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Effect of even and odd-order
aberrations on the accommodation response
Aikaterini I. Moulakaki, Antonio J. Del Águila-Carrasco, José J.
Esteve-Taboada, Robert Montés-Micó
Department of
Optics and Optometry and Vision Sciences, University of Valencia, C/Dr. Moliner
50, Burjassot
46100, Valencia, Spain
Correspondence
to:
Aikaterini I. Moulakaki. Department of Optics and Optometry and Vision
Sciences, Faculty of Physics, University of Valencia, C/Dr. Moliner 50, Burjassot 46100, Valencia, Spain.
aikaterini.moulakaki@uv.es
Received: 2016-10-21
Accepted: 2017-03-07
Abstract
AIM: To investigate
the potential effect that odd and even-order monochromatic aberrations may have
on the accommodation response of the human eye.
METHODS: Eight healthy
subjects with astigmatism below 1 D, best corrected visual acuity 20/20 or
better and normal findings in an ophthalmic examination were enrolled. An
adaptive optics system was used in order to measure the accommodation response
of the subjects’ eyes under different conditions: with the natural aberrations
being present, and with the odd and even-order aberrations being corrected.
Three measurements of accommodation response were monocularly acquired at
accommodation demands ranging from 0 to 4 D (0.5 D step).
RESULTS: The
accommodative lag was greater for the accommodative demands of 1.5, 3, 3.5 and
4 D for the condition in which the even-order aberrations were corrected, in
comparison to that obtained for the natural aberrations and corrected odd-order
aberrations for the same accommodation demands. No statistically significant
differences were found between the accommodation responses under the three
conditions.
CONCLUSION: The odd and
even-order aberrations are not helping the visual system to accommodate,
because their partial correction do not affect the accommodation performance.
KEYWORDS: accommodation response;
monochromatic aberrations; adaptive optics
DOI:10.18240/ijo.2017.06.19
Citation: Moulakaki
AI, Del Águila-Carrasco AJ, Esteve-Taboada JJ, Montés-Micó R. Effect of even
and odd-order aberrations on the accommodation response. Int J Ophthalmol
2017;10(6):955-960
Article Outline
INTRODUCTION
It is well known that the eye is capable of changing its power in order
to focus on objects that are placed on different distances[1].
The change in power of the human eye is known as accommodation and it is vital
for the improvement of the retinal image quality[2]
and for the appreciation of the details of the objects[3].
There are several cues that activate the accommodation mechanism of the
eye in order to have a proper accommodation response[4].
These cues can come from the surroundings[5] (e.g.
distance of the object) or from the optics of the eye itself[6][e.g.
longitudinal chromatic aberration (LCA)], which have an influence on the
retinal image quality[7].
Defocus caused by an incorrect accommodation response can be
characterized by a positive or negative sign, which depends on whether the
plane of the image is ahead of or behind the retina[8-9].
It has been demonstrated that LCA provides a directional signal for
accommodation[10-13].
Nevertheless, there have been cases in which the accommodation ability was not
lost when the cues of the LCA were artificially removed[14].
This indicates the co-existence of additional optical cues, which play a role
in the accommodation response[15].
The monochromatic aberrations can be also considered optical cues. More
precisely, odd-order aberrations can be considered as signed cues for
accommodation, since the images formed at the retina are different whether they
are focused in front of or behind it. Moreover, some aberrations have a greater
contribution to the accommodation response than others. This is evident in a
study conducted by Wilson et al[16]
according to which the optical system is capable of differentiating the changes
between the point spread function (PSF) of the positively and negatively
induced defocus in the presence of monochromatic aberrations. In particular,
the even-order aberrations could help to distinguish between the negative and
positive defocus, since the image formed when they are present is different
whether the light is focused in front of or behind the retina. On the contrary,
the odd-order aberrations are not intertwined with such ability[16-17]. Nonetheless, it is still under
research the exact role of the different aberrations in the accommodation
response of the eye and whether the even and odd-order aberrations contribute
as a signed cue to the direction of defocus or not.
Therefore, the aim of this study to further investigate how the
monochromatic aberrations influence on the accommodation response of the eye.
To achieve this, an adaptive optics system was used in order to measure the
accommodation response of the subjects’ eyes under different conditions: with
the natural aberrations being present, and with the odd and even-order
aberrations being corrected.
SUBJECTS
AND METHODS
Subjects Eight young adult subjects
(mean age: 31±5.24y, range: 26 to 40y) who could accommodate under
monochromatic light conditions participated in the study. The averaged
spherical equivalent refractive error was -1.00±2.37 diopters (D). Astigmatism
was limited to ≤1.00 D. All subjects had normal corrected visual acuity (20/20
or better) evaluated with the ETDRS chart (Precision Vision, USA), no ocular
pathology, no binocular vision anomalies, no previous conducted ocular surgery,
and normal clinical amplitudes of accommodation for their ages (at least 4 D). The
study followed the Declaration of Helsinki and was approved by the Ethics
Committee of the University of Valencia. The subjects were verbally informed
about the details and possible consequences of the study, and a
signed formal consent was obtained from each subject.
Equipment The crx-1 adaptive optics visual
simulator (Imagine Eyes, Orsay, France) was used to measure and correct the
wavefront aberrations of each subject’s eye (Figure 1). The system is composed
of a Hartmann-Shack wavefront sensor and a deformable mirror. The wavefront
sensor employs a square array of 1024 microlenses and a near-infrared light
source with a wavelength of 850 nm. An internal microdisplay is used to project
the target, while the Badal system is employed to change its vergence (in other
words, accommodation demand). To control the accommodation process, a
monochromatic Maltese cross (550±5 nm) is used as the target. A precise
alignment of the subject’s pupil is required, and this was achieved with an
additional Charge Coupled Device (CCD) camera. Head movements were reduced
employing a chin and forehead rest.
Figure 1 Schematic layout of the crx-1 adaptive optics
visual simulator used to measure and correct the wavefront aberrations of the
subject’s eye.
Furthermore,
the deformable mirror is comprised of 52 independent magnetic actuators, which
are used to either correct or modify the wavefront aberrations[18-20]. Prior to data collection, a
customized software based on commercially available routines (Imagine Eyes,
Orsay, France) was used to control the deformable mirror and reshape it from
its normally flat surface to the desired one.
In this study,
the Zernike coefficients of each individual up to and including 6th order
were considered and partially corrected to meet the conditions tested (i.e. natural
aberrations present, odd and even-order aberrations separately corrected).
Experimental
Procedure Before starting the
experiment, subject’s spherical refractive error was corrected using the Badal.
The experiment was divided into three conditions, each having different
wavefront aberrations present. In the first condition the subject’s natural
aberrations were present, whereas in the two other conditions the subject’s odd
and even-order aberrations were respectively corrected. To achieve this, a
customized software was made and implemented into the adaptive optics system.
This software was further controlling the deformable mirror of the system in
order to correct the aberrations corresponding to each condition. In all
conditions the measurements were performed monocularly and obtained from the
dominant eye of each subject.
The
measurements were acquired under three different conditions: 1) natural aberrations were
present, 2) odd-order aberrations were corrected, and 3) even-order aberrations
were corrected. In each condition, three measurements were acquired at the
accommodation demand from 0 to 4 D, with a step of 0.5 D. Thus, 27 wavefront
measurements were recorded per condition, with a total of 81 measurements for
each eye. The subject was allowed to blink prior recording a measurement, to
avoid increased tear film aberration that might otherwise have occurred during
an extended inter-blink interval[21]. Subjects
were also allowed to rest between trials.
Data
Analysis The wavefront data were
exported as Zernike coefficients up to 6th order. To solely identify
the accommodation response of the eyes to the accommodation stimuli, the
Zernike defocus was used[22-23].
The accommodation response was estimated in diopters employing the following equation:
(1)
where AR is the accommodation response, AD is the
accommodation demand, 
is the
second-order Zernike coefficient for defocus in μm
and r is the pupil radius in mm[24].
Data corresponding to each one of the three conditions
were fitted to linear models using Matlab 2015b (MathWorks Natick, MA, USA).
For each regression analysis, the intercept, the slope, the determination
coefficient, and the P-value were obtained. An additional ANCOVA
analysis was performed to elucidate whether the slopes of the three different
conditions were different. A P-value of less than 0.05 was considered to
be statistically significant.
RESULTS
To obtain the
values of the accommodation response, the second-order Zernike coefficient
(defocus) was converted into diopters, employing the previously described
formula (Equation 1). Then, the mean of three consecutive measurements was
displayed for each condition and accommodation demand considered in this study.
Figure 2 exhibits the mean accommodation response obtained from all
eight subjects for each accommodation demand with the natural aberrations being present,
starting from 0 D and ending at 4 D of accommodation demand, utilizing a step
of 0.5 D. The accommodation responses were acquired when the natural
aberrations were present. The dashed line shows the theoretical response of the
accommodation process (i.e. equal accommodation response for each
accommodation demand). In this case, there was a difference towards the same
direction between all accommodation responses and the theoretical line, showing
accommodative lag for all subjects and accommodation demands.
Figure 2 The mean accommodation response obtained with
the natural aberrations being present
Each data point
represents the meanstandard deviation (SD) of each accommodation demand.
The dashed line displays the theoretical accommodation response.
The mean
accommodation responses acquired when the odd and even-order aberrations were
removed, are displayed in Figures 3 and 4, respectively. Both figures
illustrate the mean accommodation response of all subjects and accommodation
demands. In both figures, the obtained accommodation responses are similar indicating a
similar accommodative lag for both conditions with reference to the theoretical
line. Nevertheless, in Figure 4 the lag of accommodation is greater for the
accommodation demands of 1.5, 3, 3.5 and 4.0 D, in comparison to that
obtained in Figure 3 for the same accommodation demands.
Figure 3 The mean accommodation response obtained with
the odd-order aberrations being corrected in the subjects’ eyes Each data point represents the mean±standard deviation
(SD) of each accommodation demand. The dashed line displays the theoretical
accommodation response.
Figure 4 The mean accommodation response obtained with
the even-order aberrations being corrected in the subjects’ eyes Each data point represents the mean±standard deviation
(SD) of each accommodation demand. The dashed line displays the theoretical
accommodation response.
As already
mentioned, a statistical analysis was conducted to analyze whether the
measurements obtained for the three different conditions were statistically
different or not.
Table 1 summarizes the results obtained for the regression analysis
performed for each condition. The referred accommodation demand of 0 D
corresponds to the far point of each subject’s eye, hence its non-accommodated
state. Therefore, this accommodation demand was excluded from the statistical
analysis. All the P-values for the three linear regression analysis were
statistically significant (P<0.001). The minimum determination
coefficient (R2), equal to 0.88, was obtained for the
condition in which the even-order aberrations were corrected. The ANCOVA
analysis revealed that the slopes of the accommodative responses for the three
conditions were not significantly different from each other (P=0.26).
Table 1 Results obtained for the
regression analysis performed for each condition
|
Condition |
Slope |
Intercept
(D) |
R2 |
P |
|
Natural
aberrations |
0.587 |
0.237 |
0.97 |
<0.001 |
|
Odd-order
corrected |
0.574 |
0.025 |
0.97 |
<0.001 |
|
Even-order
corrected |
0.471 |
0.195 |
0.88 |
<0.001 |
DISCUSSION
During the past fourteen years, several studies have been conducted to
identify the possible use of the high-order aberrations on accommodation[6-7,16,25].
Nevertheless, all of these studies came up with different results. An
additional study conducted by López-Gil et al[26]
examined once again the effect of the high-order aberrations, but exclusively
the effect of inducing third-order aberrations on the accommodationusing
customized contact lenses. On the other hand, Gambra et al[27] employed
targets, which were blurred with a certain amount of specific high-order
aberrations to identify their influence on accommodation. Although, in all of
the aforementioned studies there were differences in the methodology employed
to perform the different experiments, they all had one common parameter; they
all developed their experiments in order to study the dynamic accommodation
response. Moreover, the number of participants varied between five to ten among
these studies, with one study having only two participants[6].Additionally,
in two studies, some aspects of latency and speed of the dynamic accommodation
response were explored after the partial[6]
and complete[7] correction of the ocular aberrations
using an adaptive optics system, whereas in two other studies the gain and
phase of the dynamic accommodation response were examined by inducing ocular
aberrations[26-27].
A fifth study investigated the capability of perceiving changes between the PSF
of the positive and negative induced defocus, but it did not record
accommodation[16].
In the present study, we selected a different approach to study the
effect of the ocular aberrations on the static accommodation response. This
study was designed in this way in order to show the potential of such approach
for future research. More specifically, we selected to assess the differences
in accommodation with natural aberrations being present in the subjects’ eyes
and with the odd and even-order aberrations being respectively corrected. This
was achieved by employing an adaptive optics visual simulator and several
accommodation demands ranging from 0 to 4 D, with a step of 0.5 D.
Additionally, we chose to study solely the changes that occurred in defocus
when a total of natural, even and odd-high order aberrations were present in
the eye. In this way the changes in accommodation response can be adequately
assessed for all conditions and accommodation demands.
Our results indicate that in the presence and absence of high-order
aberrations, the static accommodation response is not altered. Although, we
were expecting that the interactions between the natural and corrected
aberrations may play a role in the precision of accommodation, such as worse
precision in accommodation in the absence of some ocular normal aberrations; in
our study this is not evident. In particular, according to our statistical
analysis we found that the obtained accommodation responses were not
significantly different between the three conditions. In other words, we would
suggest that our results show that the accuracy of accommodation response
remains unaffected with the correction of the odd and even-order aberrations.
This aspect of our results is in agreement with the corresponding aspect of the
results obtained in three previous conducted studies on the dynamic
accommodation response[6-7,26].
Therefore, from these results we conclude that if the higher-order aberrations
were helping the visual system to choose the right direction of accommodation,
then with their correction the accommodation performance would have been
reduced.
Moreover, our results yielded a certain value of accommodation lag for
all conditions and accommodation demands (Figure 5). According to previous
studies, a general accommodation lag was expected as our subjects were seeing a
Maltese cross. Using more demanding stimuli, like small letters, significantly
reduces the lag in the accommodation response[2].
Once again, the differences in accommodation lag between the different
conditions were not significantly different for each accommodation demand.
Nonetheless, a slightly increased accommodation lag is noticed in the
even-order corrected condition for the accommodation demand of 1.5, 3, 3.5 and
4 D in comparison to the lag obtained in the two other conditions for the same
accommodation demands.
Figure 5
Mean accommodation values for the three conditions and every accommodation
demand included in this experiment.
Furthermore, in this study we used a monochromatic Maltese cross in
order to impair the use of the LCA by the accommodation system, as it is well
known that commonly it is used as cue for accommodation. This way, we can focus
exclusively in the effect of the correction of the monochromatic aberrations on
the accommodation response. We selected only subjects who were able to
appropriately accommodate under monochromatic light, despite the great
reduction in information provided by the LCA and monochromatic aberrations,
respectively. In particular, in their case is indicated that by accommodating
in monochromatic light the LCA is not used as a cue of accommodation.
Additionally, no difficulties in accommodating were faced in the conditions of
correcting the odd and even-order aberrations (in other words, the partial
correction of the higher-order aberrations), as it has happened to previous
conducted studies[7].
Overall, neither of the subjects’ responses was worse without the odd
and even-order aberrations nor it was unchanged. Chen et al[7]
suggested that in such case the accommodation response does not improve as it
is not affected by the increase in the rate of change in image quality with
focus error produced with the removal of the high order aberrations.
In summary, we measured the static accommodation response of the
subjects’ eyes with the natural aberrations and with the odd and even-order
aberrations corrected using an adaptive optics system. Our results indicate
that when LCA is eliminated as cue, all of the subjects who are able to
accommodate under monochromatic light are capable of accommodating properly
despite the elimination of the odd and even high-order aberrations. For all
subjects, there is no significant difference in the accommodation response with
the natural aberrations or without the odd and even-order aberrations. In our
study, we suggest that the odd and even-order aberrations do not provide aid
for accommodation, as the accommodation response of all subjects was not
affected by the partial correction of these aberrations. Nevertheless, still is
under question the actual role of the monochromatic aberrations in the
accommodation mechanism. Therefore, further research is needed using a larger
number of subjects in order to increase our knowledge in this topic.
ACKNOWLEDGEMENTS
Foundations: Supported by the Marie Curie Grant
FP7-LIFE-ITN-2013-608049-AGEYE Grant; the Atracció de Talent (University
of Valencia) Research Scholarship (UV-INV-PREDOC14-179135).
Conflicts
of Interest: Moulakaki AI, None; Del Águila-Carrasco AJ, None; Esteve-Taboada
JJ, None; Montés-Micó R, None.
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