A device for the automatic, continuous recording of stereoscopic visual acuity

Photogrammetria

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STEREOSCOPIC VISUAL ACUITY C. E. T. KRAKAU

Department o] Exper.mental Ophthatomology, University o] Lund (Sweden) (Received August 28, 1968)

SUMMARY

An electronic device for testing stereoscopic visual acuity during an arbitrary period is described. An ink written record, suited for time series analysis, is obtained. The device can easily be connected to a tape punch. Some results of a series of tests on photogrammetric personnel is given, INTRODUCTION

Visual acuity cannot be fully determined by a single value since we know that it varies considerably with time. It is therefore reaso~aable to deal with acuity as a stochastic process and try to determine certain parameters by which it can be characterized. The aim of the present paper is to describe a procedure, which makes it possible to present the stereoscopic and other types of visual acuity as a time series. PRINCIPLE

In testing acuity with the ordinary "constant stimuli" method, a set of objects of increasing difficulty is used. Each object is shown to the experimentee a number of times and the ratio between the number of correct interpretations and the total number of trials gives an estimate of the probability of seeing the object correctly. No information on the stationarity and correlation properties of the visual acuity is obtained by this method. However, a time series analysis can be made if t h e procedure is modified in the following way. When an object has been correctly interpreted, the next object shown will be one step more difficult and when an incorrect interpretation is made the next object will be one step easier. The process obtained can then be analysed for stationarity and correlation properties; The analysis is limited to undulations of acuity which are long compared with the interval between succesive trials.

Photogrammetria, 25 ( 1969/1970~ 115- 123

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Fig.l, Experimental set up. A. Oscilloscope electronic unit and writing unit. B. Press buttons and prism device. PROCEDURE

In practice the testing is performed in the following way. The test object which is shown on an oscilloscope screen (Fig.lA), has two alternative positions. The subject, at 4 m distance from the screen, has in front of him two buttons (Fig. 1B) one for each of the two positions of the test object. He is instructed to press one of the buttons corresponding to his interpretation of the position of the test object. When the button is pressed, the test object disappears for a short pre-selectable time 7 (0.5-8 sec), and then reappears in a position chosen at random. The object then remains until the subject presses the button again. Alternatively, the test image can be suppressed after a pre-set period p (0.025-0.4 sec). This procedure is shown schematically in Fig.2. The pressing of the button means either a right or a wrong interpretation. If the wrong button is pressed the object shown next is somewhat (one step) easier than the previous one. Since we have two alternatives only, the chance of pure guessing Photogrammetria, 25 (1969/1970) 115-123

AUTOMATIC RECORDING OF STEREOSCOPIC VISUAl_ ACUITY

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Fig.2. Time relations for exposure of the test image, a = maximum reaction time; fl = exposure time; ;, -- time of suppression of test image. In A: c, ~: fl; in B: a ~ /L Vertical arrow ($) denotes pressing of a button. is as great as V2. This chance is r e d u c e d by d e m a n d i n g three consecutive interp r e t a t i o n s to be correct for the o b j e c t shown n e x t to be one step m o r e difficult. T h e m a x i m a l r e a c t i o n time ,~ in which the subject has to m a k e his choice m a y be infinite or limited t o a p r e - s e t p e r i o d ( 0 . 5 - 8 sec). If neither of the buttons is p r e s s e d within this p e r i o d an easier object is shown. T h e test process is c o n t i n u o u s l y r e c o r d e d by an inkwriter, which indicates the size of the test object. FORMATION OF THE STEREO IMAGE W h e n the nonius acuity (i.e. the ability to perceive a small step on a line, Fig.3) is t e s t e d the object is a simple p l a n e geometrical image. A n artifice m a k e s it possible to use the s a m e device for testing the stereoscopic acuity also. A n i m p r e s s i o n of d e p t h is o b t a i n e d if there is a so-called geometric disparity between the images of the two eyes. T h e definition of disparity ~ is shown with the

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Photogrammetria, 25 (1969./1970) 115-123

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aid of Hering Helmholtz' so-called peg test in Fig.4. Three vertical bars are seen,the one in the middle being placed out of the plane of the outer ones. In the illustration the middle bar has been placed nearer to the observer than the outer ones. The two plane images, which could produce the same effect, should have the middle bar displaced to the right and to the left for the right and left eye respectively. This effect

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is obtained from a simple image of three parallel horizontal lines if we iook at it through a prism device like the one in Fig.5. The image of the right eye is rotate(i 9 0 ' clockwise and that of the left eye 90 ° antictockwise and a disparity between the images is obtained. If the subject has stereoscopic vision, he will be awarc of a level difference between the structures on the oscilloscope screen. The two alternatives in the interpretation of thc image will clearly be that the middle line is see~ nearer or further from the observer as in the peg test. The degree of difficulty of the test object is determined by the size of the distance ,I a (Fig.3). The quotient between ~1 a at one step and that o f the next easiest one is always 1.2, ON THE CONSTRUCTION

The test images are formed by means of a square wave generator. A sort of "coin flipping" device chooses which of the alternatives will be shown on the oscilloscope screen. The electronic problems (such as the memory function and the judgement whether an interpretation has been correct or not) have been solved by pulse technique. For the recording and determination of object size a "slow syn" motor is used. It moves one step in a clockwise direction when three correct interpretations have been made and one step counter-clockwise for a wrong interpretation. The motor has on its axis a lever with a contact brush which rests on one of a series of contact points. The contacts are connected to a row of resistances which determine the degree of difficulty of the test object (the size of A a in Fig.3). The lever also carries an ink-pen so that the size of the object is continually monitored. The oscilloscope which shows the test image has to be of a high quality. 1 The apparatus can be connected to a tape punch, and the desired statistical parameters of the calculation are then obtained from a computer. EVALUATION

OF THE RECORDS

From the number of transitions from one state to another a set of transition probabilities (i.e., the chance of interpreting correctly an object Ei) can be estimated. For routine investigations it is a bit clumsy to have to use the whole set of values. For most purposes the type value (i.e., the state from which a transition to the next more difficult object is the most common) or the mean value of the states visited can be used. As measures of dispersion the range of states visited or the standard deviation may be used. The stationarity of the process is to some extent described by the trend of the 1 The author is greatly indebted to lic. Hjelmstrom of the Institute of Photogrammetry, Stockholm, for his checking of the oscilloscope accuracy, which has resulted in increased care at adjusting the deviations zJ a.

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recording. Denoting the type value of a period of, say, 5 min. at the beginning, middle and end of the recording by y~, y,, and y.~ we can give the approximate course of the curve by: G =

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The number of trials made per minute is another simple measure of importance. A more sophisticated analysis may comprise the calculation of the autocovariance function. As is seen in the example in Fig.6 there are u n d u l a t i ~ s in the course of testing and we may ask ourselves if these are random effects or if they really represent periods of higher and lower seeing ability. This problem has been approached along the following line. Suppose the trials in a series were all independent. Our test series is transformed by the testing procedure since only a neighbouring state can be reached at each step and the process would be a Markow chain, defined by a set of transition probabilities. The autocovariance function of such a chain has a characteristic course (with some restriction)--it falls exponentially with increasing parameter value. Now we can compare the directly calculated autocorrelation function with the one predicted from the hypothesis of a Markow chain. TEST

SERIES

A group of 34 photogrammetrists was tested at the Institute of Photogrammetry, KTH, Stockholm, for a period of 40 min. each. The test principle was immediately understood by the experimentee who rapidly adjusted the prisms for himself, and as a rule the mean level was approached in a few minutes. The average disparity level for the whole group corresponded to 16.3 (5 sec t) with a range of 10.0-19.9 ( 2 0 - 3 sec). The standard deviation was (mean of the groups) 1.96 (range 5.19-3.10). The number of trials per minute was 16.3 (mean), (range 8.3-27.4). In ten of the cases there was a trend greater than two steps and less than seven steps. (One step change corresponds to a factor 1.2 or 1.2-t). The trend was towards improvement in seven of them. The autocovariance function was calculated and in about half of the cases there were very clear undulations in the course, in several others there was a n obvious discrepancy between the directly calculated curve and the one corresponding to the independent trials hypothesis. Unfortunately we have no significance test so far for this difference. A most interesting question arises, however: does a similar autocorrelation pattern reappear when the individuals are tested repeatedly? Fig.7 shows two autocorrelatioa curves for t w o individuals tested twice. Obviously, the number of trials per minute varies considerably between different operators. This raises an important question which must be left open: how 1 Seconds are sexagesimal. Photogrammetria, 25 (1969/1970) 115-123

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much may high speed cost in lowered precision? As a contrast to the group of photogrammetrists a series of testings on 44 normal males, all car drivers, about 20 years of age may be quoted. All except ten had full vision on both eyes. In none of the cases could the subject maintain a level during the testing period (12 rain); a few of them reached a fairly good level for a short period but were not able to maintain it. Most of the cases succeeded in obtaining a stereoscopic image for short periods, but were soon back at the zero level again. Some cases (16) could not see stereoscopically at all. On the whole the material was not suitable for statistical treatment of the kind described. This deplorable result may have several explanations. F o r instance, the time allowed for the adjustment etc. had to be limited to a few minutes. Further more, the stereoscopic test came as the last one in a series of other fairly tiring eye tests and some fatigue was inevitable. However, the most important reasons why the

Photogrammetria, 25 (1969/1970) 115-123

AUTOMATIC RECORDING OF STEREOSCOPIC VISUAl. ACUIIY

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first g r o u p was so m u c h m o r e s u p e r i o r were n o d o u b t , firstly, the daily t r a i n i n g of the stereoscopic vision in this group, a n d secondly, the fact that p e o p l e w i t h o u t ;t perfect stereoscopic vision are h a r d l y a t t r a c t e d by, or ~o o n with, such m e a s u r e merits. REFERENCES

KRAKAU, C. E. T., 1967a. An automatic apparatus for time series analysis of visual acuity. Vision Res., 7: 99-t05. KRAKAU, C. E. T., 1967b. En metod f6r fortl6pande pr6vning av stereosynskiirpan: FiJrsvarsmedicin, 3:27-35 (in Swedish). KRAKAU, C. E. T., 1969. On time series analysis of visual acuity. A statistical model Acta Ophthalmol., 47:66(1 666.

Photogrammetria, 25 (1969;'19701 115-123