 
 o 
 
 
 41 
 
 rj c 
 
 U-l 
 
Target 
 Input 
 
 Tin 
 
 Sampling 
 
 t t ' 
 
 t 1 t 
 
 i i 
 
 Time 
 
 To 
 
 Definition of symbols sliov/ing inputs 
 
 occurring in sampling intervals T_ . 
 
 c 
 
 Pis. 20 
 
66 
 
 Probability 
 
 k - 
 
 f (x) = k e' 
 
 s = 61n(x/T ) 
 
 x 
 
 o o 
 
 a) Log Normal Distribution 6 
 
 Probability 
 
 1 
 a/e 
 
 = 2 
 
 b) Raylcigh Distribution 
 Probability 
 
 1 
 
 ct ' t 2a 
 
 c) Kor.--Jnci:oo:?inn fit to Raylcigh Distribution 
 
 Mathc'iiu: lical Dcicr.';)t.ions of. Latency HiF.toarans 
 
67 
 
 LATENCY 
 
 
 
 
 
 10 
 
 
 20 
 
 
 
 
 
 30 
 
 
 
 
 
 
 i 
 
 
 i 
 
 
 
 
 
 i 
 
 Hn- ii-.r 
 
 
 1 
 
 1 
 
 
 MM 
 
 1 ! ' 
 
 l ! 
 
 
 
 1 
 
 
 f I III 
 
 Ids- I5n 
 
 
 1 
 
 ! 
 
 
 1 1 I 1 
 
 ! I ! 
 
 ! 
 
 
 
 i 
 
 
 1 1 M 1 
 
 I r, n _ i r r. 
 
 
 l 
 
 ! 
 
 
 1 M 1 
 
 1 I 1 
 
 ! 
 
 
 
 1 
 
 
 1 1 M 
 
 ; r .5- i 
 
 
 I 
 
 | 
 
 
 ill! 
 
 i ! 1 
 
 ! 
 
 
 
 1 
 
 
 ! 1 Ml!! 
 
 i r, n - 1 r - r . 
 
 
 1 
 
 1 
 
 
 III! 
 
 ! I 1 
 
 ! 
 
 
 
 1 
 
 
 1 III!!! 
 
 1*5- 1.70 
 
 
 ! 
 
 | 
 
 
 1 ! ! 1 
 
 1 1 1 
 
 ! 
 
 
 
 I 
 
 
 ! 
 
 170- 175 
 
 
 | 
 
 1 
 
 
 Mil 
 
 1 I 1 
 
 I 
 
 
 
 I 
 
 i 
 
 
 1 (Mill 
 
 175- ISO 
 
 
 1 
 
 1 
 
 
 1 M 1 
 
 ! ! ! 
 
 1 
 
 
 
 1 
 
 
 1 
 
 i r -o- in 5 
 
 
 1 
 
 ! 
 
 
 i 1 i 1 1 
 
 ! 1 1 
 
 ! 
 
 
 ! 
 
 1 
 
 
 ! ! I 
 
 i. 5 - inn 
 
 
 i 
 
 1 
 
 
 MM! 
 
 ! 1 ! 
 
 ! 
 
 
 1 
 
 ! 
 
 
 ! Mil 
 
 T n n _ T n r, 
 
 
 1 
 
 l 
 
 
 MM 
 
 i ! ! 
 
 ! 
 
 
 
 I 
 
 
 1 MM! 
 
 3 n r, - o n o 
 
 
 1 
 
 I 
 
 
 ! i ! ! 
 
 1 1 M 
 
 1 
 
 
 
 1 
 
 
 I 1 ! I 1 II I 
 
 200- 20s 
 
 
 1 
 
 ! 
 
 
 Mil 
 
 MM 
 
 1 ! 
 
 
 
 I 
 
 
 1 1 
 
 o n 5 - ? i o 
 
 
 1 
 
 ! 
 
 
 1 i I i 
 
 1 ! ! 1 
 
 1 1 
 
 
 
 1 
 
 
 1 
 
 21.0- 215 
 
 
 1 
 
 j 
 
 
 1 1 M 
 
 MM 
 
 I 1 
 
 
 
 i 
 
 
 Mill 
 
 215- 220 
 
 
 1 
 
 i 
 
 
 till 
 
 ! ! M 
 
 I I 
 
 
 
 
 
 
 220- 2 nr - 
 
 
 1 
 
 1 
 
 
 I ! I 1 
 
 MM 
 
 1 I 
 
 
 
 
 
 
 2 2 5 - 2 3 n 
 
 
 j 
 
 I 
 
 
 ! ! I ! 
 
 MM 
 
 
 
 
 
 
 
 9~3;n- 235 
 
 
 i 
 
 1 
 
 
 MM 
 
 Mil 
 
 
 
 
 
 
 
 235- 2'tn 
 
 
 1 
 
 1 
 
 
 ! 1 ! 1 
 
 
 
 
 
 
 
 
 2 u n - 2 f '- 5 
 
 
 1 
 
 1 
 
 
 1 
 
 
 
 
 
 
 
 
 2'i5- 250 
 
 
 ! 
 
 1 
 
 
 
 
 
 
 
 
 
 
 2;0- 255 
 
 
 1 
 
 ! 
 
 
 I 
 
 
 
 
 
 
 
 
 2 t, t, - ;< K i i 
 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 2 r o - 2 r 5 
 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 2f'5- 270 
 
 
 ! 
 
 
 
 
 
 
 
 
 
 
 
 2 7 n - 2 7 f- 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 275- 2SO 
 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 2SO- 2.^5 
 
 
 ! 
 
 
 
 
 
 
 
 
 
 
 
 2 " 5 - 2 " 
 
 
 ! 
 
 
 
 
 
 
 
 
 
 
 
 2in- 2ns 
 
 
 
 
 
 
 
 
 
 
 
 
 
 20 p- 300 
 
 
 1 
 i 
 
 
 
 
 
 
 
 
 
 
 
 ^05- 310 
 
 
 i 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 31 n- 3T5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3?0- 
 
 335- 3'tO 
 LATENCY 
 
 i 
 
 10 
 
 i 
 20 
 
 i 
 
 50 
 
 i 
 
 uo 
 
 Fi 5 . 22 
 
68 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 Hi-h freq, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 [ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Lov; frsq. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 - 
 
 - 
 
 
 
 
 
 
 - 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
69 
 
 *0 
 
 r: 
 o 
 o 
 GJ 
 
 CO 
 
 O 
 
 
 
 to 
 rd 
 C 
 O 
 O 
 
 c- 
 
 03 
 
 U~\ 
 CM 
 
 o 
 
 s 
 
 C\J 
 
 
 
 fcD 
 H 
 
 o 
 
 m 
 a 
 c 
 
 to 
 o 
 
 e 
 
 o 
 
 H 
 
 -p 
 o 
 
 d 
 o 
 
 o 
 vo 
 
 e> 
 t-i 
 
 CJ 
 
 O 
 
 r. 
 
 o 
 
70 
 
 LT\ 
 CM 
 
 H 
 ft 
 
 M 
 O 
 
 H 
 
 B 
 
 O 
 
 8 
 
 hn 
 
 r: 
 
 fcD 
 C 
 
 C 
 H 
 
 CO 
 
 O 
 
 E 
 
 d 
 
 o 
 
 H 
 P 
 O 
 
 S 
 
 o 
 
 O 
 O 
 
 I 
 
 n 
 H 
 d 
 
 c 
 
 0) 
 
71 
 
 *^-.s 
 
 c ^ 
 
 O .0 
 
 j; to 
 
 : 5 
 
 ^* 
 
 O 
 O 
 
 to 
 
 "O 
 
 o 
 
 o 
 
 (D 
 
 O r 
 
 to .- 
 
 
 
 
 o 
 
 IT) 
 I 
 
 o 
 
 
 
 
 t.o 
 
 H 
 
 U) 
 
 o 
 
 c 
 o 
 
 o 
 
 n3 
 0) 
 
 G) 
 
 ra 
 o 
 o 
 
 3 
 u 
 
 o 
 o 
 
 c 
 
 w 
 H 
 d 
 
 Q> 
 -P 
 
 H 
 O 
 
 C 
 o 
 
 fH 
 45 
 
 eo 
 
 o 
 
 C 
 o 
 
 g. 
 
 OJ 
 
 
 
 0) 
 
c 
 o 
 
 +> O 
 3 C 
 
 O 
 ~ cj 
 
 -r* 
 
 to 
 
 O-H 
 
 HrS 
 
 w r., 
 
 fe) 
 
 
 < *-fc* snc *-* -y^r ~. - : 
 V,"vaa j.'**-t_e_t* j . 
 
 P 
 
 O 
 
 
 * 
 
 H 
 
 n 
 
 
 *-m 
 
 G. 
 
 % rH 
 
 V I ' ; f 1 
 
 % 
 
 o 
 
 E 
 
 v-J 
 
 V."-'^ 
 
 M 
 
 JJ 
 
 O' 
 
 s 
 
 O 
 
 
 
 t I 
 
 ^-, 
 
 
 " . -i-i>_- wr^.j 
 
 V 
 
 c- 1 
 
 C C 
 
 fcO 
 
 CVJ 
 rH 
 
 cd 
 
 A 
 
 ( % 
 
 o 
 
 H 
 
 IS 
 
 H> 
 C 
 a) 
 
 0) 
 
 a> 
 ^ 
 o, 
 
 0) 
 
 o 
 o 
 
 OT 
 fl) 
 
 I! 
 
GENERAL LIBRARY U.C. BERKEL 
 
H5$ ' M