Open Journal of Ophthalmology, 2012, 2, 54-59
http://dx.doi.org/10.4236/ojoph.2012.23012 Published Online August 2012 (http://www.SciRP.org/journal/ojoph)
Optical Modeling and Analysis of Peripheral Optics of
Contact Lenses
Jie Shen, Frank Spors
College of Optometry, Western University of Health Sciences, Pomona, USA.
Email: jshen@westernu.edu
Received March 15th, 2012; revised April 27th, 2012; accepted May 7th, 2012
ABSTRACT
Background: Degraded peripheral vision has been hypothesized to be a stimulus for the development of foveal refrac-
tive error. Contact lenses have been widely used to correct central vision, but their impacts on peripheral v ision are still
unknown. The purpose of this study was to use optical model software to evaluate the peripheral optics of rigid gas
permeable (RGP) and soft contact len ses (SCLs) in isolation. This will better assist us in understand ing their peripheral
optical performances on human eyes. Methods: An optical design software package (Zemax EE) was used to model
peripheral optics of Menicon RGP lens and Acuvue 2 SCLs. Profiles of sphero-cylindrical power and major higher-
order aberrations were computed in 10˚ steps out to 40˚ off-axis eccentricity for –3.0 D central focal power contact lens.
The results of optical modeling were analyzed and compared with previously published experimental data. Results:
–3.0 D RGP lenses and SCLs had –1.4 D and –2.0 D dioptric power at 40˚ eccentricity, respectively. The reduced diop-
tric power in the periphery of the analyzed contact lenses quantitatively matched with the reduc ed amount of hyperopic
field curvature found from experimental data when these contact lenses fitted on human eyes. Cylindrical power in-
creased to 0.3 D ~ 0.4 D at 40˚ eccentricity for both lens types. In addition, both contact lens types produced higher
order aberrations, namely 1.2 µm coma and 0.15 µm spherical aberration at 40˚ eccentricity. Conclusions: Compared to
SCLs, RGP lenses with equal focal power had less dioptric power in the periphery. Both RGP lenses and SCLs pro-
duced the same amount of major higher-order aberrations with increasing of the field angle. Some of these results can
be used to predict and understand the peripheral optical performance of contact lenses on human eyes.
Keywords: Contact Lens; Peripheral Optics; Aberrations; Optical Model
1. Introduction
Degraded peripheral vision has been hypothesized to be a
stimulus for the development of foveal refractive error.
[1-4]. Based on the “grow to compensate hyperopic de-
focus” [1-3] or the “grow to clarity” [4] hypothesis and
local retinal mechanisms [5-8], eyes of individuals even
with perfect central vision, but with peripheral hyperopic
refractive error or blurred peripheral image, might still
develop myopia.
Contact lenses (CLs) are widely used treatments for
correcting foveal defocus and astigmatism. With fully
corrected foveal vision achieved, peripheral refractive
error and aberratio ns with contact lens correctio n are still
largely unknown. Some recent studies have shown the
effects of CLs on peripheral refraction and image quality
[9-11]. Results from those studies indicated that, after
CLs correction, peripheral refraction will be influenced
by the contact lens design and materials when a contact
lens is prescribed to correct on-axis refractive error. Our
previous study [9] compared peripheral refraction with
correction of Rigid Gas Permeable (RGP) lenses and Soft
Contact Lenses (SCLs) and suggested that both lens
types reduced the degree of hyperopic field curvature
present in the periphery of myopic eyes, with RGP lenses
having a greater effect. Moreover, our results have
shown that RGP lenses introduced more oblique astig-
matism than SCLs, which as a tradeoff, limited the pos-
sible effect of RGP lenses on myopia progression con-
trol.
The above studies were based on experimental meas-
urements of the peripheral optics of the human eye with
and without CLs. The experimental methods are time
consuming and labor intensive since investigators n eed to
repeat the measurements along horizontal or vertical me-
ridians in 5˚ or 10˚ steps out to 40˚ off-axis eccentricity
using different instruments [2,12-19]. Although new
techniques have been developed to facilitate easy and
fast measurements of human eyes’ peripheral optics, [20,
21] it is still a major methodological obstacle for re-
searchers who are interested in studying peripheral vi-
sion.
Copyright © 2012 SciRes. OJOph
Optical Modeling and Analysis of Peripheral Optics of Contact Lenses 55
Optical modeling results of off-axis optical character-
istics of human eyes with CLs correction have also been
previously reported [22,23]. However, there are few stu-
dies focused on characterizing peripheral optics of CLs
in isolation. We anticipate th at the different types of CLs
with varying design characteristics and materials have a
major impact on the differences in peripheral image qua-
lity. To characterize the off-axis optics of different CLs,
we can either experimentally measure their peripheral re-
fraction and aberrations in isolation or use optical design
software for modeling off-axis optical characteristics of
those CLs. Percy et al. [10] used a “Power Mapper” sys-
tem, which scans a narrow laser beam parallel to the op-
tical axis across the entire lens surface, to measure power
profiles across the optic zone (OZ) of the CLs. However,
this method did not measure the actual off-axis power of
the contact lens which needs pencils of light coming
from varying off-axis field angles. A physical human
model eye has been developed recently and provided the
ability to assess the optical performance of CLs in vary-
ing off-axis positions [24]. In this study we use the po-
pular optical design software Zemax to evaluate the pe-
ripheral optics of different contact lenses, SCLs and RGP
lenses, in isolation. This will better assist us in under-
standing their peripheral optical performances when fit-
ted on human eyes.
2. Methods
An optical design software package (Zemax EE, Zemax
Corporation, San Diego, Feb. 2010 version) was used to
run a ray-tracing program to model the peripheral optics
of Menicon XT RGP lenses (Z material, Menicon Co.
Ltd.) and Acuvue 2 SCLs (Vistakon Division, J & J Vi-
sion Care, Inc.). The parameters of the different lens de-
signs were obtained from the manufacturers. In the fol-
lowing text the abbreviations RGP lenses refers to Me-
nicon Z XT contact lenses and SCLs refers to Acuvue 2
contact lenses.
A Zernike aberrations table was generated and ex-
tracted from the Zemax modeling results. The sphero-
cylindrical power components were converted from the
Zernike coefficients using the following equations .
0
2
2
2
0
2
2
45 2
2
43
26
26
2
M
C
r
J
C
r
J
C
r
(1)
where M represents the spherical equivalent, J0 repre-
sents with-the-rule (WTR) astigmatism and against-the-
rule astigmatism (ATR), J45 represents oblique astigma-
tism with axes at 45 degrees and 135 degrees. , ,
0
2
C2
2
C
2
2
C
are Zernike coefficients for defocus, WTR or ATR
astigmatism and obliqu e astigmatism terms, respectively.
In these equations, r is the pupil radius, or aperture ra-
dius.
Based on the contact lenses parameters as provided by
the manufacturers, profiles of sphero-cylindrical power
and major higher-order aberrations (up to the 4th Zernike
order) were computed in 10˚ steps out to 40˚ off-axis
eccentricity for –3.0 D RGP lenses and –3.0 D SCLs. All
computations were done for an aperture size of 6 mm.
Peripheral profiles of field curvature, astigmatism, coma
and spherical aberration of CLs with varying central di-
optric power from –1.0 D to –6.0 D in 1.0 D steps have
also been modeled. The results of optical modeling were
analyzed and compared with previously published ex-
perimental data [9,25].
3. Results
Both types of contact lenses produced less negative
power for off-axis incident pencils of light than for on-
axis pencils of light. Figure 1 is a comparison of the
mean spherical equivalent (M) across the lens up to 40
degrees of off-axis angle in the two types of contact
lenses, both havin g a centra l focal power of –3.0 D.
As shown in Figure 1, at a 40 degrees off-axis field
angle the dioptric power of the RGP lens decreased to
–1.4 D and the dioptric power of the SCL decreased to
–2.0 D.
Contact lenses, just like other optical elements, pro-
duce more cylindrical power with increasing off-axis
angle. As depicted in Figure 2, both the RGP lens and
SCL introduce ATR astigmatism in off-axis eccentrici-
ties. However the RGP lens has a stronger effect. At 40˚
Figure 1. Refractive power variation in relation to the field
angle for different contact lenses modeled by Zemax soft-
ware. The contact lenses used in this simulation had -3.0 D
central focal power. The power profile of the RGP lens is
represented by the red curve and the power profile of the
SCL is represented by the blue curve.
Copyright © 2012 SciRes. OJOph
Optical Modeling and Analysis of Peripheral Optics of Contact Lenses
Copyright © 2012 SciRes. OJOph
56
eccentricity, –3.0 D the RGP lens and the SCL produce
–0.38 D and –0.32 D astigmatism, respectively. Com-
pared to the changes in the spherical power profiles the
increases in off-axis astigmatism are small.
in the off-axis field angle. Both RGP lenses and SCLs
produced negative spherical aberration (SA) which be-
came more negative toward the contact lenses peripheries
(Figure 4).
The experimental results showed that the effect of
contact lenses on the peripheral curvature of field was
depended on the CLs central dioptric power. The higher
the corrective power of the lens, the more effect it had on
the changes of peripheral curvature of field. The optical
modeling of contact lenses in isolation also supports
these empirical data (Figure 3). Both contact lenses
showed increased positive focal power values of Periph-
eral Relative M (PRM) when the central dioptric power
varied from –1.0 D to –6.0 D. The amounts of J0 intro-
duced by both types of CLs also increased systematically
in the periphery with increased len s power. Comparing J0
profiles of RGP lenses with SCLs, RGP lenses intro-
duced more cylindrical power in the periphery than did
SCLs.
Figure 2. Cylindrical power variation in relation to the field
angle for different contact lenses modeled by Zemax soft-
ware. The contact lenses used in this simulation had -3.0 D
central focal power. The power profile of the RGP lens is
represented by the red curve and the power profile of the
SCL is represented by the blue curve.
Simulation of Major Higher-Order Aberrations
The optical modeling of major higher-order aberration
coefficients indicated that RGP lenses and SCLs with
same central power introduced the same amount of coma
Figure 3. Contact lens power profiles varied depending on the contact lenses central focal power. The upper two panels show
the profiles of peripheral relative defocus (M) and the lower two panels show the profiles of peripheral WTR and ATR
astigmatism (J0).
Optical Modeling and Analysis of Peripheral Optics of Contact Lenses 57
The amount of off-axis coma and spherical aberration
increased with dioptric lens power for both RGP lenses
and SCLs (Figure 4). However it has to be noted that the
Zemax modeling of higher-order aberrations induced by
the contact lenses were done in isolation. Therefore the
results of these simulations may differ from experimental
findings when the lenses interact with the optical com-
ponents of the pat i e nt s’ co rneas.
4. Discussion
One purpose of the current study was to investigate how
efficient the optical characteristics of contact lenses can
be transferred to the eye when fitting CLs. The results
presented in this study indicate that the optical properties
of CLs in isolation change at various field angles. The
comparison of these results with previous experimental
data allows a better understanding and prediction of the
peripheral optical profiles for different types of contact
lenses when fitted in the eyes. Table 1 allows a com-
parison of experimental findings for a –3.0 D myopic eye
with optical modeling results for a –3.0 D RGP lens and
a –3.0 D SCL respectively.
For field angles ranging from 5 degrees up to 25 de-
grees, both the RGP lens and the SCL induced a relative
myopic defocus. Whereas the SCL demonstrated this
throughout the entire peripheral field up to 35 degrees,
the RGP induced a relative hyperopic defocus for 30 de-
grees and 35 degrees field angles (Table 1).
Figure 4. Coma and spherical aberration (SA) varied with field angle in different contact lenses. The focal power values of
the contact lenses used in this Zemax modeling varied from -1.0 D to -6.0 D. The upper two panels show the profiles of coma
and the lower two panels show the profiles of spherical aberration (SA).
Table 1. A comparison of optical modeling data for contact lenses from this study and experimental data for an uncorrected
myopic eye, adapted from a previous study [9].
Field angle (degree)
Data values
(diopter) 0 5 10 15 20 25 30 35
Experimental (uncorrected eye) –3.00 –2.89 –2.77 –2.70 –2.59 –2.41 –2.29 –2.03
RGP modeling –3.00 –2.97 –2.92 –2.80 –2.66 –2.45 –2.18 –1.80
SCL modeling –3.00 –2.98 –2.95 –2.91 –2.81 –2.69 –2.53 –2.27
Copyright © 2012 SciRes. OJOph
Optical Modeling and Analysis of Peripheral Optics of Contact Lenses
58
The decreased lens power in the peripheral field can
help to explain why SCLs partially correct PRM while
RGP lenses over-correct RPM at large field angles (25˚
and 30˚). In the companion paper, one of the major
statements is “for an eccentricity of E degrees, PRM is
approximately E percent of foveal refractive error in the
naked eye” [9]. For example, when measuring at 35˚ ec-
centricity, a –3.0 D myopic eye has about 35% × 3.0 D =
1.05 D less refractive myopic error relative to its center,
which equals a remaining amount of –1.95 D myopia at
35˚ visual field angle. A RGP lens with –3.0 D central
focal power has a peripheral focal power of –1.8 D at 35
degrees field angle, which will under-correct the eye’s
refractive error at this eccentricity and result in a myopic
field curvature. On the contrary, a –3.0 D SCL has a
spherical power of –2.27 D at 35 degrees which will
over-correct the eye’s refractive error resulting in a hy-
peropic field curvature (Figure 5).
The above analysis indicated that differences of pe-
ripheral power profiles in SCLs and RGP lenses can help
to explain the experimental observations of changes in
PRM when these lenses were used to correct central re-
fractive errors. With contact lens correction the total op-
tical system of the eye consists of the contact lens, the
tearfilm, the cornea and the crystalline lens. We analyzed
the data of curvature of field profiles for the –3.0 D my-
opic uncorrected eye as well as the –3.0 D contact lenses
listed in Table 1. By ignoring the influence of the tear
film when wearing a contact lens the blue and red curves
in Figure 6 represent the normalized PRM, PRM value
as a fraction of center M, of a SCL and a RGP lens, re-
spectively. A comparison of data from the optical mod-
eling and experimental findings shows that these data
have a close match for visual field angles up t o 25 degrees.
Figure 5. Comparison of experimental data of a –3.0 D my-
opic eye’s curvature of field profile with optical modeling
data of –3.0 D contact lens power profiles for varying field
angles. The green curve represents the experimental data
adapted from a previous paper. The red and blue curves
represent the optical modeling results for a RGP lenses and
a SCL, respectively.
Figure 6. Normalized PRM as a function of varying field
angles. The green curve represents experimental data in
uncorrected eyes. The blue and red curves indicate normal-
ized PRM by subtracting uncorrected experimental data of
SCLs and RGP lenses from modeling data, respectively.
The blue triangle and the red circle symbols represent ex-
perimental data for the SCLs and the RGP lenses, respec-
tively. The error bars indicate the standard error of the
mean.
This suggests that the dioptric power of the contact
lenses can be effectively transferred to the eye from the
center to the mid periphery. When wearing contact lenses
the tear film plays a minor role in the formation of pe-
ripheral defocus.
Optical modeling data for astigmatism (J0) and other
major higher-order aberrations (Coma and SA) of the
RGP lenses and SCLs did not generate comparable re-
sults with the experimental data [9,25]. This might be due
to the conformity of the co ntact lenses with the front co r-
neal surface which was not taken into account in the Ze-
max modeling.
In conclusion, RGP lenses with equal focal power had
less dioptric power in their periphery compared to SCLs.
Both RGP lenses and SCLs produced the same amount of
major higher-order aberrations with the increase of the
field angle. Optical modeling of peripheral optics of CLs
in isolation can be a good predictor for changes in PRM
up to a field angle of 25 degrees. Within this range the
modeling matched appropriately with previously ob-
served experimental findings.
5. Acknowledgement
The authors thank Prof. Larry Thibos for co-authoring
and providing comments in preparing the ARV O abs trac t
of the same content in this article. Also thanks Audrey
Vazquez for proofing reading this paper.
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