Compensation of corneal aberrations by the internal optics in the human eye.

Abstract

The objective was to study the relative contribution of the optical aberrations of the cornea and the internal ocular optics (with the crystalline lens as the main component) to overall aberrations in the human eye. Three sets of wave-front aberration data were independently measured in the eyes of young subjects: for the anterior surface of the cornea, the complete eye, and internal ocular optics. The amount of aberration of both the cornea and internal optics was found to be larger than for the complete eye, indicating that the first surface of the cornea and internal optics partially compensate for each other's aberrations and produce an improved retinal image. This result has a number of practical implications. For example, it shows the limitation of corneal topography as a guide for new refractive procedures and provides a strong endorsement of the value of ocular wave-front sensing for those applications.

Full text

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Journal of Vision (2001) 1, 1-8. http://journalofvision.org/1/1/1 1
DOI:10:1167/1.1.1 Received February 1, 2001; published May 1, 2001. ISSN 1534-7362 © 2001 ARVO
Compensation of corneal aberrations by the internal
optics in the human eye
Pablo Artal

Antonio Guirao

Esther Berrio

David R. Williams

Laboratorio de Optica, Universidad de Murcia,
Campus de Espinardo (Edificio C), 30071 Murcia, Spain
?
Laboratorio de Optica, Universidad de Murcia,
Campus de Espinardo (Edificio C), 30071 Murcia, Spain
?
Laboratorio de Optica, Universidad de Murcia,
Campus de Espinardo (Edificio C), 30071 Murcia, Spain
?
Center for Visual Science, University of Rochester,
Rochester, NY, USA 14627
?
The objective was to study the relative contribution of the optical aberrations of the cornea and the internal ocular optics
(with the crystalline lens as the main component) to overall aberrations in the human eye. Three sets of wave-front
aberration data were independently measured in the eyes of young subjects: for the anterior surface of the cornea, the
complete eye, and internal ocular optics. The amount of aberration of both the cornea and internal optics was found to be
larger than for the complete eye, indicating that the first surface of the cornea and internal optics partially compensate for
each other’s aberrations and produce an improved retinal image. This result has a number of practical implications. For
example, it shows the limitation of corneal topography as a guide for new refractive procedures and provides a strong
endorsement of the value of ocular wave-front sensing for those applications.
Key Words: optical aberrations, eye, cornea, lens, retinal image quality
Introduction
Optical aberrations in the human eye impose a major
physical limit on spatial vision. Interest in the study of ocular
optics was evident centuries ago. Now the field is booming
because of new optical technology to correct ocular aberrations
beyond defocus and astigmatism. New technology could allow a
generation of high-resolution ophthalmoscopes and better than
normal vision with contact lenses or refractive surgery procedures
customized to correct an individual's optical aberrations.
Although a great deal of applied research is ongoing (Liang,
Williams, & Miller, 1997; Vargas-Martín, Prieto, & Artal, 1998),
fundamental questions concerning ocular aberrations remain
unanswered. The answers to these questions will impact the
development of these new ophthalmic technologies. For
example, what are the relative contributions of aberrations in the
crystalline lens and the cornea to the quality of images on the
retina? Thomas Young, as early as 1801, performed an
experiment in his own eye to measure the contribution of the
lens to the ocular astigmatism (Young, 1801). He neutralized the
corneal contribution by immersing his eye in water and found
that his astigmatism persisted. In clinical practice, it is commonly
accepted that the lens compensates for moderate corneal
astigmatism. Recent studies, designed to separate aberrations of
the cornea and the lens, concentrated on spherical aberration (El
Hage & Berny, 1973; Tomlinson, Hemenger, & Garriott, 1993),
or used only indirect estimates of the aberrations of the internal
surfaces (Artal & Guirao, 1998), or were based on studies of
crystalline lenses in vitro (Glasser & Campbell, 1998).
We performed three different and complementary sets
of wave-front aberration (WA) measurements in the eyes of
a group of healthy young subjects and showed clearly the
relative contribution of the corneal surface and the internal
optics of the eye to the ocular aberrations.
The WA is a function that characterizes the image-forming
properties of any optical system (Born & Wolf, 1985). It is defined
as the optical deviation of the wave front along a certain ray from
the perfect spherical wave front. The WA is related to the image of
a point source produced by the system (point-spread function
[PSF]) through an integral equation (Goodman, 1996). First, the
WAs of both the cornea and the complete eye were measured. By

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Artal, Guirao, Berrio & Williams 2

combining these two sets of data, the aberrations of the internal
optics were estimated by direct subtraction. Then the WA of the
eye was measured after neutralizing the cornea using swimming
goggles filled with saline water. The aberrations measured with the
filled goggles correspond approximately to those of the internal
ocular optics. The crystalline lens is the most important contributor
to the aberrations of the internal ocular optics that also includes
the posterior surface of the cornea and the ocular media.
Methods
Figure 1 shows a schematic diagram of the experimental
procedure. From the aberrations of the complete eye and
the cornea, those of the internal optics are estimated by
direct subtraction. The aberrations of the internal optics
are directly measured after neutralizing the aberrations of
the first corneal surface.
+
=
+
=
internal optics = eye - cornea
internal optics (directly)

Figure 1. Schematic diagram of the experiments performed.
The WA of the eye was measured with a Hartmann-
Shack (H-S) sensor (Liang, Grimm, Goelz, & Bille, 1994; Liang
& Williams, 1997; Prieto, Vargas-Martín, Goelz, & Artal, 2000).
A narrow infrared beam that acts as a beacon source is
produced by a super-luminescent diode and is projected
into the subject's retina. In the second pass, a microlens
array, conjugated with the eye pupil, produces an image of
spots on a charged-coupled device camera (CCD) (Figure
2A). The relative displacements of the spots are
proportional to the WA local slopes. Then the WA is
reconstructed as a Zernike polynomial expansion (Noll,
1976). The aberrations introduced by the anterior surface
of the cornea were calculated from the corneal shape,
measured by a videokeratographic device (MasterVue
corneal topography system; Humphrey Instruments, San
Leandro, CA). Once the anterior corneal surface was
modeled, the difference in optical path between the chief
ray and a marginal ray over the pupil yields the WA for the
cornea (Guirao & Artal, 2000). From these two WA maps,
the relative contributions of the cornea and the internal
optics to the overall ocular aberration were evaluated. The
geometric center of the pupil was used as the reference point
for the registration between H-S and corneal measurements.
In a simple model with the two series of Zernike coefficients
for the cornea and the eye, the aberrations of the internal
optics were obtained by direct subtraction of each pair of
coefficients. It was assumed that the wave aberrations were
the same axially along small distances.
In addition, the WA for the internal optics was directly
measured with the H-S sensor when refraction and
aberrations of the corneal surface were cancelled by
immersing the eye in saline water using swimming goggles
(Millodot & Sivak, 1979). Light reached the eye through a
hole along the optical axis of the goggles that was covered by
a high-quality optical window. When the corneal surface
power is cancelled, the eye becomes highly hyperopic. To
obtain H-S images adequate for processing, this large defocus
was compensated with a Badal optometer formed by two
photographic objectives (Figure 2B). By using this
procedure, several problems may affect the estimates of the
aberrations of the internal optics. When the H-S sensor is
used at the extreme vergence required for correcting the eye’s
hyperopia, the apparatus itself introduces large aberrations
that may affect the results. This issue was overcome by using
a reference image of the system, recorded in the same
conditions, to compute the aberrations of the internal ocular
optics. This removes any systematic aberrations present in
the apparatus. In addition, the optical window placed in
front of the goggles and the water act as a plane parallel plate
that introduces spherical aberration for those vergences. The
spherical aberration was calculated with a ray-tracing
program and incorporated into the data analysis.
objective
(50 mm)
objective
(50 mm)
focus
corrector
microlens
array
CCD
SLD
saline
water
hyperopia
correction
(46 D)
goggles
(a)
(b)

Figure 2. A. Schematic diagram of the Hartmann-Shack wave-
front sensor used to measure the aberrations of the complete
eye. SLD indicates super-luminescent source; CCD, charged-
coupled device camera. B. Diagram of the part of the set-up
modified to measure the aberration of the internal optics. The
eye was equipped with swimming goggles filled with saline
water. Defocus was compensated by the relative position of the
two 50-mm objectives.

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Artal, Guirao, Berrio & Williams 3

Figure 3 shows 2 examples of H-S images recorded in
the naked eye (A) and in the eye with filled goggles (B).
From independent measurements, we have the estimates of
wave-front aberrations for the different optical components
(anterior surface of the cornea and internal optics);
therefore, the comparison of these estimates indicates the
validity of the methods.
(ab)

Figure 3. Examples of Hartmann-Shack image in the naked eye
(A) and in the eye with filled goggles (B).
Aberrations of the cornea, measured both directly from
the shape and by subtraction of the aberrations obtained
with goggles from those of the whole, were found to be
similar within the experimental variability. Figure 4 further
explains this comparison. Figure 5 shows the Zernike
coefficients of the aberrations for the anterior corneal
surface obtained both directly (videokeratography) and
indirectly (goggles) for 2 subjects. This result provides
strong evidence for consistency of the complete procedure,
supporting the simple model where corneal and internal
optics aberrations are added in a single plane to produce
the overall ocular aberrations.
-
WA
(complete eye)
WA
(internal)
WA
(cornea)
indirect
direct
from corneal
opography
from goggles

Figure 4. Schematic procedure to estimate the aberrations of the
cornea directly and from indirect measurements (complete eye
and anterior corneal surface).
We carried out the indirect set of measurements (with
and without filled goggles) on the eyes of 5 subjects and the
measurement of corneal and complete eye aberrations in
another group of 6 subjects. In 2 of the subjects for which
goggle measurements were performed, corneal topography
for comparison (Figure 5) was also available. All of the
subjects analyzed had normal vision (corrected visual acuity
1 [20/20] or better). Their ages ranged from 24 to 38 years.
The study followed the tenets of the Declaration of
Helsinki, and signed informed consent was obtained from
every subject after the nature and all possible consequences
of the study had been explained. The H-S images were
recorded with paralyzed accommodation (using
cyclopentholate 1%) and infrared light (780 nm). The
aberrations were estimated for different pupil diameters
(4.7 mm when aberrations of the internal optics were
obtained directly from the goggle experiment and 5.9 in the
remainder of the cases).
microns
-0.4
-0.2
0.0
0.2
0.4
microns
-0.4
-0.2
0.0
0.2
0.4
(a)
(b)
C
-4
4
C
-2
2
C
2
2
C
Zernike terms
-1
3
C
1
3
C
3
3
C
-3
3
C
0
4
C
-2
4
C
2
4
C
4
4

Figure 5. Zernike coefficients of the aberrations of the cornea for
2 subjects, obtained from the shape (circles) and by subtraction
of the aberrations of the whole eye and the internal surfaces
(triangles), as described in Figure 4.

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Artal, Guirao, Berrio & Williams 4

Results
The results presented in this section are direct measurements
of the aberrations of the anterior corneal surface and the complete
eye, and indirect estimates of the aberrations of the internal
surfaces. Figure 6 shows a representative example of the results for
1 of the subjects: the WA maps for the cornea (A), the internal
optics (B), and the complete eye (C) together with their associated
PSFs calculated at the best image plane (D-F). In this subject, the
magnitude of aberrations is larger in the cornea than in the
complete eye. This can be easily noted in the wrapped
representation of the WAs by counting the number of
phase-steps appearing in the maps for the cornea and for
the complete eye, or, alternatively, by comparing the
spreads of the associated PSFs.
Figure 7 shows the Zernike terms for the aberrations of
the cornea (solid symbols) and the internal optics for all
subjects. The magnitude of the most important aberration
terms is similar for the two components, but with a change
in sign. This produces an eye with smaller amounts of
aberrations than its main components, indicating that the
internal optics partially compensate for the aberrations of
the anterior surface of the cornea. Figure 8 shows the root
mean square of the WA (a parameter indicating the
magnitude of the aberration) for the eye, the anterior
surface of the cornea, and the internal optics for 6 eyes
after defocus was removed. In every case, the aberrations of
the corneal surface and the isolated internal optics are
larger than those of the total eye.
a
b
c
de
f

Figure 6. A-C. Wave-front aberration (WA) maps for the cornea
(A), the internal optics (B) and the complete eye (C). These WAs
are represented as modulo-π. The pupil diameter was 5.9 mm.
D-E. Associated point-spread functions (PSFs) calculated at the
best image plane from WA panels A-C. Each image subtends 20
minutes of arc of visual field.
C
-2
2 C
2
2
Zernike terms
C
-1
3C
1
3 C
-3
3 C
3
3C
0
4C
2
4C
-2
4
microns
-0.8
-0.4
0.0
0.4
0.8
C
4
4

Figure 7. Zernike terms for the cornea (solid symbols) and the
internal optics (open symbols) for all subjects.
RMS (microns)
subject
eye
cornea
internal
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4

Figure 8. Root mean square of the wave-front aberration of the
eye (squares), the cornea (circles), and the internal optics
(triangles) for 6 eyes after defocus was removed.
Figure 9 shows the values of the Zernike terms up to
fourth order (from 5 to 14) for all subjects for the corneal
surface versus the internal optics. There is a significant
negative correlation between corneal and internal optics
aberrations (regression coefficient, 0.86). This result
indicates a significant coupling of individual aberration
terms between the cornea and the internal ocular optics.
Astigmatism for the cornea and internal optics (Zernike
terms 5 and 6) had opposite signs. Figure 10 shows the
astigmatism of the corneal surface versus the internal
optics. This supports a well-known fact in clinical practice:
the internal optics tend to compensate for the corneal
astigmatism. However, what is more surprising is that this
compensation also takes place for higher order aberrations.
Third- and fourth-order aberrations were also partially
compensated. A large fraction of the spherical aberration of
the cornea is cancelled by the internal optics. The
magnitude of comalike aberrations of the cornea is also
significantly reduced by the internal optics. Figure 11 shows

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Artal, Guirao, Berrio & Williams 5

the values of third-order coma and triangular astigmatism
for the cornea versus the internal surfaces. Figure 12 shows
the fraction of the spherical aberration and coma in the
cornea that is compensated by the internal surfaces.
anterior cornea (microns)
-0.8-0.4 0.00.40.8
internal surfaces (microns)
-0.8
-0.4
0.0
0.4
0.8

Figure 9. Values of Zernike terms up to fourth order (5-14) for
the aberrations of the cornea versus the internal optics for all
subjects.
anterior cornea (microns)
internal surfaces (microns)
-1
-0.5
0
0.5
-0.500.51

Figure 10. Values of astigmatism for the cornea versus the
internal optics for all subjects.
anterior cornea (microns)
internal surfaces (microns)
coma
triangular
astigmatism
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
-0.4 -0.3 -0.2 -0.100.1 0.2 0.3 0.4

Figure 11. Value of third-order coma and triangular astigmatism
for the cornea versus the internal optics for all subjects.
subject
fraction compensated (%)
-60
-40
-20
0
20
40
60
80
100

Figure 12. Fraction of spherical aberration (solid circles) and
coma (open circles) of the cornea that are compensated by the
internal surfaces in every subject.
Discussion
This balance of corneal and internal aberrations
represents a typical example of a coupling of 2 optical
systems. In this case, the corneal surface and the internal
ocular optics, both with a relative poor optical quality,
combine to form a system with a better optical
performance. In optical engineering, a series of lenses in
cascade are usually used to optimize the overall quality of
the system (Smith, 1990); however, the situation in the eye is
different in that there is not a simple access to every lens as