JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
VOLUME 65, NUMBER 3
MARCH 1975
Chromostereopsis with small pupils* D. A. Owens and H. W. Leibowitz Pennsylvania State University, University Park, Pennsylvania 16802 (Received 15 October 1974) Index Headings: Vision; Dispersion.
Vos 1 analyzed the phenomenon of chromostereopsis, the difference of the apparent depth of coplanar colored s t i m uli, in t e r m s of two opposing effects. The f i r s t fol lows from the divergence between the optic and the vi sual axes, i. e . , the angle α. Because the fovea typi cally lies on the temporal side of the optical axis, the visual and optical axes do not coincide. This d i s c r e p ancy r e s u l t s in differential dispersion of light as a func tion of wavelength; the s h o r t e r wavelengths a r e refract ed to relatively nasal locations on the retina, compared with longer wavelengths. Thus, equidistant red and blue stimuli can be expected to stimulate noncorresponding points, such that the red stimulus appears n e a r e r than the blue. Vos attributes this explanation to Bruecke and, l a t e r , Einthoven. Vos points out that (1) with the natural pupil, the ob served magnitude of chromostereopsis is considerably l e s s than would be predicted on the b a s i s of the differ ence between the optical and the visual axes, and (2) some o b s e r v e r s r e p o r t a r e v e r s a l of the expected effect; for them, blue a p p e a r s n e a r e r than red, which suggests that the Bruecke-Einthoven explanation alone is not adequate for c h r o m o s t e r e o p s i s . Vos proposed that the Stiles-Crawford effect may resolve these apparently contradictory data. He suggested that the decentration of the effective optical axis of the eye, which r e s u l t s from the orientation of the foveal cones in relation to the pupil, tends to counteract the effects of dispersion of light on the retina, by reducing the sensitivity to the light r a y s that enter along the physical axis. That i s , because of their orientation, the cones a r e most s e n s i tive to light that e n t e r s the eye along an axis that lies on the opposite side of the visual axis from the optical axis. There a r e individual differences of the magnitudes of both the angle α and the decentration of the pupil. Also, because the effective magnitude of the S t i l e s Crawford effect is determined by the size of the natural pupil, which v a r i e s in s i z e , it is not s u r p r i s i n g that r e p o r t s of the magnitude and even the direction of c h r o m o s t e r e o p s i s vary among different e x p e r i m e n t e r s . It follows from V o s ' s explanation that observations made under conditions in which the Stiles-Crawford ef fect is minimized will r e s u l t in the unopposed manifesta tion of the role of the angle α. He has reported such data for a study in which subjects adjusted r e d and blue vertical lines to appear equidistant while they viewed the stimuli through two stenopaeic a p e r t u r e s , which w e r e adjusted to simulate various interpupillary distances (narrow-beam s t e r e o s c o p y . ) His data agree well with predicted values based on the calculated retinal light dispersions. We have confirmed V o s ' s observations, utilizing red 358
(Kodak Wratten filter #29, dom λ = 632.7 nm) and blue (Wratten #47, dom λ = 470 nm) vertical slits subtending 2. 5 by 12. 5 min of a r c at a viewing distance of 2. 5 m. The photopic luminance of both stimuli was 74. 3 m L . The subjects wore a precision t r i a l frame in which blanks that provided 1. 0 or 2. 0 mm artificial pupils w e r e in s e r t e d in the normal manner. The pupils w e r e dilated by administration of two drops of 10% neosynephrine to each eye to p e r m i t a wide range of interpupillary adjust ment. This dosage had no appreciable effect on the amplitude or the resting focus of accommodation, as determined by a l a s e r optometer. The subjects' task was to r e p o r t at what point the red and blue slits appeared to be equidistant, while the ex p e r i m e n t e r moved the left-hand side, variable stimulus toward the right-hand side, standard stimulus in depth. F o r half of the t r i a l s , red was the variable stimulus,: for half, blue was variable. Half of the t r i a l s w e r e be gun with the variable stimulus at a clearly n e a r e r and half at a clearly f a r t h e r position. The l a t e r a l s e p a r a tion of the stimuli remained constant at 3. 6 degrees of a r c for all depth d i s p a r i t i e s . Order of presentation was counter-balanced for color, starting positions, and in terpupillary distance. F i g u r e 1 i l l u s t r a t e s the settings at which the variable stimulus appeared to be equidistant to the standard s t i m ulus, which was always at 2. 5 m, as a function of interpupillary distance. Angular disparity is given on the left ordinate and linear disparity (calculated from the angular values, assuming a 65 mm interpupillary
FIG. 1. Physical disparity between apparently equidistant red and blue stimuli as a function of relative interpupillary dis tance. Positive angular values indicate that the red stimulus was set nearer to appear equidistant with the blue. Zero on the abscissa represents the subject's natural IP distance.
Mar. 1975
L E T T E R S TO THE
TABLE I. Slopes and intercepts of functions illustrated in Fig. 1. The slope values indicate the change of retinal disparity (in min. of arc) for a 1 mm change and IP distance. The intercepts give the retinal disparity for the natural IP distance.
distance) on the right ordinate. Positive angular (or negative linear) values indicate that, in order to appear equidistant, the red stimulus was positioned nearer than the blue stimulus. The reference, or natural, interpupillary distance (0 on the graph) was determined optically with a Titmus P-D Scope. Linear functions were fitted to the data by the method of averages. In all cases, the data are described closely by functions with a negative slope. This is in accord with the fact that when the stimuli were physically equidistant, the red stimulus appeared farther than the blue for narrow interpupillary distances, and nearer than the blue for the natural and wide interpupillary distances. This finding is consistent with Vos's hypothesis. In accordance with Vos's observations, the magnitude of the chromostereopsis effect is large. The slopes and intercepts of the functions illustrated in Fig. 1 are presented in Table I. The slope values represent the change of retinal disparity produced by a 1 mm change of interpupillary distance. Mean changes of 3. 0 and
EDITOR
359
2. 7 min of arc per mm were obtained for the 1 mm and 2 mm pupils, respectively. That a somewhat greater slope was obtained for the 1 mm pupil is consistent qualitatively with the greater influence of the StilesCrawford effect with increased pupil size hypothesized by Vos. Also consistent with most previous findings, the intercept values show that, with physically equidistant stimuli and the natural IP distance, all subjects would judge the red stimulus to be nearer. Differences between the intercepts for the 1 and 2 mm pupils are probably not reliable, because they were measured during different experimental sessions and, thus, may be affected by slight differences of position of the trial frames. Because all interpupillary distances for a given pupil size were tested without removing the frames, this problem does not apply to the slopes. The magnitude of the chromostereopsis effect is particularly relevant to the use of binocular instruments, such as microscopes, which typically have small exit pupils. Under such conditions, the size of the illusory depth effect that results from chromostereopsis not only represents a strikingly large error, but also can be expected to vary with slight changes of the interpupillarydistance settings of the instrument. This represents a very real problem for optical-instrument design, because (1) small variations of interpupillary distance result in large changes of chromostereopsis, and (2) few presently available instruments make provision for accurate setting of interpupillary distance. *Supported by grant MH08061 from the National Institute of Mental Health, The assistance of Professor Jay Enoch and Hope Green is gratefully acknowledged. 1 J. J. Vos, J. Opt. Soc. Am. 50, 785 (1960).
VOLUME 65, NUMBER 3
MARCH 1975
Chromostereopsis with small pupils* D. A. Owens and H. W. Leibowitz Pennsylvania State University, University Park, Pennsylvania 16802 (Received 15 October 1974) Index Headings: Vision; Dispersion.
Vos 1 analyzed the phenomenon of chromostereopsis, the difference of the apparent depth of coplanar colored s t i m uli, in t e r m s of two opposing effects. The f i r s t fol lows from the divergence between the optic and the vi sual axes, i. e . , the angle α. Because the fovea typi cally lies on the temporal side of the optical axis, the visual and optical axes do not coincide. This d i s c r e p ancy r e s u l t s in differential dispersion of light as a func tion of wavelength; the s h o r t e r wavelengths a r e refract ed to relatively nasal locations on the retina, compared with longer wavelengths. Thus, equidistant red and blue stimuli can be expected to stimulate noncorresponding points, such that the red stimulus appears n e a r e r than the blue. Vos attributes this explanation to Bruecke and, l a t e r , Einthoven. Vos points out that (1) with the natural pupil, the ob served magnitude of chromostereopsis is considerably l e s s than would be predicted on the b a s i s of the differ ence between the optical and the visual axes, and (2) some o b s e r v e r s r e p o r t a r e v e r s a l of the expected effect; for them, blue a p p e a r s n e a r e r than red, which suggests that the Bruecke-Einthoven explanation alone is not adequate for c h r o m o s t e r e o p s i s . Vos proposed that the Stiles-Crawford effect may resolve these apparently contradictory data. He suggested that the decentration of the effective optical axis of the eye, which r e s u l t s from the orientation of the foveal cones in relation to the pupil, tends to counteract the effects of dispersion of light on the retina, by reducing the sensitivity to the light r a y s that enter along the physical axis. That i s , because of their orientation, the cones a r e most s e n s i tive to light that e n t e r s the eye along an axis that lies on the opposite side of the visual axis from the optical axis. There a r e individual differences of the magnitudes of both the angle α and the decentration of the pupil. Also, because the effective magnitude of the S t i l e s Crawford effect is determined by the size of the natural pupil, which v a r i e s in s i z e , it is not s u r p r i s i n g that r e p o r t s of the magnitude and even the direction of c h r o m o s t e r e o p s i s vary among different e x p e r i m e n t e r s . It follows from V o s ' s explanation that observations made under conditions in which the Stiles-Crawford ef fect is minimized will r e s u l t in the unopposed manifesta tion of the role of the angle α. He has reported such data for a study in which subjects adjusted r e d and blue vertical lines to appear equidistant while they viewed the stimuli through two stenopaeic a p e r t u r e s , which w e r e adjusted to simulate various interpupillary distances (narrow-beam s t e r e o s c o p y . ) His data agree well with predicted values based on the calculated retinal light dispersions. We have confirmed V o s ' s observations, utilizing red 358
(Kodak Wratten filter #29, dom λ = 632.7 nm) and blue (Wratten #47, dom λ = 470 nm) vertical slits subtending 2. 5 by 12. 5 min of a r c at a viewing distance of 2. 5 m. The photopic luminance of both stimuli was 74. 3 m L . The subjects wore a precision t r i a l frame in which blanks that provided 1. 0 or 2. 0 mm artificial pupils w e r e in s e r t e d in the normal manner. The pupils w e r e dilated by administration of two drops of 10% neosynephrine to each eye to p e r m i t a wide range of interpupillary adjust ment. This dosage had no appreciable effect on the amplitude or the resting focus of accommodation, as determined by a l a s e r optometer. The subjects' task was to r e p o r t at what point the red and blue slits appeared to be equidistant, while the ex p e r i m e n t e r moved the left-hand side, variable stimulus toward the right-hand side, standard stimulus in depth. F o r half of the t r i a l s , red was the variable stimulus,: for half, blue was variable. Half of the t r i a l s w e r e be gun with the variable stimulus at a clearly n e a r e r and half at a clearly f a r t h e r position. The l a t e r a l s e p a r a tion of the stimuli remained constant at 3. 6 degrees of a r c for all depth d i s p a r i t i e s . Order of presentation was counter-balanced for color, starting positions, and in terpupillary distance. F i g u r e 1 i l l u s t r a t e s the settings at which the variable stimulus appeared to be equidistant to the standard s t i m ulus, which was always at 2. 5 m, as a function of interpupillary distance. Angular disparity is given on the left ordinate and linear disparity (calculated from the angular values, assuming a 65 mm interpupillary
FIG. 1. Physical disparity between apparently equidistant red and blue stimuli as a function of relative interpupillary dis tance. Positive angular values indicate that the red stimulus was set nearer to appear equidistant with the blue. Zero on the abscissa represents the subject's natural IP distance.
Mar. 1975
L E T T E R S TO THE
TABLE I. Slopes and intercepts of functions illustrated in Fig. 1. The slope values indicate the change of retinal disparity (in min. of arc) for a 1 mm change and IP distance. The intercepts give the retinal disparity for the natural IP distance.
distance) on the right ordinate. Positive angular (or negative linear) values indicate that, in order to appear equidistant, the red stimulus was positioned nearer than the blue stimulus. The reference, or natural, interpupillary distance (0 on the graph) was determined optically with a Titmus P-D Scope. Linear functions were fitted to the data by the method of averages. In all cases, the data are described closely by functions with a negative slope. This is in accord with the fact that when the stimuli were physically equidistant, the red stimulus appeared farther than the blue for narrow interpupillary distances, and nearer than the blue for the natural and wide interpupillary distances. This finding is consistent with Vos's hypothesis. In accordance with Vos's observations, the magnitude of the chromostereopsis effect is large. The slopes and intercepts of the functions illustrated in Fig. 1 are presented in Table I. The slope values represent the change of retinal disparity produced by a 1 mm change of interpupillary distance. Mean changes of 3. 0 and
EDITOR
359
2. 7 min of arc per mm were obtained for the 1 mm and 2 mm pupils, respectively. That a somewhat greater slope was obtained for the 1 mm pupil is consistent qualitatively with the greater influence of the StilesCrawford effect with increased pupil size hypothesized by Vos. Also consistent with most previous findings, the intercept values show that, with physically equidistant stimuli and the natural IP distance, all subjects would judge the red stimulus to be nearer. Differences between the intercepts for the 1 and 2 mm pupils are probably not reliable, because they were measured during different experimental sessions and, thus, may be affected by slight differences of position of the trial frames. Because all interpupillary distances for a given pupil size were tested without removing the frames, this problem does not apply to the slopes. The magnitude of the chromostereopsis effect is particularly relevant to the use of binocular instruments, such as microscopes, which typically have small exit pupils. Under such conditions, the size of the illusory depth effect that results from chromostereopsis not only represents a strikingly large error, but also can be expected to vary with slight changes of the interpupillarydistance settings of the instrument. This represents a very real problem for optical-instrument design, because (1) small variations of interpupillary distance result in large changes of chromostereopsis, and (2) few presently available instruments make provision for accurate setting of interpupillary distance. *Supported by grant MH08061 from the National Institute of Mental Health, The assistance of Professor Jay Enoch and Hope Green is gratefully acknowledged. 1 J. J. Vos, J. Opt. Soc. Am. 50, 785 (1960).
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