DEPENDENCE OF ACCOMMODATION RESPONSE ON THE SPATIAL FREQUENCY SPECTRUM OF THE OBSERVED OBJECT W. N. CHAILM~Vand JILL TUCKER Department of Ophthalmic Optics, University of Manchester Institute of Science and Technology, Manchester M60 1QD. England (Received
ZS Ocrober
1975; in revised form
8 April
1976)
Abstract-Experiments are described in which the monocular, steady-state, accommodation response to sinusoidal grating targets was assessed as a function of the spatial frequency of the grating and its vergence at the eye. using a laser optometer. At all levels of stimulus, the response is found to be dependent upon the grating frequency. At very low spatial frequencies the response is often substantially in error and is closely related to the accommodation exercised by the observer when viewing an empty held. At higher frequencies the response becomes more accurate and its exact value is probably dependent upon the observing conditions and upon the ocular aberrations and. other properties of
the observer. Further experiments with Snellen targets suggest that the accommodation to a target with a complex spatial frequency spectrum cannot be predicted from a knowledge of that spectrum and of the observer’s response to its component frequencies, under the same viewing conditions. The significance of the findings to theories of accommodation is indicated.
1. fNTRODLKTtON
iMuch attention has been devoted in recent vears to studies of the dynamics of the accommodation response (e.g. Allen, 19%; Campbell and Westheimer, 1960; Phillips, Shirachi and Stark, 1972) and to the development of theoretical models of the accormnodation system (e.g. Stark, 1965; Toates, 197i, 1972a). Curiously, however, the nature of the characteristics of the object which determine the final level of response has been comparatively neglected. Nadell and Knoll (1956) used a rather motley collection of targets to demonstrate that the response varied with target co~guration. Heath (1956) in a rather more systematic investigation, modified the spatial frequency spectrum of his letter targets by optical blurring. He found that, for a given target vergence, the blurred or lower frequency-content targets elicited a generally smaller amount of accommodation. It has also been shown that the response to a given stimulus tends to fall with the level of illumination of the target (Campbell, 1954; Nadell and Knoll, 1956). Green and CampbelI (1965) have illustrated that, when viewing sinusoidal gratings, the optimum refraction of an eye whose accommodation has been paralysed may depend upon the spatial frequency spectrum of the grating, due to the spherical aberration of the eye. In general, then, it might be expected that, for any fixed object vergence, the steady-state accommodation response would depend upon the spatial frequency spectrum of the object. We have therefore presented an observer with a series of sinusoidal grating targets at each of a number of fixed vergences and have studied the corresponding monocular acco~odation response. 1. APPARATUS
viewing. is shown in Fig. 1. Monocular viewing was chosen for this exploratory investigation to eliminate the influence of convergence on the responses. 2.1. Target system Gratings with a sinusoidal variation of luminance were produced on the 10 x 12cm face of a Tektronix 7403X oscilloscope having a Pit phosphor; conventional techniques were employed (Campbell and Green, 1965). The use of an oscilloscope display has many advantages but presents problems in that, for any fixed viewing distance, the dimensions of the display limit the lowest spatial frequency available, while the finite oscilloscope resolution sets the high frequency limit. For these reasons. our target vergences were kept constant by using fixed effective optical distances, rather than by observing the dispIay directly at fixed distances. The gratings were viewed through a refractor head equipped with lenses of variable power. Appropriate combinations of actual target distance, lens power and grating frequency allowed the full range of spatial frequencies 0.4-40 c/deg to be explored for each target
Laser l-l
Chopper ’
1 +
A.YD METHODS
Subject
basic experimental arrangement, consisting of a target display and a laser optometer system for monocular The
129
Fig. I I. Schematic
view
of the target system and laser optometer.
[ _;I)
h’
S. CHARMAN and JILL TI_CKER
vergence. at constant grating modulation, Correcnons were mJde for the ini-luence oi lens effectivity on the apparent spatial frequencies. In the present experiments the gratings were of high contrast. a constant grating modulation of SO’,, being used. At k;lst 10 complete cycles were included in the held at all spatial frequencies except the lowest 10.-lc deg). where onlv_ seven were employed. This minimised possible distortions in visual response associated with the use of less sxrcnsive gratings (Hoekstra.Van der Goat. Van den Brink and Bilsen. 1974: Van den Brink .rnd Bilsen. IYi5; Kelly. 19-S). .\n obvious problem in using grating targets for studies of the present type is that the target boundary must not itself constitute a significant stimulus to accommodation and. similarly. that fixation marks cannot be used. The oscilloscope display was therefore viewed through an illuminated surround whose uniform luminance matched the space-averaged luminance of the gratings. The circular inner aperture of this surround subtended a slightly smaller angle at the eye than the minimum dimension of the rectangular grating display. By placing the surround as close to the eye as possible. its vergence at the eye (h10D.S.) was made to ditTer by the maximum amount possible from thJt of the grating and was normally beyond the accommodative powers of the observer. The grating thus appeared within a blurred circular margin: the subtense of the grating held diameter varied from 1s’ to 2.0’ for the coarsest and finest erstings respectively. The outer margin of the surround~tield subtended about 1s’. this being set by the mount of the refractor head lenses. Beyond this limit the field appeared dark. Both the gratings and their surround were viewed through a narrow-cut green g&tine filter. The combined effect of the filter and PI 1 phosphor was to produce illumination with a mean wavelength of 535 nm and a bandwidth of about 25 nm. The tinal space-averaged luminance of the gratings and their surround. as seen by the obsener through the optometer beam-splitter. was 10 cd. m:. 1.2. Laser opiolllrrer Accommodation when viewing the object field was assessed with a laser optometer (Knoll, 1966; Baldwin and Stover. 1968; Ingelstam and Ragnarsson. 1972) where essentially the image of a laser speckle pattern is made conjugate with that of the target. The use of a speckle pattern for reference purposes has obvious advantages; its spatial power spectrum corresponds to the incoherent transfer function of the pupil of the eye (Lowenthal and ,\rsenault. 1970; Hariharan and Hegedus, 1974) and is broadband. It thus lacks pronounced features at any particular spatial frequency-. unlike many other possible reference targets. Ltght from a I-mW He-se laser (i. = 633 nm) was directed via a diverging lens and beam-splitter onto the surface of a slowly moving drum ( - I2 rev’hr). The subtense of the illuminated patch at the eye was kept constant with drum distance by making the focal point of the diverging lens lie at the same distance from the drum as the eye. The chopper and beam-splitters allowed the observer to view the resultant moving speckle pattern superimposed on the grating target for 65 set every 5 sec. Hennessy and Liebowitz (1970) have shown that exposures of this duration do not themselves affect the estimated accommodation. As substantial differences between the target vergence and the level of accommodation exercised were frequently found and it n-as desired to keep the apparatus as compact as possible. additional low-power lenses were inserted when necessary into the optical path of the optometer to provide addi;ional control of the effective drum vergencc. The basic measurement consisted essentially in moving the drum along the optomster axis until the superimposed speckle pattern appeared stationary to an observer who
was accommodated on a gratmg target. The level of accommodation could then be calculated from the position of the plane of stationaritv of the speckles (Charman. 1975) and the powers and positions of the lenses between the drum and the eye. The peripheral portions of the observer’s field were well screened to avoid any possibility of indirect observation of the position of the drum or of the oscilloSCOp
ZS Ocrober
1975; in revised form
8 April
1976)
Abstract-Experiments are described in which the monocular, steady-state, accommodation response to sinusoidal grating targets was assessed as a function of the spatial frequency of the grating and its vergence at the eye. using a laser optometer. At all levels of stimulus, the response is found to be dependent upon the grating frequency. At very low spatial frequencies the response is often substantially in error and is closely related to the accommodation exercised by the observer when viewing an empty held. At higher frequencies the response becomes more accurate and its exact value is probably dependent upon the observing conditions and upon the ocular aberrations and. other properties of
the observer. Further experiments with Snellen targets suggest that the accommodation to a target with a complex spatial frequency spectrum cannot be predicted from a knowledge of that spectrum and of the observer’s response to its component frequencies, under the same viewing conditions. The significance of the findings to theories of accommodation is indicated.
1. fNTRODLKTtON
iMuch attention has been devoted in recent vears to studies of the dynamics of the accommodation response (e.g. Allen, 19%; Campbell and Westheimer, 1960; Phillips, Shirachi and Stark, 1972) and to the development of theoretical models of the accormnodation system (e.g. Stark, 1965; Toates, 197i, 1972a). Curiously, however, the nature of the characteristics of the object which determine the final level of response has been comparatively neglected. Nadell and Knoll (1956) used a rather motley collection of targets to demonstrate that the response varied with target co~guration. Heath (1956) in a rather more systematic investigation, modified the spatial frequency spectrum of his letter targets by optical blurring. He found that, for a given target vergence, the blurred or lower frequency-content targets elicited a generally smaller amount of accommodation. It has also been shown that the response to a given stimulus tends to fall with the level of illumination of the target (Campbell, 1954; Nadell and Knoll, 1956). Green and CampbelI (1965) have illustrated that, when viewing sinusoidal gratings, the optimum refraction of an eye whose accommodation has been paralysed may depend upon the spatial frequency spectrum of the grating, due to the spherical aberration of the eye. In general, then, it might be expected that, for any fixed object vergence, the steady-state accommodation response would depend upon the spatial frequency spectrum of the object. We have therefore presented an observer with a series of sinusoidal grating targets at each of a number of fixed vergences and have studied the corresponding monocular acco~odation response. 1. APPARATUS
viewing. is shown in Fig. 1. Monocular viewing was chosen for this exploratory investigation to eliminate the influence of convergence on the responses. 2.1. Target system Gratings with a sinusoidal variation of luminance were produced on the 10 x 12cm face of a Tektronix 7403X oscilloscope having a Pit phosphor; conventional techniques were employed (Campbell and Green, 1965). The use of an oscilloscope display has many advantages but presents problems in that, for any fixed viewing distance, the dimensions of the display limit the lowest spatial frequency available, while the finite oscilloscope resolution sets the high frequency limit. For these reasons. our target vergences were kept constant by using fixed effective optical distances, rather than by observing the dispIay directly at fixed distances. The gratings were viewed through a refractor head equipped with lenses of variable power. Appropriate combinations of actual target distance, lens power and grating frequency allowed the full range of spatial frequencies 0.4-40 c/deg to be explored for each target
Laser l-l
Chopper ’
1 +
A.YD METHODS
Subject
basic experimental arrangement, consisting of a target display and a laser optometer system for monocular The
129
Fig. I I. Schematic
view
of the target system and laser optometer.
[ _;I)
h’
S. CHARMAN and JILL TI_CKER
vergence. at constant grating modulation, Correcnons were mJde for the ini-luence oi lens effectivity on the apparent spatial frequencies. In the present experiments the gratings were of high contrast. a constant grating modulation of SO’,, being used. At k;lst 10 complete cycles were included in the held at all spatial frequencies except the lowest 10.-lc deg). where onlv_ seven were employed. This minimised possible distortions in visual response associated with the use of less sxrcnsive gratings (Hoekstra.Van der Goat. Van den Brink and Bilsen. 1974: Van den Brink .rnd Bilsen. IYi5; Kelly. 19-S). .\n obvious problem in using grating targets for studies of the present type is that the target boundary must not itself constitute a significant stimulus to accommodation and. similarly. that fixation marks cannot be used. The oscilloscope display was therefore viewed through an illuminated surround whose uniform luminance matched the space-averaged luminance of the gratings. The circular inner aperture of this surround subtended a slightly smaller angle at the eye than the minimum dimension of the rectangular grating display. By placing the surround as close to the eye as possible. its vergence at the eye (h10D.S.) was made to ditTer by the maximum amount possible from thJt of the grating and was normally beyond the accommodative powers of the observer. The grating thus appeared within a blurred circular margin: the subtense of the grating held diameter varied from 1s’ to 2.0’ for the coarsest and finest erstings respectively. The outer margin of the surround~tield subtended about 1s’. this being set by the mount of the refractor head lenses. Beyond this limit the field appeared dark. Both the gratings and their surround were viewed through a narrow-cut green g&tine filter. The combined effect of the filter and PI 1 phosphor was to produce illumination with a mean wavelength of 535 nm and a bandwidth of about 25 nm. The tinal space-averaged luminance of the gratings and their surround. as seen by the obsener through the optometer beam-splitter. was 10 cd. m:. 1.2. Laser opiolllrrer Accommodation when viewing the object field was assessed with a laser optometer (Knoll, 1966; Baldwin and Stover. 1968; Ingelstam and Ragnarsson. 1972) where essentially the image of a laser speckle pattern is made conjugate with that of the target. The use of a speckle pattern for reference purposes has obvious advantages; its spatial power spectrum corresponds to the incoherent transfer function of the pupil of the eye (Lowenthal and ,\rsenault. 1970; Hariharan and Hegedus, 1974) and is broadband. It thus lacks pronounced features at any particular spatial frequency-. unlike many other possible reference targets. Ltght from a I-mW He-se laser (i. = 633 nm) was directed via a diverging lens and beam-splitter onto the surface of a slowly moving drum ( - I2 rev’hr). The subtense of the illuminated patch at the eye was kept constant with drum distance by making the focal point of the diverging lens lie at the same distance from the drum as the eye. The chopper and beam-splitters allowed the observer to view the resultant moving speckle pattern superimposed on the grating target for 65 set every 5 sec. Hennessy and Liebowitz (1970) have shown that exposures of this duration do not themselves affect the estimated accommodation. As substantial differences between the target vergence and the level of accommodation exercised were frequently found and it n-as desired to keep the apparatus as compact as possible. additional low-power lenses were inserted when necessary into the optical path of the optometer to provide addi;ional control of the effective drum vergencc. The basic measurement consisted essentially in moving the drum along the optomster axis until the superimposed speckle pattern appeared stationary to an observer who
was accommodated on a gratmg target. The level of accommodation could then be calculated from the position of the plane of stationaritv of the speckles (Charman. 1975) and the powers and positions of the lenses between the drum and the eye. The peripheral portions of the observer’s field were well screened to avoid any possibility of indirect observation of the position of the drum or of the oscilloSCOp
