PHILIP B. KRUGER e/ t/l .... short wavelength light focuses behind the retina rather than in front. ..... short wavelength light focusing before long wavelength light.
t’oion Res. Vol. 33, No IO. pp. 1397-141 I. 1993 Printed in Great Britain. All rights reserved
Copyright
Chromatic Aberration Fincham Revisited PHILIP
B. KRUGER,*
STEVEN
Receioed 10 Junr 199.2; in recked fhn
MATHEWS.*
0042-6989,93 $6.00 + 0.00 4, 1993 Pergamon Preab Ltd
and Ocular Focus: KARAN
R. AGGARWALA,*
NIVTAN
SANCHEZ*
30 Nocember 1992
Longitudinal chromatic aberration of the eye (LCA) produces “color fringes” at edges that specify focus. Fincham [(1951) British Journal of Ophthalmology, 35, 381-3931 concluded that these chromatic effects were important for accommodation, but most investigators disagree. We monitored accommodation in 25 subjects while they viewed a sinusoidally moving target (1.5-2.5 D at 0.2 Hz) in a Badal optometer. The target was monochromatic (590 nm with 10 nm bandwidth), or white (3000 K) with LCA normal, neutralized or reversed. Sensitivity to the effects of LCA is profound and widespread. Gain decreases substantially and phase-lag increases when LCA is eliminated, and reversing the aberration severely disrupts accommodation. The ordered arrangement of spectral foci produced by LCA seems to be a fundamental aspect of the stimulus for “reflex” accommodation. Accommodation
Stimulus
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INTRODUCTION Chromatic dispersion by the ocular media results in considerable longitudinal chromatic aberration (Wald & Griffin, 1947; Bedford & Wyszecki, 1957). Short wavelength light comes to focus much further forward in the eye than long wavelength light so that for a “white” target the difference in focus between the blue (400 nm) and red (700 nm) ends of the spectrum is about 2 D. Object points have corresponding image points that are actually a spectrum of foci, and the luminance gradients and edges that comprise the retinal image are characterized by subtle color “fringes”. Focus behind the retina (under-accommodation) produces a point spreadfunction with a red fringe, while focus in front of the retina (over-accommodation) produces a blue fringe. Chromatic dispersion also results in transverse (lateral) chromatic aberration if the pupil is not centered on the optical axis, and for points that are off the optical axis of the eye (Thibos, Bradley, Still, Zhang & Howarth, 1990). The transverse aberration produces a small change in angular magnification or a change in lateral image location for different wavelengths, but these effects are minor when compared to the effects of longitudinal chromatic aberration (Simonet & Campbell, 1990). These chromatic effects have implications for resolution and depth of focus, but in the present investigation we have concentrated on the degree to which longitudinal chromatic aberration (LCA) helps direct the focusing system of the eye. A central issue in accommodation research has been how the accommodative system knows which way to go;
*Schnurmacher Institute for Vision Research, State College of Optometry. State University of New York, NY 10010, U.S.A. 1397
Focus
that is, how it distinguishes over- from under-accommodation. Under normal conditions, accommodation is linked to binocular vergence, so that changes in convergence are usually accompanied by concomitant changes in accommodation (Morgan, 1944). In addition, both accommodation and binocular vergence are influenced by monocular and binocular depth cues, which provide unambiguous directional information for oculomotor control (Ittelson & Ames, 19.50; Kruger & Pola. 1985, 1986, 1987; Erkelens & Regan, 1986; Enright, 1987; McLin, Schor & Kruger, 1988). What has puzzled investigators is that the focusing system continues to operate effectively, even when all the usual cues to depth are eliminated. The conventional explanation for this response to dioptric vergence is that the eye accommodates to reduce defocus blur and to maximize contrast, and that negative feedback in the form of blur reduction is an important part of the process (Toates. 1970; Phillips & Stark, 1977). In addition, the ongoing highfrequency oscillations of accommodation may play an important role (Charman & Heron, 1988). But there is also the possibility that the system has more direct sensitivity to the vergence of light (wavefront curvature) or the degree of convergence or divergence of raybundles. In this context Hartridge suggested to Fincham that LCA might be involved in the process (Fincham, 1951)--the chromatic effects that result from LCA provide an index of focus that might help direct accommodation. Fincham was familiar with the techniques of clinical refraction. and was aware of the sensitivity of most patients to extremely small amounts of defocus. He was particularly interested in the “reflexive” type of accommodation that maintains the focus of the eye, and compensates for small amounts of hyperopia. and he
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was acquainted with the precautions that must be taken to avoid such accommodation during clinical refraction. Fincham reasoned that if this “reflexive” system operated in a trial-and-error manner to determine focus, it would be more unstable than it is, particularly under monocular conditions. Fincham interposed low power (l--I .5 D) plus and minus lenses in front of the eye of his subjects and monitored their response with a coincidence optometer. In polychromatic “white” light most subjects accommodated appropriately to the step changes in lens power. However in monochromatic sodium light (590nm) Fincham found that 60% of his subjects had diffculty accommodating or they could not accommodate at all. He obtained the same result when LCA was neutralized by an achromatizing lens. Fincham suggested that a chromatic mechanism, sensitive to the effects of LCA, provides a measure of light vergence for most subjects. He also postulated that an achromatic mechanism invotving the Stiles-Crawford effect might provide a directional cue for those individuals who continue to accommodate effectively in the absence of chromatic aberration. Fincham’s findings with regard to chromatic aberration gained some support from Campbell and Westheimer (1959), but most investigators have disagreed (Troelstra, Zuber, Miller & Stark. 1964; Stark & Takahashi, 1965; Van der Wildt, Bouman & Van de Kraats, 1974; Charman & Tucker, 1978; Wolfe & Owens, 1981; Bobier, Campbell & Hinch, 1992). In a previous series of experiments, we have confirmed that the accommodative system is sensitive to the effects of LCA, and that sensitivity to these effects varies among individuals (Kruger & Pola, 1986, 1987, 1989). Similar findings have recently been reported for accommodation in the monkey (Flitcroft & Judge, 1988). Pilot studies in our lab now suggest that sensitivity to LCA is much more profound and more widespread than Fincham and others have reported. In the present investigation we have taken a more definitive look at the influence of LCA in a large group of subjects by using more sensitive methods than in previous investigations.
The subject was instructed to fixate the center of a target (a Maltese cross) as it moved toward and away from the eye in a Badal stimulus system. The target was
presented in monochromatic light or white light. and the LCA of the subject’s eye was altered by specially designed lenses that neutralized or reversed the normal LCA of the eye. Accommodation was monitored continuously by a high-speed infra-red recording optometer. hstrumentation The infra-red optometer and the principles on which it operates have been described previously (Kruger, 1979). Its response is linear over a 6 D range, resolution is better than one-tenth of a diopter, and the cut-off frequency is 10 Hz. The system is insensitive to changes in pupil size and to eye movements up to 3 deg from the fixation point. The stimulus system is a modified Badal optometer (Crane & Cornsweet, 1970) that allows the dioptric stimulus for accommodation (target vergence or accommodative demand) to be varied sinusoidally without change in the visual angie subtended by the target (Ogle. 1968). The target is shown in Fig. 1. It subtends 4 deg at the eye, each limb of the cross forms an angle of 10 deg at the center of the cross, and the central points of the cross subtend approx. 1 min arc at the eye. The radial form of the target provides a central fixation point for the subject. The target is presented in white light (3000 K) or monochromatic light (590 nm with 10 nm bandwidth) at a luminance of 200cd/m’. The main components of the system are shown in Fig. 1. There are two superimposed optical systems: an illumination system represented by dashed lines, and a target system represented by solid lines. The illumination system will be described first. Light from source S {quartz tungstenhalogen lamp) is collimated by lens Ll and brought to focus by lens L2 at S’. The light is then re-collimated by lens L3 and reflected four times at the surfaces of right angled prisms PI and P2 as shown. (The entrance and exit faces of the prisms are mirror coated, while the hypotenuse of the prisms remains clear.) The collimated light is then brought to focus by lens L4 in the pupil of the subject’s eye E. An image of aperture A is formed in the pupil of the eye where it serves as a 3 mm artificial pupil. The target system (represented by solid lines in Fig. I) completes the stimulus system. Light from the target T is collimated by lens L2 and brought to focus by lens L3 at T’ after reflection at prisms Pl and P2. The subject
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FIGURE 1. Schematic representation of the Badal stimulus system. The illumination system is in dashed lines and the target system in solid lines.
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views an image of this real aerial image in Badal lens L4. If the target image T’ is in the focal plane of lens L4, the target appears to the eye at optical infinity. If the image T’ is closer to lens L4, the target appears blurred (if the eye is focused for infinity) and the eye must accommodate to clear it. Prism P2 can be moved, as shown by the arrow, to vary the distance between the image of the target (T’) and lens L4. The position of the prism is controlled by a servo-motor and computer which produce sinusoidal changes in the position of the target image. Such changes in target position stimulate accommodation through changes in the dioptric vergence of the target. To alter the LCA of the eye, one of two specially designed lenses can be positioned in the stimulus system at aperture A. The lenses are cemented doublets made of standard crown (SK16 620603) and flint glass (F2 620364) and having plano front and back surfaces. They have zero power at 588 nm and appropriate power at shorter and longer wavelengths to neutralize or reverse the normal LCA of the eye. The neutralizing lens is designed to focus all wavelengths approximately in the same plane in the eye so that there is no LCA. The reversing lens reverses the normal LCA of the eye so that short wavelength light focuses behind the retina rather than in front. and long wavelength light focuses in front of the retina rather than behind. Procedures Control experiments. The design of the zero-power doublets was tested by measuring the longitudinal chromatic aberration, transverse chromatic aberration and contrast sensitivity of the eye through the Badal stimulus system, with and without the lenses in place. These control experiments were run to examine the effect of the lenses on LCA, and to determine whether they introduce additional aberrations that might impair accommodation and confound our results (Powell, 1981; Simonet & Campbell, 1990). The left eye of the subject was carefully positioned in the apparatus by using a telescope to focus and align the cornea1 reflection of the target, and a forehead rest and bite-plate were used to ensure that the subject did not move during the measurements. (1) The LCA of the eye was measured in five subjects through the Badal stimulus system, with and without the lenses in place. The eye was cyclopleged by instilling two drops of 1% cyclopentolate hydrochloride 30 min before testing. Measurements of the subject’s far point were made at eight wavelengths between 450 and 670 nm using a method similar to Howarth and Bradley (1986). The subject used a potentiometer control and the method of adjustment to focus the target at each wavelength. Five measures were taken at each wavelength with target luminance at 200 cd/m2. We compensated for the ametropia of each subject by subtracting the average refractive error found in the neutralized condition (480-570 nm) from the optometer measures. Data from the five subjects were then averaged. (2) Transverse (lateral) chromatic aberration was measured in six subjects through the system with and
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without the lenses in place. These measures were also made under cycloplegia. For this procedure the target was replaced by two vertical vernier lines that were each 1.7 deg long and 0.5 min wide. The two vernier lines were imaged one above the other in the target plane of the stimulus system (at T in Fig. 1) by means of a twochannel optical system (not shown). The top vernier line was red (650 nm interference filter with a 10 nm bandwidth) and it could be moved laterally by the subject by turning a rotary dial connected to a precision linear stage. This allowed the line to be positioned with a resolution of 2 set arc. The bottom vernier line was blue (470 nm interference filter with a 10 nm bandwidth) and its position was fixed. Measurements were made for fovea1 viewing, as well as at 2 deg to the left and 2 deg to the right of the fovea (the position of the lateral edges of the cross target). Since transverse chromatic aberration should be measured with longitudinal chromatic aberration neutralized (Simonet & Campbell. 1990) our measures represent true transverse chromatic aberration only in the neutralized condition. It should also be clear that for the foveal-viewing condition the center of the target is OIZthe optical axis of the stimulus system. and therefore no lateral chromatic aberration can result from the stimulus itself. But transverse chromatic aberration can arise at the fovea from the optics of the eye since the optical axis is about 5 deg from the visual axis. and the pupil is usually somewhat decentered. In the case of peripheral targets, transverse chromatic aberration comes about from the stimulus system and from the eye. After the cycloplegia was complete the subject adjusted the focus of the two vernier lines while both were illuminated by monochromatic (590 nm) light. This position of focus was used for all the subsequent measures. The verniers were aligned 10 times and the average alignment position was used as the zero position for subsequent measures with the red and blue vernier targets. The targets were aligned 10 times by the subject, the red vernier being brought into alignment with the blue vernier from the opposite side on alternate trials. Measures were made at the fovea, as well as 2 deg to the left and 2 deg to the right of fixation. For the peripheral measures a small fixation light was used to maintain fixation at the center of the field. Subjects were instructed to make the alignments using their peripheral vision and they were urged not to look at the verniers. (3) Contrast sensitivity was measured in five subjects through the Badal system with and without the lenses in place. For this experiment the usual target was replaced by sine-wave gratings (1-21 c/deg) produced on a Joyce display-scope (white P4 phosphor). The display was imaged through the stimulus system with a mean luminance through the apparatus of 17 cd/m’. A twoalternative (spatial) forced-choice procedure was used to measure threshold contrast of the subjects (Stone, Kruger & Mathews, 1990). A small fixation target (black cross) was positioned at the center of a 6 deg field to serve as an accommodative stimulus. Both the fixation target and sinusoidal gratings were positioned at the subject’s dark focus to minimize accommodative error.
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The subjects indicated by pressing a keypad whether the vertical gratings appeared in the left or right half of the stimulus field. Muin experiment. Before each experimental trial the subject was carefully positioned in the apparatus using a telescope to focus and align the cornea1 reflection of the target. A bite plate and forehead rest kept the subject still, trial lenses before the left eye compensated for any refractive error, and the right eye was patched. The room was dark and the apparatus shielded so that the target was the only visible stimulus. The subject was instructed to “concentrate on the center of the target” (Maltese cross) as it moved sinusoidally toward and away from them. There were four stimulus conditions: (1) normal (white target with the usual LCA); (2) neutralized (white target with no LCA); (3) reversed (white target with LCA opposite to normal), and (4) monochromatic (orange target of 590 nm light with 10 nm bandwidth). Changes in the dioptric vergence of the target were produced by moving the target image (T’) sinusoidally toward and away from the subject’s eye, so that the stimulus varied sinusoidally over a 1 D range between 1.5 and 2.5 D. The four stimulus conditions were presented in random order at 0.2 Hz and four trials of 41 set duration were run for each stimulus condition. Stimulus motion was controlled by computer, and the stimulus and accommodative response were recorded by polygraph and computer. Output of the infra-red optometer was sampled at 100 set -I and stored for analysis. The analysis program removed the effects of blinks, scaled the data according to the subject’s calibration (see below), and performed a fast Fourier transform on the data from each trial, to derive the amplitude and phase of the accommodative response. Gain is the amplitude of the response divided by the amplitude of the stimuius, and phase-lag is the distance in degrees from the peak of the stimulus to the peak of the response. Gain and phase measures for the four trials for each condition were vector-averaged to provide mean gain and phase, and standard errors for each condition. Calibration of the infra-red optometer was performed at the beginning of each session. The subject was instructed to focus the target, which was then stepped through 0, 1, 2, 3, and 4 D of accommodative demand. The target paused for 10 set at each stimulus level and the procedure took about a minute. The accommodative response to the four stimulus levels was disptayed on the computer screen, the average responses to the 1 and 3 D stimuli were estimated from the display, and these two measures were stored in the computer for subsequent use in the analysis procedure. The estimated measures were highly repeatable and they changed very little for each subject over the course of the experiment. This method of calibration does not provide an absolute calibration of accommodation because the accommodative response does not necessarily equal the stimulus at all distancessubjects tend to over-accommodate for targets at optical infinity and under-accommodate for targets at near.
1’1d.
However, these measures allow relative accommodative performance to be evaluated with confidence. su/?jt?cts Twenty-five subjects took part in the experiment. All had normal vision and were free of ocular pathology. Their ages ranged from 22 to 38 yr and all had sufficient accommodative amplitude for the experiment. Two of the investigators participated in the experiment. All the other subjects were naive to the purpose of the experiment and were paid for their participation. The subjects gave informed consent. RESULTS
Control experiments
LCA was measured for five subjects through the stimulus system, with and without the lenses in place. Figure 2 shows the lens power needed to correct the aberration for wavelengths between 450 and 670 nm. In addition to the data for the reversing and neutralizing lenses, the figure includes a plot for normal LCA. The reversing lens essentially reverses the lens power needed to correct the aberration at each wavelength. The neutrahng lens focuses most wavelengths of light in the same plane but there is a small amount of residual LCA (under-correction) at long wavelengths. The measures of normal LCA are similar to those of Bedford and Wyszecki (1957). Transverse chromatic aberration (TCA) was measured for six subjects. Figure 3 shows data for each of the six subjects for fovea1 viewing, as well as for 2 deg to the left and 2 deg to the right of fixation. TCA at the fovea with no lenses in place ranges from - 68 to + 73 set arc with an absolute mean of 46 set arc for the six subjects. These are similar to previous measures of TCA at the fovea (Ogboso & Bedell, 1987; Simonet & Campbell, 1990). Mean TCA remains essentially the same (48 set arc) with the neutralizing lens in place, and increases to 87 set arc 2
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-2”“‘1”‘,1”“‘,“*““.i”‘-J 4004!505fn550300650700 WAVEtENGTH (nm) FIGURE
2. Longitudinal chromatic aberration (mean of five subjects)
with no lens in place (normal) and with the neutralizing and reversing lens in place. The y-axis shows the lens power needed to correct the aberration. The lenses operate essentially as designed. Error bars show +I SEM.
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FIGURE 3. Lateral chromatic aberration for six subjects measured through the Badal stimulus system with and without the special lenses in place. Data are for fovea1 viewing and for 2 deg to the left and 2 deg to the right of the central fixation point. Error bars show k 1 SEM.
with the reversing lens in place. It is not unusual for individuals to show TCA of 1 or 2 min arc at the fovea, although TCA is usually < 1 min arc (Simonet & Campbell, 1990). These relatively small amounts of TCA are not likely to be of consequence in the present experiment. We also measured the contrast sensitivity of five subjects through the system, with and without the lenses in place. Mean data for the five subjects are shown in Fig. 4. Contrast sensitivity is essentially the same for the three conditions, even at high spatial frequencies where the effects of aberrations should be most prominent. Main
is a little smaller than the amplitude of the stimulus, and accommodation follows the stimulus with a small phase lag. When LCA is neutralized the amplitude of the response is reduced substantially, while in monochromatic light and with LCA reversed the response is barely perceptible. The high frequency oscillations of accommodation, with about 0.25 D amplitude at 2-3 Hz, are prominent under all four experimental conditions. The second subject shows a similar pattern.
experiment
It became clear early in the study that many subjects are highly sensitive to the effects of LCA. When the chromatic cues are removed by the neutralizing lens or through the use of monochromatic light, the amplitude of the response is reduced and the response becomes erratic. When the aberration is reversed, accommodation is often totally disrupted. Data for three typical subjects under each of the four experimental conditions are shown in Fig. 5. For each subject the stimulus is the top trace and four response traces are shown below (normal, neutralized, monochromatic and reversed). The first subject accommodates well in the normal condition, the amplitude of the response
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FIGURE 4. Contrast sensitivity (mean of five subjects) measured through the Badal stimulus system with no special lens present, and with the neutralizing or reversing lens in place.
PHILIP B. KRUGER c/ (11. 4-
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FIGURE 5. Typical data from three subjects for each of the four experimental conditions. For each subject the top trace is the stimulus and the traces below are the responses to each condition. Each trace is from one 40 set trial. The large transients in the neutralized and reversed conditions are blinks.
Accommodation is good in the normal condition, the response is reduced in the neutralized and monochromatic conditions, and there is little response in the reversed condition. However, unlike the first subject, some accommodative tracking is present in monochromatic light and also when the aberration is reversed. The third subject shows more erratic behavior. Although this subject accommodates well in the normal condition, he often uses large accommodative “saccades” to clear the target as it moves away, and these “saccadic” responses become prominent when LCA is removed or reversed. The data in Fig. 5 are typical of most subjects, especially for the normal, neutralized and monochromatic conditions. But subjects show a wider range of behaviors in the reversed condition. Figure 6 shows data from six subjects with LCA reversed (one trace from each subject). Their responses are more variable and more erratic than most subjects. Large oscillations of accommodation are common, and accommodation often changes
abruptly from one relatively steady-state level to another. Some subjects show considerable over-accommodation while others under-accommodate, and this behavior sometimes changes abruptly during the course of a trial. Only one subject out of 25 showed little or no deficit when LCA was removed, but even this relatively insensitive subject showed a drop in gain when LCA was reversed. Examination of the color vision of this subject (anomaloscope) showed him to be deuteranomalous. The data were analyzed by computer to give measures of gain and phase at the temporal frequency of the stimulus and the four measures for each condition were vector averaged for each subject. Although it is not clear from the data in Fig. 6, at least one-quarter of the subjects show some evidence of counterphase tracking when LCA is reversed. In these subjects phase-lag is particularly large, ranging from about 180 to 300 deg, but because the response is so small in the reversed condition, the effect of such counterphase tracking is easily obscured in Fig. 6. Figure 7 shows the average 1.0 0.8
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6. Accommodative response from six subjects with LCA reversed. Each trace is from one 40 set trial.
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FIGURE 7. Mean accommodative gain and phase for the four experimental conditions for 25 subjects. Error bars (k 1 SEM) are sometimes smaller than the symbols.
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gain and phase for all 25 subjects for the four experimental conditions. Gain is reduced successively in the neutralized, monochromatic and reversed conditions, and phase-lag increases in each successive condition. In the reversed condition the standard error for phase-lag is large because some subjects track in counterphase. A one-way ANOVA was used to compare accommodative gain across the four experimental conditions. The conditions differed significantly from one another [F(3,96) = 57.2, P < 0.011. Planned comparisons indicated significant differences between all sets of means taken two at a time [normal and neutralized, r(96) = 4.47, P < 0.01; normal and monochromatic, t(96) = 8.79, P < 0.01; normal and reversed, ~(96) = 12.35, P < 0.01; neutralized and monochromatic, t(96) = 4.32, P < 0.01; neutralized and reversed, t(96) = 7.89. P < 0.01; monochromatic and reversed, ~(96) = 3.56, P < 0.011. DISCUSSION
The measures of LCA that were made with the special lenses in place show that the lenses function essentially as designed. In addition, the measures of lateral chromatic aberration and contrast sensitivity show that the lenses do not introduce aberrations that reduce the contrast of the retinal image. Therefore, the effects of the lenses on gain and phase of accommodation are presumably not due to blur introduced by the lenses, but rather to the elimination or reversal of the effects of LCA. In a related experiment we doubled the amount of LCA and found that neither contrast sensitivity nor accommodation were affected (Kruger, Mathews & Fox, 1987). The chromatic cues seem to be effective as long as they are in their normal ordered configuration with short wavelength light focusing before long wavelength light. Our findings with regard to LCA and contrast sensitivity agree with the results of other investigations in which MTF and visual discrimination showed no improvement under monochromatic or achromatized conditions (Krauskopf, 1964; Bour, 1980). Explanations include the filtering effects of the yellow macular pigment and crystalline lens of the eye, and the spectral sensitivity of the cone photoreceptors (Walls, 1942; Reading & Weale, 1974). LCA is most severe at short wavelengths where the macula lutea absorbs most effectively, and where visual sensitivity is at a minimum. In addition, the short-wavelength cones have poor spatial discrimination which may serve as a further “spectrum-shortening device” (Boynton, 1979). Despite the variety of mechanisms that serve to minimize these “image-degrading” effects, the focusing mechanism remains remarkably sensitive to the effects of LCA. A related issue is the depth of focus of the eye. If the neutralizing or reversing lenses alter depth of focus, this might explain our findings-a larger depth of focus might reduce the accommodative response (gain), while a smaller depth of focus might actually improve the response. This explanation does not fit our results. For example, the neutralizing lens should improve the qual-
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ity of the retinal image (by removing LCA), this should decrease depth of focus, allow greater sensitivity to defocus blur, and perhaps more accurate accommodation. This clearly is not the case, since accommodation is impaired with the neutralizing lens in place. On the other hand, with the reversing lens in place the amount of LCA should be essentially unchanged, since the lens simply inverts the order of spectral foci (Fig. 2). Thus with LCA reversed, depth of focus should be similar to the normal condition and accommodation should not be impaired. Finally, we find that doubling the amount of LCA has no effect on accommodation (Kruger et al., 1987). Doubling the aberration should increase depth of focus, and following this line of reasoning, should impair accommodation, but this did not happen either. Depth of focus does not seem to be an important factor in the present experiment. It is clear from our data (particularly Fig. 7) that the use of monochromatic light to eliminate the effects of LCA is more debilitating than use of the achromatizing lens. This result is puzzling and disagrees with Fincham’s report that accommodation is impaired equally by the use of monochromatic light or by an achromatizing lens (Fincham, 1951). Although Fincham’s method was less exacting than ours and may not have allowed him to discern the difference, our result is still difficult to explain. If the effects of LCA are important for accommodation, it should make no difference whether they are removed by an achromatizing lens or by the use of monochromatic light. Perhaps the small undercorrection of LCA by our achromatizing lens for long wavelength light allows the residual chromatic aberration to assist accommodation in the achromatized condition. The residual aberration is only about $ D between 570 and 630 nm, but this may be enough to improve the accommodative response. Another possibility is that 590 nm light may be particularly debilitating, and accommodation might improve if 550 nm light had been used instead. Pilot studies in our lab suggest that accommodation does improve to a small degree when the illumination wavelength is shorter than 590 nm, but accommodation remains poor even in 550 nm light. Finally, the broadband nature of “white” light may somehow be important for accommodation, even without the effects of LCA. In the natural environment the source of light and the reflectance of surfaces usually have broad spectral bandwidth, and the perceptual processes that evolved under these conditions might be compromised in narrowband monochromatic illumination. For example, the mechanisms of color constancy that separate reflectance (object color) from illumination, seem to depend on broadband illumination for their operation (Land & McCann, 1971; Rubin & Richards, 1982; Daw, 1984; Gershon, Jepson & Tsotsos, 1986). If the chromatic aspect of accommodative control depends on mechanisms like those that mediate color constancy, this might contribute to the particularly poor performance in monochromatic illumination. Whatever the basis for the impairment, the poor response in monochromatic light suggest that pure contrast change
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(together with negative feedback) is a relatively ineffective stimulus for regexive accommodation. It is also clear from our results that reversing LCA is even more debilitating than the use of monochromatic light. A likely explanation is that when LCA is reversed the color “fringe” drives accommodation in the wrong direction, but blur feedback reveals the error and restrains the response. If this explanation is correct, accommodation should improve under open-loop conditions where blur feedback cannot disturb the response. Pilot experiments conducted under open-loop conditions lend some support to this view-most subjects track in counterphase when LCA is reversed, but the accommodative gain remains relatively low. Reversing LCA does not simply drive accommodation in the wrong direction; under open-loop conditions there seems to be an achromatic directional cue that counteracts the chromatic cue when LCA is reversed (Kruger, Mathews, Aggarwala & Nowbotsing, 1992). Only one other study has used sinusoidally moving targets to examine the effect of chromatic aberration on accommodation. As part of a larger investigation, van der Wildt et al. (1974) examined one subject in white and monochromatic light and found no difference in accommodation for the two conditions. The present data suggest that such individuals are rare, and points to the danger of generalizing from small numbers of subjectsin the present study only one of 25 subjects showed little or no deficit in monochromatic light. All other investigations of the effect of LCA on accommodation used stationary targets, or targets that step to a new position, to examine sensitivity to these chromatic cues (Troelstra et al., 1964; Stark & Takahashi, 1965; Charman & Tucker, 1978; Bobier et al., 1992). Such stimuli are much easier to focus than moving targets, and voluntary accommodation can inffuence the results of such experiments. Many subjects can readily alter focus to manipulate the contrast of the retinal image, and such conscious trial-and-error behavior can mask the influence of subtle cues like LCA, especially when the stimulus is stationary or when it steps to a new position. The problem is compounded by the use of averaged data from static stimuli, which can obscure the variable and erratic behavior that is typical of many subjects when the effects of LCA are disturbed. We believe the methods used in some of the previous investigations may have allowed voluntary accommodation to conceal the role of LCA. The related issues of attention and prediction were addressed by van der Wildt et al. (1974). Their study showed that careful instruction can profoundly influence the degree of anticipation that subjects display. If the subject was specifically instructed to maintain focus and to keep the target “clear”, gain increased and phase lag decreased. But if the subject was instructed to “concentrate” on the form of the target, rather than to maintain its clarity, gain and phase were consistent with results obtained from unpredictable input signals. In the present experiment we carefully instructed our subjects to “concentrate” on the target, and avoided the terms “ciear” or “focus”. With this type of instruction, we believe that
et al.
sinusoidally moving targets provide a more sensitive method of examining the stimuli for accommodation with minimal intrusion of voluntary behaviors. We find that the rhythmical nature of the blur stimulus is often barely perceptible when the amplitude of target motion is moderate (1 .OD). If the subject is carefully instructed the appearance of a “beat” from defocus-blur seems to be of little help to the system. We have compared the phase-lags from our experimental data, with calculated phase-lags derived from experimental gains and a firstorder linear model of accommodation, and find that the experimental and calculated data are very similar (Mathews, 1989). This suggests that with careful instruction sinusoidally changing dioptric stimuli afford little anticipation. We believe that our method effectively isolates the “reflexive” aspect of the accommodative system that responds automatically to small changes in focus, and operates even in the absence of depth cues and other non-dioptric influences. Our results show that sensitivity to the effects of LCA is widespread and not limited to a subgroup of individuals. Our data support Fincham’s conclusion that color fringes at edges provide directional information for accommodation, and that sensitivity to these cues varies among the population. But our results also show that Fincham under-estimated the number of subjects that respond to these cues. Of his subjects 40% were able to accommodate effectively in monochromatic light, and Fincham concluded that they were insensitive to the effects of chromatic aberration. His methods may have made it difficult to identify subjects that have moderate or low sensitivity to LCA. The present investigation and others also suggest that chromatic aberration does not provide the only stimulus for reflex accommodation. Subjects accommodate to some degree in monochromatic light, albeit with reduced effectiveness, and some tracking ability remains even under open-loop conditions, where blur feedback cannot assist the process (Kruger ef al., 1992). Our findings suggest that “achromatic” and “chromatic” mechanisms operate in unison as complementary components of the “reflexive” focusing system. The achromatic system is rather slow and inefficient on its own (reduced gain and increased phase-lag), but when the chromatic system supplements its activity, there is much finer control of accommodation and a more accurate and effective response. It is noteworthy that our subjects respond to these chromatic effects on first exposure to dioptric blur, and do not learn to use the cues during the experiment. Data collected during the first trials of our experiments, and then over months and even years in some subjects, shows no improvement over time. Subjects who respond readily, respond well on their first practice trial, and those who are less sensitive remain that way despite repeated exposure. When LCA is reversed, accommodation is debilitated during the first practice trial, and the response remains poor throughout the experiment and on repeated exposure. The strength of these cues in so many subjects, and the severe disruption of accommodation that results from their removal or reversal,
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suggests that the ordered arrangement of chromatic foci, with short wavelength light focusing before long wavelength light, is a fundamental aspect of the stimulus for reflex accommodation, and may be a basic feature of the proximal visual stimulus. Most of the luminance gradients that comprise the retinal image are characterized by the effects of LCA, and these gradients and edges play a fundamental role in the perceptual process (Krauskopf, 1963; Shapley & Tolhurst, 1973; Kulikowski & King-Smith, 1973; Marr & Hildreth, 1980; Graham, 1980; Gershon, Jepson & Tsotsos, 1986). The issue calls for a critical look at the nature of the image on the retina, and the changes that take place with change in focus. .?Tfect
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0.5D DEFOCUS 74% CONTRAST
1.25D DEFOCUS 43% CONTRAST
qf chromatic aberration on the retinal image
The target in the present experiment has a complicated spatial structure with broad spatial frequency content. Its image on the retina is blurred by scatter, diffraction, aberrations and defocus, and the effect is particularly severe at high spatial frequencies (Fry, 1955; Charman, 1983). Spherical aberration, irregular and asymmetric monochromatic aberrations, chromatic aberration (longitudinal and transverse) and inaccurate focus all influence the MTF of the eye (Van Meeteren, 1974; Bour, 1980; Charman, 1983; Thibos, 1987). But if we limit discussion to relatively low spatial frequencies (3 c/deg) and moderate pupil sizes (3 mm) the situation is less complicated. At 3 c/deg, diffraction. off-axis imagery (angle alpha), lateral chromatic aberration, and even spherical aberration have minimal effect on contrast, and the principle cause of retinal blur is LCA (van Meeteren, 1974; Charman, 1983). Accommodation responds well at 3 c/deg (Owens, 1980; Ward, 1987; Mathews, 1989) and single sine-wave gratings can be as effective as more complex stimuli (Phillips, 1974; Charman & Tucker, 1977). Moreover, sensitivity to the effects of LCA is prominent at 3 c/deg (Kruger. Stevens & Mathews, 1989). It is important to understand that a distant 3 cjdeg “white” sine-wave grating target actually forms a spectrum of (aerial) grating images in the eye-long wavelength components of the image come to focus further back in the eye than short wavelength components. As a consequence, for any condition of focus, the contrast on the retina varies across wavelength. As an example, if long wavelength light (650 nm) from a “white” sinewave grating target is focused on the retina, contrast at this wavelength is at a maximum; but light of shorter wavelength focuses in front of the retina, and its contribution to the retinal image is blurred and has reduced contrast. The retinal image of a white sine-wave grating can be treated as approximating the sum of longmediumand short-wavelength components, each of different contrast. These relations are illustrated in Fig. 8(a). We used the method of Hopkins (1955) and Flitcroft (1990) to calculate Michelson contrast for three conditions of focus. The example is for an eye with a 3 mm pupil viewing a 3 c/deg sine-wave grating in monochromatic (550 nm) light. The top function is the lumi-
FIGURE 8. Luminance profile for a 3 qdeg sine-wave grating imaged on the retina through a 3 mm pupil with various degrees of defocus. (a) Monochromafic (550 nm) grating: the top luminance profile is for an in-focus image with 80% contrast, the second luminance profile is for i D of defocus with 74% contrast. and the third profile is for I .25 D of defocus with 43% contrast. (b) Broadband poiychromuric sine-wave grating (3 c/deg) to show the effect of LCA. Mean luminance is the same at each wavelength. Long wavelength light (650nm) comes to focus on the retina with 80% contrast, medium wavelength light (540 nm) comes to focus : D in front of the retina with 74% contrast, and short wavelength light comes to focus I .25 D in front of the retina with 43% contrast.
nance profile of an “in focus” image of a sine-wave grating (80% contrast), the middle function is for the same image defocused by 0.5 D (contrast is reduced to 74%) and the bottom function is for 1.25 D of defocus (contrast is 43%). At 3 c/deg, defocus-blur simply reduces the contrast of the grating image, without altering its spatial frequency or phase. In white (polychromatic) light, all three “components” are present simultaneously. Figure 8(b) shows the luminance profile of such a broadband aberrated image of a sine-wave grating. Long wavelength light (650 nm) is focused on the retina with 80% contrast, medium wavelength light (540 nm) is focused about i D in front of the retina with 74% contrast, and short wavelength light (450 nm) is focused about l;D in front of the retina with only 43% contrast. When the eye changes focus (accommodates) the contrast at each wavelength changes, increasing for some and decreasing for others. In the example above, if accommodation is reduced (relaxed) by i D, medium wavelength light (540 nm) will now be focused on the retina with maximum contrast, long wavelength light (650 nm) will focus behind the retina with reduced contrast, while short wavelength light (450 nm) will still be focused in front of the retina but with increased
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contrast. The ordered arrangement of spectral foci ensures that for a given source, and for any particular condition of focus, contrast of the long-, medium- and short-wavelength components of the retinal image specifies focus. The image on the retina is replete with these effects, and they are prominent at spatial frequencies where accommodation responds best (3-5 c/deg). At higher spatial frequencies the effects of defocus (and LCA) are much more severe. For example, at 10 c/deg, defocus in the amount of 0.75 D is sufficient to reduce contrast from over 80% to zero (Walsh & Charman, 1988). Accommodation may respond poorly at high spatial frequencies because small amounts of defocus have such severe effects on MTF. In addition, spatial acuity of the color mechanisms is limited to about 10 c/deg (Mullen, 1985). Is accommodation color -blind? In a novel experiment, Wolfe and Owens (1981) used a stimulus for a~ommodation that had no luminance contrast but only chromatic contrast (isoluminant stimulus). They found that accommodation fails under such conditions, and concluded that accommodation is “color-blind”. Following this conclusion they could not understand how the accommodative system could use the subtle effects of chromatic aberration to direct accommodation. Their results were confirmed by Switkes, Bradley and Schor (1990), using sinusoidal gratings consisting of either isochromatic luminance modulations or isoluminant red-green gratings. We have used the present (dynamic) methods to examine the accommodative response to isoluminant stimuli, and our results agree with the previous investigations (Mathews & Kruger, 1990). When the target is an isoluminant edge separating red and green hemifields, it is extremely difficult to focus the edge. The impairment of accommodation at isoluminanc~ is more severe than the deficit from removing or even from reversing LCA, and is probably related to the poor performance of many other visual functions at isoluminance (Livingstone & Hubel, 1988; Troscianko & Fahle, 1988; Logothetis, Schiller, Charles & Hurlbert, 1990). In the natural environment isoluminant edges are extremely rare, and the usual combination of luminance and color changes at edges may be vital for perceptual processes that evolved under normal ecological conditions. For example, analysis of luminance and color changes at edges seems to be important for distinguishing between edges that specify shadows, highlights. material (color) changes, and the shading that results from changes in surface orientation (Rubin & Richards, 1982; Gershon, Jepson & Tsotsos, 1986). While the physiological basis for the impairment at isoluminance is controversial, an important factor seems to be the way in which the visual system encodes color and luminance information. Recent evidence suggests that color and luminance signals are mixed or “multiplexed” in a single channel, rather than separated in independent channels (Logothetis et al., 1990; Billock, 1991; Gur & Akri, 1992). Thus isoluminance may not be an appropriate method to determine whether accommo-
dation is color-blind. Although luminance contrast seems to be essential For reflex accommodation, a truly color-blind system shouid not respond to the subtle chromatic effects of LCA. Besides the neurophysiological considerations, the nature of the blur spread-function may also play a role in the failure at isoluminance. Previous investigators seem to confuse the conventional type of color contrast that is an inherent property of isoluminant red-green edges and gratings, with the subtle chromatic contrast that is produced by LCA and is superimposed on luminance edges and gratings. Their argument seems to be that because color contrast is present at isoluminant edges, and a~ommodation fails, accommodation must be color blind. But conventional color contrast is not equivalent to the ordered arrangement of spectral contrast at luminance edges; and conventional color contrast does not change in the same way as it does at luminance edges, when focus changes. Figure 9 illustrates the essential differences between luminance and isoluminant edges and emphasizes the effects of LCA. The edge spread-functions were generated by convolving an edge with a series of Gaussian functions. The effects of defocus (due to LCA) were simulated by varying the standard deviation of the Gaussian according to the methods of Fry (1955). The example is for a reduced eye with a 4mm pupil. The illustrations at the top show the distribution of light across the image of a luminance edge composed of four wavelengths of light (500, 550, 600 and 650 nm). In the example on the left, red light (650 nm) is in focus on the retina, and shorter wavelength light focuses in front of the retina; while on the right green light (500 nm) is in focus and longer wavelength light focuses behind the retina. As a result of LCA the distribution of light varies as a function of wavelength, and subtle chromatic contrast is produced across the luminance border. This dioptric type of chromatic contrast extends for several minutes of arc on either side of the border, and its chromatic structure varies with the wavelength of light that is focused on the retina. The color “fringe” that forms on the dark side of the luminance edge ostensibly specifies focus--overaccommodation for a “green” fringe (left side of Fig. 9) and under-accommodation for a “red” fringe (right side of Fig. 9). The lower half of Fig. 9 shows the distribution of light across the image of a red-green isoluminant edge that is similar to the targets used by Wolfe and Owens (1981). The red and green components each have a bandwidth of 50nm and each color is represented by two wavelengths of light-650 and 600nm for red; 550 and 500 nm for green. The illustration on the left is for 650 nm light in focus on the retina, while on the right 500 nm light is in focus. At red-green ~sol~inant edges the red and green edge spread-functions extend in opposite directions from the border, and do not overlap as they normally do at broadband luminance edges (top of Fig. 9). As a result, the ordered chromatic spectrum that normally forms at luminance edges is disturbed at isoluminant edges, and the color “fringe” that normally
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FIGURE 9. Distribution of light across the retinal image of a broadband luminance edge (top) and a red--green isoluminant edge (bottom) for two conditions of focus. On the left 650 nm (red) light is in focus on the retina. and on the right 500 nm (green) light is in focus.
forms at luminance edges is largely concealed. While conventional chromatic contrast certainly exists at isoluminant edges, the subtle contrast that results from LCA is obscured. A similar situation holds for sinusoidal grating stimuli, like those used by Switkes et ul. (1990). Figure IO illustrates the differences between luminance and isoluminant gratings, and emphasizes the effects of LCA. We used the methods of Hopkins (I 955) and Flitcroft (1990) to calculate Michelson contrast for a 5 cjdeg sine-wave grating viewed through a 4mm pupil. The figure shows the distribution of light across one cycle of the retinal image. The top illustrations are for broadband “isochromatic” luminance gratings showing the luminance profile of the retinal image for four wavelengths of light (500,550,600 and 650 nm). The example on the left is for 650 nm (red) light in focus on the retina (80% contrast), and the example on the right is for 500 nm (green) light in focus (80% contrast). Light that comes to focus behind or in front of the retina has reduced contrast. The figure clearly illustrates the effects of LCA on contrast. For luminance gratings, the entire grating essentially becomes a “color fringe” that specifies focus-over-accommodation on the left and under-
accommodation on the right. The systematic ordering of the wavelength components of the image depends on focus, and the order reverses in the peaks and troughs of the gratings (on either side of the zero-crossings). Most important is the subtle chromatic contrast between the peaks and troughs of the luminance grating, which changes with change in focus. The situation is quite different for red-green isoluminant gratings. The bottom illustrations (Fig. 10) show the distribution of light across the retinal image of an isoluminant red-green grating, in which the red components of the grating (650 and 600 nm) are in spatial counterphase with the green components (550 and 500nm). In the example on the left 650nm light is in focus with maximum contrast (80%). and contrast is reduced for shorter wavelength components of the image. On the right, 500 nm light is in focus, and contrast is reduced for longer wavelength components, LCA thus introduces substantial luminance artifacts in the retinal image of isoluminant gratings, and the artifacts depend critically on focus (Bradley, Zhang & Thibos, 1992). But more important is that the long- and medium-wavelength components of the image are in spatial counterphase, and this disturbs the normal arrangement and behavior of the color
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FIGURE IO. Distribution of light across the retinal image of a broadband sinusoidal luminance grating (top), and a red-green isoluminant grating (bottom) for two conditions of focus. On the left 650 nm (red) light is in focus on the retina, and on the right 500 nm (green) light is in focus.
“fringe” that is a typical feature of broadband luminance gratings. For luminance edges and gratings the combination of luminance contrast (from the edge or grating) and chromatic contrast (from LCA), seems to be important for accommodation. At isoluminant borders and gratings not only are luminance gradients missing, but the usual effects of LCA are disturbed and obscured as well. If (as we suggest below) the accommodative system monitors focus by comparing the contrast of long- and medium-wavelength components of the grating image, accommodation might be confused by isoluminant gratings.
The mechanisms that support this chromatic aspect of the focusing system have hardly been explored. Crane (1966) introduced an early model that incorporates three receptor types and the effects of LCA to simultaneo~ly sample the retinal image at three levels of focus. The idea is particularly appealing, but scant attention has been paid to the subject. Recently Flitcroft (1990) modeled the behavior of “typical” cortical neurons using a difference-of-Gaussians (DOG) paradigm, and showed that spatially bandpass chromatically opponent neurons can perform the
necessary chromatic analysis between 2 and 8 c(deg. The mechanism could be similar to that proposed by Land (1983), in which the quality of the image in each cone mechanism or “retinex” is compared. In the present context, the ratio of “effective contrast” in each of the three cone systems might specify focus, and the changes in effective contrast that accompany defocus might activate accommodation. The process would require comparison of contrast by conventional red-green (and perhaps blue-yellow) opponent mechanisms. Flitcroft (1989) has also addressed some of the implications for calorimetry and visual physiology. In particular, he showed that the theoretical color spaces based on the “Silent Substitution” method (MacLeod & Boynton, 1979; Derrington, Krauskopf & Lennie, 1984) are sensitive to the effects of LCA and defocus. Small amounts of defocus can have significant effects on the results of psychophysical and electrophysiological experiments. There is also the possibility that LCA is more directly involved in the perceptual process. Recently Cobb (1991) used an anomaloscope to examine the color vision of subjects, both with and without the effects of LCA. Color vision was “adversely affected” when the effects of LCA were removed. Along these lines,
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Funt and Ho (1989) have shown that in theory a type of “spectral photometry” could be performed on the spread-function at edges, to extract the spectral power distribution of the light. Such information could assist the mechanisms of color constancy. With regard to the neurophysiology, changes in focus are likely to influence the activity of midget ganglion cells (P cells) in the retina, and Type I cells in the parvocellular layers of the LGN (Wiesel & Hubel, 1966; Shapley & Perry, 1986; Kolb, 1991). These cells have long- and medic-wavelength color and spatial opponency (e.g. center R+ and surround G-), and they transmit a mixture of luminance and hue information (Billock, 1991). They respond well to luminance edges, and the activity of some of these cells is likely to modulate in response to the effects of defocus that are illustrated at the top of Figs 9 and 10. Besides such retinal and geniculate involvement, the effects of LCA and defocus should be detected by cells like the double opponent cells that are found in the “blobs” of the striate visual cortex (Michael, 1978; Livingstone & Hubel, 1984; Ts’o & Gilbert, 1988; Born & Tootell, 1991). These cortical cells have a chromatically opponent center-surround receptive field organization (e.g. center R+ G - and surround G+ R-) that responds well to the chromatic effects of defocus (Flitcroft, 1990). Connections from cortex to midbrain were originally suggested by Jampel (1959) but direct chromatic pathways from retina or LGN to the oculomotor nucleus may also exist. Sensitivity to light vergence
Fincham’s idea that the visual system might be sensitive to light vergence (wavefront curvature) was provocative, because such sensitivity does not fit with conventional views of visual optics. The issue was addressed by Heath (1956) soon after Fincham published his findings. In Heath’s experiment, subjects viewed a Snellen target in a Badal optometer. Target vergence was varied by moving the target toward or away from the eye, and the focus of the eye was measured with a subjective optometer. In addition to producing defocus blur, Heath could blur the targets themselves by means of a ground glass diffusing screen. He found that the accommodative response decreased steadily as acuity was reduced from 20,llOO (6 c/deg) to 20~400 (1 c/deg), and when the target was extremely blurred the response became independent of the stimulus. These findings agree with what we now know about accommodative sensitivity to the spatial frequency content of the target (Owens, 1980; Mathews & Kruger, 1993). But Heath reasoned that if the eye is sensitive to light vergence it should be able to accommodate effectively even if the target was extremely blurred (20/600 or 1 c/deg). He seemed to have the view that the vergence of light from the target should be effective independent of the spatial frequency content of the target. This assumption led Heath to conclude that the eye is insensitive to light vergence, and the issue has remained dormant.
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Acknowledgements-We thank Dr Edwin Bechtold for designing the doubling, neutralizing, and reversing lenses. The research was supported by grants from the Schnurmacher Institute for Vision Research (91-92-026), the Research Foundation of the State University of New York (FY89-91), and the National Eye Institute (EY07494: EY08953; EY05901). We acknowledge the help of Dean Yager, Alan Lewis, Milton Katz, Harry Wyatt, Jordan Pola and Sheldon Ebenholtz, and thank John Orzuchowski, Matthew Polasky. Diane Schiumo and Wayne Grofik for technical assistance.
