Progress in The Spectacle Correction of Presbyopia PDF
Progress in The Spectacle Correction of Presbyopia PDF
Progress in The Spectacle Correction of Presbyopia PDF
surface astigmatism or cylinder, generally oriented at an Unfortunately, the lack of rotational symmetry and the dual-
oblique axis, in the lateral regions of the lens surface. The surface nature of the Aves design made it impractical for
use of a plus-cylinder at an oblique axis to seamlessly join mass production as a prescription sphero-cylindrical lens, so
sections of two surfaces with different curvatures can be it was never introduced commercially. Shortly thereafter,
1
appreciated with the aid of Figure 2. Henry Orford Gowlland invented a single-surface
progressive lens design that employed a section of a
Progressive lens surfaces are often described as
paraboloid on the back surface.3 Other progressive lens
“continuously smooth” surfaces that are “locally toric.” A
designs followed over the years,4,5 although the marginal
surface free of ledges and other physical discontinuities
performance characteristics of these early lens designs,
must have a continuous surface height. A surface that is
combined with the manufacturing challenges associated with
physically smooth, with no sharp peaks or valleys and no
the machining techniques available at the time, relegated
abrupt changes in prism, must also have a continuous first
this form of multifocal correction to little more than a novelty.
derivative (that is, surface slope). Finally, a surface that
provides only smooth, continuous changes in power and In fact, because of these limitations, progressive lenses
magnification must have a continuous second derivative failed to enjoy any real commercial success until the 1960s.
(that is, surface curvature) as well. Such surfaces are Before the advent of computer-numerically-controlled
sometimes called "C2" surfaces to reflect this mathematical grinding techniques, the mass production of complex
constraint. progressive lens surfaces that lacked the symmetry of a
If a constant power law with a linear increase in addition Unless the surface is quite steep, the horizontal and vertical
power is assumed for this surface, a fairly simple and well- curvatures of this simple elephant trunk surface, which
documented mathematical model may be derived for the utilizes a linear power law, remain roughly equal into the
elephant trunk progressive surface. Although progressive periphery. Maximum surface astigmatism occurs, however,
lens designs generally employ a power law that varies non- through the oblique meridians of the lens at axis 45 degrees.
linearly along the umbilic in order to provide stabilized zones This surface astigmatism increases linearly away from the
of distance and near vision, this mathematical model is umbilic, producing significant quantities of unwanted cylinder
nevertheless useful for deducing some fundamental power at axis 45 degrees. Minwitz’s theorem states that the
principles of progressive lens surfaces. Expressing this unwanted cylinder power lateral to the umbilic of this type of
linear power law in terms of surface curvature, in units of progressive surface increases twice as rapidly as the
reciprocal millimeters, yields: addition power increases along the umbilic, so that:9
z ( x, y ) = 16 g ⋅ y 3 + 12 g ⋅ y ⋅ x 2 δAdd
[6] δCyl = 2 ⋅ ⋅1000 ⋅ (n − 1) = 2 ⋅ δAdd
1000 ⋅ (n − 1)
which can also be expressed as:
Ultimately, Minkwitz’s theorem demonstrates that it is not
z ( x, y ) =
g 3
6
(
y + 3 yx 2 ) …Elephant trunk surface [7] possible to produce a change in “spherical” addition power
along the progressive corridor without introducing surface
astigmatism away from the corridor. Further, Minkwitz’s
+2.00 Add +4.00 Add +2.00 Add, Long Corridor +2.00 Add, Short Corridor
Figure 7. As a consequence of Minkwitz’s theorem, the Figure 8. As a second consequence of Minkwitz’s theorem,
unwanted surface astigmatism and cylinder power in the shorter progressive corridor lengths produce greater levels of
periphery of a progressive lens is roughly proportional to the unwanted cylinder power, smaller viewing zone sizes, or a
add power of the lens. combination of both.
2.0
Significant technological advancements over the past four
1.5
decades have provided progressive lens manufacturers with
2.5
0
1.
2.5 1.5
2.0 0
3.
2.0 sophisticated tools to design and fabricate progressive
3.0
lenses. The introduction of numerically-controlled cutting,
either to grind glass lens surfaces directly or to shape
Astigmatism Plot Mean Add Power Plot
refractory materials suitable for “slumping” glass at high
Figure 9. Contour plots show the distribution of an optical
temperature, has eliminated most manufacturing limitations,
quantity—such as unwanted astigmatism (cylinder power) or
while the introduction of high-speed computing has made
mean add power—across the lens by indicating the magnitudes
of the quantity at fixed intervals (for example, 0.50 diopters). possible lens designs of virtually unlimited complexity.
Today, progressive lens designers are constrained only by
Typically, each progressive lens has a unique astigmatism
the inherent mathematical limitations of these surfaces.
contour plot, so these plots also serve as a kind of
“fingerprint” of the lens design. Mean add power contour Although early progressive lenses were quite crude in
plots, on the other hand, indicate the size and location of the design, and enjoyed only limited success, modern
near zone as well as regions of excess plus power that may progressive lenses generally perform quite well for most
contribute to blur during far vision. spectacle wearers. In fact, numerous studies have
demonstrated that progressive lenses are now preferred
Plots of surface power provide a convenient way to evaluate
over conventional bifocal lenses by the vast majority of
the optics of a lens design, but they are only indicative of
subjects.14,15 It has even been estimated that progressive
performance. Furthermore, plots of surface quantities are
lenses are preferred to conventional bifocal lenses by
usually less meaningful than plots of ray-traced optical
roughly four to one.16
performance, which typically rely on modeling the lens in the
“position of wear” in order to determine how the wearer
Distribution of Power and Astigmatism
actually perceives the optics of the lens. The position of
wear represents the intended position of the glazed and No longer faced with the limitations imposed by early lens
fitted spectacle lens relative to the visual system of the design and manufacturing techniques, lens designers have
actual wearer, including the vertex distance and any lens tilt. been free to pursue more generalized surfaces of greater
Although plots of surface astigmatism and mean add power complexity. Improvements to early progressive lens designs
are the most common measures of optical performance, focused on reducing unwanted astigmatism in the periphery
they fail to represent the combined interaction of these to its mathematical limits while better managing the overall
effects upon vision. Both unwanted cylinder power and distribution of addition power and astigmatism across the
excess—or insufficient—addition power contribute to blur. lens surface. This could be accomplished both by varying
RMS (root-mean-square) power combines both the the horizontal curvatures of the surface appropriately and by
astigmatic and mean power errors into a single measure of carefully managing the progression of addition power along
of optical performance, and a useful predictor of blur and The horizontal cross-sections of the basic progressive lens
13
visual acuity. It is also possible to characterize the optics of model presented earlier are essentially circular, resulting in
a progressive lens using wavefront analysis. Wavefront an extremely rapid increase in unwanted astigmatism in the
analysis evaluates “high-order” aberrations of the lens in periphery of the lens surface, particularly when a non-linear
addition to the “low-order” aberrations represented by power law is utilized. This was especially problematic for
astigmatism and excess addition power (or defocus). The many early progressive lenses, which often concentrated
significance and application of wavefront analysis in unwanted astigmatism into relatively small regions of the
progressive lens design will be described in detail in the lens periphery. The use of non-circular, aspheric cross-
second part of this series. sections, including conic sections that varied in eccentricity
down the corridor, reduced the rapid increase in surface unwanted cylinder power in the periphery. Because of
astigmatism in the periphery while allowing some of the this, harder progressive lenses generally offer wider
surface astigmatism to be distributed into the distance distance and near viewing zones, but higher levels of
periphery without overly compromising the utility of the blur and distortion in the periphery. Hard designs will
17,18
central distance viewing zone. generally work better for sustained viewing tasks
requiring good visual acuity, and tend to offer the kind of
The eventual use of “spreading” or “smoothing” functions
utility that current bifocal wearers enjoy.
further reduced levels of surface astigmatism to its
mathematical limits, while also providing considerable • Soft type lens designs spread the progressive optics
freedom in defining the viewing zone configuration of the across larger regions of the lens surface, thereby
lens design. One such approach applied Dirichlet’s principle, reducing the gradients and overall magnitude of
or the principle of minimum potential energy, to the problem unwanted cylinder power at the expense of narrowing
of distributing power and astigmatism in the smoothest the areas of clear vision. Because of this, softer
possible way between the distance and near zones by progressive lenses generally offer less blur and
19
minimizing a Dirichlet integral. For “modern” progressive distortion in the periphery, but narrower viewing zones.
lenses, the peak level of unwanted cylinder power seldom Soft designs will generally work better for dynamic
exceeds the magnitude of the addition power of the lens by viewing tasks, and tend to improve visual comfort and
more than 20 percent. adaptation for emerging presbyopes.
In addition to developing novel lens surfaces with minimal Essentially, the gradients of surface power and astigmatism
unwanted astigmatism, lens designers also began across the lens design must increase as the area of the lens
investigating the optimal distribution of surface optics across surface used to "blend" the distance and near zones is
the lens. The spatial distribution and rates of change—or decreased. Since the overall utility of the lens design relies
gradients—of power and astigmatism across the surface are on a careful balance between clarity of vision and visual
fundamental aspects of the lens design that define the gross comfort, modern progressive lenses are seldom strictly
optical performance of the lens. Often, progressive lens "hard" or "soft" in design, but instead represent a well-
designs are broadly categorized as either “hard” type considered compromise between these two approaches. It is
designs or “soft” type designs based upon the distribution of equally important that the relative balance between the
power and astigmatism (Figure 10): distance zone size and the near zone size reflect the typical
wearer’s use of the lens. Lens designers often seek to find
• Hard type lens designs concentrate the progressive
the best overall balance between the utility of the three
optics into smaller regions of the lens surface, thereby
central viewing zones and the periphery of the lens.20
expanding the areas of clear vision at the expense of
elevating the gradients and overall magnitude of The distribution of power and astigmatism across the lens
surface may be tuned differently for different addition
powers, as well as for different base curve and addition
Close Spacing: Wide Spacing:
High Gradients Low Gradients power combinations. For instance, the progressive lens may
employ a “softer” lens design with a longer corridor length
for low additions and a “harder” lens design with a shorter
corridor length for high additions, or vice versa, depending
upon the design strategy. In some cases, the progressive
lens design may vary the size of the central viewing zones
by base curve in order to provide more consistent fields of
“Hard” Type Design “Soft” Type Design view by accounting for the effects of spectacle magnification.
Lens designs that vary as a function of addition power are
Figure 10. Unwanted astigmatism is spatially distributed over
much of the lens surface in “soft” type designs, which referred to as multi-design lenses, whereas lens designs
therefore exhibit relatively low gradients of astigmatism, that vary as a function of both base curve and addition
whereas unwanted astigmatism is confined to smaller regions power are sometimes referred to as design by prescription
of the lens surface in “hard” type designs, which therefore
lenses.
exhibit relatively high gradients of astigmatism.
with a relatively rapid progression of addition power. A graph across a wide range of frame styles. Progressive lenses first
of addition power as a function of the vertical position within became popular in the 1970s and 1980s—decades that
the progressive corridor is known as the power profile of the represented the peak of large spectacle frame styles. The
lens design, as shown in Figure 11. capacious frame styles in vogue during these early decades
afforded the typical progressive lens wearer with more than
The ergonomic utility of the lens design for many viewing
sufficient vertical clearance for the intermediate and near
tasks depends upon carefully locating the distance and near
zones of traditional progressive lens designs. By the 1990s,
zones in order to minimize unnecessary head and eye
however, the fashion trend in frame styles was decidedly
movements while ensuring clear, comfortable vision during
“minimalist,” with frame dimensions shrinking dramatically.
both sustained and dynamic viewing tasks. Ideally, the
design of the power profile should reflect the wearer’s typical Eventually, progressive lenses designed specifically for
use of the near and intermediate zones for reading and mid- smaller frame styles were introduced.21 This new class of
range viewing tasks while minimizing unwanted blur from progressive lenses utilizes significantly shorter corridor
excess plus power within the central distance zone. The lengths that afford lower minimum fitting heights. Of course,
length of the progressive corridor should represent a reducing the corridor length of the lens design necessitates
sensible balance between the various tradeoffs involved: various optical compromises, in accordance with Minkwitz’s
theorem. Since shorter corridor lengths result in smaller
• Shorter corridor lengths afford the wearer with a more viewing zone sizes or higher levels of unwanted cylinder
readily accessible near zone and sufficient reading power in the periphery, lens designers must carefully
utility across a wider range of frame sizes and fitting manage the optics of these designs in order to ensure
heights. Since every one millimeter of corridor length at sufficient visual utility.
the spectacle plane necessitates roughly two degrees of
Binocularity
+6 +6
+4 +4
Early progressive lenses designs were completely
From Pupil Center (mm)
+2 +2
+0 +0
symmetrical with respect to the umbilic. The desired near
Power Change
Power Change
-2 -2
-4 -4 zone inset for near vision was achieved mechanically by
-6 -6
-8 Δy -8 Δy simply having each lens rotated by nine degrees or more. In
-10 -10
ΔAdd ΔAdd
-12 -12 effect, the same lens blank could be used for either eye prior
-14 -14
-16 -16 to surfacing. This process would rotate the more deleterious
-18 -18
-20 -20 optics of the surface, however, into the upper nasal (medial)
+0.00
+0.50
+1.00
+1.50
+2.00
+0.00
+0.50
+1.00
+1.50
+2.00
binocular field of view was restricted by excess blur in the The inherent surface astigmatism and rapid changes in
nasal field of the opposite lens (Figure 12). power and prism in the peripheral “blending” regions of
Eventually, lens designers began altering the design of the progressive lens designs produce several optical
lens on either side of the umbilic in order to achieve the phenomena that may be visually disturbing to the wearer
desired near zone inset optically, instead of mechanically. initially, particularly under dynamic viewing conditions.
Asymmetric lens designs were an early application of this Fortunately, much progress has been made over the past
concept; these designs essentially constrained the nasal few decades in minimizing these “optical side-effects” by
surface astigmatism below a fixed horizontal axis as the better managing the optical design of the lens periphery.
umbilic was effectively rotated nasally. 22
By designing the With more sophisticated lens design tools and a better
path of the umbilic with an optical inset, better alignment understanding through vision research of the most visually
could be obtained between the right and left viewing zones significant imaging defects, progressive lens designers have
during binocular vision, maximizing the binocular field of been able to minimize rapid undulations in power and prism
view. Nevertheless, while asymmetric lens designs increase and to achieve better overall orthoscopy, or lack of
the binocular field of view through the lenses, the nasal geometric distortion, in the periphery of the lens.
surface astigmatism of these lens designs is often Recall that the cylinder power in the periphery of a
considerably higher than the temporal astigmatism, since progressive lens is generally oriented at a highly oblique
the astigmatism becomes more “concentrated” as the near axis. This unwanted cylinder power produces differential
zone is effectively rotated into the nasal region. spectacle magnification at a similar orientation. This optical
The next innovation in improving binocular vision imaging defect is known as skew distortion, and causes
performance was obtained by more carefully balancing the objects—such as straight edges—to appear tilted, sheared,
optics to either side of the umbilic. Horizontal symmetry or even curved (Figure 14). Minimizing skew distortion and
ensures that the power, prism, and magnification remain improving orthoscopy can be achieved by orienting the
relatively equal for corresponding points across the right and surface astigmatism more vertically or by reducing the
example, blurred vision or slowness of refocusing), some degree of far vision utility.26 The distance zone of
asthenopia (for example, eyestrain or headache), and even these lenses is typically smaller and higher compared with
24
musculoskeletal strain (for example, neck and back pain). general-purpose progressive lenses, and some designs
In fact, one investigation of clinical studies pertaining to the provide a low addition within the distance zone (for example,
prevalence of computer vision symptoms concluded that 50 +0.50 diopters), which still allows for mobility indoors. These
percent or more of computer users complain of some form of lenses are generally available in a full range of additions and
25
eye problems associated with computer use. base curves, and are also fitted like traditional progressive
lenses. Enhanced single vision lenses, on the other hand,
The viewing zone configuration and range of addition power
typically provide only mid-range and reading utility, but
offered by occupational progressive lenses reflect the more
frequently offer wider intermediate and near zones that are
sedentary visual demands of typical office and computer
more readily accessible.27 These lenses are generally
work, providing very little—if any—far vision utility. These
available in only one or two possible power changes—each
progressive lenses are generally characterized by
associated with a range of prescribed additions—and are
exceptionally wide intermediate and near zones, often
fitted like either progressive lenses or single-vision lenses,
combined with a marked reduction in unwanted astigmatism
depending upon the recommendations of the manufacturer.
in the periphery of the lens design. Of course, the wider
intermediate and near viewing zones and reduced unwanted
References
astigmatism are achieved at the expense of the distance
zone. Further, these lenses typically offer a smooth power
law, or rate of change in addition power, by utilizing a 1 Meister D. (2006) Fundamentals of Progressive Lens Design.
VisionCare Product News. 6(9), 5-9.
relatively long progressive corridor and by reducing the total
2 Aves O. (1908) Improvements in and relating to Multifocal
change in addition by starting the addition at an intermediate
lenses and the like, and the method of Grinding Same. GB
power intended for mid-range working distances. Patent 15,735.
Occupational progressive lenses are sometimes categorized 3 Orford H. (1909) Manufacture of Lenses for Spectacles or
as either “computer progressive lenses” or “enhanced single Eyeglasses. US Patent 943,449.
vision lenses,” which are distinctions that reflect the extent of 4 Poullain A. and Cornet D. (1910) Improvement in and relating to
Optical Lenses. French Patent 418,583.
the range of clear vision typical of each lens design as well
5 Glancy A. (1923) Ophthalmic Lens. US Patent 1,518,405.
as the overall design strategy (Figure 15).
6 Cretin-Maitenaz B. (1959) Multifocal Lens Having a Locally
Computer progressive lenses are similar to traditional Variable Power. US Patent 2,869,422.
general-purpose progressive lenses, and may even offer 7 Maitenaz B. (1966) Four Steps that Led to Varilux. Am. J.
Optom. Arch. Am. Acad. Optom. 43, 441-450.
Distance Near Distance Near 8 Bennett A. (1973) Variable and Progressive power lenses.
Manufacturing Optics Int. Mar, 137-141.
+0.00 +0.50 +1.00 +1.50 +2.00 +0.00 +0.50 +1.00 +1.50 +2.00
9 Sheedy J., Campbell C., King-Smith E., and Hayes J. (2005)
Progressive Powered Lenses: the Minkwitz Theorem. Optom.
Far Mid-Range Vis. Sci. 82(10), 1-9.
.00
+1
50 10 Sheedy J., Buri M., Bailey I., Azus J., and Borish I. (1987) The
0.
0
+1.0
+
optics of progressive lenses. Am. J. Optom. Physiol. Opt. 64,
+1.5 90-99.
.50 0
+1
11 Sheedy J., Hardy R., and Hayes J. (2006) Progressive addition
+1
.50 lenses–measurements and ratings. Optom. 77(1), 23-39.
+2.00
+2.00
lenses had been relegated to a highly involved, mass prescription sphere and cylinder curves normally applied to
2
production environment. Free-form surfacing has made the back of the lens blank. Since the progressive lens
possible the production of complex lens designs on a per-job design may be surfaced directly onto the back of the lens
basis at the laboratory level, on the other hand, by providing blank along with the prescription curves, only a small range
laboratories with the means to surface progressive and other of “pucks,” or semi-finished lens blanks with spherical front
complicated lens designs directly onto a lens blank. surfaces corresponding to the desired base curves, is
necessary for lens production, thus obviating the need for a
The inherent visual benefit of progressive lenses produced
large inventory of semi-finished progressive lens blanks.
using free-form surfacing is minimal compared with similar
Although there may be a minor reduction in certain
lenses produced using traditional lens casting and surfacing.
unwanted magnification effects, free-form progressive
Although the free-form surfacing process may arguably offer
lenses of this type essentially replicate the performance of
more precise replication of progressive lens designs, this
traditional lenses made from mass-produced, semi-finished
benefit relies on meticulous process engineering in order to
progressive lens blanks. Consequently, one should
ensure lens surfaces of consistently good quality and
distinguish between so-called “smart” free-form progressive
accuracy. Traditional lens casting, on the other hand, is a
lenses that are truly designed for the wearer in real time and
highly repeatable process that delivers relatively consistent
free-form progressive lenses that are produced directly from
quality, albeit with some loss of fidelity in reproducing certain
surface description files with little optical modification for the
lens design features due to factors such as shrinkage while
wearer, if any.3
the liquid monomer polymerizes. Furthermore, although the
precision of free-form surfacing is not limited by the
Free-Form Lens Surfacing
availability of hard lap tools, often stocked in only tenth- or
eighth-diopter increments, these lenses are still held to
A “traditional” lens surfacing process cannot produce the
typical optical tolerances and subject to manufacturing
complex surfaces utilized for complicated lens designs like
variances, particularly in the absence of adequate process
progressive lenses due to limitations in both the range of
engineering.
possible geometries and the “quality” of surfaces produced
When used in conjunction with sufficiently advanced lens by conventional generators. Conventional generators were
design software, however, a free-form delivery system can designed with an emphasis on efficient stock removal from
produce a completely arbitrary progressive lens design that simple spherical and toroidal surfaces of revolution, which
has been fully parameterized using input specific to the can be smoothed and polished using rigid (that is, “hard”)
individual wearer. Consequently, if the visual and optical lap tools of similar curvature in combination with various
requirements of a particular wearer are known prior to the abrasives. However, unlike these basic surfaces of
optical design stage, it becomes possible to customize the revolution, complex progressive surfaces must be smoothed
design of the progressive lens accordingly. Alternatively, and polished with flexible (that is, “soft”) lap tools, since the
since free-from surfacing is not subject to the inventory curvature does not remain constant across the surface.
constraints of semi-finished lenses, a suitable progressive
The accuracy and finish of a machined surface is generally
lens may be selected from a range of possible lens designs,
evaluated for several different qualities, including surface
thus allowing for a greater degree of freedom in matching
roughness prior to polishing and errors from the desired
the lens design to the specific wearer. Therefore, as a
shape, or form, including waviness (Figure 1). Conventional,
“technology enabler,” free-form surfacing can serve as a
two-axis generators can produce only simple surfaces of
critical vehicle to deliver considerable visual benefits to the
revolution. Newer, three-axis generators were not designed
wearer. When the potential of individualized progressive
to produce complex lens surfaces to the level of precision
lens production via free-form surfacing is fully realized,
and smoothness required for soft lap polishing. The surface
optical performance and wearer satisfaction are maximized.
roughness off both two-axis and three-axis generators is still
It is also possible to utilize free-form surfacing to deliver relatively high, and often comparable in magnitude to the
traditional-type progressive lenses on demand, often by errors in form necessary to create visible optical effects,
mathematically combining a “fixed” progressive lens design such as “waves.” These generators rely on hard lap tools
from a predefined surface description file with the affixed with abrasive pads to correct errors in form and
curvature while bringing the surface to a level of smoothness this surface represents the combination of a progressive
suitable for polishing. lens design with the required prescription curves, which will
be surfaced onto a spherical “puck.” In a sufficiently
A “free-form” lens surfacing process, on the other hand, can
advanced process, this lens surface may also be optically
produce even highly complex surfaces like progressive lens
modified using various parameters specific to the wearer.4
designs in a matter of minutes. Free-form generators are
Alternatively, the surface may represent optically-optimized
highly sophisticated machines capable of producing very
(or “atoric”) prescription curves only, which will be surfaced
precise surfaces of high complexity using a computer-
onto a semi-finished progressive lens blank with the
controlled, single-point cutting process (Figure 2). Free-form
progressive lens design prefabricated on the front surface.5
polishers utilize a flexible, computer-controlled “soft lap” tool
capable of polishing the complex lens surfaces produced by The final surface is then rendered as a digital cutting file, or
free-form generators. Common free-form generators utilize “points” file, which is transmitted to the computer controller
single-point diamond turning, with a combination of diamond of the free-form generator. The back surface of a semi-
tools, to produce accurate surfaces of sufficient smoothness finished lens blank with a prefabricated front surface is then
that require only a short polishing cycle using a soft lap tool, subjected to a three-stage cutting process by the generator,
since excess polishing can distort the surface of the lens. which utilizes a multi-blade tool for rough cutting, a
polycrystalline diamond tool for smooth cutting, and a
natural diamond tool for a high quality finishing pass. After
Axis 1 Diamond Tip generating, the lens blank is transferred to a free-form
Spiral polisher, where it undergoes a computerized polishing
Axis 2
Cutting Path process that utilizes a dynamically-controlled, soft lap tool
Axis 3
made from a compliant foam or similar material.
Prescription Customization
Figure 4. A sophisticated
prescription optimization process,
used in conjunction with free-form Transformations
lens surfacing, can achieve the
ideal performance of the lens
design for virtually any
prescription, as demonstrated by
these plots of ray-traced optical
astigmatism. Note the distortion of
the viewing zones that occurs due
to the prescription in the absence
Target: Plano Rx, +2.00 Add Initial: +2.00 −1.50 × 45 Optimized: +2.00 −1.50 × 45
of optimization.
Zone Degrees of
Width Freedom
HARD
SOFT
Balance
SH
NG
LO
Multi-Dimensional
Corridor Customization Space
Length
Figure 7. Dispensing tools for taking accurate position of wear
measurements include highly sophisticated digital centration Figure 8. The degrees of freedom available for manipulating the
systems capable of capturing a variety of measurements (photo geometry of a progressive lens design represent a multi-
courtesy of Carl Zeiss Vision GmbH). dimensional customization space of lens design possibilities.
process of optical design in real time. However, the without unnecessarily compromising optical performance in
customization afforded by this latter approach will be limited other regions of the lens (Figure 9). This allows the optics of
by the number of suitable options available in the free-form the lens design to take full advantage of the available lens
lens supplier’s repository of possible lens designs, including area. Typically, this customization is based on the standard
the number of lens designs available with unique corridor fitting height measurement supplied to the laboratory. A
lengths, unique viewing zone balances, and so on. progressive lens design having the most suitable corridor
length for the frame can then be chosen from a range of two
Of course, determining how to best manipulate these lens
or more corridor length options, or the corridor length of the
design parameters for a given wearer requires the
design may be continuously varied over a range of possible
application of extensive vision science and clinical research.
values with the use of sufficiently advanced software.
In some cases, new dispensing technologies designed to
capture critical measurements and wearer feedback may be In addition to customization based on fitting height or frame
required. Currently, advanced free-form lens designs are size, it is also possible to manipulate the optics and form of
available that are tailored to the wearer’s chosen frame the lens based on the overall “shape” of the frame and other
style, visual demands typical of the wearer’s lifestyle, and opto-mechanical requirements. For instance, the optics and
physiological behavior patterns captured from biometric form of the lens design can be tailored to facilitate glazing in
measurements of the wearer. exotic frames styles or to the use of non-standard base
curves. With the increasing popularity of steeply curved and
Frame Style Customization highly wrapped eyewear, which often necessitate complex
atoric lens designs for optimal performance, this application
Most general-purpose progressive lenses are designed to of free-form technology is becoming increasingly relevant.
work well in conservative frame styles. Although many
modern progressives will perform adequately at 17- or 18- Lifestyle Customization
millimeter fitting heights, many lens designs may not achieve
optimal optical performance with fitting heights below 20 to The ideal progressive lens design for a given wearer will
22 millimeters. Although various “short corridor” progressive depend in no small part upon the visual demands specific to
lenses are now available for shorter fitting heights, these his or her lifestyle. It has been demonstrated that preference
lens designs are not without their compromises. The shorter for progressive lens designs can vary with the unique visual
the length of the progressive corridor, the more the optics of needs of the wearer.9 Progressive lens wearers more
the lens design must be “compressed,” leaving wearers to frequently engaged in tasks associated with far vision will
tolerate reduced intermediate utility, higher levels of often prefer lens designs with larger distance zones,
peripheral blur, and narrower viewing zones, in accordance whereas wearers with greater near vision demands may
with Minkwitz’s theorem. prefer lens designs with larger near zones (Figure 10).
Moreover, a low hyperope who only wears her spectacles
Moreover, many recent short-corridor progressive lenses
while reading may prefer a larger near zone, whereas a low
have been engineered for ultra-small frames requiring
extremely short fitting heights. Eye care professionals may
be forced to choose between lens designs engineered to
work well either in conservative frames or in ultra-small
frames, and to determine at what fitting height to switch from
one to the other. Inevitably, unless the corridor length of the
chosen lens design happens to coincide with the optimal
length required for a particular wearer’s chosen frame style,
+1
.7
+1
“Distance Priority” Design “Near Priority” Design For some wearers, the limited width of the viewing zones of
a progressive lens may restrict lateral eye movement,
Figure 10. The geometry of a progressive lens design can be
customized based on visual lifestyle requirements by altering necessitating an increase in head movement gain by the
13
the balance between the size of the distance viewing zone and wearer. Even when eye movement is not significantly
the size of the near zone. restricted, reading efficiency may be noticeably reduced by
narrower viewing zones, subsequent to an increase in gaze
myope who removes her spectacles to read may prefer a
stabilization time and in the number of reading
larger distance zone.
14
regressions. It has been suggested that these factors
Lifestyle customization relies on assessing the relative visual contribute to the adaptation problems experienced by some
demands of the wearer in order to determine the ideal progressive lens wearers.
balance between the distance and near viewing zones of the
Consequently, “eye movers” may potentially benefit from the
lens design. Relevant lifestyle information may be captured
use of progressive lens designs with wider central viewing
using computer screening or a questionnaire of some form.
zones. “Head movers,” on the other hand, will fixate an
A progressive lens design having the most suitable viewing
object with a ballistic eye movement, during which vision is
zone configuration for the wearer can then be chosen from a
suppressed, while initiating a much slower compensatory
range of possible lens designs, or the viewing zone balance
head movement. During this head movement, the visual field
of the design may be continuously varied to match the exact
may be disrupted by the changing prism and magnification
balance indicated for the wearer.
effects across the progressive lens design as the gaze
The relative suitability of common progressive lens designs remains relatively stable. Therefore, “head movers” may
for different viewing tasks has been previously evaluated.10 benefit from designs with softer gradients of power and
Many of these lens designs are positioned as “general- astigmatism that minimize image swim, skew distortion, and
purpose” lenses in the marketplace, suggesting that these other optical imaging defects associated with prism and
lens designs do not intentionally differ from a viewing zone magnification gradients (Figure 11).
balance consistent with equal distance and near vision
requirements. The range of possible viewing zone balances
available commercially is therefore limited, at best.
Customized progressive lenses delivered via free-form lens Softer Gradients Wider Zones
surfacing, however, are not constrained by the same
limitations in availability. Additionally, while choosing one of
these lens designs based on measurements of viewing zone
size offers some degree of freedom, this relies on an
accurate assessment of the optical performance of each
lens, which may not be readily accessible in many cases.
Biometric customization relies on the measurement of the the actual progressive lens design is directly surfaced. An
physiological interaction of the wearer with his or her visual alternative approach employs a semi-finished (that is,
environment. For biometrically customized progressive prefabricated) progressive surface on the front and free-
lenses, a head-tracking device or similar instrument is form-surfaced prescription curves on the back that have
required. Head-tracking measurements are captured by a been optically optimized. There is also a class of “dual
computer during key viewing tasks, which often involve surface” configurations that employ a partial or “split”
either fixating flashes of light presented at two lateral progressive surface on the front and a partial progressive
viewing angles or performing an actual reading task (Figure surface on the back that has been combined with the
15
12). Again, the progressive lens design having the most prescription curves.
suitable geometry for the wearer can be chosen from a
Although it is sometimes claimed that “splitting” the
range of possible lens designs, or the geometry of the
progressive design between the front and back surfaces
design may be continuously varied to match the exact
reduces unwanted astigmatism, the actual differences in
balance indicated for the wearer, depending upon the
performance are generally small. Because a typical
sophistication of the free-form supplier’s software tools.
spectacle lens represents an “optical system” of fairly
negligible thickness, the optics of each surface are
Lens Surface Configuration essentially additive. The optical powers across the lens can
be distributed between both surfaces with very little change
With two separate surfaces to work with, the optical design in effective optical performance. Consequently, the
and prescription components of a free-form progressive lens placement of the actual progressive optics, whether on the
can be applied to the lens blank in variety of possible front surface, back surface, or split between both, has very
configurations. Each configuration represents a particular little impact on the inherent unwanted astigmatism of the
combination of factory-finished, traditionally-surfaced, and lens design (Figure 13).
free-form-surfaced lens curves. The lens surfaces involved
The magnitude of astigmatism produced by a progressive
range in complexity from simple spherical surfaces to
lens design is not significantly influenced by the choice of
optimized progressive surfaces that have been combined
surface placement. Nevertheless, there may be some minor
with the prescription sphere and cylinder curves.
optical benefits to the use of a back-surface progressive lens
As described earlier, a common configuration employs a configuration. Although the vertex power will remain
semi-finished spherical surface on the front and a free-form- unchanged, the equivalent power and magnification across
surfaced progressive surface on the back that has been the lens will vary depending upon the surface used for the
combined with the normal prescription curves. In this case, progressive optics. In particular, differences in curvature on
the front surface will contribute to spectacle magnification
effects. Therefore, a slight reduction in skew distortion may
Comparable Astigmatism
For free-form lens suppliers, the choice of free-form surface wavefront error is the separation, or difference in optical
configuration is often influenced by many non-optical factors, path length, between the actual wavefront and the ideal
such as ease of manufacturing and any limitations imposed wavefront. In the presence of uncorrected refractive errors
by existing patents and similar intellectual properties. For and other optical aberrations, the actual wavefront is often
instance, back-surface progressive lens configurations limit flatter or steeper than necessary and distorted in shape.
the number of surfaces that must be “worked,” which offers After the errors in height between the actual, aberrated
certain production advantages while eliminating the potential wavefront and the ideal wavefront surface have been
for misalignment between the front and back surfaces. determined, these error measurements are typically fitted
Front-surface progressive lens configurations, on the other with one of several possible sets of basis functions. These
hand, may be available in a wider prescription range, since functions allow the complex shape of the wavefront errors to
the rear prescription surface is not limited by the dynamic be broken down, or decomposed, into an assortment of
defocus and astigmatism have been substantially specifically, the third-order Zernike aberrations known as
17
ameliorated. coma and trefoil.
Additionally, each Zernike mode has a coefficient associated The presence of coma across a progressive lens surface
with it indicating the quantity of that particular Zernike can be deduced from Figure 14. Classic coma is due to an
aberration present in the actual wavefront surface. The asymmetric variation in refractive power and magnification
overall magnitude of the wavefront errors is often stated in across the lens for off-axis object points. The change in
terms of the RMS (or root-mean-square) error of the refractive power across a progressive lens surface produces
wavefront. The RMS error is essentially equal to the a very similar effect. As the line of sight passes down the
standard deviation—a statistical measure of variation—of progressive corridor of the lens, the power at the upper
the wavefront errors from the ideal wavefront across the margin of the pupil differs from the power at the lower
reference pupil. The RMS wavefront error can be calculated margin by an amount roughly equal to the product of the
directly from Zernike coefficients by taking the square-root of pupil diameter and the rate of change in addition power at
the sum of the squares of the coefficients. that particular location. In fact, coma is directly proportional
to the rate of change in mean addition power.
Wavefront Aberrations in Progressives
Some additional insight into the nature of wavefront
aberrations in progressive lenses may be deduced by
Conventional single vision and bifocal spectacle lenses that
comparing the shape of a progressive lens surface directly
have been properly fabricated to the intended prescription
to the actual basis functions used to “build” a given
will produce no second-order Zernike aberrations along the
wavefront (Figure 15). The Zernike basis functions used to
optical axis of the lens. Second-order Zernike aberrations
-1
will occur, however, at oblique angles of view due to the represent the contribution of vertical coma (Z3 ) and oblique
-3
introduction of the primary Seidel optical aberrations known trefoil (Z3 ) to the overall shape of a wavefront surface are
18
as oblique astigmatism (producing Zernike astigmatism) and given by the following functions in Cartesian form:
curvature of the field (producing Zernike defocus). These
two optical aberrations are generally minimized with the use
(
Z 3−1 = N 3 yx 2 + 3 y 3 − 2 y ) …Vertical coma [3]
Increase in
Surface Power 6 mm
primarily due to unwanted surface astigmatism (producing 6
0.5 1.0
Pupil
Zernike astigmatism) and excess addition or plus power for 1.5
1.5
Moreover, because progressive lens surfaces utilize
6
1.0
0.5
6 7
progressive change in addition power, this class of surfaces
has non-zero third derivatives. Consequently, progressive Figure 14. The progression of addition power across a
progressive lens surface causes the power to vary over the
lenses produce certain levels of the higher-order wavefront
finite diameter of the wearer’s pupil, introducing a coma-like
aberrations associated with the third derivatives of a surface, wavefront aberration.
This equation is identical in form to that of the surface height Next, the approximate refractive power of the elephant trunk
function z of the simple “elephant trunk” progressive lens surface z is expressed in terms of a wavefront profile
19 -3
model described in the companion paper, namely: function w, in microns (μm or mm ), using:
z ( x, y ) =
g 3
(
y + 3 yx 2 ) …Elephant trunk surface [6] w(x, y ) = z ( x, y ) ⋅ 1000(n − 1)
6
An analytical model has been described for computing the where C3 is the Zernike coefficient of the combined third-
third-order wavefront aberrations of the elephant trunk order coma and trefoil functions. This coefficient essentially
surface.20 This analytical model can be derived with the aid represents the amount by which to “scale” the coma and
of some basic algebraic manipulation. Zernike basis trefoil functions in order to produce the desired wavefront
functions are calculated over a unit circle. Therefore, the x profile of the elephant trunk progressive surface. It is also
and y terms of these basis functions must first be equal to the RMS wavefront error of the Zernike modes.
“normalized” by dividing each by the maximum pupil radius Canceling like terms and solving for the Zernike coefficient
ρ: C3 yields:
⎡⎛ y ⎞3 y ⎛x⎞
2
⎤ δAdd
f ZZ ( x, y ) = 2 8 ⎢⎜⎜ ⎟⎟ + 3 ⎜⎜ ⎟⎟ ⎥ C3 = ρ3 …Third-order coefficient [12]
ρ
⎢⎣⎝ ⎠ ρ ⎝ρ⎠ ⎥⎦ 12 8
-1 -3
Unlike the simple progressive lens model presented earlier,
Zernike Coma (Z 3 ) Zernike Trefoil (Z 3 )
modern progressive lenses employ non-circular cross-
Figure 15. The action of a simple progressive lens surface can sections and a power law that varies non-linearly along the
be described by a combination of vertical coma and oblique corridor. Nevertheless, the third-order aberrations in these
trefoil wavefront aberrations.
lenses will vary with the rate of change in surface power at minimizing high-order aberrations in any particular region
any point. Coma and trefoil will be highest in regions will be at the expense of inducing higher levels of high-order
wherein the addition power and surface astigmatism are aberrations elsewhere.
changing most rapidly (Figure 16). Moreover, since high-
Although higher-order aberrations may result in a reduction
order aberrations are dependent on the rate of change in
in image quality and a loss of contrast, low-order aberrations
surface power, these aberrations will be more significant in
generally account for the greatest impact on vision quality in
progressive lenses with shorter corridor lengths or higher
progressive lenses. In particular, unwanted astigmatism
addition powers, in accordance with Minkwitz’s theorem.
dominates much of the lens surface. Further, in contrast to
Recently, progressive lens designers have begun paying the case of low-order aberrations, clinical research has
closer attention to high-order aberrations, and in some demonstrated that the high-order aberrations in progressive
cases even patenting progressive lens designs with reduced lenses are seldom any greater in magnitude than the
21
high-order aberrations, such as coma. Unfortunately, you inherent high-order aberrations of a typical wearer’s eyes.23
cannot eliminate the high-order aberrations produced by a
Research has also demonstrated that the impact of high-
progressive lens surface, just as you cannot eliminate
order aberrations on visual acuity in the progressive corridor,
unwanted surface astigmatism. In fact, for modern
where these aberrations are often highest, are negligible.
progressive lens designs at least, average levels of high-
Additionally, the caustic focus produced in the presence of
order aberrations calculated globally over the central lens
small amounts of high-order aberrations may possibly
surface are fairly similar in magnitude.22 Nevertheless, you
improve the wearer's depth of focus and tolerance to the blur
can judiciously manage both the low- and high-order
caused by the second-order aberrations of the lens. In fact,
aberrations in a progressive lens.
aberration coupling between the high-order aberrations of
Just as there are two general approaches to the the progressive lens and the high-order aberrations of the
management of second-order astigmatism, by either eye can sometimes yield better visual acuity than obtained
spreading it out to "soften" the design or confining it to with the naked eye.24 Nevertheless, the high-order
smaller regions to "harden" the design, there are also two aberrations produced by a progressive lens will have at least
intimately related approaches to the management of third- some impact on the wearer’s vision, and therefore represent
order aberrations. A "soft" lens design with gradual power a meaningful quantity to evaluate during the optical design
changes will frequently yield relatively low levels of high- process.
order aberrations over the entire lens, whereas a "hard" lens
design with rapid power changes will yield lower levels of Spectacle Correction of Ocular Aberrations
high-order aberrations in the central distance and near
viewing zones while creating greater levels at the viewing It should be emphasized that, in general, minimizing the
zone boundaries and within the progressive corridor. In high-order wavefront aberrations produced by a spectacle
general, for a given corridor length and addition power, lens will not provide the wearer with better than his or her
best corrected visual acuity. The high-order aberrations of
the eye can only be reduced after first measuring the eye
Regions of Regions of with a wavefront sensor, such as an aberrometer, and then
sm
High Coma
w er High Trefoil ati precisely customizing an optical component based on those
Po tigm
n As measurements.25 The technical limitations involved,
M ea
however, in the spectacle correction of high-order ocular
aberrations make the application of this type of technology
challenging, if not prohibitive.