THE EFFECT OF PUPIL SIZE ON ACCOMMODATION’ ROBERT T. HENXSSY.~ Thri~o IIDA.~ KEN SHIISA' and H. W. LEIBOWITZ The Pennsylvania State University, University Park. PA 16862. U.S.A. (Receicetl 10 Jirl.r 1975) Abstract-Accommodation was measured with a laser optometer while viewing letter charts through a series of artificial pupils over a range of distances. As pupil size is reduced, the amplitude of accommodation is diminished, approaching a fixed intermediate resting focus corresponding to approx I m. These data are interpreted as supporting the intermediate as opposed to the classical infinity resting focus hypothesis. Implications for instrument myopia and the relationship between perceived distance and accommodation are discussed.
Two opposing viewpoints regarding the resting state of accommodation exist in the current literature. According to classical theory. the focus of the relaxed, emmetroptc eye corresponds to optical infinity (Helmholtz. 1963: Duke-Elder, 1969; Brown. 1965; Borish, 1970; Ogle. 1968). The intermediate resting position (Akkotnmodationsruhelage) hypothesis (Schober. 1954; Morgan, 1946, 1957: Otero, 1951). maintains that the resting focus does not correspond to infinity,
but rather to an intermediate distance of the order of 1 m. A method of experimentally comparing these theoretical points of view is to reduce the size of the pupil. With smaller pupils, the retinal image is determined progressively less by dioptrics, with a corresponding widening of the depth of field. Thus, if pupil size is reduced, there is less functional need for accommodation and it would be expected that the lens would tend to return to its equilibrium or resting focus. In the present study, the accommodative response to targets at various distances is determined for binocular and monocular viewing with the natural pupil, and for a series of artificial pupils. Accommodation is evaluated by means of a laserBadal optometer. METHOD
Five students between the ages of 23 and 30 served as subjects. Each exhibited uncorrected acuity of at least X22 at infinity and at 43 cm when tested with a Titmus Professional and Industrial Vision Tester (Model OV-7M). A series of letter charts, each consisting of a 12 x 12 matrix of black upper case letters on a white background were used as fixation targets. The charts were scaled such that each letter subtended II’ at the viewing distances of 50. 100. 350 and 600 cm. Each subject viewed these charts binocularly with natural pupils, monocularly with the right eye and natural pupil. and through artificial pupils 3.0, ’ Supported by grant MH08061 from the National Institute of Mental Health. The authors are indebted to D. .A. Owens for assistance in the preparation of the manuscript. ’ Present address: Human Factors Research, Goleta. Cal. J Present address: Industrial Products Research Institute. Tokyo, Japan. ’ Present address: Fachbereich Psychologie. Universitat Konstanz, Konstanc W. Germany.
2.0. 1.5, 0.75 and 0.5 mm dia. Two luminance conditions were used; in the first, the white portion of the chart was maintained at I6ft-L at all distances. Under the second condition, the luminance of the white portion of the chart was adjusted for the artificial pupil viewing conditions so that retinal illuminance was constant at 62.5 td. The order of presentation of the letter charts for each subject was either near to far or the reverse, counterbalanced across subjects. The order of pupil conditions was randomized across subjects. The subjects were instructed to fixate a letter, designated in terms of coordinates. and to maintain fixation while accommodation was determined. While the subject was fixating the letter chart under each combination of the various experimental conditions. the refractive state of the left eye was measured using a laserBadal optometer. Laser light possesses properties which facilitate the rapid and accurate measurement of refractive state (Baldwin and Stover, 1968; Knoll, 1966: Hennessy and Leibowitt 1972; Ingeistam and Ragnarsson, 1972). When the diverged beam of a low energy laser is directed at a slowly rotating cylinder, a moving speckled pattern of interference points is apparent to the observer. The direction of this apparent motion is related to refractive state. If the speckles appear to move in the direction of rotation of the cylinder. the subject’s eye is conjugate to a point in front of the axis of the cylinder. Similarly. if the apparent motion is in the opposite direction, the observer’s eye is conjugate to a point behind the axis of the cylinder. By utilizing this revolving cylinder as the target of a Badal optometer (Ogle, 1968), refractive state can be measured by noting the point of reversal of motion as the optical distance of the cylinder is changed. A beamsplitting prism is used to superimpose the interference points into the subject’s field of view, and a shutter limits exposure duration to @S sec. A bracketing procedure is employed to determine the reversal point. which, in turn, can be converted into diopters. In all measurements reported here, axial chromatic aberration due to the monochromatic nature of the laser light is corrected to 56Onm using the tables of Bedford and Wyszecki (1957). For details of this technique see Hennessy and Leibodtz (1972). RESULTS
Figure 1 presents the mean refractive state as a tunctton of distance with target luminance constant at 16 ft-L for the various viewing conditions. It can be seen that the slope of the line for binocular observation with the natural pupil most nearly corresponds to target distance. With smaller pupil sizes. the in587
Naturalpupil-blnoculcr 3 Naturalpupil-monocular
/
.
r 3
Artificial
/
pupils (mm)
; : i=
3 3.0
x Tcrge! lumlnarce
o
6-
Retinal
iilumlnance
constant
1 ! Monoc
I
I
017 a4 (6m) (2.h) Dtoptric
,
/
L%
&%
Distance
of
Torqet
Fig. 1. Accommodation as a function of dioptric distance for various sized artificial pupils. The theoretical line indicates values expected if accommodation corresponded to target distance.
Huence of target distance is diminished, the total range of accommodation is reduced, and the slopes of the accommodative response functions become progressively flatter. Figure 2 presents the slopes of the functions, as determined by least squares, for the constant target luminance as well as the constant retinal illuminance condition. These functions are essentially identical. DlSCUSSlOiU
The decrease in accommodative amplitude with smaller pupils is to be expected in terms of the expanded depth of field as pupil size is decreased (Ripps, Chin, Siegel and Breinin, 1962). Of greater theoretical interest is the distance to which the focus of the eye approaches when the need for accommodation is reduced with smaller pupils. This corresponds to approx 1 m5 which is consistent with the intermediate resting focus hypothesis as opposed to classical view that the relaxed eye is accommodated for optical infinity. The intermediate resting state hypothesis, supported by the present data, implies that when the need for accommodation is reduced the focus of the eye returns passively to its resting state corresponding to an intermediate distance. These findings suggest a parsimonious explanation for instrument myopia, the unnecessary accommodation observed when viewing through optical instruments. In many optical instruments, in particular light microscopes, the exit pupil is of the order 2.Omm and with higher magnification become even smaller. Under these conditions, the depth of field of the eye is enlarged permitting a range of optical distances over which the image will be m clear focus. In effect, ’ Subsequent research on the resting focus on large populations indicates marked intersubject variability. For a population of more than 120 college-age observers, tested in total darkness. the mean is 1.7 D with a S.D. of 0.7 D. (See Leibowitz and Owens. 1975.)
5
I.0 Artificial
1.5
x
constant
2.0
Pupil Diameter
3.0 hms)
Natural Pupil
Fig. 2. The slope of the accommodation-distance function as a function of artificial pupil diameter with constant target luminance and with constant retinal illuminance.
the eye adjusts its focus to the resting state. For a detailed analysis see Hennessy (1975). The present experiment is also relevant to the question of the effect of perceived distance on accommodation (Ittelson and Ames. 1950: Schober. Dehler and Kassel. 1970). The data of the present experiment were gathered in a large well-illuminated laboratory room: between each test condition the subject saw the next chart being placed at its appropriate distance and was therefore aware of the approximate distance of each chart. If perceived or known distance affects accommodation, it would be expected that this would become manifested particularly under the 05 mm artificial pupil viewing condition since variation in accommodation would have minimal inAuence on the clearness of the retinal image. Inspection of the data shows that at this pupil size there is very little change in accommodation with chart distance. The slope of this function is Q I1 with constant target luminance and 049 with constant retinal illuminance. It therefore seems unhkely that perceived distance has a significant effect on accommodation under normal viewing conditions. REFERENCES Baldwin W. R. and Stover W. 9. (1968) Observation of laser standing wave patterns to determine refractive status. Am. J. Optom. 43. 14;150. Bedford R. E. and Wyszacki G. (1957) Ax131 chromatic aberration of the human eye. J. Opr. Sot. rim. 47. 564-565. Borish I. M. (1970) Clinical Refraction. The Professional Press, New York. Brown J. L. (1965) The structure of the visual system. In Msfon and Visual Perception (Edited by Graham C. H.). Wiley, New York. Duke Elder S. (1969) The Practice of‘ Refraction, pp. 1X?131. Mosby. St. Louis. Helmholtz H. W. (1962) Physiological Oprics. Vol. I. pp. 136-137. Dover. New York. Hennessy R. T. (1975) Instrument myopia. J. opt. Sot. Am. 63, 1114-11’0. Hennessy R. T. and Leibou-itz H. \V. (19711 Laser optometer incorporating the Badal principle. Behar. Rrs. .Cfeth. Instrum. 4, 237-239.
The effect of pupil size on accommodation Ingelstam E. and Ragnarsson S. I. (1972) Eye refraction examined by aid of speckle pattern produced by coherent light. Vision Res. 12. 411420. Ittelson W. H. and Ames A. (1950) Accommodation. convergence and their relation to apparent distance. J. Ph.~siol.. Lond. 30, 43-62. Knoll H. A. (19661 Measuring ametropia with a gas laser. Am. J. Oprom. 43, 415-418. Leibowitz H. W. and Owens D. A. (1975) Anomalous myopias and the intermediate dark-focus of accommodation. Science 189, 646-648. Morgan M. W. (1946) A new theory for the control of accommodation. .-lm. J. Oprom. 23. 99-110.
589
Morgan M. W. (19571The resting state of accommodation. Am. J. Optom. 34, 347-353. Ogle K. (1968) Optics (2nd ed.). Thomas, Springfield. IIL Otero J. IM.(195 1) Influence of the state of accommodation on the visual performance of the human eye. J. opt. Sot. Am. 41, 942-948. Ripps H., Chin N.. Siegel and Breinin G. (1962) The effect of pupil size on accommodation, convergence and the ACA ratio. Inrrstce. Oohth. 1. 127-135. :. Schober H. A. W. (1954) Uber die Akkommodationsruhelaae. Optik 11, 282-290. Schober H., Dehler H. and Kassel R. (1970) Accommodation during observations with optical instruments. J. opt. Sot. Am. 60(l). 103-107.
Two opposing viewpoints regarding the resting state of accommodation exist in the current literature. According to classical theory. the focus of the relaxed, emmetroptc eye corresponds to optical infinity (Helmholtz. 1963: Duke-Elder, 1969; Brown. 1965; Borish, 1970; Ogle. 1968). The intermediate resting position (Akkotnmodationsruhelage) hypothesis (Schober. 1954; Morgan, 1946, 1957: Otero, 1951). maintains that the resting focus does not correspond to infinity,
but rather to an intermediate distance of the order of 1 m. A method of experimentally comparing these theoretical points of view is to reduce the size of the pupil. With smaller pupils, the retinal image is determined progressively less by dioptrics, with a corresponding widening of the depth of field. Thus, if pupil size is reduced, there is less functional need for accommodation and it would be expected that the lens would tend to return to its equilibrium or resting focus. In the present study, the accommodative response to targets at various distances is determined for binocular and monocular viewing with the natural pupil, and for a series of artificial pupils. Accommodation is evaluated by means of a laserBadal optometer. METHOD
Five students between the ages of 23 and 30 served as subjects. Each exhibited uncorrected acuity of at least X22 at infinity and at 43 cm when tested with a Titmus Professional and Industrial Vision Tester (Model OV-7M). A series of letter charts, each consisting of a 12 x 12 matrix of black upper case letters on a white background were used as fixation targets. The charts were scaled such that each letter subtended II’ at the viewing distances of 50. 100. 350 and 600 cm. Each subject viewed these charts binocularly with natural pupils, monocularly with the right eye and natural pupil. and through artificial pupils 3.0, ’ Supported by grant MH08061 from the National Institute of Mental Health. The authors are indebted to D. .A. Owens for assistance in the preparation of the manuscript. ’ Present address: Human Factors Research, Goleta. Cal. J Present address: Industrial Products Research Institute. Tokyo, Japan. ’ Present address: Fachbereich Psychologie. Universitat Konstanz, Konstanc W. Germany.
2.0. 1.5, 0.75 and 0.5 mm dia. Two luminance conditions were used; in the first, the white portion of the chart was maintained at I6ft-L at all distances. Under the second condition, the luminance of the white portion of the chart was adjusted for the artificial pupil viewing conditions so that retinal illuminance was constant at 62.5 td. The order of presentation of the letter charts for each subject was either near to far or the reverse, counterbalanced across subjects. The order of pupil conditions was randomized across subjects. The subjects were instructed to fixate a letter, designated in terms of coordinates. and to maintain fixation while accommodation was determined. While the subject was fixating the letter chart under each combination of the various experimental conditions. the refractive state of the left eye was measured using a laserBadal optometer. Laser light possesses properties which facilitate the rapid and accurate measurement of refractive state (Baldwin and Stover, 1968; Knoll, 1966: Hennessy and Leibowitt 1972; Ingeistam and Ragnarsson, 1972). When the diverged beam of a low energy laser is directed at a slowly rotating cylinder, a moving speckled pattern of interference points is apparent to the observer. The direction of this apparent motion is related to refractive state. If the speckles appear to move in the direction of rotation of the cylinder. the subject’s eye is conjugate to a point in front of the axis of the cylinder. Similarly. if the apparent motion is in the opposite direction, the observer’s eye is conjugate to a point behind the axis of the cylinder. By utilizing this revolving cylinder as the target of a Badal optometer (Ogle, 1968), refractive state can be measured by noting the point of reversal of motion as the optical distance of the cylinder is changed. A beamsplitting prism is used to superimpose the interference points into the subject’s field of view, and a shutter limits exposure duration to @S sec. A bracketing procedure is employed to determine the reversal point. which, in turn, can be converted into diopters. In all measurements reported here, axial chromatic aberration due to the monochromatic nature of the laser light is corrected to 56Onm using the tables of Bedford and Wyszecki (1957). For details of this technique see Hennessy and Leibodtz (1972). RESULTS
Figure 1 presents the mean refractive state as a tunctton of distance with target luminance constant at 16 ft-L for the various viewing conditions. It can be seen that the slope of the line for binocular observation with the natural pupil most nearly corresponds to target distance. With smaller pupil sizes. the in587
Naturalpupil-blnoculcr 3 Naturalpupil-monocular
/
.
r 3
Artificial
/
pupils (mm)
; : i=
3 3.0
x Tcrge! lumlnarce
o
6-
Retinal
iilumlnance
constant
1 ! Monoc
I
I
017 a4 (6m) (2.h) Dtoptric
,
/
L%
&%
Distance
of
Torqet
Fig. 1. Accommodation as a function of dioptric distance for various sized artificial pupils. The theoretical line indicates values expected if accommodation corresponded to target distance.
Huence of target distance is diminished, the total range of accommodation is reduced, and the slopes of the accommodative response functions become progressively flatter. Figure 2 presents the slopes of the functions, as determined by least squares, for the constant target luminance as well as the constant retinal illuminance condition. These functions are essentially identical. DlSCUSSlOiU
The decrease in accommodative amplitude with smaller pupils is to be expected in terms of the expanded depth of field as pupil size is decreased (Ripps, Chin, Siegel and Breinin, 1962). Of greater theoretical interest is the distance to which the focus of the eye approaches when the need for accommodation is reduced with smaller pupils. This corresponds to approx 1 m5 which is consistent with the intermediate resting focus hypothesis as opposed to classical view that the relaxed eye is accommodated for optical infinity. The intermediate resting state hypothesis, supported by the present data, implies that when the need for accommodation is reduced the focus of the eye returns passively to its resting state corresponding to an intermediate distance. These findings suggest a parsimonious explanation for instrument myopia, the unnecessary accommodation observed when viewing through optical instruments. In many optical instruments, in particular light microscopes, the exit pupil is of the order 2.Omm and with higher magnification become even smaller. Under these conditions, the depth of field of the eye is enlarged permitting a range of optical distances over which the image will be m clear focus. In effect, ’ Subsequent research on the resting focus on large populations indicates marked intersubject variability. For a population of more than 120 college-age observers, tested in total darkness. the mean is 1.7 D with a S.D. of 0.7 D. (See Leibowitz and Owens. 1975.)
5
I.0 Artificial
1.5
x
constant
2.0
Pupil Diameter
3.0 hms)
Natural Pupil
Fig. 2. The slope of the accommodation-distance function as a function of artificial pupil diameter with constant target luminance and with constant retinal illuminance.
the eye adjusts its focus to the resting state. For a detailed analysis see Hennessy (1975). The present experiment is also relevant to the question of the effect of perceived distance on accommodation (Ittelson and Ames. 1950: Schober. Dehler and Kassel. 1970). The data of the present experiment were gathered in a large well-illuminated laboratory room: between each test condition the subject saw the next chart being placed at its appropriate distance and was therefore aware of the approximate distance of each chart. If perceived or known distance affects accommodation, it would be expected that this would become manifested particularly under the 05 mm artificial pupil viewing condition since variation in accommodation would have minimal inAuence on the clearness of the retinal image. Inspection of the data shows that at this pupil size there is very little change in accommodation with chart distance. The slope of this function is Q I1 with constant target luminance and 049 with constant retinal illuminance. It therefore seems unhkely that perceived distance has a significant effect on accommodation under normal viewing conditions. REFERENCES Baldwin W. R. and Stover W. 9. (1968) Observation of laser standing wave patterns to determine refractive status. Am. J. Optom. 43. 14;150. Bedford R. E. and Wyszacki G. (1957) Ax131 chromatic aberration of the human eye. J. Opr. Sot. rim. 47. 564-565. Borish I. M. (1970) Clinical Refraction. The Professional Press, New York. Brown J. L. (1965) The structure of the visual system. In Msfon and Visual Perception (Edited by Graham C. H.). Wiley, New York. Duke Elder S. (1969) The Practice of‘ Refraction, pp. 1X?131. Mosby. St. Louis. Helmholtz H. W. (1962) Physiological Oprics. Vol. I. pp. 136-137. Dover. New York. Hennessy R. T. (1975) Instrument myopia. J. opt. Sot. Am. 63, 1114-11’0. Hennessy R. T. and Leibou-itz H. \V. (19711 Laser optometer incorporating the Badal principle. Behar. Rrs. .Cfeth. Instrum. 4, 237-239.
The effect of pupil size on accommodation Ingelstam E. and Ragnarsson S. I. (1972) Eye refraction examined by aid of speckle pattern produced by coherent light. Vision Res. 12. 411420. Ittelson W. H. and Ames A. (1950) Accommodation. convergence and their relation to apparent distance. J. Ph.~siol.. Lond. 30, 43-62. Knoll H. A. (19661 Measuring ametropia with a gas laser. Am. J. Oprom. 43, 415-418. Leibowitz H. W. and Owens D. A. (1975) Anomalous myopias and the intermediate dark-focus of accommodation. Science 189, 646-648. Morgan M. W. (1946) A new theory for the control of accommodation. .-lm. J. Oprom. 23. 99-110.
589
Morgan M. W. (19571The resting state of accommodation. Am. J. Optom. 34, 347-353. Ogle K. (1968) Optics (2nd ed.). Thomas, Springfield. IIL Otero J. IM.(195 1) Influence of the state of accommodation on the visual performance of the human eye. J. opt. Sot. Am. 41, 942-948. Ripps H., Chin N.. Siegel and Breinin G. (1962) The effect of pupil size on accommodation, convergence and the ACA ratio. Inrrstce. Oohth. 1. 127-135. :. Schober H. A. W. (1954) Uber die Akkommodationsruhelaae. Optik 11, 282-290. Schober H., Dehler H. and Kassel R. (1970) Accommodation during observations with optical instruments. J. opt. Sot. Am. 60(l). 103-107.
