Pupil size and stereoacuity S. M. Luria Naval Submarine Medical Research Laboratory, Groton, Connecticut 06340 (Received 7 June 1975)
Stereoacuity and visual acuity a r e affected similarly by a wide variety of variables, such as luminance, 1 wavelength, 2 contrast, 3 retinal locus, 4 target movement, 5 ocular pursuit of a moving test object, 6 and observation distance 7 —the latter has been shown in both cases to be artif actual. 8 But not all variables affect them similarly. The introduction of apertures or lenses between the observer and the test object, for example, has a different effect on the two p r o c e s s e s . 9 One comparison that does not appear to have been made is the effect of pupil size. Both Cobb10 and Lei157
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bowitz 11 have shown that as pupil size increases, visual acuity typically improves up to a point and then d e clines as pupil diameter further i n c r e a s e s . The poor acuity with small pupil diameters is due to diffraction, and the decline in acuity with a pupil diameter of more than 5 mm is thought to be caused by spherical a b e r r a tions. 11, 12 Consequently, it has been suggested that the main result of the changes in pupil size is not the control of the amount of light entering the eye but the p r o duction of the optimal depth of focus and the maximization of visual acuity. 1 3 Since stereoacuity is often related to visual acuity Copyright © 1976 by the Optical Society of America
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and depends on those factors which affect visual acuity, 1 4 the question a r i s e s as to how changes in pupil size affect stereoacuity. I measured stereoacuity with a three-rod HowardDolman apparatus. The subject saw the middle portion of three vertical, black rods (1.57 cm thick and 7.6 cm apart) through an aperture 1.2° high by 3. 5° wide. The two outer rods were fixed in position 6 m from the subject in a line parallel to the aperture, which was 5.75 m from the subject. The middle rod was movable. The specific measure of stereoacuity was the variability of the setting which the subject made when he judged the middle rod to be the same distance from him as the two outer rods. F i r s t I determined the settings of the middle rod which the subject reported as either farther from him or n e a r e r to him than the outer rods about 90% of the time. I then measured the localization e r r o r of the equidistant setting by the method of constant stimuli. I set the middle rod at various positions r a n domly and asked the subject to report whether each s e t ting was closer or farther than the two outer r o d s . There were five to seven settings, equally separated, during each determination, depending on the subject's initial performance. Typically, the settings were 4.5 sec arc apart, but I also used separations of 2.25 and 9 sec arc for subjects who were more or less sensitive. I presented each setting an equal number of times (at least five and as many as ten times). Thus a threshold determination was based on from 25 to 50 judgments, depending on the subject's consistency. I plotted a f r e -
quency-of-seeing curve (percentage of "farther" judgments versus the absolute difference in distances of the test and reference rods) on cumulative probability paper and read the standard deviation of the equidistance setting from the plot. The subject sat with his head in a chin rest and viewed the apparatus through artificial pupils (1. 6, 3.2, 4.0, and 6.0 mm diam.) cut in black aluminum disks and worn in precision trial frames, as close to the cornea as possible. If the artificial pupils are too far from the eyes, they will act more as a field stop than a pupil. If they are adequately close to the eyes, then the change in diameter will have little effect on the visual angle of the field seen by the subject. In an attempt to check on this point, I measured the visual angle of the field visible through the various pupils. Although the pupil diameter varied by a factor of nearly four, the extent of the visual field was only about 4° larger through the largest pupil than through the smallest in a total field of 30°. The subject wore the various sizes in counterbalanced order during the session. The subject equated the brightnesses of the background seen through the various pupil sizes by haploscopic matching. He first equated a second white field of the same apparent size as the background (but positioned 1 m from him) to the background while wearing the smallest artificial pupils. This set the level of the maximum luminance of the background in the apparatus at about 13 fL. Then I varied the luminance of the ap-
FIG. 1. Mean variability, (standard deviation of angular stereoscopic disparity) of equidistance settings as a function of pupil diameter for all subjects (open circles) and for the five subjects whose natural pupil diameter exceeded 6.0 mm (filled circles) under the highest experimental luminance. 158
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paratus background, as seen through the largest pupil by the right eye, until the subject reported that it matched the second field viewed through each of the smaller pupils by the left eye. Ten emmetropes who had had extensive practice in making the required judgments through artificial pupils served as subjects. After the experiment was over, I measured the diam eters of the subjects' natual pupils from photographs taken while they were viewing the apparatus at its high est luminance. Five subjects had pupil diameters ex ceeding 6.0 mm. All had pupil diameters exceeding 4.0 mm. Figure 1 shows the variability of the equidistance settings (ησ) with the various pupil s i z e s . The mean results of all 10 subjects are shown for the three smallest artificial pupil diameters. The mean vari ability decreased as pupil diameter increased. The mean results for the five subjects whose natural pupil diameter exceeded 6.0 mm are shown separately for all four artificial pupil sizes. Again, variability de creased as pupil diameter increased from 1.6 to 4.0 mm, but there was an increase in variability with a further increase to 6.0 mm. It may be noted that essentially the same curve was obtained when the luminances were equated as if for a Maxwellian view 15 despite the fact that the subjects now reported that the background was much brighter through the smaller pupil sizes. It is clear that stereoacuity is affected by pupil diam eter. These results are similar to those that Leibowitz 11 reported for visual acuity and suggest that both spherical aberrrations (with larger pupil diameter) and
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diffraction (with a small pupil) interfere with stereoacuity as they do with visual acuity. 1
Compare S. Shlaer, J. Gen. Physiol. 21, 165 (1937) and C. G. Mueller and V. V. Lloyd, Proc. Nat. Acad. Sci. 34, 223 (1948). 2 S. Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553 (1942); R. H. Young and A. Lit, Percep. Psychophys. 11, 213 (1972). 3 C. D. Hendley, J. Gen. Physiol. 31, 433 (1948); A. Lit, J. P. Finn, and W. M. Vicars, Vision Res. 12, 1241 (1972). 4 J. Mandelbaum and L. L. Sloan, Am. J. Ophthal. 31, 581 (1947); K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, Pa., 1950). 5 A. Burg and S. F. Hulbert, J. Appl. Psychol. 45, 111 (1961); A. Lit, Am. J. Optom. 43, 283 (1966). 6 E. Ludvigh and J. W. Miller, J. Opt. Soc. Am. 48, 799 (1958); S. M. Luria and S. Weissman, J. Exp. Psychol. 76, 51 (1968). 7 W. H. Teichner, S. L. Kobrick, and R. F. Wehrkamp, Am. J. Psychol. 68, 193 (1955); E. Freeman, J. Opt. Soc. Am. 22, 285 (1932). 8 H. R. Blackwell. -T- Ont. Son. Am. 38. 1097 (1948); K. N. Ogle, ibid. 48, 794 (1958). 9 S. M. Luria and J. A. S. Kinney, Percep. Psychophys. 13, 76 (1973). 10 P. W. Cobb, Am. J. Physiol. 36, 355 (1915). 11 H. Leibowitz, J. Opt. Soc. Am. 42, 416 (1952). 12 J. Krauskopf, J. Opt. Soc. Am. 52, 1046 (1962); G. Westheimer and F. W. Campbell, ibid. 52, 1040 (1962). 1040 (1962). 13 F. W. Campbell and A. H. Gregory, Nature 187, 1121 (1960); F. W. Campbell and D. G. Green, J. Physiol. London 181, 576 (1965). 14 K. N. Ogle, Ref. 4. 15 Although an analysis of variance showed these means to be significantly different (F = 4.89, df = 3/12, p< .05), the rise in variability when the pupil diameter was increased to 6.0 mm was not significant, according to the Tukey (a) test. But only one of the five subjects showed less variability with the 6.0 than with the 4.0 mm pupil.
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Stereoacuity and visual acuity a r e affected similarly by a wide variety of variables, such as luminance, 1 wavelength, 2 contrast, 3 retinal locus, 4 target movement, 5 ocular pursuit of a moving test object, 6 and observation distance 7 —the latter has been shown in both cases to be artif actual. 8 But not all variables affect them similarly. The introduction of apertures or lenses between the observer and the test object, for example, has a different effect on the two p r o c e s s e s . 9 One comparison that does not appear to have been made is the effect of pupil size. Both Cobb10 and Lei157
J. Opt. Soc. Am., Vol. 66, No. 2, February 1976
bowitz 11 have shown that as pupil size increases, visual acuity typically improves up to a point and then d e clines as pupil diameter further i n c r e a s e s . The poor acuity with small pupil diameters is due to diffraction, and the decline in acuity with a pupil diameter of more than 5 mm is thought to be caused by spherical a b e r r a tions. 11, 12 Consequently, it has been suggested that the main result of the changes in pupil size is not the control of the amount of light entering the eye but the p r o duction of the optimal depth of focus and the maximization of visual acuity. 1 3 Since stereoacuity is often related to visual acuity Copyright © 1976 by the Optical Society of America
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and depends on those factors which affect visual acuity, 1 4 the question a r i s e s as to how changes in pupil size affect stereoacuity. I measured stereoacuity with a three-rod HowardDolman apparatus. The subject saw the middle portion of three vertical, black rods (1.57 cm thick and 7.6 cm apart) through an aperture 1.2° high by 3. 5° wide. The two outer rods were fixed in position 6 m from the subject in a line parallel to the aperture, which was 5.75 m from the subject. The middle rod was movable. The specific measure of stereoacuity was the variability of the setting which the subject made when he judged the middle rod to be the same distance from him as the two outer rods. F i r s t I determined the settings of the middle rod which the subject reported as either farther from him or n e a r e r to him than the outer rods about 90% of the time. I then measured the localization e r r o r of the equidistant setting by the method of constant stimuli. I set the middle rod at various positions r a n domly and asked the subject to report whether each s e t ting was closer or farther than the two outer r o d s . There were five to seven settings, equally separated, during each determination, depending on the subject's initial performance. Typically, the settings were 4.5 sec arc apart, but I also used separations of 2.25 and 9 sec arc for subjects who were more or less sensitive. I presented each setting an equal number of times (at least five and as many as ten times). Thus a threshold determination was based on from 25 to 50 judgments, depending on the subject's consistency. I plotted a f r e -
quency-of-seeing curve (percentage of "farther" judgments versus the absolute difference in distances of the test and reference rods) on cumulative probability paper and read the standard deviation of the equidistance setting from the plot. The subject sat with his head in a chin rest and viewed the apparatus through artificial pupils (1. 6, 3.2, 4.0, and 6.0 mm diam.) cut in black aluminum disks and worn in precision trial frames, as close to the cornea as possible. If the artificial pupils are too far from the eyes, they will act more as a field stop than a pupil. If they are adequately close to the eyes, then the change in diameter will have little effect on the visual angle of the field seen by the subject. In an attempt to check on this point, I measured the visual angle of the field visible through the various pupils. Although the pupil diameter varied by a factor of nearly four, the extent of the visual field was only about 4° larger through the largest pupil than through the smallest in a total field of 30°. The subject wore the various sizes in counterbalanced order during the session. The subject equated the brightnesses of the background seen through the various pupil sizes by haploscopic matching. He first equated a second white field of the same apparent size as the background (but positioned 1 m from him) to the background while wearing the smallest artificial pupils. This set the level of the maximum luminance of the background in the apparatus at about 13 fL. Then I varied the luminance of the ap-
FIG. 1. Mean variability, (standard deviation of angular stereoscopic disparity) of equidistance settings as a function of pupil diameter for all subjects (open circles) and for the five subjects whose natural pupil diameter exceeded 6.0 mm (filled circles) under the highest experimental luminance. 158
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paratus background, as seen through the largest pupil by the right eye, until the subject reported that it matched the second field viewed through each of the smaller pupils by the left eye. Ten emmetropes who had had extensive practice in making the required judgments through artificial pupils served as subjects. After the experiment was over, I measured the diam eters of the subjects' natual pupils from photographs taken while they were viewing the apparatus at its high est luminance. Five subjects had pupil diameters ex ceeding 6.0 mm. All had pupil diameters exceeding 4.0 mm. Figure 1 shows the variability of the equidistance settings (ησ) with the various pupil s i z e s . The mean results of all 10 subjects are shown for the three smallest artificial pupil diameters. The mean vari ability decreased as pupil diameter increased. The mean results for the five subjects whose natural pupil diameter exceeded 6.0 mm are shown separately for all four artificial pupil sizes. Again, variability de creased as pupil diameter increased from 1.6 to 4.0 mm, but there was an increase in variability with a further increase to 6.0 mm. It may be noted that essentially the same curve was obtained when the luminances were equated as if for a Maxwellian view 15 despite the fact that the subjects now reported that the background was much brighter through the smaller pupil sizes. It is clear that stereoacuity is affected by pupil diam eter. These results are similar to those that Leibowitz 11 reported for visual acuity and suggest that both spherical aberrrations (with larger pupil diameter) and
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diffraction (with a small pupil) interfere with stereoacuity as they do with visual acuity. 1
Compare S. Shlaer, J. Gen. Physiol. 21, 165 (1937) and C. G. Mueller and V. V. Lloyd, Proc. Nat. Acad. Sci. 34, 223 (1948). 2 S. Shlaer, E. L. Smith, and A. M. Chase, J. Gen. Physiol. 25, 553 (1942); R. H. Young and A. Lit, Percep. Psychophys. 11, 213 (1972). 3 C. D. Hendley, J. Gen. Physiol. 31, 433 (1948); A. Lit, J. P. Finn, and W. M. Vicars, Vision Res. 12, 1241 (1972). 4 J. Mandelbaum and L. L. Sloan, Am. J. Ophthal. 31, 581 (1947); K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, Pa., 1950). 5 A. Burg and S. F. Hulbert, J. Appl. Psychol. 45, 111 (1961); A. Lit, Am. J. Optom. 43, 283 (1966). 6 E. Ludvigh and J. W. Miller, J. Opt. Soc. Am. 48, 799 (1958); S. M. Luria and S. Weissman, J. Exp. Psychol. 76, 51 (1968). 7 W. H. Teichner, S. L. Kobrick, and R. F. Wehrkamp, Am. J. Psychol. 68, 193 (1955); E. Freeman, J. Opt. Soc. Am. 22, 285 (1932). 8 H. R. Blackwell. -T- Ont. Son. Am. 38. 1097 (1948); K. N. Ogle, ibid. 48, 794 (1958). 9 S. M. Luria and J. A. S. Kinney, Percep. Psychophys. 13, 76 (1973). 10 P. W. Cobb, Am. J. Physiol. 36, 355 (1915). 11 H. Leibowitz, J. Opt. Soc. Am. 42, 416 (1952). 12 J. Krauskopf, J. Opt. Soc. Am. 52, 1046 (1962); G. Westheimer and F. W. Campbell, ibid. 52, 1040 (1962). 1040 (1962). 13 F. W. Campbell and A. H. Gregory, Nature 187, 1121 (1960); F. W. Campbell and D. G. Green, J. Physiol. London 181, 576 (1965). 14 K. N. Ogle, Ref. 4. 15 Although an analysis of variance showed these means to be significantly different (F = 4.89, df = 3/12, p< .05), the rise in variability when the pupil diameter was increased to 6.0 mm was not significant, according to the Tukey (a) test. But only one of the five subjects showed less variability with the 6.0 than with the 4.0 mm pupil.
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