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The effect of ocular aberrations on steady-state errors of accommodative response
Abstract
It is well accepted that the accommodation system is characterized by steady-state errors in focus. The purpose of this study was to correlate these errors with changes in ocular wavefront aberration and corresponding image quality when accommodating. A wavefront analyzing system, the Complete Ophthalmic Analysis System (COAS), was used in conjunction with a Badal optometer to allow continuous recording of the aberration structure of the eye for a range of accommodative demands (up to 8 D). Fifty consecutive recordings from seven subjects were taken. Monocular accommodative response was calculated as (i) the equivalent refraction minimizing wavefront error and (ii) the defocus needed to optimize the modulation transfer function at high spatial frequencies. Previously reported changes in ocular aberrations with accommodation (e.g., the shift of spherical aberration to negative values) were confirmed. Increased accommodation errors for near targets (lags) were evident for all subjects, although their magnitude showed a significant intersubject variability. It is concluded that the one-to-one stimulus/response slope in accommodation function should not always be considered as ideal, because higher order aberrations, especially changes of spherical aberration, may influence the actual accommodative demand. Fluctuations may serve to preserve image quality when errors of accommodation are moderate, by temporarily searching for the best focus.
History
Received August 15, 2004; published May 23, 2005
Citation
Plainis, S., Ginis, H. S., & Pallikaris, A. (2005). The effect of ocular aberrations on steady-state errors of accommodative response.
Journal of Vision, 5(5):7, 466-477,
Keywords
accommodation, steady-state errors, spherical aberration, image quality, wavefront
When we observe an object in the distance, the retinal
image of the target is supposed to be in focus. When we decide to look at a
nearby object, the accommodative system generates signals to elicit ciliary
muscle contraction and an increase in lens power that is sufficient to maintain
a clear retinal image (Campbell & Westheimer, 1960). Defining the stimulus for
accommodation has been a prime area of investigation. Among a variety of
non-optical cues, such as binocular disparity (Jaschinski, 2001; Tsukamoto et al., 2001), stimulus proximity (Hung, Ciuffreda,
& Rosenfield, 1996; Rosenfield, Ciuffreda,
& Hung, 1991) and changes in
stimulus size (Koh & Charman, 1998; McLin,
Schor, & Kruger, 1988) that may dominate
depending on the circumstances, defocus blur is considered to be the primary
stimulus that controls the accuracy of monocular accommodative
response (Toates, 1972).
Moreover, it has been suggested that ocular aberrations
other than defocus, which normally degrade the quality of the in-focus retinal
image (Charman, 1983), constitute cues that
drive the accommodative mechanism. Specifically, it has been shown that
accommodation is more accurate to broad-band than to monochromatic targets
(Aggarwala, Kruger, Mathews, & Kruger, 1995) and that longitudinal chromatic
aberration (LCA) favorably influences accommodative response (Kruger et al., 2004; Stone, Mathews, & Kruger, 1993). In addition, there is evidence that
asymmetric monochromatic aberrations, such as astigmatism and coma, provide
useful directional cues for accommodation (Campbell & Westheimer, 1959; Charman, 2000; Wilson, Decker, & Roorda, 2002).
It is of interest that, even if objects are at a fixed
distance, small changes in focus may be required to optimize image quality
(Howland & Buettner, 1989). These
steady-state errors form an intrinsic part of the accommodative control system
and are of two types. First, the system is characterized by over-accommodation
for far targets, known as "lead" of accommodation, and under-accommodation for
near targets, known as "lag" of accommodation (Charman, 1995; Morgan, 1944): Clinical refraction techniques accept
the lead and leave the eye slightly myopic for true distance vision, relying on
ocular depth-of-focus to give adequate retinal image quality. Second, under all
conditions, the accommodation response changes rapidly and continuously, showing
small fluctuations with typical values of about 0.20 D (Charman &
Heron, 1988; Stark & Atchison, 1997; Winn, Charman, Pugh, Heron, & Eadie,
1989). These fluctuations are thought to
contribute in the maintenance of the steady-state response to any stimulus by
producing temporal changes in retinal image quality (Charman, 2000; Hofer, Artal, Singer, Aragon, &
Williams, 2001).
Further evidence regarding optical changes in the
retinal image when accommodating is provided by studies that demonstrated
changes in higher order aberrations, and especially spherical aberration, which
causes significant degradation near the fovea (Atchison, Collins, Wildsoet,
Christensen, & Waterworth, 1995; He,
Burns, & Marcos, 2000; Lopez-Gil, Iglesias,
& Artal, 1998). As has been widely
publicized, most eyes suffer from positive spherical aberration when
unaccommodated, with a trend toward negative spherical aberration being observed
with increasing the accommodation level (Atchison et al., 1995; Cheng et al., 2004; He et al., 2000; Ivanoff, 1956).
Since spherical aberration is coupled to the refraction
of the eye, it is expected (especially for large pupils) that accommodation
measured with commonly used auto-refractometers could be biased (Collins, 2001; Hazel, Cox, & Strang, 2003).
The change of image quality with accommodation has been
evaluated in the past using the variance of wavefront error or the root mean
square (RMS) of the overall wave aberrations (Atchison et al., 1995; He et al., 2000; Lopez-Gil et al., 1998). The above studies showed a large
variability between subjects, with mean RMS increasing at high accommodation
levels. There is a trend for retinal image quality to be optimal at the resting
point of accommodation (at about 1–2-D vergence), with aberrations
increasing for targets both nearer and farther from the eye's resting point
(Charman, 1999; He et al., 2000). However, these studies have not taken into
account the pupil constriction, which accompanies accommodation and reduces the
total effect of higher order aberrations.
Small pupils (<3 mm) are expected to produce larger
errors in accommodation by increasing depth-of-focus and reducing high spatial
frequency information from the retinal image due to diffractive effects (Ward
& Charman, 1985).
In this study we use a wavefront sensor in conjunction
with a purpose-built Badal optometer to allow continuous recordings of the
wavefront aberration of the eye for a range of accommodative demands. The
defocus needed to optimize image quality at each accommodative level is
evaluated using two different image quality metrics. It is shown that the
steady-state errors in focus in accommodative response can be partially
explained in terms of focusing of the eye to achieve best image
quality.
Seven right eyes of seven subjects between the ages of
23 and 33 years were tested (mean age: 28 years). Four were emmetropes and three
were low myopes (range: –2.00 to –2.50 D) corrected with spectacles.
All subjects had visual acuity better than 6/6 (20/20), normal binocular vision,
phoria and near point of convergence, and no ocular pathology. None of the
participants had a history of refractive or other ocular surgery. Prior to data
collection, subjective accommodative amplitudes were measured to ensure that
values were normal for the age group tested. Informed consent was obtained from
all participants after they received a written explanation of the nature of the
study. The experiment followed the tenets of the Declaration of Helsinki, and
conformed to a protocol approved by the Institutional Research
Board.
The monochromatic wavefront aberration function of the
eye was measured using the Complete Ophthalmic Analysis System (COAS, Wavefront
Sciences Ltd), which is based on the Shack-Hartmann principle (Thibos, 2000). COAS provides a real-time display of
pupil image, which is used to align the patient’s line of sight with the
instrument’s axis. COAS uses an 840-nm
wavelength super-luminescent diode as the light source and utilizes a square
lenslet array of 33 x 44 (a total of 1452 lenslets) with each lenslet having a
width of 144 μm. According to the manufacturer, the pupil magnification
factor is 0.685, which means that the lenslet array samples the exiting
wavefront every 210 μm in pupil plane. Based on the number and the
distribution of the active Shack Hartmann elements, pupil size can be calculated
with a resolution of 0.1 mm.
The software allows continuous recording of
Shack-Hartmann images and pupil size about every 130 ms for each frame capture
(i.e., a temporal frequency of 7.7 Hz). The data extracted from COAS consist of
a set of Zernike coefficients (up to fourth order) in Malacara format that
quantify the type and the magnitude of aberrations present.
A purpose-built Badal optometer, depicted in Figure 1, is mounted on top of the COAS sensor. The
particular optometer has two target arms that can be illuminated separately. In
the present experiment only one target was used. Accommodation was controlled
with a target viewed through a beam splitter, allowing for continuous recordings
of the wavefront aberration of the tested
eye. The Badal
focusing block features a two-element Badal lens. Adjusting manually the
stimulus back and forth provides changes in target vergences between +1 and
–12 D. This is achieved without changing the apparent size of the target,
thus inducing a blur-only stimulus for accommodation.
Figure 1. Schematic diagram of the Badal
optometer used in conjunction with the Complete Ophthalmic Analysis System
(COAS) to allow recording of the wavefront aberration of the tested eye while
accommodating.
The target was a high-contrast (>80%) single letter
E, printed on white paper and illuminated by an incandescent lamp. The letter
had an angular subtence of 1.75° (having limbs with widths subtended 21'
arc, equivalent to a 6/126 or 20/420 letter). The center of the letter coincided
with the optical axis of the Badal optometer that was also aligned with the
optical axis of the COAS. The luminance of the background was 5
cd/m2. However, retinal illuminance was not constant for each subject
and accommodation level because of differences in pupil
sizes. All measurements were performed with natural pupils
without administering any mydriatic or cycloplegic
drug. Room lights were dimmed to
maintain large pupil diameters. The subject positioned his/her head on the chin
rest. The operator manually aligned the subject’s pupil center with the
optical axis of the device by means of six dots (that lie on a circle concentric
with the pupil) displayed on a video monitor. This ensured that the
subject’s line of sight was coaxial with the instrument’s optical
axis. For each condition 50 consecutive measurements were taken (with a duration
of 6.5 s at 7.7 Hz) for the full pupil without re-alignment being needed. Right
eyes were tested, whereas left eyes were occluded. Subjects were asked to blink
prior to all measurements.
Subjects were given a short practice session to
familiarize themselves with the procedure. They were also encouraged verbally to
direct their attention to the target and maintain best possible focus at all
times. Shack-Hartmann images and the resulting wavefront aberration data were
initially recorded for positive target vergence (i.e., the target was placed behind the subject's far point at
+0.84 D). In subsequent trials, the target was brought progressively closer to
the subject to increase the stimulus vergence up to –8.00 D in about
1.00-D steps. A complete measurement session for each subject lasted about 30
min. Target vergence was corrected for effectivity when spectacles were used,
using Equation 1:
where
A is the
accommodation demand,
L the
target vergence,
a the
vertex distance (13 mm), and
K
the refractive power of the correcting
lens.
The files containing wavefront information were
downloaded on removable media and analyzed off-line (e.g., plotting of wavefront
maps) using custom-written scripts in MatLab (V 5.2; The Mathworks Inc.,
Nantick, MA) mathematical software. The Zernike expansion coefficients derived
from the wave inclination data for the full pupil were initially transposed to
the OSA format (recommended by the Optical Society of America; Thibos,
Applegate, Schwiegerling, & Webb, 2000)
and corrected for chromatic aberration (from 840 to 550 nm) (see Appendix A in
Ginis, Plainis, & Pallikaris, 2004). Accommodative response for each target vergence was evaluated:
(i) by calculating the equivalent quadratic of a
wavefront aberration map (given in Equation
2) using "paraxial curvature matching" (i.e., the second-order paraxial
focus
[c20]
and the fourth-order spherical aberration
[c40]
Zernike coefficients). This forms an approximation of spherical equivalent used
in common ophthalmic calculations, and was found to be the most accurate method
in predicting subjective refraction (Thibos et al., 2004),
(ii) by using a computational method that calculates
the power of a focusing lens needed to optimize retinal image quality of the
accommodating eye. This was calculated using a “weighted” sum of the
modulation transfer function (MTF) image metric, the “optimized” MTF
with a weighting function (WF) peaking at a spatial frequency of 18 c/deg (see
Figure 1b). This was chosen because it has been
suggested that while low spatial frequency components of a target provide a
"coarse" accommodation guidance, it is the high spatial frequencies or edges of
the target that refine in accuracy the final response (Charman & Tucker, 1977).
Figure 1b.
Presentation of the calculations employed to compute optimized through focus
modulation transfer function (MTF) using the Zemax-EE software. The weighting
function (black line-circles) forms a weighted sum of the MTF amplitudes at five
spatial frequencies, tuned at 18 c/deg. Examples of two MTFs of an eye for two
different corrections are shown: minimized wavefront aberration (MTF, green
dashed line) and high frequency optimized MTF (w-MTF, red dashed line).
Other studies (Mathews & Kruger, 1994; Owens,
1980) argued against this hypothesis, suggesting that intermediate spatial
frequencies (~5 c/deg) are the most
important for accommodation. Even if high spatial frequency content of the
target is not the primary feedback feature in monocular accommodation, we feel
that, because high spatial frequencies are more sensitive to focus errors, a
high frequency tuned MTF is expected to be more effective in detecting small
changes in focus. This can be achieved with the WF, which substantially improves
high spatial frequencies of the MTF that minimizes RMS wavefront aberration (see
Figure 1b).
The effect of Stiles-Crawford apodization under
photopic conditions was also included in the calculation of the MTFs. All
computational simulations were performed using the ZEMAX-EE (Version 10; Zemax
Development Corporation, San Diego, CA). Given that tilt does not influence
retinal image quality, first-order terms were not included in any of the
analyses performed.
Because accommodation represents an increase in the
power of the eye, which counteracts the negative vergence of the accommodation
stimulus, positive notation is used in the graphs to describe accommodative
response.
Figure 2 plots mean
monocular accommodative responses (as evaluated by the spherical equivalent of
the wavefront aberration; see Equation 2)
as a function of target vergence for all subjects tested. The intrinsic focusing
errors of the accommodation system are confirmed: Observers failed to
accommodate "accurately" both at low (over-accommodation) and high
(under-accommodation) dioptric stimulus levels. The effects of these errors on
retinal image quality are considered in Discussion.
Figure 2. Accommodative response for all subjects
as calculated by the
z20
and
z40
Zernike coefficients (see Equation
2) of the wavefront aberration. Each data point represents the mean of 50
measurements and errors bars ±1
SD. The dotted line is the ideal 1:1
relationship, and the dashed bold line is the least square regression fit for
the linear portion of the curve (for vergences >0). Note that the
“resting" points, estimated from the response/stimulus curve
intersections, show a significant inter-subject variability.
Moreover,
it is apparent that, when averaged, the stimulus and response are equal at a
vergence in the vicinity of about –1.75 D. This intersection in the
response/stimulus curve, which is thought to represent the "resting" or "tonic"
level of accommodation (Toates, 1972),
varies considerably between subjects tested (range –0.25 to –3.25
D).
The usual accommodation-induced pupillary miosis is
clearly shown in Figure 3, where pupil diameter
is plotted as a function of accommodative response. It is evident that the
higher the accommodative response, the greater the degree of miosis, with the
relationship being linear: When averaged across subjects, each diopter of
accommodation (A) elicits 0.18 mm of pupil constriction (P) (i.e., the P/A ratio
is –0.18 mm/D). However, there is a considerable intersubject variability
(P/A ranged between –0.12 and –0.27 mm/D with the correlation
coefficient,
r,
being higher than 0.85 in all cases). Note also that this linear relationship
holds up to a degree of accommodative response, and that pupil constriction does
not cease when the accommodative response reaches its
limit.
Figure 3. Pupil
diameter as a function of accommodative response. Data from all subjects are
shown. Each data point represents the mean of 50 measurements and errors bars
±1 SD. The dashed lines represent
the least square regression fit for each subject.
The overall changes in higher order aberrations with
accommodation are qualitatively described in Figure
4, which illustrates wavefront aberration maps for each refractive state
from unaccommodated to approximately 8 D of accommodation over the natural pupil
diameter. Only higher order terms are included in the calculation of the
aberration maps. Data from three subjects are shown. Wavefront error maps were
drawn for all subjects and show a considerable variation in the wavefront
patterns from individual to individual at each accommodation level. For example,
for subject SP it is evident that the higher order wavefront error is minimized
at intermediate dioptric stimulus levels (around his resting point of
accommodation), whereas for subject AT higher order aberrations increase with
accommodation, being maximal at the highest accommodation level (where spherical
aberration reaches its maximum magnitude). In contrast, for subject IK the
lowest aberrations occurred at the highest accommodation level.
Figure 4. Wave
aberration maps of total higher order wavefront error for increasing target
vergences (shown on the top of the maps) for subject SP (top), AT (middle), and
IK (bottom). The contour interval in the wavefront map is 0.1 μm. Diameter of full-size
(natural) pupils is also shown. (Accommodation-induced miosis is apparent for
all subjects.)
Figure 5 depicts for all individual subjects the
changes with accommodation in three higher order aberration modes: primary
spherical aberration
(c40),
vertical
(c31),
and horizontal coma
(c3-1).
The most systematic change occurs for the spherical aberration,
c40,
which always moves in the negative direction. The magnitude of the change in
c40
is linearly related to the accommodative response for all the subjects (on
average 0.048μm/D, the correlation coefficient,
r, being higher than 0.93 in all
cases). Regarding the coma modes, although there is a tendency (more pronounced
for
c3-1)
for a change to more positive values with accommodation, there is a significant
intersubject variability. Note that, when averaged across all subjects, both
mean spherical-like and coma-like aberrations approximate to zero when the
response equals –1.5 D, close to the mean tonic accommodation level (the
intersection in the response/stimulus curves), although this is not the case for
all individual subjects. This is further discussed in Conclusions. The other
third- and fourth-order wavefront terms underwent small nonsystematic changes.
It has to be stressed that the aberration data correspond to different pupil
sizes (because of the accommodation-induced pupillary miosis). This analysis was
purposely chosen to evaluate retinal image quality under real
conditions.
Figure 5. Plot of spherical aberration
(c40),
vertical
(c3-1),
and horizontal
(c31)
coma for a range of accommodative responses. Data from all subjects are shown.
Each data point represents the mean of 50 measurements and errors bars ±1
SD. The dashed lines in the top figure
represent least square regression fit for each subject. The dashed bold line is
the least square regression for all subjects. Natural pupils are used for
analysis.
Figure 6 plots
simulated retinal images of a 6/6 (20/20) letter for a –0.15-D and a
–8.05-D vergence target simulated for three different refractive states:
the recorded accommodative response (mean of 50 continuous measurements)
calculated directly from the wavefront map, the 1:1 "ideal" response (i.e.,
accommodation fully counteracts target vergence), and the response that
maximizes the weighted MTF (see Methods).
Figure 6. Plots
of simulated retinal images (a 6/6 letter is used) for two target vergences
(left, –0.15 D for subject TD; right, –8.05 D for subject AT) as
computed by three different estimations of the mean accommodative response: the
actual accommodative response (top), the "ideal" 1:1 response (middle), and the
dioptric response, which optimizes the MTF (bottom). Note that for the distant
target (left), subject TD over-accommodates (0.76-D response corresponds to a
–0.15-D target), whereas for a near target (right), subject AT
under-accommodates (5.39-D response corresponds to an 8.05-D target).
As can be seen in Figure
6 (first row), when actual accommodative response is used, the simulated
retinal image is significantly degraded, and this is more pronounced for higher
target vergences. This is mainly due to the observed steady-state errors in
accommodative response (see Figure 2).
Furthermore, even if the subjects were achieving a 1:1 accommodative/target
response, the simulated image of the letter would not demonstrate optimal
sharpness (see middle images in Figure 6). This
is mostly achieved when high spatial frequencies are brought to focus.
As a result, the "ideal"
accommodative response is not necessarily the 1:1 relationship, but varies
depending on the polarity of spherical aberration: Positive
c40
produces a lead (over-accommodation) for far targets, whereas negative
c40
results in a lag (under-accommodation) for near targets. For example, for
subject AT (see Figure 6), an accommodative lag
equal to 1.05 D (compared to the overall 2.65 D) can be attributed to the high
negative
c40
when accommodating, with the resulting optimal image response occurring at 7.00
D and not at 8.05 D, which equals the target vergence. Similarly, for subject
TD, an accommodative lead equal to 0.18 D (compared to the overall 0.61 D) can
be attributed to the positive
c40
with the resulting optimal image response occurring at 0.33 D instead of
the 0.15-D target vergence.
This is further justified in Figure 7, which presents the characteristic
focusing errors derived by the optimized MTF as a function of spherical
aberration
(c40).
These errors are calculated for each subject by the difference between the ideal
1:1 response and the optimized MTF. They take a positive value when
corresponding to a "lag" and a negative value when resulting in a "lead." The
linear trend proves that spherical aberration is the main higher order
aberration that contributes to image quality changes during accommodation.
Figure 7. Plot
of the errors in focus derived from the response needed to optimize MTF as a
function of spherical aberration
(c40).
The positive signs in y-axis indicate a
"lag" and the negative a "lead." Data from all subjects are shown. Correlation
coefficient r is higher than 0.93 in
all cases.
Figure 8 compares the
steady-state errors in focus, as calculated by the wavefront aberration maps and
by the optimized MTF, as a function of target vergence. The errors in focus
("lead" for far targets, "lag" for near targets) increase linearly with target
vergence for all subjects (see upper graph), although there is a notable
between-subject variability (the slope of the regression coefficient ranges from
0.31 D to 0.56 D of focusing error per diopter of target
vergence:
r being higher than 0.89 in all
cases). It is also evident that predicted focusing errors computed by the
optimized MTF response are lower in magnitude, and thus can partly explain the
observed accommodative "lag" and "lead."
Figure 8. Plot
of errors in focus while accommodating for a range of target vergences, as
calculated by the wavefront error (upper graph) and the optimized MTF (lower
graph). Errors bars represent ±1
SD. Positive signs in
y-axis indicate a "lag," negative signs
a "lead." Data from all subjects are shown.
Figure 9 plots the RMS
amplitude of fluctuations (i.e., the standard deviation of the accommodative
response) for a range of accommodative demands. It is evident that, although
there is a considerable variation in the amplitude of accommodation fluctuations
among subjects, the RMS amplitude is minimal for all subjects for a target at
infinity. Moreover, there is a strong indication that fluctuations increase in
magnitude when near objects are observed. Of particular interest is the
observation that the vergence where fluctuation activity is maximal varies among
subjects tested (between 2-D and 8-D target vergence).
Figure 9.
Changes in root mean square (RMS) fluctuations as a function of target vergence.
Data from all subjects are shown.
This effect is better illustrated in Figure 10, which presents dynamic response traces
(fluctuations of response) for a wide range of target vergences for two
representative subjects. For subject AT fluctuations are more powerful as the
stimulus is brought closer to the eye: Mean accommodation effort increases by a
factor of 3 over the stimulus vergence range (from 0.07 D for a –0.15-D
target to 0.22 D for a –8.05-D target). However, this is not always the
case (i.e., for most of the subjects [see subject SP in Figure 10] fluctuations are higher at intermediate
target vergences, decreasing at higher accommodative
demands).
Figure 10. Plots
of continuous accommodative response to a stationary target for a range of
accommodative demands for subjects AT (left) and SP (right). Total recording
period is 6.5 s (50 measurements).
The effects of these dynamic changes in accommodative
response on retinal image quality are demonstrated in Figure 11, which is a 50-frame (6.5 s) video clip
showing microfluctuations of a continuous accommodative response to a 4.11-D
target for one subject. The mean response is 3.55 D
(SD, 0.17), ranging between 3.23 and
4.02 D. Mean pupil diameter is 5.54
mm.
Figure 11. Video clip of continuous accommodative
responses to a stationary target at –4.11-D vergence. Mean accommodative
response is 3.55 D, ranging between 3.23 and 4.02 D (see Figure 10; the error in focus ranged between 0.09
and 0.88 D). Total recording period is 6.5 s (50 measurements). Mean natural
pupil diameter is 5.54 mm (range: 5.31–5.75 mm).
The effect of monochromatic wavefront aberrations on
the accuracy of the accommodative response is central in this study. A
purpose-built badal optometer (Figure 1) was
used in conjunction with a COAS wavefront sensor to achieve recordings of the
accommodating eye. Monocular viewing and the use of a Badal optometer allowed us
to eliminate the target proximity cues and vergence-accommodation interactions,
producing a blur-only stimulus for accommodation. Moreover, analysis was
performed over a natural pupil diameter to simulate real conditions.
The intrinsic steady-state errors of accommodation
response (i.e., "lags" at high dioptric stimulus levels and "leads" at low
levels; see Figure 2) reported by a number of
authors (Charman, 1999; Hazel et al., 2003; He et al.,
2000; Kasthurirangan, Vilupuru, & Glasser, 2003; Schaeffel, Wilhelm, &
Zrenner, 1993) were confirmed.
Although the increased errors in focus for near targets
were evident for all the subjects, the exact value of the accommodative lag, as
well as the resting state of accommodation (represented by the intersection in
the stimulus/response curves), showed a significant intersubject variability,
confirming previous research (e.g., for a review, see Charman, 1995). The magnitude of focusing errors,
however, was somewhat higher than reported in early studies. This is not
surprising because accommodative lag is expected to increase with monocular
viewing (Jaschinski, 2001) and when
retinal disparity and convergence, which also drive accommodative response
(Fincham & Walton, 1957), are not in
play. Moreover, the accuracy of accommodative response is known to depend on
stimulus characteristics, such as luminance (Johnson, 1976) contrast (Tucker & Charman, 1987; Ward, 1987), color (Aggarwala et al., 1995), and spatial frequency (Charman &
Tucker, 1977), of the target. As a
consequence, the fairly large target (1.75° angular size) used in the
present study might have produced focusing errors of higher magnitude.
Furthermore, early measurements of accommodative response were taken with
auto-refractometers, which record sphero-cylindrical refraction over a small
measurement zone, resulting in an underestimation of the focusing errors at
higher accommodation levels (Collins, 2001;
Hazel et al., 2003).
Another observation is that pupil size decreases
linearly with accommodative response until the accommodative system can no
longer respond (Figure 3). The lower P/A values
found in this study (average was –0.18 mm/D compared to –0.45 mm/D
reported by Alpern, Mason, & Jardinico, 1961) are probably due to the restriction of
the accommodation stimulus to image blur; it is known that pupil constriction is
triggered by other variables, such as image size and accommodative convergence.
Moreover, our calculations were based on pupil responses up to 8-D stimulus
(compared to a 4-D stimulus by Alpern et al., 1961), and it is known that P/A ratio is
exaggerated for low limits of accommodative response (Schaeffel et al., 1993).
It would be expected that pupillary miosis, by
increasing depth of focus, would demand less precision from the accommodative
system, resulting in an increasing accommodative lag. However, this is true only
for pupils below ~3 mm (Tucker &
Charman, 1975; Ward & Charman, 1985). Moreover, in this study pupil
constriction was found to be less than 1 mm in most cases, which means that
changes in depth of focus relax the criterion of accommodative response by less
than ±0.05 D (Campbell, 1957).
The present changes of the wavefront aberration pattern
when accommodating, as well as the high intersubject variability (Figure 4), have been previously reported by a
number of authors (Atchison et al., 1995;
Cheng et al., 2004; Vilupuru, Roorda, &
Glasser, 2004). Although there is a
tendency for coma-like
(c3-1,
c31)
aberrations to change to the positive direction, the most prominent transition
occurs for symmetric spherical aberration
(c40),
which consistently moves into the negative direction with increasing
accommodation demand (Cheng et al., 2004; He
et al., 2000; Vilupuru et al., 2004). These are attributed to changes in the
shape, refractive index distribution, and position of the crystalline lens
during accommodation (Drexler, Baumgartner, Findl, Hitzenberger, &
Fercher, 1997; Roorda & Glasser, 2004).
In spite of the fact that the systematic negative
change in
c40
is evident for all subjects, there are three characteristic patterns: (1)
subjects with positive
c40
in the unaccommodated state, which shifts to negative values with
accommodation (most common); (2) those with positive
c40,
which changes to less positive values without crossing through zero; and (3)
those with negative
c40,
which changes progressively to more negative values with accommodation.
Since spherical and coma-like aberrations are the
predominant aberrations for foveal vision (Atchison et al., 1995; Howland & Howland, 1977; Walsh & Charman, 1985), it is expected that wavefront error and
consequently overall retinal image quality would be affected during
accommodation. However, due to the different patterns observed between subjects
tested, overall image quality is differentially affected: Some subjects show
best image quality at far, others at near, and others at intermediate
accommodative levels. Finally, because monochromatic aberrations are in play
only when pupil diameter is large, it is expected that pupil constriction at
near would improve image quality. Considering this intersubject variability, it
is not surprising that previous studies have reached confounding conclusions
regarding image quality during accommodation (Cheng et al., 2004; He et al.,
2000; Vilupuru et al., 2004).
Overall, it appears that optical factors may play an
important role in the accommodation response. In any case, optimal monochromatic
performance will be achieved only if the eye is precisely focused, with dioptric
defocus affecting accuracy of the accommodative response. Considering that
spherical aberration is the most significant higher order aberration in defining
the equivalent refractive power of the eye (Charman & Walsh, 1989), the shift in its polarity with
increasing accommodative response is expected to contribute to the focusing
errors of the accommodative response.
To test the effect of higher order aberrations
(especially spherical aberration) on the dioptric errors of the eye, the
accommodative response needed to optimize image sharpness (optimized MTF) was
estimated. It was found (see Figure 6) that if
the criterion that drives the accommodative mechanism is image sharpness, the
one-to-one matching between the dioptric stimulus level and corresponding
accommodative response is not always the ideal: Optimal image quality would
result in a "lag" for near targets (when negative
c40
is present) and a "lead" for far targets (when positive
c40
is present).
It follows that the steady-state errors in
accommodation can partly be explained by optical factors (i.e., the change in
spherical aberration that differentially affects image quality) (Figures 7 and 8).
The precise estimation of the errors in accommodative response is very
important, as increased errors have been reported to contribute to myopia
development and progression (Charman, 1999;
Flitcroft, 1998; Gwiazda, Thorn, Bauer,
& Held, 1993; Seidel, Gray, & Heron
2003).
It has to be noted that the refraction based on
computations maximizing optical or visual quality varies substantially between
different metrics (Thibos, Hong, Bradley, & Applegate, 2004). This means that the use of another
metric (i.e., the minimum RMS spot size) would produce different results. The
optimized MTF criterion applied here, with the inclusion of Stiles-Crawford
apodisation effect, is expected to improve high spatial frequency content of the
target, which is supposed to preferentially drive accommodation response.
One possible limitation is that the wavefront
aberration functions and image metrics reported in this study apply for
monochromatic light of wavelength 550 nm. However, the accommodative target was
lit with a source that emits white (broad-band) light. Generalizing these
metrics to polychromatic light may yield reasonable image quality over a large
range of defocus, because longitudinal chromatic aberration attenuates the
degrading effect of monochromatic aberrations on MTF (Charman & Chateau, 2003).
Regarding the stability of accommodative response, the
highest is exhibited for targets at infinity (< 0.1 D), with fluctuations
increasing (up to 0.3 D) as the target is moved toward a vergence of about
–5 D (see Figures 9 and 10). Moreover, in agreement with the literature
(e.g., Charman & Heron, 1988; Stark
& Atchison, 1997), there is a
considerable variation among subjects in both the magnitude of the fluctuations
and in their changes with target vergence. Miege and Denieul (1988) postulated that fluctuations show maximal
activity near the center of accommodative range, and thus would strongly depend
on the full amplitude of accommodation achieved by each subject. Note that
microfluctuations in pupil diameter may also contribute to the RMS fluctuations
of accommodation: This is expected to be more significant for near targets, as
pupil noise was found to be maximal for small diameters, while independent of
the mean accommodation response level (Stark & Atchison, 1997; Usui & Stark, 1978).
It has been suggested that although these fluctuations
stem from feedback instability (i.e., the elastic and mechanical characteristics
of the crystalline lens, and the structure of the ciliary muscle and the
zonules; Charman, 1983; Charman &
Heron, 1988), they may play a functional
role in optimizing image quality by producing temporal changes in the contrast
of the retinal image (Alpern, 1958; Charman
& Tucker, 1977; Howland &
Buettner, 1989; Miege & Denieul, 1988). As a result, fluctuations of higher
magnitude are required to maintain the system at higher level of response when
moderate errors in accommodation are present (Charman, 2000; Miege & Denieul, 1988). This is validated in Figure 11 (movie), which illustrates that, despite
the mean error in focus is about 0.5 D, fluctuations of increased amplitude in
one direction tend to improve the out-of-focus image by guiding the
accommodative response, and thus help to maintain an optimal state of focus for
the eye. If the above hypothesis is valid, the shape of the stimulus/response
curve and the variation of fluctuations with target vergence are expected to be
systematically dependent on each other. This issue and the impact of fluctuation
on image perception itself are being addressed in a separate study.
To summarize, it should be emphasized that although
focusing errors of accommodation response increase when viewing near targets,
the change in higher order aberrations may influence the accuracy of the
resulting response. Thus, when an image metric that optimizes focus for high
spatial frequency information is used as the criterion to estimate accommodative
response, focusing errors in accommodation can partially be explained.
It follows that the one-to-one stimulus/response
relationship should not necessarily be considered as the ideal: For a spherical
aberration shifting from positive to negative values with increasing
accommodation, a “lag” for near targets and a “lead” for
far targets can be predicted.
Moreover, fluctuations in accommodation seem to play an
important role in providing a feedback mechanism in accommodative response.
Their increased amplitude, when errors of accommodation are moderate (of
~1-D magnitude), contribute in
maintaining the system at high levels of response by temporarily bringing the
image to the best focus.
Finally, when changes in aberrations upon accommodation
are considered, population-averaged data may lead to erroneous results as a
consequence of the significant intersubject variability in the pattern of
aberrations and other factors, such as pupil size and full amplitude of
accommodation.
The authors acknowledge Professor W. N. Charman for
essential comments on the manuscript. SP is funded by the Greek State
Scholarship Foundation.
This work is partially supported by SHARP-EYE: Adaptive
Optics for Retinal Imaging and Improved Vision, a funded Research Training
Network under the 5th Framework of the European Union (http://www.sharpeye.org/).
Preliminary results of this study were presented at the
Association for Research in Vision and Ophthalmology, Ft. Lauderdale, FL, in
April 2004. Commercial relationships:
none.
Corresponding author: Sotiris Plainis.
Email: plainis@med.uoc.gr.
Address: VEIC, School of Medicine, University
of Crete, Heraklion 71003, Crete,
Greece.
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