Tucker** supported this view, but Owens'^ showed that if voluntary focusing ..... Owens^ with a peak response between 3 and 5 c/deg. Ophthal. ..... Wayne Grofik.
I
Accommodation and chromatic aberration: effect of spatial frequency I
Debra Stone, Steven Mathews and Philip B. Kruger
l_Schnurmacher Institute for Vision Re.search, State College of Optometry, State University of New York, WO East 24th Street, New York, NY WOW, USA (Received 28 August 1992, in revised form 11 March 1993)
When subjects view an edge in white light, a colour fringe, produced by longitudinal chromatic aberration (LCA) of the eye, is formed at the edge. The colour fringe changes with changes in focus, and serves as a complex colour-coded cue for reflex accommodation. Fincham found that 60% of his subjects failed to accommodate appropriately when the colour fringe was removed with an achromatizing lens or by the use of monochromatic light. Our experiment sought to determine the spatial frequencies at which LCA is most efTcctivc. We monitored accommodation in 10 subjects while they viewed sinusoidaily moving sine-wave gratings (I -3 D at 0.2 Hz; 1-10.5 c/deg) in a Badal optometer. The targets were 'white' gratings with LCA normal, doubled, neutralized or reversed. Doubling the aberration has minimal effect, removing the aberration reduces gain and increases phase-lag, and reversing the aberration severely disrupts accommodation. Sensitivity to these chromatic cues exists at all spatial frequencies tested, but is most prominent between 3 and 5 c/deg. These results support the view that the system monitors focus by comparing contrast in red-green and perhaps blue-yellow colour-opponent mechanisms.
When an emtnetropic observer with adequate accommodative amplitude and facility is presented monoculariy with a distant static target, and a negative lens is introduced before the eye, the subject makes the appropriate accommodative increase to resolve the target. If the lens is then removed, the observer decreases accommodation as dictated by the stimulus. The possibility that an accommodative response is made in the proper direction and amount on the basis of light vergence alone, as the above description would suggest, was explored in the early 1950s. Fincham' reasoned that if defocus blur was the only cue available for determining the accommodative state of the eye, then a trial-anderror process would ensue, showing fluctuations of the accommodative response until the appropriate direction and level were achieved. Since this oscillatory behaviour did not typify the normal accommodative response, Fincham looked for other cues as a basis for signalling the direction of accommodation, Fincham suggested that longitudinal chromatic aberration (LCA) may signal the direction of the stimulus, as 60% of 55 subjects tested showed either partial or total absence of an accommodative response when they were presented with a target viewed in monochromatic sodium light. But why should this absence of spectral light be so devastating to the accommodative system? Fincham observed that LCA produces a characteristic colour fringe pattern around the target when viewed in white light. The fringe characteristics change with varying amounts of light vergence so that when a myopic state is created, a blue band appears on
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the outside of the colour fringe, while in a hyperopic state, a red band assumes the outside position. In monochromatic light, all colour fringe information is lost. It would appear, then, that those 60% of the subjects tested within Fincham's monochromatic experiment relied on chromatic cues to a significant degree. Fincham concluded that for subjects who are sensitive to the presence of colour fringes, "Without the information given by the chromaticity of the image, . . . there is no clue to the direction the adjustment should take, and the brain is unable to give the necessary innervation'. In another condition, Fincham substituted an achromatizing lens with the target viewed in white light, for the monochromatic light source. He speculated that if the loss of accommodative responsiveness was due to the absence of colour fringes, then he would find similar results with the achromatizing lens, since all wavelengths of light would be focused at the same point, leaving no chromatic cues to guide the system. Fincham reported that the results of this test were, "precisely the same as that found in monochromatic light'. But the issue is more complicated as 40% of the subjects produced a response in monochromatic light equal to that found when tested under normal viewing conditions (that is, when colour fringes were present). How did they maintain their response despite the loss of chromatic cues? Fincham speculated that scanning eye movements in conjunction with a reflexive assessment of the Stiles-Crawford effect could yield the directional cues necessary to guide the accommodative system. For those subjects that rely on this mechanism, brightness Q 1993 Butterworth-Heinemann for British College of Opiometrists 0275-5408/93/030244-09
Accommodation,, chromatic aberration and spatial frequency: D. Stone et al. may provide the necessary information. There is also considerable evidence that a variety of non-dioptric cues, such as changing size and apparent distance, also contribute to the accommodative signal under normal viewing conditions- ^ Certainly, a variety of cues are available for directing the accommodative system. The way in which they are combined for interpretation most likely depends upon their ecological validity for a given individual''. More specifically, the environmental circumstances within which we have adapted may act as the primary factor in determining the relative strength of each accommodative cue. But in the present study we concentrate on the dioptric stimulus for reflexive accommodation and in particular the spatial frequency content of the target. The conventional view of accommodation is that the eye changes focus to maintain a clear high-resolution image on the retina. In this view, the fine details of the image are particularly important, and therefore accommodation should respond well at high spatial frequencies. Early studies by Phillips^ and Charman and Tucker** supported this view, but Owens'^ showed that if voluntary focusing strategies are discouraged by instructing the subjects 'to view the gratings naturally, without straining the eye', optimal accommodative performance was obtained for intermediate spatial frequencies between 3 and 5 c/deg. Instructional and motivational factors can have a large infiuence on the response to step and stationary targets'"". Owens* findings were confirmed by Mathews'^'' using the same methods and instructions used in the present study; if voluntary focusing behaviours are kept to a minimum, accommodation responds best between 3 and 5 c/deg. Our present interest is in the role of LCA, and the spatial frequencies at which the efFects of LCA influence accommodation. In the conventional view chromatic aberration should have greatest effect at high spatial frequencies, where the influence of aberrations and defocus are most prominent''"^ On the other hand, the effects of LCA and defocus remain conspicuous even at relatively low spatial frequencies {down to about I c/deg), while the chromatic mechanisms that most likely detect these subtle chromatic effects also operate at relatively low spatial frequencies (below about 10 c/deg)"'. If the efi!"ects of LCA influence reflexive accommodation at intermediate spatial frequencies (3 to 5 c/deg), this will support the view that conventional colour-opponent mechanisms are involved in accommodative control'^'**. In the present experiment, we will examine the effects on the accommodative response when sine-wave gratings and their associated colour fringes are first viewed normally, that is, with the effects of LCA in their normal configuration. Then we will manipulate the colour fringe pattern in three ways: by doubling the amount of LCA so that each spectral colour in the fringe is approximately twice its normal size; by neutralizing (removing) the colour fringe with an achromatizing lens; and by reversing the layout of the colour fringe so that a red outer band will now signal the myopic state while a blue outer band will signal the hyperopic state. An important feature of this project entails the use of a dynamic target: the spatial frequency gratings will oscillate sinusoidaily toward and away from the eye at a temporal frequency of 0.2 Hz. At this temporal frequency the response is quite good, but the task is
demanding enough to reveal the influence of LCA**. A recurring problem in accommodation research is that voluntary effort can significantly alter the accommodative response. We find that the sinusoidaily moving stimulus together with careful instruction, reduces the amount of voluntary accommodation the subject can use in viewing the target, when compared to static target methods'". While a more static form of accommodation may be required for most of our daily visual tasks, reducing the amount of voluntary input allows more effective isolation of the effect of the chromatic component of the stimulus for "reflex' accommodation.
Methods Subjects were asked to view single spatial frequency sine-wave gratings in a Badal stimulus system. LCA was manipulated by interposing one of three specially designed zero-power doublets that either doubled, neutralized, or reversed the aberration. The target oscillated toward and away from the eye while a highspeed infrared recording optometer monitored accommodation continuously. Instrumentation The infrared recording optometer and the principles upon which it operates have been described previously'*'. Briefiy. the optometer works as a dynamic retinoscope. monitoring accommodation at 240 samples per second. The eye is scanned by an infrared beam and the retinal refiex is monitored by a high-speed detection system. The optometer responds linearly over a 6 D range, its resolution is < 0.1 D, and the cut-off frequency is 10 Hz. The recording system operates effectively as long as the pupil is 3 mm in diameter or larger, and eye movements are kept to a maximum of 3" deviation from the point of fixation. The essential components of the Badal stimulus system are shown in Figure I. Details of the stimulus system have been described previously'^ Sine-wave gratings are produced on a Joyce display scope (JDS) with a 'white' {P4) phosphor. The spectral output ofthe P4 phosphor is shown in Figure 2. In Figure I lens Ll forms a real (minified) image of the grating display at T. Light from the grating target (T) is collimated by lens L2 and brought to focus by lens L3 at T', after reflection at prisms PI and P2. Prism P2 can be moved, as shown by the arrow, to vary the distance between the image ofthe target (T') and Badal lens L4. When the target image is in the focal plane of lens L4. light from the target is collimated by lens L4. and comes to focus on the retina ofthe eye (E). Motion of prism P2 reduces the distance between the target image (T') and Badal lens L4. and the eye must accommodate to keep the target clear. The position ofthe prism is controlled by a servo-system and computer, which produce sinusoidal changes in target vergence. Aperture A is imaged in the pupil of the eye where it serves as a 3 mm artificial pupil. The infrared recording optometer operates off a hot mirror positioned between the Badal lens and the eye. The stimulus gratings subtend 6 at the eye and are surrounded by a blurred circular margin produced by a field stop (not shown) positioned 6 D beyond optical infinity. The Badal system ensures a constant angular size f'or the
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Figure 1 Diagrammatic representation illustrating the Badal stimulus system
target so that target vergence can be changed without providing an additional size cue for accommodation'''. Several spatial frequency gratings are employed: 0.98, 3.11, 5.25, 7.62, and 10.50c/deg. Each grating has a luminance contrast of 0.8 and the mean luminance of the target is 20cdm"'. Manipulation of the longitudinal chromatic aberration of the eye lies at the root of the experiment. One of three specially designed zero-power lens doublets can be positioned at A {Figure I) to alter the LCA of the eye. Details of the design and performance of these lenses have been described previously'^ The doubling lens creates twice as much LCA as in the normal condition. The neutralizing lens eliminates LCA to a large degree, and the reversing lens reverses the normal LCA of the eye. The effects of the lenses on focus are shown in Figure 3. The data are averaged measures from five subjects taken through the Badal stimulus system using a method of adjustment similar to Howarth and Bradley^". The figure shows the lens power needed to correct LCA for wavelengths between 450 and 670 nm. The lenses operate essentially as designed, although the neutralizing lens shows a small amount of residual LCA for long wavelength light. This small under-correction by the neutralizing lens is ^0.3 D between 570 and 670 nm, and recent findings suggest that even this small amount of LCA can be of some assistance to accommodation-'.
The use of a simple "doublet' design for these lenses precludes complete elimination of LCA in the neutralized condition. To avoid introducing lateral chromatic aberration the lenses were carefully positioned in the Badal stimulus system using a laser to assist alignment of the optics, and the three lenses were mounted in a rotating multiple-filter holder with preset positions for each lens. The subject's eye was positioned accurately by using a telescope to focus and align the corneal reflection (Purkinje image) of the target. Contrast sensitivity and transverse chromatic aberration were measured through the stimulus system, with and without the lenses in place'\ The lenses have no effect on contrast sensitivity measured through the stimulus system, and they introduce very little if any lateral chromatic aberration that might impair the quality of the retinal image"*. Lateral chromatic aberration measured through the system without the special lenses in place averages 46 sec arc, it remains essentially the same with the neutralizing lens in place (48 sec arc), and through the reversing lens averages 87 sec arc'*'. These measures of lateral chromatic aberration are not unusual, the amount of lateral chromatic aberration varies widely among subjects, and can be both positive and negative in direction^^-^\ The position of our lenses in the stimulus
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Figure 3 Lens power necessary to correct the longitudinal chromatic aberration ofthe eye for wavelengths between 450 and 670 nm. Data are for chromatic aberration: , doubled; , normal; , neutralized; and . . ., reversed; error bars show + t SEM
Accommodation, chromatic aberration and spatial frequency: D. Stone et al. system rather than directly in front ofthe subject's eye^''. allows accurate alignment of the lens, and introduces little if any additional lateral chromatic aberration to the stimulus system. Procedures The instructions given to the subjects were designed to avoid voluntary accommodation while encouraging active attention to the appearance ofthe target. Subjects were instructed lo fixate the centre of the grating as it oscillated toward and away from their eye, and they were reminded on several occasions to fixate the target as though reading a book. Subjects were urged to attend actively to the target, but it was emphasized that voluntary accommodation (conscious manipulation of contrast) was to be avoided. Subjects were positioned on a bite plate, secured by a forehead rest, shielded from all other activities in the room so that only the target was visible, and their non-viewing eye was patched. Trial lenses were positioned in front of their eye to correct for any refractive error and they were dark-adapted for several minutes before beginning the session. The four chromatic stimulus conditions (normal, doubled, neutralized and reversed) at five spatial frequencies, were presented in random order. Three trials, each 40 s in duration, were run for each spatial frequency and chromatic condition. Typically 20 runs constituted a session, with each session lasting ^ I h. Subjects ran for 40 s and then rested for two minutes while the next condition was set up. The subjects were in the dark for the entire session. Calibration oi' the infrared optometer was performed at the beginning of each experimental session. For the calibration, the grating target was replaced with a highluminance (200 cdm ^) white Maltese cross target with broadband spatial frequency content, to ensure an optimal response. The target was positioned at T in Figure I and illuminated by a tungsten-halogen source (not shown). The illumination system has been described previously**'-. The subjects were told, "keep the target clear as it steps towards you". The target stepped toward the subjects through 0. 1, 2. 3. and 4 D of vergence. pausing at each level for 10 s before making the next step. An entire calibration sequence took < 1 min and the response at each level was displayed on a computer monitor. The average accommodative response to the 1 and 3 D stimuli were estimated from the display and were later used in the analysis. These estimated averages were highly repeatable and changed very little during the course of the experiment. While these methods do not provide an absolute calibration of accommodation (since the accommodative response does not necessarily equal the accommodative stimulus), the relative measures are adequate for the present experiment. Stimulus motion, controlled by a sinusoidal computergenerated signal, varied between I and 3 D at a temporal frequency of 0.2 Hz. Accommodative responses were recorded by polygraph and computer'-. Output from the optometer was sampled at 100 Hz and stored for later analysis. Blinks were removed, the data were scaled according to the subject's calibration from that session, and a fast Fourier transform was run on the data for each trial to derive the amplitude and phase of the accommodative response. Gain was obtained by dividing the amplitude of the accommodative response
by the amplitude ofthe stimulus. Phase was obtained by comparing the phase ofthe accommodative stimulus to that ofthe subject's response. Gain and phase measures were calculated for each ofthe three trials at each spatial frequency and chromatic condition. The three values were then vector averaged to provide the mean gain and phase measures as well as their respective standard errors for each experimental condition. Subjects Ten subjects participated in the experiment. Their ages ranged from 23 to 38 years. Seven subjects were naive, and the three investigators also served as subjects. Each subject was given a standard vision examination and corrected to emmetropia. They all had normal binocular vision and were free of ocular pathology. All subjects gave informed consent. Results Data from one typical subject are shown in Figure 4. The figure shows one 40 s trial for each of the four experimental conditions, at the five spatial frequencies tested. At the lowest spatial frequency (1 c/deg) there is a small response, mainly in the normal and doubled conditions. When LCA is neutralized there is no discernible response, although the target certainly was visible to the subject during the trial. In the reversed condition (1 c/deg) the response is intermittent and somewhat erratic. At 3 c/deg accommodation is good in the normal, doubled and neutralized conditions, but there is essentially no response when LCA is reversed. The subject responds well at 5 c/deg in the normal and doubled conditions, but there is no response when LCA is neutralized or reversed. At 7 c/deg the response is minimal, even in the normal and doubled conditions, and at 10 c/deg there is no response for any condition. At the higher spatial frequencies (7 and 10 c/deg) the target was visible to the subjects as it came in and out of focus, but they were unable to track it. In summary, for this subject accommodation is best between 3 and 5 c/deg especially with LCA normal or doubled. When LCA is neutralized, adequate tracking ability is maintained only at 3 c/deg. and reversing LCA severely disrupts the subject's ability to track the target at all spatial frequencies. The response of each subject varies to some degree from trial to trial, but generally follows the pattern shown in Figure 4. Averaged gain and phase plots for the same subject are shown in Figure 5. At the lowest spatial frequency (1 c/deg) gain is reduced for all four chromatic conditions, and the influence of LCA is difficult to discern. But at 3 and 5 c/deg the normal response is substantial, and the influence of LCA becomes prominent. At 3 c/deg reversing LCA clearly reduces gain and increases phase-lag, although neutralizing the aberration results in only a small reduction in gain. It is only at 5 c/deg that gain is substantially reduced in both the neutralized and reversed conditions. At higher and lower spatial frequencies the response is so small that it is difficult to demonstrate the influence of LCA, although at 7 c/deg phase-lag is clearly larger when LCA is neutralized and reversed. The response to spatial frequency follows the pattern suggested by Owens^ with a peak response between 3 and 5 c/deg.
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Accommodation, chromatic aberration and spatial frequency: D. Stone et al. 1 c/d
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Accommodation, chromatic aberration and spatial frequency: D. Stone et al. Most of our subjects respond in this manner, although there are some individual differences as detailed below. Figure 6 shows data from an unusual subject whose accommodative tracking ability remains remarkably accurate even at higher spatial frequencies. Doubling LCA has no effect on gain or phase, except at 1 c/deg where it seems to improve gain to a small degree. Neutralizing and reversing LCA reduces gain at all spatial frequencies, even at 7 and 10 c/deg. This subject is highly sensitive to the effects of LCA. in that removing or reversing LCA has a profound effect on accommodative gain. Although we have been unable to find others who respond as well as this subject at high spatial frequencies'-, these data suggest that the effects of LCA on accommodation are largely independent of spatial frequency, that is, the chromatic cues are effective at all the spatial frequencies that stimulate accommodation. Figure 7 shows data from another unusual subject, in this case one who is relatively insensitive to the chromatic cues at any spatial frequency. The accommodative response is best between 1 and 5 c/deg and neutralizing LCA has no deleterious effect at all. However, doubling as well as reversing the aberration reduces gain at 5 c/deg. Subjects like this are unusual, they are relatively unaffected when LCA is disturbed, and they seem to rely on an achromatic directional cue to guide accommodation'\ We have examined about 40 subjects in a series of experiments and find that perhaps 10% of subjects behave in this manner"*. Average gain and phase for all 10 subjects at each spatial frequency and chromatic condition are shown in Figure 8. Although each individual subject responds somewhat differently to both spatial frequency content and chromatic condition, an overall trend exists. The normal condition produces the best accommodative gain at 3 c/deg, the doubled condition seems to reduce the gain at 3 and 5 c/deg, the neutralized condition reduces gain at 3. 5 and perhaps 7 c/deg. and the reversed condition severely impairs the response at all spatial frequencies. For the group as a whole, phase-lag is only 1.0 0.8 Z
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Figure 7 Gain and phase plot for an unusual subject who shows little sensitivity to the various chromatic manipulations: , normal; , doubled; . neutralized; reversed. The subject seems to respond well to an achromatic directional cue. Error bars show ± 1 SEM
