U.S. patent application number 10/234993 was filed with the patent office on 2003-05-01 for ophthalmic lenses with induced apertures.
Invention is credited to Griffin, Richard A..
Application Number | 20030081171 10/234993 |
Document ID | / |
Family ID | 24637706 |
Filed Date | 2003-05-01 |
United States Patent
Application |
20030081171 |
Kind Code |
A1 |
Griffin, Richard A. |
May 1, 2003 |
Ophthalmic lenses with induced apertures
Abstract
Multifocal and single focus lenses are defined by nonconical
aspheric optical surfaces. Various alternative surface shapes
provide one or more vision regions bounded by optical steps. Each
optical step has rapidly and smoothly changing power in the radial
direction which creates an induced aperture through which the
cortical elements of the human vision system are induced to
concentrate. The induced aperture results in increased clarity and
enhanced vision. In various configurations, the induced aperture
decreases spherical aberration to further enhance vision. To
increase correction intensity at one or more powers, redundant
power regions are provided in repeated optical steps or annular
apertures. In several embodiments, the redundant power regions
create multiple induced apertures at one or more optical powers
directed at one or more vision distances.
Inventors: |
Griffin, Richard A.;
(Gainesville, FL) |
Correspondence
Address: |
Sven W. Hanson
PO Box 357429
Gainesville
FL
32635-7429
US
|
Family ID: |
24637706 |
Appl. No.: |
10/234993 |
Filed: |
September 4, 2002 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
10234993 |
Sep 4, 2002 |
|
|
|
09657562 |
Sep 8, 2000 |
|
|
|
6474814 |
|
|
|
|
Current U.S.
Class: |
351/159.05 ;
351/159.41 |
Current CPC
Class: |
G02C 7/028 20130101;
G02C 7/063 20130101; G02C 7/042 20130101; G02C 7/061 20130101; G02C
7/044 20130101; A61F 2/164 20150401; A61F 2/1618 20130101; A61F
2250/0036 20130101; G02C 7/041 20130101; A61F 2/1613 20130101 |
Class at
Publication: |
351/161 |
International
Class: |
G02C 007/04 |
Foreign Application Data
Date |
Code |
Application Number |
Sep 6, 2001 |
PCT/US01/28156 |
Claims
I claim:
1. An ophthalmic lens comprising: an apex and apical power at the
apex; at least one annular vision region, each of the at least one
annular vision regions having a respective local maximum or minimum
power; and each annular vision region bounded by optical steps
having rapidly changing power; and an optical surface creating a
power distribution that varies smoothly from the apical power and
through all annular vision regions.
2. An ophthalmic lens according to claim 1, wherein: the apical
power is a distance sight corrective power; and the at least one
annular vision region has a near sight corrective power greater
than the distance sight corrective power.
3. An ophthalmic lens according to claim 1; wherein: the at least
one annular vision region comprises a first annular aperture having
a distance power less than the apical power.
4. An ophthalmic lens according to claim 3, wherein: the apical
power is sufficiently high to prevent the human cortical vision
system from resolving an image from any plane-of-regard passing
through the apex.
5. An ophthalmic lens according to claim 4, wherein: the apical
power more than 3.0 diopters greater than the distance power.
6. An ophthalmic lens according to claim 3, wherein: the at least
one annular vision region further comprises at least one second
annular aperture having an intermediate power that is less than the
apical power and greater than the distance power.
7. An ophthalmic lens comprising: at least one optical surface
creating a symmetric smooth radial power distribution, the power
distribution having at least one local maximum and at least one
local minimum, each maximum and minimum bounded by optical steps;
the power distribution changing sufficiently rapidly in each
optical step to induce a user receiving images from a
plane-of-regard associated with the respective maximum and minimum
to view the portion of the image passing through optical surface at
the respective maximum or minimum.
8. An ophthalmic lens according to claim 7, wherein: all local
minimums have equal power.
9. An ophthalmic lens according to claim 7, wherein: all local
minimums have distinct powers.
10. An ophthalmic lens according to claim 7, wherein: all local
maximums have distinct powers.
11. An ophthalmic lens according to claim 7, wherein: all local
maximums have equal power.
12. An ophthalmic lens according to claim 7, wherein: all maximums
and minimums have mutually distinct powers.
13. An ophthalmic lens according to claim 8; wherein: the power at
each minimum is a distance sight power; and at least one local
maximum comprising at least one near sight region having a near
sight power no more than 3.0 diopters greater than the distance
sight power.
14. An ophthalmic lens according to claim 13, wherein: the at least
one near sight region comprises an apical region.
15. An ophthalmic lens according to claim 14, wherein: at least one
local maximum further comprising an annular aperture having an
intermediate power less than the near sight power and greater than
the distance power.
16. An ophthalmic lens according to claim 7, wherein: the power
distribution is defined by at least one cyclic function.
17. An ophthalmic lens according to claim 7, wherein: the at least
one optical surface comprises the surface of a human cornea.
18. An ophthalmic lens according to claim 7, wherein: the at least
one optical surface is a anterior surface of a contact lens; and a
posterior surface of the lens has a reverse geometry such that a
centering force is created on the lens when fitted to an eye.
19. An ophthalmic lens comprising: a contact lens body having an
optical surface having a symmetric radial power distribution; the
power distribution having at least one annular induced aperture,
each aperture having a respective local maximum or minimum power
and each aperture bounded by optical steps; and each optical step
having smoothly and rapidly changing power such that a user
receiving images passing through the lens is induced to selectively
accept the portions of the image passing through the induced
apertures.
20. An ophthalmic lens according to claim 19, wherein; the power
distribution is smooth from an apex to the extents of a lens
mesopic pupillary region;
Description
RELATED APPLICATIONS
[0001] The present application is a continuation-in-part of, and
claims priority from, both the U.S. application having Ser. No.
09/657,562 and filed Sep. 8, 2000, and International Application
No. PCT/US01/28156, filed Sep. 6, 2001.
BACKGROUND OF THE INVENTION
[0002] The present invention relates to ophthalmic lenses having
more than a single focal length. The methods and structures
provided are applicable to proximal and spectacle lenses and other
lenses for correcting human vision.
[0003] The majority of vision-correcting lenses are designed to
correct sight solely for distance viewing-with a single focal
length. When a person views near objects, the eye accommodates the
divergent, rather than parallel, light arriving from the near
object. The act of accommodation by the human eye results in a
physical change in shape of the crystalline lens within the eye,
the flexure of this lens causes the incoming divergent light
emitted by near objects to re-converge and focus on the retina.
Accommodation increases the convergence of light waves by causing
the lens surfaces to be more steeply curved, which in turn adds
focal power to the optical system of the eye. The closer an object
is viewed, the greater the accommodative demand placed on the eye.
As the human crystalline lens ages, it slowly loses its gel-like
flexibility. Although the process goes unnoticed for the better
part of four decades, the lens body expands in girth and hardens,
losing the ability to change shape with a resulting loss in
accommodative ability. This condition is known as presbyopia.
Typically, corrective lens wearers begin to notice presbyopia near
the end of the fourth decade and then begin to require more than
one lens in order to see clearly and efficiently at all distances.
The convergent focal power requirement of this multiple lens system
then typically increases gradually over the next fifteen years.
[0004] Early versions of multiple corrective spectacle lens systems
for the human eye simply added an additional spectacle lens below
the distance lens and designated the two-lens system a bifocal. The
additional focal power afforded by this arrangement was known as
the add-power for near vision. Eventually a third lens was placed
between these two lenses to improve vision at intermediate
distances, and the system became a trifocal. Because of recent
innovations in the field of ophthalmic lens design, spectacles are
now available in multifocals that are made in a continuous array of
focal powers. These spectacles are made to accommodate the eye for
distances from infinity to the reading plane, and are known as
progressive-addition lenses. Although multifocal spectacle lenses
have been largely successful in satisfying the needs of spectacle
wearers, multifocal lenses that are positioned on or in the eye
(proximal lenses): contact lenses, intra-ocular lenses and the
alternative surgically imparted corneal lenses have been much less
successful. Many recently emerging presbyopes are life-long wearers
of contact lenses that correct only the distance vision. As
presbyopia develops, most of these patients are forced to wear
reading glasses over their contact lenses or to wear a distance
lens in one eye and a near lens in the opposite eye (mono-vision).
These two modes are very inconvenient, and sometimes hazardous to
the wearer. Wearers of the so-called mono-vision modality must
necessarily forfeit the natural binocular function that is needed
to judge depth. Another growing population in need of multifocal
correction is the pseudo-aphakic post-cataract surgery patient
whose natural lenses have been replaced with implanted polymeric
lenses. These patients must wear spectacles for reading after
successful surgery, but many of them could benefit if the implanted
lenses were efficiently shaped multifocals. Such a multifocal
implant must be capable of replacing the variable focusing ability
of their youthful natural lenses. Yet another large and growing
group of lens wearers are the recent recipients of corneal surgery
who find themselves forced to wear reading glasses after a very
expensive surgical procedure that corrects only the distance
vision. If corneal surgery could introduce a multifocal into the
corneal stroma of proper shape and focal power distribution, it
would alleviate the necessity of wearing reading spectacles in
post-operative presbyopes.
[0005] Previous attempts to provide multifocal power to the human
eye using contact lenses or other proximal lenses (those on or in
the eye) have had limited success. Mimicking the simple bifocal
spectacle, the device as described in U.S. Pat. No. 4,693,572 to
Tsuetaki, et.al. is an example of segmented alternating bifocal
contact lenses. This type of lenses must be caused to translate on
the cornea of the wearer by pressure from the sensitive lower lid
margin when the wearer gazes downward. Despite the discomfort of
the lip pressure, this design has experienced some niche success.
That success comes in part from the wide field of vision afforded
the wearer as the pupillary aperture is exposed to a very large
component of either the lower (near) lens or the (upper) distance
lens in the two positions of gaze.
[0006] More recent designs, as found in U.S. Pat. No. 5,436,678 to
Carroll depend upon the phenomenon of simultaneous focus to obtain
addition power along with distant vision correction. Using this
method, multiple foci: far, near and intermediate are presented
within the pupillary zone at the same time. These devices depend
upon discrimination by the cortical vision system to select the
best focus available for the distance that is being viewed. Though
this approach has had considerable success, most designs can
correct only moderate amounts of presbyopia and are usually most
successful when the surface shape treatment is applied to the
corneal side of rigid gas-permeable contact lenses. In these
designs, extreme curvatures are applied to the base curve, often
creating metabolic problems for the cornea. The devices of the
Carroll patent are modified in U.S. Pat. No. 5,835,187 to Martin to
include a plurality of spherical zones on the front surface while
maintaining conic curves on the posterior surface so that
multifocal addition power is obtained from both surfaces.
Unfortunately, the spherical zones are pieced together and are not
a continuous array or radii with continuous first and second
derivatives, with the result that diffraction will play a roll in
degrading the optical performance of these lenses.
[0007] Various shapes have been applied to lens surfaces to improve
simultaneous focus lenses. Aspheric multifocal lenses have been
designed using multiple zones of conicoid surfaces. In concentric
designs such as contact lenses or intra-ocular lenses, adjacent
surfaces of revolution of differing shapes are smoothed
mathematically to develop addition power that increases radially on
the lens surfaces. Conicoids evolved as usable shapes for
ophthalmic lenses primarily because of their variable shape and
innate ease of manipulation. Consequently, aspheric contact lenses
evolved from these conic functions. Though highly effective in
generating variable foci, lenses designed around conic shapes do
not always provide acceptable optics for the eye and can be
somewhat unwieldy when used with interconnecting lens surfaces.
Examples of more successful bifocal (not multifocal) lenses are
discussed in U.S. Pat. Nos. 5,448,312 and 5,929,969 to Roffman. The
Roffman bifocal is generated by alternating rings of two radii, one
for distance power and another for near power in such a way as to
maintain excellent near power for typical pupil sizes and ambient
light conditions. Distance vision suffers from diffractive effects
caused apparently by the centermost rings that surround the
distance power zone, and by the loss of light and optical clarity
created by the grooves between radii. An improvement on this design
would seek to use an aspheric central and intermediate zone with
alternating rings in only the outer add-power zone.
[0008] In most multifocus lenses adjacent power zones have
boundaries which induce diffraction and other optical aberrations
which degrade visual acuity. Various smoothing and transition
methods have been developed to reduce this problem. U.S. Pat. No.
5,815,236 to Vayntraub discloses use of a logarithmic function in
defining smoother transitions between lens zonal curves. U.S. Pat.
No. 4,640,595 to Volk discloses using a variable shape (e-value) in
smoothing conicoid surfaces. U.S. Pat. No. 5,452,031 to Ducharme
discloses use of piece-wise polynomials or splining techniques to
smooth zonal curve transitions. Unfortunately, the optical areas
taken up by these transitions are at best wasted for vision
correcting benefit and typically still introduce unfocused regions
that reduce overall visual clarity. Optical discontinuities and
ineffective transitions are particularly problematic within or
adjacent to lens regions used for distance vision where they are
more perceptible to the user than within near vision regions. Clear
distance vision requires clear optics and the preponderant myopic
population will not tolerate distance blur. Good pupil economics is
also essential for the success of any lens placed on or within the
eye itself Given the limited size of the pupillary aperture, an
array of lenses introduced to the eye-optical system must be
applied with great precision and without wasted or unused optical
area.
[0009] Other devices have been studied for the improvement of
distance vision. The ability of the eye to see distance more
clearly with a relatively fixed small aperture is well known.
Consequently, methods of correcting distance vision have been
proposed that use pinholes devices or similar small aperture
designs. U.S. Pat. Nos. 3,794,414 to Wesley and 5,192,317 to Kalb
provide examples of this approach. Although benefits can be gained
for correcting presbyopia, most of these designs suffer from
defects caused by diffraction at the edge of a dark ring or masked
area, a phenomenon that detracts from any possible improvement
obtained from these small aperture designs. In addition, the
perimeter masking that is used to create these devices precludes
multifocal functioning that is desired for correcting
presbyopia.
[0010] Lenses made according to the above mentioned patents and
methods reflect the optical limitations resulting from a large
number of requirements for clear human vision at all distances and
under a wide range of light conditions. These conditions can be
more nearly met if the special attributes and abilities of the eye
are fully utilized and applied economically within the limited
pupillary zone. Uniquely, the human vision system is comprised of a
rather simple optical device that often needs optical correction
because of its diminutive size and organic changes. This
rudimentary device is yoked to a complex cortical vision system
that can control and suppress blurred areas advantageously if
presented with carefully designed optics. What is needed is a
method of forming an ophthalmic lens providing multiple focal
lengths without loss of optical efficiency or acuity from
ineffective transition regions, particularly adjacent distance
vision regions. Preferably, such a lens also effectively creates a
small aperture to improve viewing at any distance without the
problems inherent to typical small aperture devices.
SUMMARY OF THE INVENTION
[0011] The present invention defines single focus and multifocal
ocular lenses providing optical power for correcting vision over a
continuous range from infinity to near sight distances. In a lens
power distribution, radial optical steps are introduced having
rapidly changing power. The optical steps produce enhanced vision
in part by inducing an effective aperture, the image through which
the cortical elements of the vision system are induced to
concentrate. The enhanced vision effect of the induced aperture is
applied to single focus and multiple focus lenses. One or more
apical and/or annular induced apertures are used in various
configurations to address specific correction requirements. In each
configuration, the various induced apertures may have common or
distinct minimum or maximum powers in the power distribution. Each
such distinct power addresses correction for a specific
plane-of-regard. In addition, the repeated nature of the power
distribution provides redundant correction points within the
optical steps which are integrated by the cortical system to
increase acuity for intermediate distances distinct from the
planes-of-regard addresses by the induced apertures. In this way,
continuous correction may be provided by the inventive lens.
[0012] In certain embodiments, the optical surface shape producing
the induced aperture power distribution also reduces spherical
aberrations over conical shaped lenses adding to the enhanced
vision effect. In one such embodiment, a positive lens having a
single annular induced aperture is applied as a enhanced vision
single focus lens.
[0013] In exemplary embodiments, cyclic power functions defining
nonconical aspheric optical surfaces, are used to produce the
desired optical power distributions. Cyclic power functions have
benefits in ease of manipulation to fit various specific design
requirements. The smooth and continuous nature of the power
distributions used ensures no diffraction or other blurring effects
exist in the mesopic pupillary region. The surface functions may be
provided in form of polynomial series for simplicity of use in
computer driven lathes for shaping contact lenses. For the same
purpose, the power and surface functions may be reduced to
representative tabular values.
[0014] The present power distributions are applicable to contact
lenses, scleral lenses, intraocular lenses, and lenses impressed or
surgically shaped within the corneal tissue. Equations are provided
for creating anterior optical surfaces having the desired
properties. However, optical devices generating the defined power
distributions from posterior surfaces are also contemplated.
Although nominally positive power lenses are also within the
present invention, negative lenses gain particular benefit due to
decreased lens thickness at the lens perimeter and consequent
reduced spherical aberration. Spectacle lenses may also be defined
using the power distributions of the present invention, although
without the benefit of an effective aperture.
[0015] The present invention includes also methods of fitting
lenses in which equations defining lens surface shapes are
manipulated to produce a lens to meet specific user geometry and
performance needs. Additional benefits and advantages of the
present invention will become clear from the following detailed
examples and associated figures.
DESCRIPTION OF THE DRAWINGS
[0016] FIG. 1 is a graph of optical power as a function of radius
for one embodiment of the invention.
[0017] FIG. 2a depict a contact lens according to present
invention.
[0018] FIG. 2b is a graph of optical power as a function of radius
for the embodiment of FIG. 2a.
[0019] FIG. 3 are three graphs of optical power as a function of
radius for an alternative power distribution equation having
various values for a shape factor.
[0020] FIG. 4 is a graph of a power distribution of the present
invention modified to balance distance vision with near sight
vision.
[0021] FIG. 5 is a graph of an optical surface of a contact lens
according to one embodiment of the invention.
[0022] FIG. 6 is a graph of add power for various cyclical power
distributions according to the present invention.
[0023] FIG. 7 is a graph of a cyclical power distribution used in
an optical step and in a decreasing power transition region with an
intervening near vision region.
[0024] FIG. 8 is a graph of power as a function of radial dimension
in an embodiment of the present invention having multiple power
peaks.
[0025] FIG. 9 depicts an axi-symmetric lens surface as a plot of
sagittal depth as a function of radial dimension for the anterior
optical surface of a lens having a multiple-peak power distribution
according to the present invention.
[0026] FIG. 10 depicts a power distribution of one embodiment of
the invention including induced apertures at two distinct
powers.
[0027] FIG. 11 depicts a power distribution of one embodiment of
the invention including multiple annular induced apertures at
multiple distinct powers.
[0028] FIG. 12 depicts a power distribution of yet another
embodiment of the invention having a single annular aperture with a
higher apical power.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0029] FIG. 1 depicts a plot of the local optical power
distribution 20 as a function of radial dimension from an apex of
one embodiment of the invention. The vertical axis is optical power
P(r) while the horizontal axis is radial dimension from the apex. A
centrally located distance vision region 22 has a distance
correction power which is effectively approximated by the apical
power 24. The distance correction power is that power required to
correct vision for viewing of objects infinitely distant. The
required distance correction power may vary with the specific
requirements of the users. Focal power increases gradually with
increasing radius in the distance vision region 22 until a design
level power 28 is reached. The incremental power addition from the
apical power 24 (distance vision power) to the power addition that
causes blur at the entrance pupil margin is defined here as the
design level 28. The incremental power that causes blur in most
persons is found to be between +0.25 and +1.25 diopters
(meters.sup.-1) and the design level power is selected to be in
this range. The variation in power addition for the design level
power is a result, in part, of the somewhat subjective analysis of
what is considered blurred vision. For example, if the design level
power value chosen by the lens designer is +0.50, and the nominal
distance power in the central region is +1.00 diopter, then the
effective aperture is that region bounded by +1.50 diopters of
power. From the design level 28, the power rapidly increases with
radius in what is termed an optical step 26. The rise in the power
in the optical step 26 is sufficiently high that, during distance
viewing, the cortical aspect of a user's vision system is unable to
resolve through the surrounding blur of the optical step 26. As a
result, the user is induced to view distant objects solely through
the distance vision region 22. The perceived effect is similar to
that known to be achieved by small aperture devices such as
pinholes devices. The optical device having this effect, resulting
from the combination of the distance vision region and surrounding
optical step, is referred to here as an induced effective aperture.
Unlike pinhole devices and masked apertures, the present effective
aperture is not bounded by an opaque area which reduces the light
entering the pupil. The effective aperture of the present invention
is surrounded by regions functioning optically for vision
correction upon attempted focusing at distances closer than
infinity. The boundary and dimension of the effective aperture is
not precisely definable as it is determined in part by a subjective
cortical response. However, the bounds of the effective aperture
can be approximated by the design level 28. As this region is
circular in shape in the embodiment of the figure, the effective
aperture can be quantified as twice the radial dimension to the
design level 28. For greatest effect, the diameter of the effective
aperture should be in the range of 0.1 to 3.5 mm (millimeters). Due
to limitations of the mechanics of centering on the eye, a
practical minimum may be 0.5 mm.
[0030] The optical step includes continuously increasing local
power from the design level 28 to a maximum power 29, therein
providing corrective power associated with all distances from
infinity to near sight distances. "Near sight" is generally
considered in the art to be at distances of approximately 40 mm
from the eye. The power above the apical power 24 is generally
referred to herein as "add" power. The add power of the distance
vision region is effectively zero by definition. The add power
required to fully correct for near sight vision is usually in the
range of 1.0 to 3.0 diopters, depending upon the age of the wearer
and the specific near sight distance used by the wearer. Outside
the optical step, the power drops smoothly in a reduced power
region 27 to approach the apical power. The pupil diameter for
mesopic vision, during moderate lighting levels, ranges from 3.5 to
4.0 mm (millimeters) for the average person. The distance vision
region and optical step occurs within the dimensions of the mesopic
pupil to be effective at normal light levels. In low light
conditions the pupil typically opens to a diameter of about 6 to 8
mm. In low light conditions, distance correction rather than near
sight correction is desired as distance viewing is the dominant
mode in low light for most persons. For this reason it is often
desired that the lens power be reduced in the region beyond the
mesopic diameter of the pupil. The power distribution in the
diminished light or scotopic zone takes various forms in
alternative embodiments In one embodiment the scotopic zone power
is more negative than the apical distance power. This is desirable
due to the generally recognized increased negative correction
required by most persons for night vision.
[0031] For clear vision at any plane-of-regard, the power
distribution must be continuous within and proximate the bounds of
the distance vision regions. To obtain the required power
distribution it is necessary to form a lens surface shape having
first decreasing and then increasing radius of curvature. In
various embodiments of the present invention, this is obtained by
using a catenary-like equation having combined exponential growth
and decay functions. Optical surfaces based on catenaries have
superior optical characteristics for multifocus lenses due to the
occurrence of the centers of radius near the optical axes, rather
than skewed from the axis as in the case of conic functions. The
present invention manipulates the catenary-like equations by
allowing the base of the function to vary from the natural
logarithmic base.
[0032] The power distribution in FIG. 1 is produced on a lens
anterior optical surface by a surface of revolution obtained from
the following equation:
Z(x)=c.sub.1.multidot.P.sup.k.multidot.x+c.sub.1.multidot.P.sup.-k.multido-
t.x+c.sub.2 Eq. 1
[0033] where:
[0034] Z(x) is the sagittal depth from a common datum
[0035] x is a perpendicular distance from the apex in
millimeters
[0036] k is the inverse of the apical radius of curvature;
(mm.sup.-1)
[0037] P is a variable exponential power base
[0038] c.sub.1, c.sub.2 are coefficients determined by the known
boundary conditions
[0039] Equation 1 has continuous values from the apex to the limits
of the effective lens area. The first and second derivatives are
continuous as well. The apical radius of curvature is defined in
the typical manner by the particular wearer's eye geometry,
material properties, and the distance vision correction required.
The constants c.sub.1 and c.sub.2 are determined from the known
boundary conditions to be:
c.sub.1=(2.multidot.k.multidot.(ln P).sup.2).sup.-1
c.sub.2=(k.multidot.(ln P).sup.2).sup.-1 Eq. 2
[0040] The power base P may be any positive number greater than 1
but is, for practical contact lenses, less than about 60, although
in some cases P may be as high as 100. The values of P are
dependent upon the units of measure and in these values are with
respect to the equations herein expressed in millimeters. By using
different values of P, the shape and maximum power of the power
distribution shown in FIG. 1 is altered for a particular lens
design. Preferably, to obtain useful near vision correction power,
a P value is selected such that the value of the power distribution
reaches the near vision power at or before the mesopic pupillary
boundary. This ensures near vision correction is available to the
user in normal light conditions. In order to obtain corrective
power beneficial to the user for intermediate distances--between
near sight and infinity--the power distribution first derivative
should not be excessive. Practical upper limits on the slope of the
power distribution are not known and may be user dependent. Proper
modification or selection of the power distribution, by
modification or selection of the power base P, may necessarily be
guided by empirical feedback obtained from the user. In some cases,
increased clarity of vision at one distance may require sacrifice
of clarity at a second distance. At P values which produce the
required near vision power within the mesopic pupil the resulting
power distribution typically rises radially well above the required
add power.
[0041] Example contact lens designs according to the present
invention are provided in Table 1 below for various combinations of
parameters. These lenses are based on HEMA-based hydrogel having an
index of refraction of 1.4.
1TABLE 1 Distance Effective Mesopic Lens Near Add Power Aperture
Pupil Max Add # (diopters) (diopters) P Dia. (mm) Dia. (mm)
(diopters) 1 2.50 -5 13.9 1.85 3.5 7.66 2 2.50 +5 9.93 1.79 3.5
4.62 3 2.50 -20 58.9 1.91 3.5 18.02 4 1.25 -5 9.4 2.64 3.5 7.66 5
1.25 +5 7.8 2.55 3.5 1.87 6 1.25 -20 23.2 2.70 3.5 9.31
[0042] A base curve radius of 8.5 mm and a mesopic pupillary
diameter of 3.5 mm was assumed in each case. The lenses were
designed to have the near add power at this mesopic boundary. The
effective aperture is calculated from a critical design power of
+0.75 diopters above the distance power. The value of power in
diopters in the above table and elsewhere herein is in
meters.sup.-1.
[0043] All but two of the above example lenses are negative power
lenses (inducing increased divergence of incident light rays). A
negative contact lens generally increases in thickness with
increasing radius from the lens center. The thickness of the lens
is known to produce spherical aberration which degrades clarity of
vision capable with the lens. In each case above, the maximum add
power of the lens is significantly greater than the required near
add power. In each of the negative lenses, the maximum add is at
least threes times the near add power. The surface shape that
produces this high power outside the optical step also results in
thinning of the lens at the perimeter. An advantage of the present
design in negative lenses is a reduced thickness resulting when the
surface shape defined by Equation 1 is applied to a lens anterior
surface. This reduced thickness reduces spherical aberration and
increase clarity for the user.
[0044] The optical step at the edge of the effective aperture is
termed such because its rapid power rise is analogous to a "step"
function between the distance vision region 22 and maximum power
29. To ensure clear vision it is necessary to create the optical
step without discontinuities which might induce light diffraction
or other unfocused alteration of incident light. Such effects are
particularly deleterious when occuring in distance vision regions
because the human eye is more sensitive to unfocused light in
distance vision than in near vision. Prior methods of forming
regions of different optical power that include such
discontinuities do not provide optimum vision. Various methods
previously suggested by others that require optically nonfunctional
transitions or smoothing regions suffer from this detraction. It is
desired in the present invention to provide an optical step as a
smooth continuum of the lens power curve if optimum distance vision
is to be obtained. The terms of Equation 1 are defined and
continuous over the full range of the lens surface. By avoiding
multiple discontinuous functions or shapes producing discrete power
zones for distance vision, the consequent necessary transitions and
their effects are avoided.
[0045] Equation 1 can be transformed by Taylor expansion into the
following polynomial equation 1 Z ( x ) = 1 2 k x 2 + 1 24 k 3 ( ln
P ) 2 x 4 + 1 720 k 5 ( ln p ) 4 x 6 + Eq . 3
[0046] which can also be expressed as the summation: 2 Z ( x ) = n
= 1 m k 2 n - 1 ( ln P ) 2 ( n - 1 ) ( 2 n ) ! x 2 n Eq . 4
[0047] where the terms are as previously defined and m is less that
15 and preferably less than 5 for convenience of manufacture. This
equation is convenient for lens design and fabrication operations.
The rapid convergence of the power function of this invention
requires use of as few as two terms of the above equation in many
cases. Such surface equations expressed as polynomials are easily
applied in computer lathing systems for machining lens surfaces or
molds for casting lens surfaces. Similarly, these equations
defining the present inventive lenses may be expressed in tables of
discrete values of radius and associated sagittal dimension.
[0048] Mathematically, a surface of revolution must contain only
even exponents as shown in the above form; however, modern
computerized lens lathing systems are able to generate surfaces of
revolution for odd exponents by utilizing the absolute values of
those terms. This allows additional odd exponent terms to be added
to the above equation to manipulate the result for design effect.
Other polynomial expressions are possible to express the same basic
function including expressions including fractional exponent terms.
In addition, the first term of Equation 3 may be modified from its
simple parabolic form to include other conic shapes which provide
occasional benefit without detracting from the advantages of the
power form. The following equation is a general expression of an
alternative power distribution including a general conic term: 3 Z
( x ) = kx 2 2 [ 1 - ( 1 - S k 2 x 2 ) 1 2 ] [ 1 + ( 1 - S k 2 x 2
) 1 2 ] - 1 + ( 2 k ( ln P ) 2 ) - 1 P k x + ( 2 k ( ln P ) 2 ) - 1
P - k x - ( k ( ln P ) 2 ) - 1 Eq . 5
[0049] Where S is an asphericity or shape factor. For S=0, the
entire first term vanishes to obtain the original exponential form
of Eq. 1. The following conic shapes are defined in Eq. 5 by the
value of S applied:
2 Conic Shape S Value Hyperboloid S < 0 Paraboloid S = 0
Ellipsoid (prolate) 0 < S < 1 Ellipsoid (oblate) S > 1
Sphere S = 1
[0050] Lenses produced using this equation and method have similar
characteristics with the previous examples, but with the added
degree of freedom provided by the included shape factor S which can
be manipulated to change the size of the effective aperture and
shape of the optical step.
[0051] FIG. 3 contains graphs of add power for lenses defined by
Equation 5 with various values of the shape factor S. For each
power distribution shown, the value of P has been adjusted such
that the power distribution passes through the near vision power 34
at the same radial dimension. By adjusting S and P in this manner,
the shape of the optical step and slope of the power distribution
between the distance vision region and the near vision power may be
manipulated. For most contact lenses, the shape factor S will have
a value in the range of -5 to 2. At S values beyond this range, the
value of P becomes excessively small or large resulting in a
distorted power distribution. Table 2 provides example lens designs
according to the present invention with various values of S.
3TABLE 2 Distance Effective Mesopic Near Add Power Aperture pupil
Max Add Lens # (diopters) (diopters) S P Dia (mm) Dia (mm)
(diopters) 7 2.50 -5 +1 7.17 1.86 3.5 7.32 8 2.50 -5 -1 22.4 1.90
3.5 10.44 9 2.50 +20 -2 19.5 2.56 3.5 10.67 10 1.25 -5 +1 4.1 2.64
3.5 4.35 11 1.25 -5 -1 16.3 2.72 3.5 5.55 12 1.25 +20 -2 17.9 3.21
3.5 8.43
[0052] As in the previous examples, a base curve radius of 8.5 mm
and a mesopic pupillary diameter of 3.5 mm was assumed in each
case. The lenses were designed to have the near add power at this
mesopic boundary. The effective aperture is calculated from a
critical design power of +0.75 diopters above the distance
power.
[0053] Because the power distributions obtained from the above
equations are typically continuously increasing at the near vision
power, the area of the lens providing near vision power is also
typically small. A consequence for some users may be reduced near
vision clarity. To provide increased near vision correction in
mesopic conditions, the power distributions above are modified
outside the central distance vision region to enhance near vision
correction. FIG. 2a depicts such a contact lens according to a
preferred embodiment of the invention. FIG. 2b is a plot of the
optical power of the lens of FIG. 2a as a function of radial
dimension from the lens apex. The lens 30 includes central region
32 with a power distribution 32a corresponding to the distance
vision region 22, and optical step 26, as shown in FIG. 1. The
power distribution 32a is produced in various distinct embodiments
by alternate application of the above equations. The focal power in
the central region rises steeply in an optical step 26 to create an
induced aperture as discussed above. The maximum power reached is
the specifically required near vision power 34. At this power, the
optical step is truncated and the near vision power 34 is
maintained through an annular near vision region 36 extending
outward from the central region 32. The central region 32 and near
vision region 36 both lie within the mesopic pupillary dimension.
In alternative embodiments, the near vision region 36 has a varying
power distribution which follows various shapes to allow more
smooth transition between the optical step and a transition region
38. From the outer perimeter of the near vision region 36, the
optical power decreases rapidly in a transition region 38 to a
power equal the apical power 24. Preferably, the outer perimeter of
the transition region 38 is approximately at outer limit of the
mesopic pupil. In this example the transition power distribution
38a in the transition region 38 follows a simple hyperbolic. It is
important that the transition region be as smooth as possible so as
to not introduce blurring, while at the same time retracing power
rapidly so that a minimum of radial extent is used. Other curves
may also accomplish these requirements, such as may be expressed by
various polynomials. Radially outside the transition region 38 is a
lens scotopic vision region 40 having distance vision power--apical
power 24. As discussed above, in an alternative embodiment the
scotopic vision region has a reduced power which is less than the
apical power. Outside the scotopic region of the lens is an
lenticular flange 42. The flange 42 does not provide optical
effect, but provides physical support to the lens. It is important
that any smoothing or blending that is required between the above
regions is outside the primary distance vision zone which is within
the central region. Such smoothing may be carried out in any of a
variety of known methods.
[0054] In alternative embodiments, to provide balanced near and
distant vision, the power distributions are manipulated to adjust
the respective corrective areas on the lens. It is believed that a
more effective combination of near vision and distance vision may
be obtained by providing a region of near vision power at least as
large as the distance vision power lens area. That is, using areas
normal to the optical path, the area within the annular near vision
region is equal or greater the area within effective aperture.
Manipulation of both P and S is required to obtain the desired
result from Equation 5. This can be carried out by an iterative
process as now described with respect to FIG. 4 which is a graph of
a power distribution 20. It is presumed that the user and lens
specific parameters have been defined and inserted into Equation 5.
The required near vision power is also determined from the user's
requirements. A trial shape factor is selected: S=-1 is suggested.
A first estimate of the near vision power radial dimension
(R.sub.NADD), less than the user's mesopic pupillary radial
dimension 50, is chosen. Equation 5 is then evaluated for various P
values and the resulting add power (ADDP(r)) calculated at
R.sub.NADD. When the power distribution at R.sub.NADD equals the
required near vision power 34, the effective aperture 51 is
determined from the equation and the selected design level (see
above). This may be done by iterative trial and error. The
respective areas of the near vision region and within the effective
aperture are then calculated. If the near vision region is
insufficient--less than within the effective aperture--the shape
factor is decreased. If the near vision region is too
large--greater than within the effective aperture--the shape factor
is increased. Iteration on P may be used again to obtain the
desired near vision power and verify the areas. In the lens
produced from this method, the power distribution is truncated at
the near vision power to form a near vision region 36 extending to
the pupillary dimension 50 as described with respect to FIG. 3. The
near vision region 36 has constant power over its area. The lens
regions outside the mesopic pupil may be designed as described with
respect to FIG. 3. The above iterative processes may be automated
by computer methods. Tabulated values for common parameters may
also be used to simplify the process. Other methods of executing
these steps are also available to those skilled in the art.
[0055] FIG. 5 is a graph of an optical surface corresponding to the
power distribution and corrective regions depicted in FIG. 2b. From
the apex, a central surface region 61 curves inward from a
spherical reference line 62. The spherical reference line 62
corresponds to the surface of a single power lens. The central
surface region 61 corresponds to the central vision region power
distribution (32a in FIG. 2b). The central surface region 61 ends
at a sulcus surface 63 corresponding to a near vision power. From
the sulcus surface 63 extends a scotopic surface region 65 having
increasing radius of curvature which corresponds to the transition
and scotopic region powers. At the outer edge of the surface is a
lenticular flange surface 67.
[0056] An approximation of the above power distributions is
obtained in a distinct embodiment by use of cyclic functions which
provide additional benefits. The following equation for a lens add
power provides improved transition between the intermediate powers
and the near vision power while also providing control of the
maximum power and its radial location. 4 ADD ( x ) = ADDM 2 [ 1 +
cos [ ( Xc - x Xc ) ] ] Eq . 6
[0057] Where:
[0058] ADD(x) is the add power at a point x as defined above, ADDM
is the maximum power which is selected to be equal the required
near vision power, and Xc is the desired location of the maximum
power.
[0059] FIG. 6 is a graph of power distributions 69, 69', 69"
generated by this equation for various values of ADDM and Xc in the
above equation. Lenses formed with these power distributions
exhibit the same optical benefits provided by the effective
aperture and optical step discussed previously. Due to the ability
to control the maximum power of the distribution they are
particularly well suited for modification by introduction of a
extended near vision region in the manner of the previous
embodiment. FIG. 7 depicts a lens power distribution formed by
extending such a cyclic power distribution 70, from the maximum
power ADDM, with a near vision region 72 having constant near
vision power in the radial direction. The shape of the cyclic power
distribution 70 provides a smooth transition to the near vision
region and improves optical quality. A mirror image 74 of the
cyclic power distribution 70 is used at the outer boundary of the
near vision region 72 to define a smooth transition reducing
optical power in the radial direction to the apical distance
power.
[0060] The complete surface function can be derived for Equation 6,
but results in an equation that is unwieldy to apply in manufacture
of lenses. An effective approximation of the optical surfaces
associated with the power distribution of Equation 6 can be
developed from the following equation: 5 Z ( x ) = 1 2 k x 2 + M 10
- 3 2 ( n - 1 ) [ 1 2 x 2 + ( T 2 2 ) ( cos ( T x ) - 1 ) ] Eq .
7
[0061] Where:
[0062] M and T are variables which must be determined.
[0063] In order to arrive at the proper surface shape, Equation 7
is manipulated in the typical manner to arrive at a corresponding
approximate power function in terms of M and T. Appropriate values
of M and T are determined by iteration and comparison of the
approximate power function shape with the desired power function of
Equation 6. When the two power function shapes are sufficiently
similar, the corresponding values of M and T are applied to
Equation 7. This surface is then applied to create a lens optical
surface producing the desired power function of Equation 6.
[0064] The above equations for optical surface shape generate the
desired optical power distributions when applied to the anterior
surface of a contact lens. Although they may be used to form
positive lenses, additional benefits are obtained when used to form
negative lenses as mentioned above.
[0065] Due to the small size of the centrally located distance
vision region, it is desirable that the optical axis of the lens be
centered, in use, with respect to the vision axis of the pupil.
Currently available hydrophilic soft contact lenses generally
center well on the eye and are therefore preferred for carrying out
the invention over typical rigid lenses which generally do not
center as well. However, in any contact lens that can be maintained
in centered position, the concepts here are equally applicable. One
method of improving lens centering with rigid gas permeable lenses
uses a reverse geometry base similar to concepts known and used for
corneal molding in orthokeratology. The reverse geometry base
applies to the posterior surface of a lens a relatively flat curve
centrally to the corneal apex and surrounds that region with a
steepening radius portion that creates a suction to the cornea.
Surrounding these regions is a third region having a curvature
which aligns with the cornea. A combined effect of these features
is a centering force applied to the lens. The surface shapes
defined by the above Equations 1 and 5 can also be applied to the
rigid gas permeable lens base curve and, utilizing these shapes'
natural flat-steep-flat characteristics, provide the same centering
effect.
[0066] In the above examples, it is presumed that the pupil's
optics are centered on the pupil body geometric. This is often not
the case as a natural geometric offset of the pupils is found in
some persons. In order to position a contact lens eccentrically
with respect to the pupil body geometry, in alternative embodiments
an eccentric bevel is applied to the perimeter of the posterior
surface. Similarly, an eccentric flange may be used for the same
effect. By establishing a lens eccentricity, with respect to the
pupil geometry, that equals the optical eccentricity, the lens may
be centered with the optical axis. These embodiments are most
effectively used in soft and rigid gas permeable lenses.
[0067] Contact lenses according to the present invention include
hard, soft lenses, and rigid gas permeable lenses formed of any of
the materials typically used. The preferred lens is a hydro-gel or
silicone based hydro-gel soft lens. The optical power of a lens is
a function of both the lens shape and material properties. The lens
shapes and functions discussed herein are with respect to the lens'
intended condition during use. This means, for example, that lenses
designed with a significant water content are fully hydrated.
Current lathe systems are capable of transforming input parameters
to account for material properties changes such as occur in contact
lenses having a high water content in use. Similarly, cast lenses
can be formed taking into account the same material
transformations.
[0068] Although the discussions above have been primarily with
respect to contact lenses, the invention includes other lenses
incorporating the novel concepts herein, including but not limited
to, scleral lenses, intraocular lenses, and lenses impressed or
surgically shaped within the corneal tissue. In particular, power
distributions having optical steps creating effective apertures are
formed in these alternative optical devices. In Table 3 below
design parameters are given for an IOL and a formed corneal surface
profile according to the present invention.
4TABLE 3 Distance Effective Mesopic Near Add Power Aperture Pupil
Lens (diopters) (diopters) S P Dia. (mm) Dia. (mm) IOL 2.50 +20 0
18 1.83 3.5 Corneal 2.50 0 0 10.1 1.80 3.5 Profile
[0069] In the IOL design the index of refraction of the lens and
vitreous is presumed to be 1.49 and 1.34, respectively. The IOL is
a "D" shaped lens with a center thickness of 0.50 mm. The corneal
index of refraction is taken to be 1.376 with a 7.7 mm corneal
radius. The details of forming such devices with the herein defined
optical surfaces is known to those skilled in the art.
[0070] In an alternative embodiment, the benefits of the above
adjustable power and surface functions are achieved in spectacle
lenses. Due to their lack of proximity with the pupil, the effects
of an induced aperture are lessened in spectacle lenses according
to present invention. However, the above power and surface
equations provide unique methods of forming progressive spectacle
lenses where a first power distribution defines an umbilical line
along one axis of the lens. Orthogonal power distributions are
defined with coincident power values at the intersection points
with the first power distribution on the umbilical line.
[0071] The effect of the induced aperture produced by the present
invention is also of value to correct distance vision when near
vision correction is not required. The present invention includes
contact lenses having an optical step and induced aperture without
a specific need for near sight correction.
[0072] In yet further alternative embodiments of the invention, the
lens power distribution has a plurality of power peaks at
incremental radial dimensions. One example embodiment is shown in
FIG. 8 which provides a plot of power as a function of radial
dimension for such an embodiment. Three optical power peaks 80
reach a maximum power 82 which is equal, or greater than, the
design near vision power 81. From the apex to the first peak, the
power distribution is defined in the same manner as expressed in
prior embodiments. At the lens apex, the power is equal the desired
distance power 84 and rises rapidly in the radial direction to
affect an induced aperture. However, the power distribution 83 does
not level off or flatten at the maximum power 82. The power
distribution is then reflected symmetrically about the peak such
that power descends in like manner to near the distance power 84.
The subsequent peaks are defined by repeating this power
distribution in the radial dimension. The radial location of the
inner-most peak is at or within the mesopic pupillary dimension.
Although FIG. 8 depicts three peaks, two, or more than three peaks
may be included--the maximum being limited by the need to locate
them all within the design maximum pupil dimension to be effective
on vision. These power distributions having multiple peaks provide
improved distance vision as a consequence of the induced aperture
effect previously discussed. As well, the repeated peaks provide at
least two additional benefits. The first benefit is improved
intermediate and near vision due to the fact that each peak
provides an incremental effective region of power 85 at
intermediate and near distance powers less than the maximum power
82. An additional benefit is the consequent thinning of the lens
that results from the associated lens surface shape.
[0073] FIG. 9 depicts an axi-symmetric lens surface 90 shown as a
plot of sagittal depth as a function of radial dimension for the
anterior optical surface of a lens. This surface provides a power
distribution as described with respect to FIG. 8, but having two
peaks. Each power peak is associated with a sulcus 91 in the lens
surface 90. Although each sulcus is shown as having a discontinuous
trough, practicalities of manufacture dictate that these will be in
fact somewhat rounded or blended. Although these potentially may
induce some level of diffractive interference, it is believed to be
of minimal effect in most lenses. Embodiments of the invention
having multiple power peaks are characterized in part by a
plurality of radial sulci. At the outer radial dimensions, the
thinning effect of the sulci can be seen as the lens surface
follows closely the lens base curvature line 93. The lens surface
shape to produce the above described power distribution between the
apex and the first peak is defined in various embodiments by the
equations discussed above. This shape may then be reflected
symmetrically about the peak and imposed over the lens curvature
using known methods. Such operations are easily carried out using
modern numerically controlled lathes designed for the purpose. In
alternative embodiments, the several peaks may each have a distinct
surface shape. That is, one or more surface inclines, or declines,
defining the individual peaks may be specified by a surface shape
distinct from the other inclines and declines. For example, the
surface shape from the lens apex to the first peak may be specified
by Equation 5 above with a first set of parameters (i.e. values of
P and S) while the surface shape declining from the first peak, and
subsequent peaks, are defined by Equation 5 with a second distinct
set of parameters (reflected as necessary in each case).
[0074] FIG. 10 depicts a power distribution of an embodiment of the
invention including multiple induced apertures at two distinct
powers 101, 103. The power distribution includes multiple local
maximum powers and local minimum powers at powers 101, 103. The
meaning of local maximum or minimum should be clear but may be
determined by the following: a maximum is preceded, in the power
distribution, by positive slope and followed by negative slope. The
reverse identified a local minimum. Each effective local maximum
105 and local minimum 107 is bounded by steps of increasing or
decreasing power. The nature of these steps is as discussed above:
smooth and with rapidly changing power. In the figure, all local
maximums have a maximum power associated with correction for a
single specific plane-of-regard. Herein "plane-of-regard" is term
indicating a spatial plane a specific distance from the subject
optical surface and requiring a specified optical correction in
application. For example, the plane-of-regard for what is generally
considered distance viewing or sight is at infinity. Likewise, for
typical near sight, the plane-of-regard is about 40 cm
(centimeters) from the eye. Between these typical extremes,
intermediate planes-of-regard may be of interest to a viewing
subject and require distinct corrective power. In FIG. 10, two
planes-of-regard are provided greatest intensity of correction.
These are the associated with the optical powers of the local
minimums and local maximum. If these planes are near vision and
distance vision, planes-of-regard between these distances will
often be provided reduced corrective power intensity. This is due
to the relatively smaller incremental radial element that provides
effective power at any particular point within the rapidly changing
optical step 109. To increase the corrective intensity at these
"intermediate" planes-of-regard the power distribution is made to
repeatedly pass through the associated intermediate power 110 for
each such intermediate plane-of-regard. This "redundant" power
distribution provides increased intensity as a result of its
integration by the human cortical vision system. Each repeated
radial point of power for a plane-of-regard must be bounded by a
smooth power distribution for acceptance of the produced image by
the human cortical system as discussed above. Any portion of the
power distribution bounded by optical discontinuity will not be
effective.
[0075] In FIG. 10, each local maximum and minimum, when bounded by
optical steps, will produce an induced aperture with increased
clarity at the subject maximum or minimum power. In the case of
nonapical maximums and minimums, the induced aperture is annular in
geometry. Each of multiple induced apertures having a common
maximum or minimum power contributes to the corrective effect at
the associated plane-of-regard.
[0076] FIG. 11 depicts an alternative lens power distribution
according to the invention which provides an apical (center)
induced aperture 112 and multiple annular induced apertures 120
directed at various planes-of-regard. The power distribution has
repeated induced apertures 112, 121 at a minimum power 103 for
emphasized intensity at the associated plane-of-regard. This, in
application, may, for example, provide power for distance vision.
Annular induced apertures are provided at three distinct power
levels 113, 115, 117 directed at three distinct planes-of-regards.
For example, these may be directed at near vision for distinct
reading and intermediate working distances. At the same time, the
repeated or redundant nature of the power distribution provides
corrective power for planes-of-regard between those addressed by
the induced aperture. This is accomplished, as discussed with
respect to the embodiment of FIG. 10, as intermediate power 110 is
repeatedly provided at radial distinct points 123 of the
distribution, each contributing to correction for the associated
plane-of-regard. It should be clear that the embodiments of FIGS.
10 and 11 are only examples of an infinite number of arrangements
of apical and annular apertures and associated distinct powers that
may be combined to address corrective needs in particular
applications. Likewise, alternative embodiments include only
annular apertures with no center aperture.
[0077] FIG. 12 depicts another embodiment of a lens according to
the present invention. A power distribution 130 is shown having a
single annular induced aperture 131 and a higher apical power 132.
This power distribution may be employed effectively as a single
focus lens to provide distance viewing correction power 133. If the
apical power 132 (also the maximum power at the top of the optical
step outside the aperture) is sufficiently high, it will not be
accepted by the human cortical system at any plane-of-regard. This
design is particularly beneficial for single focus positive lenses.
The annular aperture is produced, in a positive lens, by a surface
shape resulting in a more constant thickness lens. Such a lens
produces significantly less spherical aberration compared to
conical lenses providing the same correction. A lens with enhanced
clarity and vision is thereby provided. In alternative embodiments,
the apical power 132 is designed to provide correction associated
with a near-sight plane-of-regard, whereby a multifocal lens is
produced.
[0078] To produce an optical surface having the required power
distribution, the methods discussed previously may be applied as
demonstrated in the following example. To ensure that each induced
aperture and intermediate power within the optical steps are
effective, the power distribution is defined by a continuous
function from the apex to the limit of the mesopic pupillary
region. Because of their relative ease of mathematical
manipulation, the many useful power distributions may be preferably
derived from cyclic functions. For example, the desired initial
power function may be defined as follows: 6 P ( x ) = P1 [ 1 + ( P2
- P1 P1 ) cos ( 1 x ) 4 ] Eq . 8
[0079] where
[0080] P(x) is a power at a point x
[0081] P1, P2 are defined powers
[0082] The required optical surface may be obtained in various
ways. For example, the above power function may be equated to the
basic expression of power in terms of curvature as in Equation 9. 7
P ( x ) = k [ 2 x 2 y ( x ) ] [ 1 + ( x y ( x ) ) 2 ] - 3 2 Eq .
9
[0083] This may be expanded in a Taylor series and the higher order
terms dropped. Most designs require two or more terms. The result
may be integrated and solved to arrive at an expression for the
optical surface profile, y(x). Verification of the resulting power
distribution, and adjustment by iteration, may be necessary by
substitution in the original equations. It will be obvious that
combinations of different cyclic functions may be used to define
power distributions having various local maximum and minimum powers
at induced apertures.
[0084] It will clear to one skilled in the art that other
mathematical methods can be used to define power distributions and
associated optical surfaces as defined by the invention. Symmetric
power distributions according to the invention may be defined by
multiple radially connected functions if the herein defined
requirements are satisfied at all points. Additionally, the
benefits of the power distributions herein described may be applied
to corrective devices in combination with other optical
elements.
[0085] The preceding discussion is provided for example only. Other
variations of the claimed inventive concepts will be obvious to
those skilled in the art. Adaptation or incorporation of known
alternative devices and materials, present and future is also
contemplated. The intended scope of the invention is defined by the
following claims.
* * * * *