JOSA LETTERS Variability of depth-discrimination thresholds as a function of observation distance* Alfred Lit Department of Psychology, Southern Illinois University at Carbondale, Carbondale, Illinois 62901
John Patrick Finn Department of Psychology, Goucher College, Towson, Maryland 21204 (Received 29 April 1975)
Observation distance has long been known to be a critical variable in a number of visual functions other than stereoscopic acuity (see, e. g., Freeman, 1 on visual acuity; Richards, 2 on area intensity; and Harvey, 3 on CFF). The experimental results typically show that visual performance is relatively poor at very near distances and progressively improves to a final level at about 1 m. Recent work directed at determining the neural mechanisms underlying visual functions (e.g., Richards 2 and Harvey3) has suggested that, as accommodation and convergence increase, the size of the receptive field increases (but see, also, Marg and Adams4). The increase in receptive field would, in turn, lead to poorer spatial and temporal resolution. However, Cavonius and Hilz5 have shown that the spatial frequency to which the eye is most sensitive, as measured by the modulation transfer function, was not affected by changes in either accomodation or convergence. Hennessy and Richards6 have recently provided experimental confirmation of the results by Cavonius and Hilz. 5 If the modulation transfer function is related to receptive-field sizes, these data may be interpreted to mean that receptive-field size does not change as accomodation and convergence are varied. Thus, the results of studies showing variations in visual performance as target distance is varied must be accounted for in terms of other mechanisms. Controversy still exists regarding the effects of observation distance on stereoscopic acuity. Ogle,7 Jameson and Hurvich,8 and Brown, Ogle, and Reiher, 9 for example, reported that variations in observation distance (from about 40 to 200 cm) have little effect on the stereoscopic threshold settings (expressed in terms of variability of equidistance settings in sec of arc), although there is a trend toward decreasing threshold values (i. e., smaller standard deviation values for corresponding groups of equidistance settings) as observation distance is increased. Amigo10 reported that the stereoscopic threshold at 100 cm is significantly lower than that at 50 cm; a slight trend toward increasing threshold values occurred as the observation distance was increased from 100 to 200 cm. The present Letter reports unpublished data that were collected during the course of an earlier experiment (Lit and Hyman11) on the magnitude of the Pulfrich effect. This effect (Pulfrich12) involves an interesting 740
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localization error which occurs when a target that is actually moving from left to right and right to left in a frontal plane is viewed under conditions of unequal illumination in the two eyes. The oscillating target will then appear to rotate out of its plane of oscillation, in a path that locates the target nearer than it really is for one direction of stroke, and farther than it really is for the return stroke. The "near " and "far " depth displacements become noticeable at some threshold difference in binocular retinal illuminance and progressively increase as the binocular intensity difference is increased. In an earlier study (Lit and Hyman11), data were reported on the near and far depth-displacement positions of a black vertical rod which was made to oscillate, in a frontal plane, at each of six observation distances ranging from 30 to 150 cm from the observer's eyes. The oscillating target was a black vertical rod located in the observer's upper visual field. A similar rod, located in the observer's lower visual field, served as a fixation (comparison) target whose depth position in the observer's median plane could be varied by having the observer move the lower fixation rod either towards or away from his eyes. The lower end of the upper oscillating target and the upper end of the lower comparison (fixation) target were located in the observer's horizontal plane of fixation. The observer was seated in a darkroom, and viewed both rods through a pair of artificial pupils (each 2. 5 mm in diameter). The rods were seen against the background of a uniformly illuminated rectangular light box. Horizontal and vertical screening units provided a rectangular field of view (21.6° in horizontal extent and 4. 2° in vertical extent) at all observation distances. Filters of differing optical density were placed in filter boxes located in front of each eye on the outer wall of the observer's darkroom, to produce seven conditions of increasingly unequal retinal illuminances, starting from binocular equality at each of the six observation distances. The velocity of the upper oscillating target was set, at each observation distance, so as to provide a constant angular velocity (18.91° per sec) at the observer's eyes. The extent of stroke of the oscillating target at each observation distance was kept constant at 20. 5° of visual angle, and the diameters of the oscillating and fixation rods were changed with each observation distance so as to produce a constant angular width (8.7 min of arc). The present Letter reports unpublished control datafor Copyright © 1976 by the Optical Society of America
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two observers on the variability of equidistance settings for both stationary and oscillating targets observed un der equal binocular background retinal illuminance (300 trolands). In one case, the upper target was held sta tionary and laterally displaced 5.73° to the right or left of the o b s e r v e r ' s vertical median plane. The observ e r ' s task was to position the lower (fixation) target, with respect to the upper target, by the method of ad justment (using a "bracketing " procedure) until both targets appeared to lie in the same frontal plane. Five equidistance settings were made for each l a t e r a l - d i s placement position at each of the six observation d i s tances. The standard deviation of each group of equi distance settings was used to compute the stereoscopic parallax angle ηSD.
FIG. 2. Stereoscopic threshold ηSD as a function of observa tion distance for targets oscillating in frontal planes at a con stant angular velocity (18.9 deg per sec). [Unpublished data on two observers from Lit and Hyman (Ref. 11). 1
In the second case of control data, the variability of equidistance settings for oscillating targets was ob tained by having the observer adjust the position of the lower fixation target, again by use of the "bracketing " procedure, until the fixation target appeared to lie in the same frontal plane as that containing the oscillating (upper) target. Ten equidistance settings for the o s cillating target were obtained at each observation d i s tance. The standard deviation of each group of equi distance settings was used to compute the correspond ing angular magnitude of the stereoscopic parallax an gle ηSD.
The comparison data in Fig. 1(c) a r e from six observ e r s tested by Amigo 10 for targets presented in " r e a l depth" at an exposure duration of 1 s. The curves in Fig. 1(a) a r e more similar to those in Fig. 1(b) than to those in Fig. 1(c) in substantiating the general conclu sions expressed by other investigators ( e . g . , Jameson and Hurvich 8 and Schor and Flom 13 ): the stereoscopic threshold angle ηSD is relatively uninfluenced by ob servation distance, particularly for distances greater than about 1 m. However, the sharp upturn in the value of ηSD at 30 cm for the solid curve in Fig. 1(a) is to be noted.
The results on the variability of equidistance settings for stationary targets are given in Fig. 1(a) for each of the two o b s e r v e r s . The stereoscopic threshold angle ηSD, based on the average value of the standard devia tions obtained on each group of equidistance settings at the two laterally displaced target positions is plotted as a function of observation distance. For purposes of comparison, Fig. 1(b) presents data on three observers reported by Brown, Ogle, and Reiher 9 for targets p r e sented stereoscopically at short exposure durations (100 m s for two of the observers and 20 m s for the third).
When the corresponding data of Fig. 1 on the magni tude of the constant e r r o r (expressed in angular t e r m s as η∆R) were plotted as a function of observation d i s tance, the obtained curves (not presented here) exhibited no systematic effects for distances beyond about 50 cm.
FIG. 1. Stereoscopic threshold η SD (in sec of arc) as a function of observation distance (in cm), (a) Unpublished data on two observers from LitandHyman (Ref. 11). (b) Data from Brown, Ogle, and Reiher (Ref. 9). (c) Data from Amigo (Ref. 10). 741
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The data on the variability of the equidistance settings for oscillating targets are presented for each observer in Fig. 2, where the stereoscopic threshold angle ηSD is plotted as a function of observation distance. As ex pected, the variable e r r o r s in Fig. 2 a r e consistently larger than the corresponding e r r o r s for the stationarytarget condition shown in Fig. 1(a). This finding is consistent with results on stationary versus oscillating targets reported by Lit and Hamm. 1 4 The data in Fig. 2 a r e , however, less similar for the two observers than was the case in Fig. 1(a) for stationary t a r g e t s . The curve in Fig. 2 for one observer (dashed lines) shows no systematic change in ηSD throughout the total range of observation distances; the corresponding curve for the second observer (solid lines) shows a nearly progressive decrease in the values of ηSD as the ob servation distance is increased in the range from 30 cm to about 100 cm. The geometric theory of binocular space perception predicts no variations in stereoscopic threshold as a function of observation distance, either for stationary or for oscillating t a r g e t s . The new experimental data presented here for one observer (dashed lines) confirm that prediction; for the second observer (solid lines) the stereoscopic threshold remains relatively constant for observation distances greater than about 60 or 80 cm. The results thus suggest that the effects of uncon trolled factors in this experiment such as m i c r o - o s c i l lations of the eyes and inaccuracies of binocular a c JOSA Letters
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commodation and convergence have a relatively negligible deteriorating influence on depth-discrimination thresholds. The noted deterioration at very short observation distances (less than about 30 cm) should r e ceive further experimental study, particularly in t e r m s of possible variations in the cyclorotary movements of the eyes (Krekling 15 ) and in the resting state of the oculomotor adjustments under these conditions of binocular depth discrimination, as measured with the aid of the laser optometer (Leibowitz and Hennessy 16 ). * Partial support for this study was provided by a research grant (No. NIII-EY-00383) from the Eye Institute of the U. S. Public Health Service awarded to Professor Alfred Lit. E. Freeman, J. Opt. Soc. Am. 22, 285 (1932). 2 W. Richards, Neuropsychol. 5, 63 (1967). 3 L. O. Harvey, Vision Res. 10, 55 (1970).
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E. Marg and J. E. Adams, Experientia 26, 270 (1970). C. R. Cavonius and R. Hilz, J. Opt. Soc. Am. 63, 929 (1973). 6 R. T. Hennessy and W. Richards, J. Opt. Soc. Am. 65, 97 (1975). 7 K. N. Ogle, J. Opt. Soc. Am. 48, 794 (1958). 8 D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 49, 639 (1959). 9 J. P . Brown, K. N. Ogle, and L. Reiher, Invest. Ophthalmol. 4, 894 (1965). I0 G. Amigo, J. Opt. Soc. Am. 53, 630 (1963). 11 A. Lit and A. Hyman, Am. J. Optom. Monograph No. 122 (1951). 12 C. Pulfrich, Naturwiss. 10, 553 (1922); 10, 569 (1922); 10, 714 (1922); 10, 735 (1922); 10, 751 (1922). 13 C. M. Schor and M. C. Flom, Am. J. Optom. 46, 805 (1969). 14 A. Lit and H. D. Hamm, J. Opt. Soc. Am. 56, 510 (1966). 15 S. Krekling, Percept. Psychophys. 12, 461 (1972). 16 H. W. Leibowitz and R. T. Hennessy, Am. Psychol. 30, 349 (1975). 5
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John Patrick Finn Department of Psychology, Goucher College, Towson, Maryland 21204 (Received 29 April 1975)
Observation distance has long been known to be a critical variable in a number of visual functions other than stereoscopic acuity (see, e. g., Freeman, 1 on visual acuity; Richards, 2 on area intensity; and Harvey, 3 on CFF). The experimental results typically show that visual performance is relatively poor at very near distances and progressively improves to a final level at about 1 m. Recent work directed at determining the neural mechanisms underlying visual functions (e.g., Richards 2 and Harvey3) has suggested that, as accommodation and convergence increase, the size of the receptive field increases (but see, also, Marg and Adams4). The increase in receptive field would, in turn, lead to poorer spatial and temporal resolution. However, Cavonius and Hilz5 have shown that the spatial frequency to which the eye is most sensitive, as measured by the modulation transfer function, was not affected by changes in either accomodation or convergence. Hennessy and Richards6 have recently provided experimental confirmation of the results by Cavonius and Hilz. 5 If the modulation transfer function is related to receptive-field sizes, these data may be interpreted to mean that receptive-field size does not change as accomodation and convergence are varied. Thus, the results of studies showing variations in visual performance as target distance is varied must be accounted for in terms of other mechanisms. Controversy still exists regarding the effects of observation distance on stereoscopic acuity. Ogle,7 Jameson and Hurvich,8 and Brown, Ogle, and Reiher, 9 for example, reported that variations in observation distance (from about 40 to 200 cm) have little effect on the stereoscopic threshold settings (expressed in terms of variability of equidistance settings in sec of arc), although there is a trend toward decreasing threshold values (i. e., smaller standard deviation values for corresponding groups of equidistance settings) as observation distance is increased. Amigo10 reported that the stereoscopic threshold at 100 cm is significantly lower than that at 50 cm; a slight trend toward increasing threshold values occurred as the observation distance was increased from 100 to 200 cm. The present Letter reports unpublished data that were collected during the course of an earlier experiment (Lit and Hyman11) on the magnitude of the Pulfrich effect. This effect (Pulfrich12) involves an interesting 740
J.
Opt. Soc. Am., Vol. 66, No. 7, July 1976
localization error which occurs when a target that is actually moving from left to right and right to left in a frontal plane is viewed under conditions of unequal illumination in the two eyes. The oscillating target will then appear to rotate out of its plane of oscillation, in a path that locates the target nearer than it really is for one direction of stroke, and farther than it really is for the return stroke. The "near " and "far " depth displacements become noticeable at some threshold difference in binocular retinal illuminance and progressively increase as the binocular intensity difference is increased. In an earlier study (Lit and Hyman11), data were reported on the near and far depth-displacement positions of a black vertical rod which was made to oscillate, in a frontal plane, at each of six observation distances ranging from 30 to 150 cm from the observer's eyes. The oscillating target was a black vertical rod located in the observer's upper visual field. A similar rod, located in the observer's lower visual field, served as a fixation (comparison) target whose depth position in the observer's median plane could be varied by having the observer move the lower fixation rod either towards or away from his eyes. The lower end of the upper oscillating target and the upper end of the lower comparison (fixation) target were located in the observer's horizontal plane of fixation. The observer was seated in a darkroom, and viewed both rods through a pair of artificial pupils (each 2. 5 mm in diameter). The rods were seen against the background of a uniformly illuminated rectangular light box. Horizontal and vertical screening units provided a rectangular field of view (21.6° in horizontal extent and 4. 2° in vertical extent) at all observation distances. Filters of differing optical density were placed in filter boxes located in front of each eye on the outer wall of the observer's darkroom, to produce seven conditions of increasingly unequal retinal illuminances, starting from binocular equality at each of the six observation distances. The velocity of the upper oscillating target was set, at each observation distance, so as to provide a constant angular velocity (18.91° per sec) at the observer's eyes. The extent of stroke of the oscillating target at each observation distance was kept constant at 20. 5° of visual angle, and the diameters of the oscillating and fixation rods were changed with each observation distance so as to produce a constant angular width (8.7 min of arc). The present Letter reports unpublished control datafor Copyright © 1976 by the Optical Society of America
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two observers on the variability of equidistance settings for both stationary and oscillating targets observed un der equal binocular background retinal illuminance (300 trolands). In one case, the upper target was held sta tionary and laterally displaced 5.73° to the right or left of the o b s e r v e r ' s vertical median plane. The observ e r ' s task was to position the lower (fixation) target, with respect to the upper target, by the method of ad justment (using a "bracketing " procedure) until both targets appeared to lie in the same frontal plane. Five equidistance settings were made for each l a t e r a l - d i s placement position at each of the six observation d i s tances. The standard deviation of each group of equi distance settings was used to compute the stereoscopic parallax angle ηSD.
FIG. 2. Stereoscopic threshold ηSD as a function of observa tion distance for targets oscillating in frontal planes at a con stant angular velocity (18.9 deg per sec). [Unpublished data on two observers from Lit and Hyman (Ref. 11). 1
In the second case of control data, the variability of equidistance settings for oscillating targets was ob tained by having the observer adjust the position of the lower fixation target, again by use of the "bracketing " procedure, until the fixation target appeared to lie in the same frontal plane as that containing the oscillating (upper) target. Ten equidistance settings for the o s cillating target were obtained at each observation d i s tance. The standard deviation of each group of equi distance settings was used to compute the correspond ing angular magnitude of the stereoscopic parallax an gle ηSD.
The comparison data in Fig. 1(c) a r e from six observ e r s tested by Amigo 10 for targets presented in " r e a l depth" at an exposure duration of 1 s. The curves in Fig. 1(a) a r e more similar to those in Fig. 1(b) than to those in Fig. 1(c) in substantiating the general conclu sions expressed by other investigators ( e . g . , Jameson and Hurvich 8 and Schor and Flom 13 ): the stereoscopic threshold angle ηSD is relatively uninfluenced by ob servation distance, particularly for distances greater than about 1 m. However, the sharp upturn in the value of ηSD at 30 cm for the solid curve in Fig. 1(a) is to be noted.
The results on the variability of equidistance settings for stationary targets are given in Fig. 1(a) for each of the two o b s e r v e r s . The stereoscopic threshold angle ηSD, based on the average value of the standard devia tions obtained on each group of equidistance settings at the two laterally displaced target positions is plotted as a function of observation distance. For purposes of comparison, Fig. 1(b) presents data on three observers reported by Brown, Ogle, and Reiher 9 for targets p r e sented stereoscopically at short exposure durations (100 m s for two of the observers and 20 m s for the third).
When the corresponding data of Fig. 1 on the magni tude of the constant e r r o r (expressed in angular t e r m s as η∆R) were plotted as a function of observation d i s tance, the obtained curves (not presented here) exhibited no systematic effects for distances beyond about 50 cm.
FIG. 1. Stereoscopic threshold η SD (in sec of arc) as a function of observation distance (in cm), (a) Unpublished data on two observers from LitandHyman (Ref. 11). (b) Data from Brown, Ogle, and Reiher (Ref. 9). (c) Data from Amigo (Ref. 10). 741
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The data on the variability of the equidistance settings for oscillating targets are presented for each observer in Fig. 2, where the stereoscopic threshold angle ηSD is plotted as a function of observation distance. As ex pected, the variable e r r o r s in Fig. 2 a r e consistently larger than the corresponding e r r o r s for the stationarytarget condition shown in Fig. 1(a). This finding is consistent with results on stationary versus oscillating targets reported by Lit and Hamm. 1 4 The data in Fig. 2 a r e , however, less similar for the two observers than was the case in Fig. 1(a) for stationary t a r g e t s . The curve in Fig. 2 for one observer (dashed lines) shows no systematic change in ηSD throughout the total range of observation distances; the corresponding curve for the second observer (solid lines) shows a nearly progressive decrease in the values of ηSD as the ob servation distance is increased in the range from 30 cm to about 100 cm. The geometric theory of binocular space perception predicts no variations in stereoscopic threshold as a function of observation distance, either for stationary or for oscillating t a r g e t s . The new experimental data presented here for one observer (dashed lines) confirm that prediction; for the second observer (solid lines) the stereoscopic threshold remains relatively constant for observation distances greater than about 60 or 80 cm. The results thus suggest that the effects of uncon trolled factors in this experiment such as m i c r o - o s c i l lations of the eyes and inaccuracies of binocular a c JOSA Letters
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commodation and convergence have a relatively negligible deteriorating influence on depth-discrimination thresholds. The noted deterioration at very short observation distances (less than about 30 cm) should r e ceive further experimental study, particularly in t e r m s of possible variations in the cyclorotary movements of the eyes (Krekling 15 ) and in the resting state of the oculomotor adjustments under these conditions of binocular depth discrimination, as measured with the aid of the laser optometer (Leibowitz and Hennessy 16 ). * Partial support for this study was provided by a research grant (No. NIII-EY-00383) from the Eye Institute of the U. S. Public Health Service awarded to Professor Alfred Lit. E. Freeman, J. Opt. Soc. Am. 22, 285 (1932). 2 W. Richards, Neuropsychol. 5, 63 (1967). 3 L. O. Harvey, Vision Res. 10, 55 (1970).
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E. Marg and J. E. Adams, Experientia 26, 270 (1970). C. R. Cavonius and R. Hilz, J. Opt. Soc. Am. 63, 929 (1973). 6 R. T. Hennessy and W. Richards, J. Opt. Soc. Am. 65, 97 (1975). 7 K. N. Ogle, J. Opt. Soc. Am. 48, 794 (1958). 8 D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 49, 639 (1959). 9 J. P . Brown, K. N. Ogle, and L. Reiher, Invest. Ophthalmol. 4, 894 (1965). I0 G. Amigo, J. Opt. Soc. Am. 53, 630 (1963). 11 A. Lit and A. Hyman, Am. J. Optom. Monograph No. 122 (1951). 12 C. Pulfrich, Naturwiss. 10, 553 (1922); 10, 569 (1922); 10, 714 (1922); 10, 735 (1922); 10, 751 (1922). 13 C. M. Schor and M. C. Flom, Am. J. Optom. 46, 805 (1969). 14 A. Lit and H. D. Hamm, J. Opt. Soc. Am. 56, 510 (1966). 15 S. Krekling, Percept. Psychophys. 12, 461 (1972). 16 H. W. Leibowitz and R. T. Hennessy, Am. Psychol. 30, 349 (1975). 5
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