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Ergonomics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/terg20
Preferred vertical gaze direction and observation distance a
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HERBERT HEUER , MICHAEL BRÜWER , THOMAS RÖMER , HEINZ KRÖGER & HENDRIK KNAPP
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Fachbereich Psychologie der Philipps , Universität Marburg , Gutenbergstrasse 18, Marburg/Lahn, D-3550, Germany Published online: 30 May 2007.
To cite this article: HERBERT HEUER , MICHAEL BRÜWER , THOMAS RÖMER , HEINZ KRÖGER & HENDRIK KNAPP (1991) Preferred vertical gaze direction and observation distance, Ergonomics, 34:3, 379-392, DOI: 10.1080/00140139108967321 To link to this article: http://dx.doi.org/10.1080/00140139108967321
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Preferred vertical gaze direction and observation distance HERBERT HEUER, MICHAEL BRUWER,THOMASRUMER,HEM K R ~ G E Rand HENDRIK KNAPP Fachbereich Psychologie der Philipps-Universitat Marburg, Gutenbergstrasse 18, D-3550 Marburgllahn, Germany
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K e y w o r k Vertical gaze direction; Vergence; Observation distance.
Hill and Kroemer (1986) and Kroemer and Hill (1986) found that the preferred vertical direction of gaze is lower with a nearer binocular stimulus than with a more distant one. A model is proposed that relates this phenomenon to characteristics of the resting state of the oculomotor system. Three predictions of the model were tested, based on measurements of the preferred vertical gaze direction and dark vergence in the same subject sample. On average the effect of observation distance on the preferred vertical gaze direction served to reduce the discrepancy between the resting state of vergence, operationally defined as dark vergence, and actual convergence during inspection of the binocular stimulus. Second, dark vergence data from individual subjects could be successfully used to predict whether they raised or lowered their eyes on inspection of a binocular stimulus as compared with the preferred vertical gaze direction while viewing a monocular stimulus. Finally, predictions of the size of the change of the preferred vertical gaze direction on introduction of a binocular stimulus produced only small and non-significant correlations. 1. Introduction
During visual work people prefer certain directions of gaze in the sagittal plane. T h e preferred vertical gaze direction is a n important criterion for recommendations regarding the optimal placement o f visual displays. (There appear to be terminological difficulties with the direction of gaze in the sagittal plane. Various shorter terms like inclination of gaze, declination o f line of sight, slope of regard, vertical gaze deviation, and line of sight angle have been used. There seems to be little risk that our term 'vertical gaze direction' can be misunderstood as designating a gaze direction coincident with the vertical; rather it refers to direction in a vertically-oriented plane.) However, such recommendations (for example Schmidtke 198 1, p 4 10) are less straightforward than generally thought. Hill and Kroemer (1986) and Kroemer and Hill (1986) found that the preferred vertical gaze direction depends on the observation distance, that is the distance of the display from the eyes. With the head upright they observed a preferred direction of -24.4" with an observation distance of 1 m and o f - 32.8" with a 0-5 rn.observation distance. Differences of about the same size were found with other orientations of the head and trunk. The dependency of the preferred vertical gaze direction on observation distance c a m e s important practical implications. For example, it suggests that the height o f visual displays should be adjusted to their distance, and that for displays at different heights (for example, in consoles) different distances should be used rather than only a single 'optimal' distance. However, so far the OOI&Ol39/9l 53.00 O 1991 Taylor & Francis Ltd.
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phenomenon does not really stand on firm ground. Its generality needs to be established, and it is in need of an explanation. Hill and Kroemer (1 986, p 133) hint at a possible role of different effects of gravity on the lens of the eye depending on accommodation and thus the tension of the zonula fibres. The purpose of this paper is to outline an alternative explanation and to provide a first experimental test, at the same time exploring the generality of the phenomenon. Basicafly it is modelled as resulting from certain characteristics of the resting state of the vergence system. 2. The model Two concepts are central for the model, 'eye-inclination costs' and 'vergence costs'. Both kinds of costs are assumed to be monotonically related to the discrepancy between actual eye positions and the oculomotor resting states. These concepts will be explained first, thereafter their relation to the effect of observation distance on the preferred vertical gaze direction will be outlined, and finally some testable predictions will be presented. 2.1 . Basic concepts Normally the position of the eyes is determined by the position of the fixated object. However, there is also a relatively stable eye position when no visual input to the oculomotor control systems is present. This position, which can be assessed in darkness, has been taken as a resting state from which the eyes are driven away by visual input. For the present purpose the resting state will be characterized by the vertical position of the eyes in darkness and their relative position, that is, their dark vergence. When no stimulus is present and no particular effort is made, the eyes are slightly depressed in most people (Leibowitz, Shupert, Post and Dichgans 1983). This position is the vertical resting position, and any deviation of the actual vertical gaze direction should be associated with effort or costs, which we will call 'eye-inclination costs'. Eye-inclination costs should be minimal when the eyes are in their vertical resting position, and they should reach maximum values towards extreme vertical eye positions. The latter postulate is based on the informal observation that it requires an effort to keep the eyes strongly raised or depressed (by about 30-45") for some time. When no stimulus is present and no particular effort is made, the average angle of convergence is about 3-2", corresponding to a distance of about 1.2 m (Owens and Leibowitz 1983, Owens 1987). Dark vergence again can be taken as the operational definition of the resting posture (compare, Owens and Leibowitz 1983), and any deviation of the actual angle of convergence should be associated with effort or costs, which we will call 'vergence costs'. In fact, with low stimulus quality (for example, Francis and Owens 1983) or impairment of the vergence control system through alcohol (for example Miller et al. 1 986), convergence tends to deviate from the angle required by the stimulus towards its resting state (dark vergence). This can be understood as resulting from a tendency to reduce vergence effort or vergence costs. Vergence costs are obviously related to observation distance which determines the actual angle of convergence. Less obviously, they are also related to the vertical direction of gaze, and in the model they are used as the conceptual link between observation distance and preferred vertical gaze direction. Heuer
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and Owens (1 987, 1989) (see also Heuer 1988, Heuer et 01. 1989) found that dark vergence drifts towards larger distances when the gaze is raised and smaller distances when the gaze is lowered. This change was observed when the eyes were raised or depressed, and to a lesser extent when the head was tilted forward or backward. The change of dark vergence with eye inclination turned out to be a reliable individual characteristic (Heuer and Owens 1989), and to be a static response which did not decline over a five-minute period with elevated or depressed eyes (Heuer et al. 1988). Thus, raising or lowering the eyes will modify vergence costs by way of modifying resting vergence.
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Figure 1. Illustration of the model and its predictions. ( a ) Eye-inclination costs c, as a function of eye inclination; (b) vergence costs cvas a function of dark vergence for a binocular stimulus at 0.5 m distance (angle of convergence: 7.2"); (c) dark vergence y~ as a function of eye inclination; (d) vergence costs cv as a function of eye inclination; (e) and U) sum of costs (upper curve) and eye-inclination costs (lower curve). Vergence cost in the sums is: (e) as shown in (d); as in (e) but for a stiinulus at 1 m distance (angle of convergence: 3.6"). For eye inclination, negative values refer to depressed eyes, and positive values to elevated eyes.
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2.2. Eye-inclination costs, vergence costs, and preferred vertical gaze direction Given the theoretical concepts of eye-inclination costs and vergence costs as well as the empirical fact that dark vergence depends on the vertical direction of gaze, it is possible to explain the relation between' observation distance and the preferred vertical direction of gaze. The basic assumption is that the preferred vertical direction of gaze is determined by the minimum of the sum of the two kinds of costs. Figure 1 illustrates the steps in the argument. Figure 1(a) presents eye-inclination costs (c,) as a function of eye inclination (T); the minimum in the example is at an eye inclination of -2.4". Figure l(b) illustrates vergence costs (c,) as a function of dark vergence (y,) for a given angle of convergence (y); in the example the angle of convergence is 7-2", corresponding to 0-5 m observation distance, and the costs are minimal for dark vergence identical to the angle of convergence. Both cost functions are plotted as U-shaped. For part of the argument, however, it is only essential that they have minima. Figure 1(c) shows the dependency of dark vergence (y,) on eye inclination (r); this actually is an empirical curve as measured for a single subject in the experiment reported below and smoothed by a polynomial. Since cv=f(yR)and y,=f(z), vergence costs can be expressed as a function of eye inclination, cv=f(r), as illustrated in figure l(d). The slope of this curve is important for testing the model. It is given by
that is, by the product of the slopes of the functions c,=f(y,) and y,=f(r). Figure 1(e) and (I) present the eye-inclination costs as the lower curve and the sum of the two kinds of costs as the upper curve. In figure I (e) the upper curve is the sum of the curves shown in figures l(a) and l(d); it has a minimum at an eye inclination of - 13.7". In figure 1(f) the upper curve was derived after shifting the curve of figure l(b) parallel to the abscissa so that the minimum was at 3.6", corresponding to an observation distance of 1 m. The minimum of the sum of the two kinds of costs is at - 5.0".Thus, with a larger observation distance of 1 m the preferred vertical direction of gaze should be higher (-5.0") than with a smaller observation distance of 0.5 rn (- 13.7"), given the particular types of functions and parameters used for the illustration. However, the predictions of the model are not limited to these.
2.3. Predictions T o test predictions of the model, the theoretical concepts have to be linked to measurements. First, the inclination of the eyes at which eye inclination costs are minimal can be estimated as the preferred vertical gaze direction in the absence of a binocular stimulus. These measurements serve as a baseline against which the effects of binocular stimuli, which drive vergence away from its resting level and add vergence costs, can be assessed. Second, the slope of vergence costs as a function of dark vergence (dcddy,) can be estimated from the difference between the actual angle of convergence and dark vergence. The slope is negative when the difference is positive, and it is positive when the difference is negative (cf. Fig. I(b)). If a U-shaped cost
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function is assumed, the absolute slope will increase monotonically with the absolute difference. Third, the slope of dark vergence as a function of eye inclination (dy,/d.t) can be measured directly as described below. From these two estimates the slope of vergence costs as a function of eye inclination (dcJdt) can be estimated according to equation (1). Finally, the inclination of the eyes at which the sum of the eye inclination costs and vergence costs is mimimal can be estimated as the preferred vertical gaze direction while viewing a binocular stimulus at a particular distance. The difference from the baseline (preferred vertical gaze direction in the absence of a binocular stimulus) represents an estimate of the contribution of vergence costs to the preferred vertical direction of gaze. It should be related to the slope of vergence costs as a function of eye inclination (dcJdr), provided that eyeinclination costs are related to eye inclination by a U-shaped curve. Given these relations, three predictions were tested in the experiment reported below. The first and most obvious prediction is that the effect of a binocular stimulus on the preferred vertical gaze direction in fact serves to reduce the discrepancy between actual convergence and the resting level, operationally defined as dark vergence. If this prediction were not confirmed, it would be hard to uphold the hypothesis that vergence costs play any role at all in the choice of the preferred vertical gaze direction. The other two predictions were concerned with individual differences, because the resting level of the vergence system can be modified experimentally only in a very limited range (see for example Heuer et a!. 1988). There are not only large and reliable individual differences with respect to the general level of dark vergence, but also with respect to the effect of eye inclination on dark vergence (Heuer and Owens 1989). The first prediction was concerned with the direction of change of the preferred vertical gaze direction at the introduction of a binocular stimulus (relative to the baseline). According to equation (1) the slope of the curve relating vergence costs to eye inclination (dcJd7) will be positive when the slopes of the curves relating vergence costs to dark vergence (dcJdy,) and dark vergence to eye inclination (dy,/d.r) are both positive or both negative, otherwise it will be negative. From figure I(d) it can be seen that a positive slope corresponds to a lower preferred vertical gaze direction when binocular stimuli are present; correspondingly a negative slope corresponds to a higher preferred vertical gaze direction relative to the base-line. Whether the slope will be positive or negative can be predicted from measurements of dark vergence, which allow one to determine the signs of the slopes dcJdyR and dy,/dz as described above. The third prediction was concerned with the size of change of the preferred vertical gaze direction on the introduction of a binocular stimulus. From equation (I) it is apparent that there should be monotonic relations between any of the two slopes on the right side and the slope of the curve relating vergence costs to eye inclination (dcjdz) on the left side, which again has a monotonic relation to the observed change of the preferred vertical gaze direction. Strictly speaking, these relations require that the second slope on the right side has a constant value. They will be noisy to the extent that this is not the case, and monotonicity breaks down when the sign of the second slope varies. (For example, a large positive dR/d7will result in a large positive dc4d.r when dcJdyR is positive, but a large negative dcJdr when dcJdyR is negative.) Further, the
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postulated monotonic relations require that the parameters of the curve relating eye-inclination costs to eye inclination are constant across subjects; additional noise will be added to the relations to the extent that there is interindividual variability with respect to these parameters. Given the two sources of noise, the best one can expect are only rather low correlations.
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3. Method 3.1, Subjects Twelve female and twelve male subjects, aged 15-33 years, took part in two experimental sessions. They were paid a fixed fee. All subjects had normal near and far visual acuity without correction (Titmus Vision Tester). One female subject was not included in the analysis because the measurements of dark vergence turned out to be too noisy. 3.2. The measurement of dark vergence Dark vergence was measured by means of a psychophysical procedure which is based on the law of identical visual directions and discussed in more detail by Heuer (1988) and Heuer arid Owens (1989). Stimuli were presented dichoptically. The right eye saw a stimulus in a fixed position, while the left eye saw a stimulus whose horizontal position was varied. Using a double-staircase procedure (Cornsweet 1962), that position of the left-eye stimulus was determined which appeared aligned with the right-eye stimulus. The display was placed 0.8 rn in front of the rotation axes of the subject's eyes (approximately 1a3 cm behind the cornea). It consisted of a horizontal row of 1 12 light-emitting diodes (LEDs) with 1 rnm diameter and centre-to centre distances of 2.5 mm. Above and below the 28th LED of the horizontal row a vertical row extended which consisted of 8 LEDs on both sides. Between the horizontal row and the upper part of the vertical row there was a 3 mm gap with the fixation light in the middle. The fixation light was the tip of a 0-5 mm diameter optic fibre with a diffusing filter, illuminated by a red LED that was invisible to the subject. The vertical row was in front of the right eye, and the horizontal row was on eye level. By means of polarizing filters (Polarex P-W 64) the venical row and the fixation point were presented to the right eye only and the horizontal row to the left eye. Each measurement began with the presentation of the monocular fixation light. After a few seconds the experimenter initiated the presentation of the LEDs. Every three seconds the vertical row and one LED from the horizontal row were flashed for 1 50 ms. The subject had to judge by way of pressing the right or Ieft of two keys whether the single LED was to the right or left of the vertical row. When a decision was impossible, the subject could omit a judgement. The single LEDs from the horizontal row were selected according to two different staircases in a random order. The one began at a randomly selected LED between positions 5 and 20, the other at a randomly selected LED between positions 30 and 45. Within each staircase the horizontal position of the single LED was shifted n steps to the right after the subject had pressed the left key and n steps to the left after a right-key press; it remained unchanged when the subject omitted a judgement. Initially n was set to 5. After the first change of the judgements it was reduced to 3 and after the second to 1. The measurement was
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finished when 10 positions had been recorded at which the judgements changed, given that n had been set to 1 before. The last 8 positions were transformed into angles of convergence, and the mean was used as the measure of dark vergence. The display used to measure dark vergence was placed on a lever that could be rotated in the sagittal plane around a horizontal axis that was approximately aligned with the rotation axes of the eyes. Biteboard and forehead rest for the subject were adjusted accordingly. Thus the vertical direction of gaze could be controlled by positioning the display in the appropriate direction. The angles used were -48, -33, - 18, -3, 17", negative angles indicating lowered gaze. Dark vergence was determined first for horizontal gaze. After this practice measurement and a five-minutes rest a series of five measurements with increasing eye inclinations was taken followed by a series of five measurements with decreasing eye inclinations. Each measurement took about two to three minutes. During the whole period of dark vergence measurements, which took a b u t half an hour, the subjects remained in darkness. Whenever a dim illumination had to be switched on to enable a new positioning of the lever, they closed their eyes.
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+
3.3. The assessment of the preferred vertical gaze direction The preferred vertical direction of gaze was assessed using the method of adjustment. The experimenter moved a stimulus from high to low or low to high in alternating sequence until the subject indicated that this was the most comfortable ('die angenehmste') position for viewing. Thereafter the experimenter moved the stimulus up and down following directions given by the subject. The final position of the display after the corrections was recorded. Thus each choice of the preferred vertical gaze direction was made with consideratipn. The preferred vertical gaze direction was assessed in a second room adjacent to the first one where dark vergence was measured. The apparatus was a stable balance designed to carry heavy displays. Again the axis of vertical rotation was approximately aligned with the axis of rotation of the subject's eyes; biteboard and forehead rest were adjusted accordingly. The angle of inclination of the balance was measured by means of a potentiometer and recorded by a computer. Three different stimuli were presented during the assessment of the preferred vertical gaze direction. The first was a red monocular stimulus presented to the left eye only (baseline). This was the tip of a 0-5 mrn diameter optic fibre placed at a distance of 1 m. According to Owens and Leibowitz (1975) such a stimulus has essentially no effect on accommodation. The two binocular stimuli were outline squares of 0.02 x 0.02 m with visible diagonals, generated by masks on back-illuminated diffusing glass. The lines were 1 mm wide, and the stimuli were placed at distances of 1 and 0.5 m. The monocular stimulus was straight-ahead of the subject, the binocular stimulus at 1 m was directly to the left of it and the 0.5 m binocular stimulus to the right. Afier three practice measurements, one with each of the three stimuli, the preferred vertical gaze direction was assessed for the monocular stimulus, the binocular 1 m stimulus and the binocular 0-5 m stimulus. The measurements were repeated with the three stimuli in the reverse order. For each stimulus two measurements were made. The first was an 'upward measurement' in which the stimulus was moved upward beginning at approximately - 50°, and the second a 'downward measurement', in which the stimulus was moved downward
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beginning at about +30°. The whole procedure took somewhat longer than half an hour. During.this time the subjects remained in darkness as during the darkvergence measurements.
3.4. Design
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The sequence of measurements was the same for all subjects. A fixed rather than a balanced sequence of measurements was chosen because this enables post hoc grouping of the subjects based on dark-vergence measurements. In the first session dark vergence was measured first, followed by the assessment of the preferred vertical gaze direction. In the second session, which was mostly on the next day and never on the same day, the order was reversed. The sequences of dark-vergence measurements in each session and of stimuli during assessment of the preferred vertical gaze direction were as described above. 4. Results and discussion Results will be reported separately for dark vergence, preferred vertical gaze direction, and the relation between the two sets of measurements. The first two sections are concerned mainly with replications and extensions of previous findings, while the final section is relevant for the model under examination.
4.1 . Dark vergence Mean dark vergence is presented in figure 2. In previous experiments, dark vergence decreased when the eyes were raised and increased when the eyes were depressed. A three-way fixed-effects analysis of variance (ANOVA) with the factors eye inclination, first (increasing) versus second (decreasing) series, and sessions indicated that this was a highly significant effect, F(4,88)=19.2, p>0.01. In addition dark vergence was smaller in the second session than in the first one, F(1,22)=6-7, p
Ergonomics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/terg20
Preferred vertical gaze direction and observation distance a
a
a
a
HERBERT HEUER , MICHAEL BRÜWER , THOMAS RÖMER , HEINZ KRÖGER & HENDRIK KNAPP
a
a
Fachbereich Psychologie der Philipps , Universität Marburg , Gutenbergstrasse 18, Marburg/Lahn, D-3550, Germany Published online: 30 May 2007.
To cite this article: HERBERT HEUER , MICHAEL BRÜWER , THOMAS RÖMER , HEINZ KRÖGER & HENDRIK KNAPP (1991) Preferred vertical gaze direction and observation distance, Ergonomics, 34:3, 379-392, DOI: 10.1080/00140139108967321 To link to this article: http://dx.doi.org/10.1080/00140139108967321
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
Preferred vertical gaze direction and observation distance HERBERT HEUER, MICHAEL BRUWER,THOMASRUMER,HEM K R ~ G E Rand HENDRIK KNAPP Fachbereich Psychologie der Philipps-Universitat Marburg, Gutenbergstrasse 18, D-3550 Marburgllahn, Germany
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K e y w o r k Vertical gaze direction; Vergence; Observation distance.
Hill and Kroemer (1986) and Kroemer and Hill (1986) found that the preferred vertical direction of gaze is lower with a nearer binocular stimulus than with a more distant one. A model is proposed that relates this phenomenon to characteristics of the resting state of the oculomotor system. Three predictions of the model were tested, based on measurements of the preferred vertical gaze direction and dark vergence in the same subject sample. On average the effect of observation distance on the preferred vertical gaze direction served to reduce the discrepancy between the resting state of vergence, operationally defined as dark vergence, and actual convergence during inspection of the binocular stimulus. Second, dark vergence data from individual subjects could be successfully used to predict whether they raised or lowered their eyes on inspection of a binocular stimulus as compared with the preferred vertical gaze direction while viewing a monocular stimulus. Finally, predictions of the size of the change of the preferred vertical gaze direction on introduction of a binocular stimulus produced only small and non-significant correlations. 1. Introduction
During visual work people prefer certain directions of gaze in the sagittal plane. T h e preferred vertical gaze direction is a n important criterion for recommendations regarding the optimal placement o f visual displays. (There appear to be terminological difficulties with the direction of gaze in the sagittal plane. Various shorter terms like inclination of gaze, declination o f line of sight, slope of regard, vertical gaze deviation, and line of sight angle have been used. There seems to be little risk that our term 'vertical gaze direction' can be misunderstood as designating a gaze direction coincident with the vertical; rather it refers to direction in a vertically-oriented plane.) However, such recommendations (for example Schmidtke 198 1, p 4 10) are less straightforward than generally thought. Hill and Kroemer (1986) and Kroemer and Hill (1986) found that the preferred vertical gaze direction depends on the observation distance, that is the distance of the display from the eyes. With the head upright they observed a preferred direction of -24.4" with an observation distance of 1 m and o f - 32.8" with a 0-5 rn.observation distance. Differences of about the same size were found with other orientations of the head and trunk. The dependency of the preferred vertical gaze direction on observation distance c a m e s important practical implications. For example, it suggests that the height o f visual displays should be adjusted to their distance, and that for displays at different heights (for example, in consoles) different distances should be used rather than only a single 'optimal' distance. However, so far the OOI&Ol39/9l 53.00 O 1991 Taylor & Francis Ltd.
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phenomenon does not really stand on firm ground. Its generality needs to be established, and it is in need of an explanation. Hill and Kroemer (1 986, p 133) hint at a possible role of different effects of gravity on the lens of the eye depending on accommodation and thus the tension of the zonula fibres. The purpose of this paper is to outline an alternative explanation and to provide a first experimental test, at the same time exploring the generality of the phenomenon. Basicafly it is modelled as resulting from certain characteristics of the resting state of the vergence system. 2. The model Two concepts are central for the model, 'eye-inclination costs' and 'vergence costs'. Both kinds of costs are assumed to be monotonically related to the discrepancy between actual eye positions and the oculomotor resting states. These concepts will be explained first, thereafter their relation to the effect of observation distance on the preferred vertical gaze direction will be outlined, and finally some testable predictions will be presented. 2.1 . Basic concepts Normally the position of the eyes is determined by the position of the fixated object. However, there is also a relatively stable eye position when no visual input to the oculomotor control systems is present. This position, which can be assessed in darkness, has been taken as a resting state from which the eyes are driven away by visual input. For the present purpose the resting state will be characterized by the vertical position of the eyes in darkness and their relative position, that is, their dark vergence. When no stimulus is present and no particular effort is made, the eyes are slightly depressed in most people (Leibowitz, Shupert, Post and Dichgans 1983). This position is the vertical resting position, and any deviation of the actual vertical gaze direction should be associated with effort or costs, which we will call 'eye-inclination costs'. Eye-inclination costs should be minimal when the eyes are in their vertical resting position, and they should reach maximum values towards extreme vertical eye positions. The latter postulate is based on the informal observation that it requires an effort to keep the eyes strongly raised or depressed (by about 30-45") for some time. When no stimulus is present and no particular effort is made, the average angle of convergence is about 3-2", corresponding to a distance of about 1.2 m (Owens and Leibowitz 1983, Owens 1987). Dark vergence again can be taken as the operational definition of the resting posture (compare, Owens and Leibowitz 1983), and any deviation of the actual angle of convergence should be associated with effort or costs, which we will call 'vergence costs'. In fact, with low stimulus quality (for example, Francis and Owens 1983) or impairment of the vergence control system through alcohol (for example Miller et al. 1 986), convergence tends to deviate from the angle required by the stimulus towards its resting state (dark vergence). This can be understood as resulting from a tendency to reduce vergence effort or vergence costs. Vergence costs are obviously related to observation distance which determines the actual angle of convergence. Less obviously, they are also related to the vertical direction of gaze, and in the model they are used as the conceptual link between observation distance and preferred vertical gaze direction. Heuer
381
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and Owens (1 987, 1989) (see also Heuer 1988, Heuer et 01. 1989) found that dark vergence drifts towards larger distances when the gaze is raised and smaller distances when the gaze is lowered. This change was observed when the eyes were raised or depressed, and to a lesser extent when the head was tilted forward or backward. The change of dark vergence with eye inclination turned out to be a reliable individual characteristic (Heuer and Owens 1989), and to be a static response which did not decline over a five-minute period with elevated or depressed eyes (Heuer et al. 1988). Thus, raising or lowering the eyes will modify vergence costs by way of modifying resting vergence.
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Figure 1. Illustration of the model and its predictions. ( a ) Eye-inclination costs c, as a function of eye inclination; (b) vergence costs cvas a function of dark vergence for a binocular stimulus at 0.5 m distance (angle of convergence: 7.2"); (c) dark vergence y~ as a function of eye inclination; (d) vergence costs cv as a function of eye inclination; (e) and U) sum of costs (upper curve) and eye-inclination costs (lower curve). Vergence cost in the sums is: (e) as shown in (d); as in (e) but for a stiinulus at 1 m distance (angle of convergence: 3.6"). For eye inclination, negative values refer to depressed eyes, and positive values to elevated eyes.
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2.2. Eye-inclination costs, vergence costs, and preferred vertical gaze direction Given the theoretical concepts of eye-inclination costs and vergence costs as well as the empirical fact that dark vergence depends on the vertical direction of gaze, it is possible to explain the relation between' observation distance and the preferred vertical direction of gaze. The basic assumption is that the preferred vertical direction of gaze is determined by the minimum of the sum of the two kinds of costs. Figure 1 illustrates the steps in the argument. Figure 1(a) presents eye-inclination costs (c,) as a function of eye inclination (T); the minimum in the example is at an eye inclination of -2.4". Figure l(b) illustrates vergence costs (c,) as a function of dark vergence (y,) for a given angle of convergence (y); in the example the angle of convergence is 7-2", corresponding to 0-5 m observation distance, and the costs are minimal for dark vergence identical to the angle of convergence. Both cost functions are plotted as U-shaped. For part of the argument, however, it is only essential that they have minima. Figure 1(c) shows the dependency of dark vergence (y,) on eye inclination (r); this actually is an empirical curve as measured for a single subject in the experiment reported below and smoothed by a polynomial. Since cv=f(yR)and y,=f(z), vergence costs can be expressed as a function of eye inclination, cv=f(r), as illustrated in figure l(d). The slope of this curve is important for testing the model. It is given by
that is, by the product of the slopes of the functions c,=f(y,) and y,=f(r). Figure 1(e) and (I) present the eye-inclination costs as the lower curve and the sum of the two kinds of costs as the upper curve. In figure I (e) the upper curve is the sum of the curves shown in figures l(a) and l(d); it has a minimum at an eye inclination of - 13.7". In figure 1(f) the upper curve was derived after shifting the curve of figure l(b) parallel to the abscissa so that the minimum was at 3.6", corresponding to an observation distance of 1 m. The minimum of the sum of the two kinds of costs is at - 5.0".Thus, with a larger observation distance of 1 m the preferred vertical direction of gaze should be higher (-5.0") than with a smaller observation distance of 0.5 rn (- 13.7"), given the particular types of functions and parameters used for the illustration. However, the predictions of the model are not limited to these.
2.3. Predictions T o test predictions of the model, the theoretical concepts have to be linked to measurements. First, the inclination of the eyes at which eye inclination costs are minimal can be estimated as the preferred vertical gaze direction in the absence of a binocular stimulus. These measurements serve as a baseline against which the effects of binocular stimuli, which drive vergence away from its resting level and add vergence costs, can be assessed. Second, the slope of vergence costs as a function of dark vergence (dcddy,) can be estimated from the difference between the actual angle of convergence and dark vergence. The slope is negative when the difference is positive, and it is positive when the difference is negative (cf. Fig. I(b)). If a U-shaped cost
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function is assumed, the absolute slope will increase monotonically with the absolute difference. Third, the slope of dark vergence as a function of eye inclination (dy,/d.t) can be measured directly as described below. From these two estimates the slope of vergence costs as a function of eye inclination (dcJdt) can be estimated according to equation (1). Finally, the inclination of the eyes at which the sum of the eye inclination costs and vergence costs is mimimal can be estimated as the preferred vertical gaze direction while viewing a binocular stimulus at a particular distance. The difference from the baseline (preferred vertical gaze direction in the absence of a binocular stimulus) represents an estimate of the contribution of vergence costs to the preferred vertical direction of gaze. It should be related to the slope of vergence costs as a function of eye inclination (dcJdr), provided that eyeinclination costs are related to eye inclination by a U-shaped curve. Given these relations, three predictions were tested in the experiment reported below. The first and most obvious prediction is that the effect of a binocular stimulus on the preferred vertical gaze direction in fact serves to reduce the discrepancy between actual convergence and the resting level, operationally defined as dark vergence. If this prediction were not confirmed, it would be hard to uphold the hypothesis that vergence costs play any role at all in the choice of the preferred vertical gaze direction. The other two predictions were concerned with individual differences, because the resting level of the vergence system can be modified experimentally only in a very limited range (see for example Heuer et a!. 1988). There are not only large and reliable individual differences with respect to the general level of dark vergence, but also with respect to the effect of eye inclination on dark vergence (Heuer and Owens 1989). The first prediction was concerned with the direction of change of the preferred vertical gaze direction at the introduction of a binocular stimulus (relative to the baseline). According to equation (1) the slope of the curve relating vergence costs to eye inclination (dcJd7) will be positive when the slopes of the curves relating vergence costs to dark vergence (dcJdy,) and dark vergence to eye inclination (dy,/d.r) are both positive or both negative, otherwise it will be negative. From figure I(d) it can be seen that a positive slope corresponds to a lower preferred vertical gaze direction when binocular stimuli are present; correspondingly a negative slope corresponds to a higher preferred vertical gaze direction relative to the base-line. Whether the slope will be positive or negative can be predicted from measurements of dark vergence, which allow one to determine the signs of the slopes dcJdyR and dy,/dz as described above. The third prediction was concerned with the size of change of the preferred vertical gaze direction on the introduction of a binocular stimulus. From equation (I) it is apparent that there should be monotonic relations between any of the two slopes on the right side and the slope of the curve relating vergence costs to eye inclination (dcjdz) on the left side, which again has a monotonic relation to the observed change of the preferred vertical gaze direction. Strictly speaking, these relations require that the second slope on the right side has a constant value. They will be noisy to the extent that this is not the case, and monotonicity breaks down when the sign of the second slope varies. (For example, a large positive dR/d7will result in a large positive dc4d.r when dcJdyR is positive, but a large negative dcJdr when dcJdyR is negative.) Further, the
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postulated monotonic relations require that the parameters of the curve relating eye-inclination costs to eye inclination are constant across subjects; additional noise will be added to the relations to the extent that there is interindividual variability with respect to these parameters. Given the two sources of noise, the best one can expect are only rather low correlations.
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3. Method 3.1, Subjects Twelve female and twelve male subjects, aged 15-33 years, took part in two experimental sessions. They were paid a fixed fee. All subjects had normal near and far visual acuity without correction (Titmus Vision Tester). One female subject was not included in the analysis because the measurements of dark vergence turned out to be too noisy. 3.2. The measurement of dark vergence Dark vergence was measured by means of a psychophysical procedure which is based on the law of identical visual directions and discussed in more detail by Heuer (1988) and Heuer arid Owens (1989). Stimuli were presented dichoptically. The right eye saw a stimulus in a fixed position, while the left eye saw a stimulus whose horizontal position was varied. Using a double-staircase procedure (Cornsweet 1962), that position of the left-eye stimulus was determined which appeared aligned with the right-eye stimulus. The display was placed 0.8 rn in front of the rotation axes of the subject's eyes (approximately 1a3 cm behind the cornea). It consisted of a horizontal row of 1 12 light-emitting diodes (LEDs) with 1 rnm diameter and centre-to centre distances of 2.5 mm. Above and below the 28th LED of the horizontal row a vertical row extended which consisted of 8 LEDs on both sides. Between the horizontal row and the upper part of the vertical row there was a 3 mm gap with the fixation light in the middle. The fixation light was the tip of a 0-5 mm diameter optic fibre with a diffusing filter, illuminated by a red LED that was invisible to the subject. The vertical row was in front of the right eye, and the horizontal row was on eye level. By means of polarizing filters (Polarex P-W 64) the venical row and the fixation point were presented to the right eye only and the horizontal row to the left eye. Each measurement began with the presentation of the monocular fixation light. After a few seconds the experimenter initiated the presentation of the LEDs. Every three seconds the vertical row and one LED from the horizontal row were flashed for 1 50 ms. The subject had to judge by way of pressing the right or Ieft of two keys whether the single LED was to the right or left of the vertical row. When a decision was impossible, the subject could omit a judgement. The single LEDs from the horizontal row were selected according to two different staircases in a random order. The one began at a randomly selected LED between positions 5 and 20, the other at a randomly selected LED between positions 30 and 45. Within each staircase the horizontal position of the single LED was shifted n steps to the right after the subject had pressed the left key and n steps to the left after a right-key press; it remained unchanged when the subject omitted a judgement. Initially n was set to 5. After the first change of the judgements it was reduced to 3 and after the second to 1. The measurement was
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finished when 10 positions had been recorded at which the judgements changed, given that n had been set to 1 before. The last 8 positions were transformed into angles of convergence, and the mean was used as the measure of dark vergence. The display used to measure dark vergence was placed on a lever that could be rotated in the sagittal plane around a horizontal axis that was approximately aligned with the rotation axes of the eyes. Biteboard and forehead rest for the subject were adjusted accordingly. Thus the vertical direction of gaze could be controlled by positioning the display in the appropriate direction. The angles used were -48, -33, - 18, -3, 17", negative angles indicating lowered gaze. Dark vergence was determined first for horizontal gaze. After this practice measurement and a five-minutes rest a series of five measurements with increasing eye inclinations was taken followed by a series of five measurements with decreasing eye inclinations. Each measurement took about two to three minutes. During the whole period of dark vergence measurements, which took a b u t half an hour, the subjects remained in darkness. Whenever a dim illumination had to be switched on to enable a new positioning of the lever, they closed their eyes.
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3.3. The assessment of the preferred vertical gaze direction The preferred vertical direction of gaze was assessed using the method of adjustment. The experimenter moved a stimulus from high to low or low to high in alternating sequence until the subject indicated that this was the most comfortable ('die angenehmste') position for viewing. Thereafter the experimenter moved the stimulus up and down following directions given by the subject. The final position of the display after the corrections was recorded. Thus each choice of the preferred vertical gaze direction was made with consideratipn. The preferred vertical gaze direction was assessed in a second room adjacent to the first one where dark vergence was measured. The apparatus was a stable balance designed to carry heavy displays. Again the axis of vertical rotation was approximately aligned with the axis of rotation of the subject's eyes; biteboard and forehead rest were adjusted accordingly. The angle of inclination of the balance was measured by means of a potentiometer and recorded by a computer. Three different stimuli were presented during the assessment of the preferred vertical gaze direction. The first was a red monocular stimulus presented to the left eye only (baseline). This was the tip of a 0-5 mrn diameter optic fibre placed at a distance of 1 m. According to Owens and Leibowitz (1975) such a stimulus has essentially no effect on accommodation. The two binocular stimuli were outline squares of 0.02 x 0.02 m with visible diagonals, generated by masks on back-illuminated diffusing glass. The lines were 1 mm wide, and the stimuli were placed at distances of 1 and 0.5 m. The monocular stimulus was straight-ahead of the subject, the binocular stimulus at 1 m was directly to the left of it and the 0.5 m binocular stimulus to the right. Afier three practice measurements, one with each of the three stimuli, the preferred vertical gaze direction was assessed for the monocular stimulus, the binocular 1 m stimulus and the binocular 0-5 m stimulus. The measurements were repeated with the three stimuli in the reverse order. For each stimulus two measurements were made. The first was an 'upward measurement' in which the stimulus was moved upward beginning at approximately - 50°, and the second a 'downward measurement', in which the stimulus was moved downward
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beginning at about +30°. The whole procedure took somewhat longer than half an hour. During.this time the subjects remained in darkness as during the darkvergence measurements.
3.4. Design
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The sequence of measurements was the same for all subjects. A fixed rather than a balanced sequence of measurements was chosen because this enables post hoc grouping of the subjects based on dark-vergence measurements. In the first session dark vergence was measured first, followed by the assessment of the preferred vertical gaze direction. In the second session, which was mostly on the next day and never on the same day, the order was reversed. The sequences of dark-vergence measurements in each session and of stimuli during assessment of the preferred vertical gaze direction were as described above. 4. Results and discussion Results will be reported separately for dark vergence, preferred vertical gaze direction, and the relation between the two sets of measurements. The first two sections are concerned mainly with replications and extensions of previous findings, while the final section is relevant for the model under examination.
4.1 . Dark vergence Mean dark vergence is presented in figure 2. In previous experiments, dark vergence decreased when the eyes were raised and increased when the eyes were depressed. A three-way fixed-effects analysis of variance (ANOVA) with the factors eye inclination, first (increasing) versus second (decreasing) series, and sessions indicated that this was a highly significant effect, F(4,88)=19.2, p>0.01. In addition dark vergence was smaller in the second session than in the first one, F(1,22)=6-7, p
