Comparison of Progressive Addition Lenses by Direct Measurement of Surface Shape

Abstract

Purpose:
To compare the optical properties of five state-of-the-art progressive addition lenses (PALs) by direct physical measurement of surface shape.

Methods:
Five contemporary freeform PALs (Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph, and Zeiss Individual) with plano distance power and a +2.00-diopter add were measured with a coordinate measuring machine. The front and back surface heights were physically measured, and the optical properties of each surface, and their combination, were calculated with custom MATLAB routines. Surface shape was described as the sum of Zernike polynomials. Progressive addition lenses were represented as contour plots of spherical equivalent power, cylindrical power, and higher order aberrations (HOAs). Maximum power rate, minimum 1.00-DC corridor width, percentage of lens area with less than 1.00 DC, and root mean square of HOAs were also compared.

Results:
Comfort Enhanced and Physio Enhanced have freeform front surfaces, Shamir Autograph and Zeiss Individual have freeform back surfaces, and Hoya Lifestyle has freeform properties on both surfaces. However, the overall optical properties are similar, regardless of the lens design. The maximum power rate is between 0.08 and 0.12 diopters per millimeter and the minimum corridor width is between 8 and 11 mm. For a 40-mm lens diameter, the percentage of lens area with less than 1.00 DC is between 64 and 76%. The third-order Zernike terms are the dominant high-order terms in HOAs (78 to 93% of overall shape variance). Higher order aberrations are higher along the corridor area and around the near zone. The maximum root mean square of HOAs based on a 4.5-mm pupil size around the corridor area is between 0.05 and 0.06 µm.

Conclusions:
This nonoptical method using a coordinate measuring machine can be used to evaluate a PAL by surface height measurements, with the optical properties directly related to its front and back surface designs.

Full text

Comparison of Progressive Addition Lenses
by Direct Measurement of Surface Shape
Ching-Yao Huang*, Thomas W. Raasch
†
, Allen Y. Yi*, and Mark A. Bullimore
‡
ABSTRACT
Purpose. To compare the optical properties of five state-of-the-art progressive addition lenses (PALs) by direct physical
measurement of surface shape.
Methods. Five contemporary freeform PALs (Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir
Autograph, and Zeiss Individual) with plano distance power and a +2.00-diopter add were measured with a coordinate
measuring machine. The front and back surface heights were physically measured, and the optical properties of each surface,
and their combination, were calculated with custom MATLAB routines. Surface shape was described as the sum of Zernike
polynomials. Progressive addition lenses were represented as contour plots of spherical equivalent power, cylindrical power,
and higher order aberrations (HOAs). Maximum power rate, minimum 1.00-DC corridor width, percentage of lens area with
less than 1.00 DC, and root mean square of HOAs were also compared.
Results. Comfort Enhanced and Physio Enhanced have freeform front surfaces, Shamir Autograph and Zeiss Individual have
freeform back surfaces, and Hoya Lifestyle has freeform properties on both surfaces. However, the overall optical properties
are similar, regardless of the lens design. The maximum power rate is between 0.08 and 0.12 diopters per millimeter and
the minimum corridor width is between 8 and 11 mm. For a 40-mm lens diameter, the percentage of lens area with less than
1.00 DC is between 64 and 76%. The third-order Zernike terms are the dominant high-order terms in HOAs (78 to 93% of
overall shape variance). Higher order aberrations are higher along the corridor area and around the near zone. The maximum
root mean square of HOAs based on a 4.5-mm pupil size around the corridor area is between 0.05 and 0.06 Hm.
Conclusions. This nonoptical method using a coordinate measuring machine can be used to evaluate a PAL by surface
height measurements, with the optical properties directly related to its front and back surface designs.
(Optom Vis Sci 2013;90:565Y575)
Key Words: progressive addition lenses, coordinate measuring machine, Zernike polynomials, freeform surface,
wavefront aberrations
The optical characteristics of progressive addition lenses
(PALs) are often measured by a conventional lensometer
1Y4
in the clinic, dispensary, or optical laboratory, which conve-
niently and quickly gives information about distance power, near
power, and thus add power. However, other characteristics of
PALs affect clinical performance, such as the unwanted astigma-
tism and aberrations that arise from the freeform surfaces. In this
context, ‘‘freeform’’ is used to describe any surface that deviates
from a spherocylindrical shape. Moire
´interferometry,
5Y9
wavefront
sensing,
10Y13
and point diffraction interferometers
14
have been
used to yield information about the distance power, near power,
related add power, and higher order aberrations (HOAs) across
the whole lens. These measurement methods are all based on
optical measurements.
With advanced freeform manufacturing technology, PALs
may now be fabricated to have complex surfaces on the front,
back, or both. Moreover, there are various lens designs from dif-
ferent manufacturers, and clinicians could benefit from a better
understanding of the underlying design principles. The overall
optical characteristics can be easily and accurately evaluated by
the aforementioned optical measurements. However, with the
introduction of increasingly complex lens designs, it is impor-
tant to evaluate the variation in shape for each individual lens
surface. For example, it is possible that imparting different sur-
face features to the axially separate front and back surfaces of a
1040-5488/13/9006-0565/0 VOL. 90, NO. 6, PP. 565Y575
OPTOMETRY AND VISION SCIENCE
Copyright *2013 American Academy of Optometry
ORIGINAL ARTICLE
Optometry and Vision Science, Vol. 90, No. 6, June 2013
*PhD
†
OD, PhD, FAAO
‡
MCOptom, PhD, FAAO
Department of Optometry, Shu Zen Junior College of Medicine and Man-
agement, Kaohsiung, Taiwan (C-YH); Colleges of Optometry (TWR) and En-
gineering (AYY), The Ohio State University, Columbus, Ohio; and College of
Optometry, The University of Houston, Houston, Texas (MAB).
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

PAL may influence high-order aberrations, as has been shown for
intraocular lenses.
15
One way to reveal individual surface proper-
ties of PALs is profilometry.
Optical properties of PALs have previously been derived from
direct measurement of the physical dimensions of the PAL sur-
faces.
16Y19
Mazuet
18
used a coordinate measuring machine (CMM)
to measure both surfaces of two PALs and mentioned that, by
knowing the lenses refractive index, the wearer power and astig-
matism maps can be generated. Recently, Raasch et al.
19
used a
CMM to characterize and compare three PAL surfaces in terms
of the Zernike polynomials. They performed surface height mea-
surements on the freeform front surface only based on the assump-
tion that the back surface does not contribute to the progressive
power because of a constant contribution to the second-order
(sphere and cylinder) terms. They also point out that if both
surfaces were freeform, measurement of both surfaces would be
needed, with careful registration of the measured regions of both
surfaces. Of course, the optical properties of the lens would be
the combined effect of the two surfaces.
In a recent article,
20
we compared PAL properties derived using
the CMM method with those from a Hartmann-Shack wave-
front sensor and a Rotlex Class Plus lens analyzer operating as a
moire
´interferometer. The three measurement methods were com-
parable for measuring spherical and cylindrical power across PALs.
In this study, direct physical measurements of both front and
back surfaces of five contemporary PALs were performed using
the CMM method and analyzed to derive the optical character-
istics of each surface and the overall properties of these PALs
with the expectation of revealing interesting data and insights
into these five different lens designs. The primary goal was to
compare and contrast the front and back surface optical prop-
erties among the five PALs.
METHODS
Five contemporary PALs (Varilux Comfort Enhanced, Varilux
Physio Enhanced, Hoya Lifestyle, Shamir Autograph, and Zeiss
Individual) were selected. All were right lenses, with plano distance
power with a +2.00-diopter (D) add, and plastic CR-39 (n = 1.498
for L= 589 nm). Three types of designs were assessed. The first
type was a freeform front surface with a spherical or spherocylindrical
back surface (Varilux Comfort Enhanced and Varilux Physio
Enhanced). The second was a spherical (or spherocylindrical) front
surface with a freeform back surface (Shamir Autograph and Zeiss
Individual). The third was freeform on both surfaces (Hoya Life-
style). The lenses had a similar base curve, fitting cross location,
and minimum fitting height, as shown in Table 1.
Surface height measurement was conducted using a precision
Sheffield Cordax RS-30 DCC CMM. Both front and back sur-
faces were measured. The lens was measured on a grid of points
(x,y) spaced about 0.49 mm apart or about 4.14 measured points
per square millimeter to produce data files that consist of (x,y,z)
positions. That measurement density yields about 12,100 samples
within a 61-mm diameter. The Hoya Lifestyle PAL was mea-
sured over a 40-mm diameter, as the lens blank is truncated at top
and bottom, leaving a maximum centered circular diameter of
about 41 mm. Data were saved and subsequently imported into
MATLAB for analysis. The analysis diameter of all PALs was
60 mm, except for the Hoya Lifestyle PAL at 40 mm. Each lens
was oriented so that the axis of the coma component of the free-
form surface was vertical. For measurement of the other surface,
the lens was flipped around this vertical meridian. For analysis,
the measured values were flipped back, so that corresponding
points on front and back surfaces superimposed. A detailed de-
scription of the measuring procedure and mathematical calculation
has been described elsewhere.
19
As an eye views through a given location on the lens, the region
of the lens centered at that location and equal in size to the pupil of
the eye is responsible for forming the foveal image. To find the
optical properties of the lens within that region, we find the set
of Zernike coefficients that describe the lens surface within the re-
gion. In outline, this process starts with a vector of 45 Zernike
coefficients (up through the eighth order), which defines the en-
tire 60-mm-diameter lens surface.
21
Those Zernike coefficients
are transformed to Taylor coefficients using a matrix method, and
the pupil translation and size rescaling are performed on these
Taylor coefficients. Those Taylor coefficients are then transformed
back to Zernike coefficients.
The matrix that is used to transform Zernike coefficients to
Taylor coefficients is a 45 45 matrix. The first row of the
matrix consists of the 45 Zernike terms in Cartesian coordinates.
The next two rows are the first derivatives with respect to xand y,
the next three rows are the second derivatives, and so on, through the
eighth derivatives. Each element of the matrix is in general a
function of xand y, so pupil location translations are produced by
inputting the (x,y) value for the center of the translated pupil.
TABLE 1.
Progressive addition lenses used in this study
Lens Design type Base curve, D Minimum height, mm Fitting cross, mm
Comfort Enhanced Molded progressive front surface, freeform
single-power back surface
5.75 18 4
Physio Enhanced Molded progressive front surface, freeform
single-power back surface
5.75 17 4
Hoya Lifestyle Freeform both surfaces 6.00 18 4
Shamir Autograph Molded spherical front surface, freeform
progressive back surface
6.00 19 4
Zeiss Individual Molded spherical front surface, freeform
progressive back surface
6.25 18 6
566 Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al.
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

Rescaling to a smaller pupil size is done by raising the propor-
tional change in aperture diameter to a power equal to the order
of each Taylor term. We now have a vector of translated and re-
scaled Taylor coefficients. Translating these back to Zernike coef-
ficients is done with another 45 45 matrix, which is the inverse
of the Zernike-to-Taylor matrix. This matrix, multiplied by the
vector of Taylor coefficients, yields a vector of Zernike coefficients
for the rescaled pupil translated to the given (x,y) lens location.
Optical properties of the lens are derived from the Zernike co-
efficients for subapertures arrayed across the lens surface. Spherical
equivalent (M), J
0
,andJ
45
are derived from the second-order
Zernike terms,
22
and the HOA root mean square (RMS) error is
derived from the higher order Zernike terms.
Progressive addition lenses characteristics were represented as
contour plots of spherical equivalent power, cylindrical power,
and HOAs. Maximum power rate change along the corridor,
minimum 1.00-DC corridor width, and percentage of lens area
with less than 1.00 DC were also compared.
RESULTS
Fig. 1 illustrates the front and back surface height profiles
caused by the higher order terms. In addition, the thickness pro-
files resulting from the combination of the two surface heights
are shown. These height profiles are generated from the higher
order terms only. The spherocylindrical (second-order) terms
are essentially irrelevant to the progressive power of the lens be-
cause they contribute a constant value to the sphere and cylinder
power. Because we are interested here in the variation in lens
power (and in astigmatism and aberrations) across the lens sur-
face, we can ignore the constant spherocylindrical terms. This
was done by simply setting the second-order coefficients to zero.
It is apparent that the first two lenses have a freeform front
surface and a spherocylindrical back surface. The last two lenses
are spherocylindrical on the front and freeform on the back. The
third lens is freeform on both surfaces. The third column repre-
sents lens thickness from the combination of the two surfaces. The
lenses are similar in that they all have relatively concave upper
portions (for distance vision) and relatively convex portions below
(for near vision).
Fig. 2 shows contour plots of the spherical equivalent power (M)
of these five PALs on the front, back, and combined. The negative
sphere values in the upper portion of the lens is a result of the
setting the second-order coefficients to zero, thus making the aver-
age power of the lens close to plano. The surface power profiles
along the vertical midline on the front, back, and combined surface
in the five PALs are shown in Fig. 3. These two figures clearly
show that Comfort Enhanced and Physio Enhanced have pro-
gressive front surface designs, Shamir Autograph and Zeiss Indi-
vidual have progressive back surface designs, and Hoya Lifestyle
has a freeform design on both surfaces, consistent with the manu-
facturers’ descriptions.
Astigmatism is shown in Fig. 4. The results show that the un-
wanted astigmatism from the freeform surface generally increases
laterally, away from the vertical midline. The contour plots of
unwanted astigmatism on the combined surface for the five lenses
are similar, which shows less astigmatism along the progressive
corridor, which increases laterally away from the vertical midline.
Note that, for the Hoya lens, the diameter represented here is
40 mm rather than 60 mm.
Table 2 shows a comparison of the maximum power rate
change, percentage of lens area (within a 40-mm diameter) with
less than 1.00 DC, and minimum 1.00-DC corridor width. It
shows that the Comfort Enhanced, Physio Enhanced, and Hoya
Lifestyle have progressive power changes on the front surface,
whereas the Shamir Autograph and Zeiss Individual have pro-
gressive power changes on the back surface. The maximum power
change rates along the vertical midline of the combined surface
are between 0.08 and 0.12 D/mm, and the minimum 1.00-DC
corridor widths are between 8 and 11 mm. The Hoya Life-
style distributes unwanted astigmatism across both surfaces
because both are freeform. Nonetheless, all five PALs show a similar
percentage of lens area with less than 1.00 DC, between 64
and 76%.
Table 3 compares the surface shapes, in terms of shape variance
(in square micrometers). These variance values come from the
Zernike coefficients that define the shape of the central 40-mm
diameter of each surface. Values are given for front, back, and
combined surfaces. Furthermore, shape variance values are given
for the third-order terms, that is, coma and trefoil. These are the
dominant high-order terms in the freeform surfaces responsible
for 78 to 93% of surface height variance.
Fig. 5 shows contour plots of the higher order RMS through a
4.5-mm pupil for the front, back, and both surfaces combined.
It is apparent that the freeform surface of each lens is responsible
for the HOAs, whereas the spherocylindrical surfaces show a low
level of HOA, as expected. The contour plots show that the RMS
of HOAs tends to be higher in the progressive corridor area and
the area surrounding the near power zone in all five PALs. The max-
imum RMS of HOAs around the corridor area is between 0.05
and 0.06 Km for a 4.5-mm pupil.
DISCUSSION
There are three types of PAL designs assessed in this study. The
first is a freeform front surface with a spherocylindrical back sur-
face. This is similar to the traditional approach to PAL manu-
facture. The second is a spherocylindrical front surface with a
freeform progressive back surface. The third is freeform on both
surfaces. According to the CMM surface height measurements
of the front and back PAL surfaces, the surface power profile
along the vertical midline in Fig. 2 and the maximum power
rate in Table 2 demonstrate that Comfort Enhanced and Physio
Enhanced belong to the first design, Shamir Autograph and Zeiss
Individual belong to the second design, and Hoya Lifestyle be-
longs to the third design, consistent with the manufacturers’
descriptions. Obviously, the most intriguing design is the Hoya
Lifestyle, which uses sophisticated surfaces on the front and the
back. Table 3 and Fig. 1 demonstrate that trefoil is the dominant
high-order aberration on the freeform back surface.
The lens specifications were plano distance power with a
+2.00-D add. The method used here produces different spherical
equivalent powers (M) than plano at distance and +2.00 D at near.
This difference is caused by the second-order Zernike term
(defocus) being initially set to zero in the calculation of surface
height. As a result, contour plots in Fig. 2 have a distance portion
Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al. 567
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

FIGURE 1.
Surface height and thickness (in millimeters) profile of five PALs: Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph,
and Zeiss Individual (from top to bottom), higher order terms only: front surface height (left), back surface height (middle), and thickness profile (right). The
black contour lines are at intervals of 0.1 mm. Lens diameter is 60 mm except for the Hoya Lifestyle, which is 40 mm. A color version of this figure is
available online at www.optvissci.com.
568 Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al.
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

FIGURE 2.
Variation in spherical equivalent power (in diopters) of five PALs, Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph,
and Zeiss Individual (from top to bottom), for the front surface (left), back surface (middle), and combined surfaces (right). The black contour lines are at
intervals of 0.50 D. Lens diameter is 60 mm except for the Hoya Lifestyle, which is 40 mm. A color version of this figure is available online at
www.optvissci.com.
Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al. 569
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

FIGURE 3.
Surface power profile of five PALs, Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph, and Zeiss Individual (from top
to bottom), along the vertical midline for the front surface (left), back surface (middle), and combined surface (right) based on the data shown in Fig.3.
The xaxis is the spherical equivalent power in diopters, and the yaxis is the vertical location on the lens in millimeters.
570 Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al.
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

FIGURE 4.
Contour plots of the cross-cylindrical power (J) of five PALs, Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph, and
Zeiss Individual (from top to bottom), for the front surface (left), back surface (middle), and combined surface (right). Jis the Pythagorean sum of J
0
and J
45
and half the magnitude of the total cylinder (in diopters). Lens diameter is 60 mm except for the Hoya Lifestyle, which is 40 mm. A color version of this
figure is available online at www.optvissci.com.
Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al. 571
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

that is negative and a near add that is positive, with a difference of
about 2.00 D.
A comparison of these lenses shows some similarities and some
differences. Which lens may perform optimally for any given user,
however, certainly must depend on a wide range of factors. Al-
though the lens characteristics described here are certainly im-
portant properties of a lens, they also certainly do not provide
sufficient information to predict with certainty which lens will per-
form best for a given user and purpose. The values of spherical power,
astigmatism, and HOAs were derived from surface measures, and
no adjustment was made for variations in vertex distance and
oblique incidence associated with a wearer’s eye rotating behind
the lens. Likewise, the present study only evaluated lenses with
plano distance power, a single add power, and a single material.
Caution should therefore be exercised before generalizing these
results to other distance and add powers, along with higher index
materials. Different manufacturers may use a variety of strategies
when manipulating surface geometry to account for these vari-
ables. However, modest changes in refractive index (from n
1
to n
2
)
will result in predictable changes to optical properties, propor-
tional to (n
2
j1)/(n
1
j1). That is, a change in index from 1.5 to
1.55 will result in power and aberration increases by a factor of
0.55/0.5 = 1.1.
The present study demonstrates that coma and trefoil are the
dominant high-order terms present in PAL designs regardless of
the design, with these third-order terms accounting for 78 to 93%
of the higher order shape variance. One cannot have a progressive
surface without high-order terms because they are responsible for
the variation in power across the lens. The amount of HOAs
varies with design (Table 3). In their excellent review, Meister and
Fisher
23
state that ‘‘coma is directly proportional to the rate of
change in mean addition power.’’ It is interesting to note that the
PALs with the highest overall levels of high-order aberrationsV
Varilux Comfort and Zeiss IndividualVhave relatively short cor-
ridors based on their maximum power rates (Table 2). Conversely,
the Physio Enhanced and Hoya Lifestyle have lower levels of high-
order aberrations (Table 3) and relatively long corridors (Table 2).
The Shamir Autograph is the exception, with a short corridor but
TABLE 2.
Comparison of the maximum power rate, percent of lens area, and minimum corridor width in five PALs for a lens diameter
of 40 mm
Maximum power rate, D/mm Percent of lens area e1.00 DC
PALs
Front
surface
Back
surface
Combined
surface
Front
surface
Back
surface
Combined
surface
Minimum 1.00-DC
corridor width, mm
Comfort Enhanced 0.124 0.004 0.118 64.3 100 64.2 9.0
Physio Enhanced 0.116 0.007 0.095 66.5 100 65.9 9.4
Hoya Lifestyle 0.090 0.039 0.085 49.0 50.7 76.2 10.7
Shamir Autograph 0.015 0.108 0.117 100 72.2 70.1 10.9
Zeiss Individual 0.021 0.105 0.115 100 66.1 63.7 8.0
TABLE 3.
Comparison of the whole-surface shape variance (in square micrometers) of HOAs in five PALs measured by the CMM
method for a lens diameter of 40 mm
PALs
Comfort
Enhanced
Physio
Enhanced
Hoya
Lifestyle
Shamir
Autograph
Zeiss
Individual
Front Surface HOAs 1600 1319 2006 54.7 118.4
Third order
(% of total HOA)
1335 (83%) 1043 (79%) 1933 (96%) 6.9 (13%) 5.2 (4%)
Coma 971 672 981 1.2 0.9
Trefoil 364 371 952 5.7 4.3
Back Surface HOAs 9.9 10.3 2101 1033 1375
Third order
(% of total HOA)
2.9 (29%) 3.7 (36%) 1969 (94%) 857 (83%) 1113 (81%)
Coma 0.3 3.3 7 553 745
Trefoil 2.6 0.4 1962 304 368
Combined Surface HOAs 1542 1128 1188 1017 1523
Third order
(% of total HOA)
1303 (84%) 896 (80%) 1102 (93%) 812 (80%) 1195 (78%)
Coma 924 553 883 542 828
Trefoil 379 343 219 270 367
Values are given for front, back, and combined surfaces. Shape variance values are given for all HOAs, third order, coma, and trefoil.
The proportion of HOAs accounted for by third-order aberrations is also shown.
572 Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al.
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

FIGURE 5.
Contour plots of the RMS (in micrometers) of HOAs of five PALs, Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph,
and Zeiss Individual (from top to bottom), for the front surface (left), back surface (middle), and combined surface (right). Lens diameter is 60 mm except
for the Hoya Lifestyle, which is 40 mm. A color version of this figure is available online at www.optvissci.com.
Progressive Addition Lenses Compared by Measurement of Surface ShapeVHuang et al. 573
Optometry and Vision Science, Vol. 90, No. 6, June 2013
Copyright © American Academy of Optometry. Unauthorized reproduction of this article is prohibited.

relatively low high-order aberrations. Thus, although high-order
aberrations in a PAL may be strongly influenced by the corridor
length, nuances in the surface designs may also play a role. Finally,
it does not seem possible to say that any of the designsVfront
surface, back surface, or bothVare better at controlling HOAs.
The high-order terms that determine the progressive power
nature of these lenses are also responsible for high-order aberra-
tions within any small pupil-sized aperture positioned anywhere
on the lens. Coma and trefoil tend to be highest around the
transition corridor and near zone, and coma can be expected to
have a somewhat greater impact than trefoil on image quality.
24
The extent to which these aberrations may be troublesome to
the patient depends to a large extent on pupil size. Higher order
aberrations and their impact increase with pupil size, so patients
with smaller pupils will be more resistant to their impact. For
example, decreasing pupil size from 4 to 3 mm, a 25% reduction,
will reduce the magnitude of the third-order terms coma and
trefoil by a factor of 0.75
3
or 0.422. Even with a relatively large
pupil, however, the magnitude of these HOAs is modest com-
pared with the astigmatism found in the periphery of all PALs.
A comparison of the RMS levels caused by unwanted astigma-
tism and by HOA shows that the RMS caused by astigmatism
is much larger. For example, with a 4.5-mm pupil and the Com-
fort Enhanced lens, across the lens surface, the RMS caused by
astigmatism was, on average, more than 16 times larger than the
RMS caused by HOA. The RMS caused by HOA approached
the level of astigmatic RMS only in regions of the lens with very
low levels of unwanted astigmatism.
A limitation of the present study is that measurements were
made by lateral translation of the CMM probe across a fixed
mounted lens. Thus, the results may not accurately represent the
effective power as worn by the patient when the eye rotates behind
the lens. This may be important as some lenses have their pro-
gressive surface on the front, some on the back, and one has two
freeform surfaces. For example, our analysis treats both surfaces
equally, but when worn, the back surface is closer to the eye and
a unit distance will subtend a larger angle than the equivalent
distance on the front surface. Because the two surfaces are slightly
different distances from the eye, there will also be very small effec-
tivity differences for the two surfaces. Our approach, however, does
illustrate the relationship between surface shape geometry and
power gradients and aberrations across that lens surface. For ex-
ample, in the case of the Hoya lens, the freeform nature of both
surfaces is revealed by the method used. In addition, this direct
measurement of surface height provides an accurate and complete
quantification of surface shape in (x,y,z) coordinates. From those
raw height values, surface shape descriptors and optical properties
resulting from that shape can then be derived, as we have done
here, by describing the shape of the lens surfaces with Zernike
polynomials.
The results of this method compare reasonably well with other
measurement methods, for example, Hartmann-Shack wavefront
sensing.
20
Differences between the results from various measure-
ment methods can result from a range of issues, such as alignment/
positioning variability during measurement, assumptions about
refractive indices, lens thickness, andsoon.Nevertheless,thisnon-
optical physical measurement of surface shape can be used to an-
alyze PALs, with optical properties derived directly from those
surface shapes and provides information not accessible by other
methods. This approach is potentially useful for characterizing and
designing PALs, and this article represents the first attempt to
document the front and back surface characteristics of a series of
contemporary PALs. Our data confirmed that the manufacturers’
descriptions are valid with regard to the nature of the front and
back surfaces. Understanding the properties of both surfaces may
allow clinicians to better appreciate the underlying optical design
but may not be extrapolated to patient performance and accep-
tance. An interesting next step would be to compare optical mea-
sures with clinical measures of vision, specific vision tests, and
subjective preferences.
25
Received July 11, 2012; accepted February 26, 2013.
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Mark A. Bullimore
356 Ridgeview Lane
Boulder, CO 80302
e-mail: bullers2020@gmail.com
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