Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02291548 1999-12-03
1
SHAPED OPHTHALMIC LENSES
The present invention relates to optical lenses and eyewear including
prescription
lenses and sunglass lenses, spectacles, lens blanks, sunglasses and safety
lenses.
it is known in the privy art to manufacture non-corrective eyeglasses such
as sunglasses or protective eyeglasses having wrap-around segments designed
to shield the eyQ from incident light, wind, and foreign objects in the
temporal
vision field of the wearer. Visible sight and light in the UV region may enter
the eye
from angles as high as 100° from the line of sight,
It has not been possible, however, in prior art sunglasses or protective
eyeglasses, to provide such spectacles with significant through power, whilst
maintaining a cosmetically acceptable appearance. The radius of curvature
required to provide an ophthalmic lens including a prescription surface is
such that
the spectacles would produce a bug-eyed appearance, which would be
cosmetically unacceptable.
Today, the vast majority of conventional prescription lenses are relatively
flat, single vision, Ostwalt section, miniscus lenses which are glazed like
window
panes into flat outline spectacle frames.
Applicants have developed certain novel optical lens elements fnctuding
lens elements with a prescription zone, suttable for use in wraparound or
protective eyewear. The element may also include a peripheral vision zone,
with
no prismatic jump between the zones. These lens elements are produced by
design methods for the prescription zone which include temporally rotating a
prescription section about a vertical axis through its optical center andlor
decentering the optical axis of the prescription section natative to its
geometric
axes. These lens elements and design method are described in International
Publication No. WO 97/35224 (25 September 1997) to applicants, the entire
disclosure of which is hereby incorporated by reference. This application
describes the use of close fitting prescription shields, visors or dual lens
CA 02291548 1999-12-03
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prescription sunglasses by introducing a step Change in curvature of the Rx
lenses, particularly in the fonnrard visual field of the wearer. However, the
technique involves design discontinuities in the optical constnrctian of the
lenses,
although the visual function is not impaired from the wearers viewpoint.
5 Applicants had developed certain novel lens elements and eyewear
characterised by steeply curved surfaces which are approximately spherical and
concentric with the centroid of rotation of the eye. These objects are
described in
detail in United States Patent Application Serial No 49/223,006 to Applicants,
('Wide held spherical lenses and single design spectacle therefor") filed 30
10 December 1998, the entire disclosure of which is hereby incorporated by
reference. These lenses deviate substantially from conventional, relatively
fiat
lens shapes. However, the overall shape of such lenses may be limited by the
spherical reference surfaces employed.
Accordingly, it would be a significant advance in the art If an item of
15 prescription eyewear, for example of the wrap-around type, could be
provided
which would allow for a wide range of selected styling for both horizontal
wrap
{around the brows) and vertical shape to maximise the fashion appeal.
Furthermore, It would be a further significant advance in the art if the
lenses could
provide good correction to the full visual field from central to peripheral
vision, if
20 desired. Even more preferably, it would be a significant advance if this
could be
achieved without design features that may create fitting difficulties for a
practitioner, or features such as a piano extension which ors visible to an
observer
and diminish the appeal of the product unless it is heated as a tinted or
reflective
sunglass.
25 Further, the range of lens shapes in both the horizontal and orthogonal
directions is relatively limited in the prior art. The necessity to provide
acceptable
optical quality has heretofore limited the range of lens element shapes
available,
particularly with lens elements having significant through power.
It Is accordingly an object of the present Invention to overcome, or at least
30 alleviate, one or more of the difficulties and deficiencies related to the
prior art.
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Accordingly in a first aspect of the present invention there is provided an
optical tens element including
a first surface; and
a second surtace of complementary curvature;
S at least one surtace exhibiting significant deviation in curvature from a
standard optical surface;
the first and second surfaces in combination defining an optical zone
exhibiting substantially constant mean through power along at least one
meridian.
it will be understood that the optical lens element according to the present
invention permits the production of optical lenses with a surface or surfaces
of
quite radical shape relative to standard ophthalmic lenses, but still
providing a lens
body for which the mean through power is relatively constant within normal
ophthalmic standards. This is despite the fact that the deviating surfaces may
exhibit significant optical distortions, e.g. high levels of surface
astigmatism over
substantial portions of the lens aperture.
Preferably the first and second surfaces are co-varying surfaces such that
the optical zone exhibits substantially constant mean through power. More
preferably the deviating surfaces) exhibits a substantially smooth change of
curvature, at least along a horizontal meridian, across at least a portion of
the
visual fixation field of the wearer. Thus, the deviating surfaces) may exhibit
substantially no visible discontinuity, and more preferably no optical
discontinuity.
In a preferred form, the change In curvature results In a change in sagittal
depth of at least approximately 2 mm, preferably at least approximately 4 mm,
more preferably at Isast approximately 9 mm.
In a preferred form, the optical zone of the lens element functions as a
prescription zone. More preferably, the lens element has a mean through power
between -6.0 D and +6.0 D, preferably between -4.0 D and +4.0 D.
In a further preferred form, the standard optical surface is of spherical or
tonic shape, defined at a sphere or fitting point on the surface which passes
CA 02291548 1999-12-03
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through the optical axis.
By the term "good optical quality", we mean optical quality equal to, ar
greater than, a standard aspheric lens, fvr example.
By the term "substantially constant mean through power" we mean that the
mean through power is constant within 10.75 D, preferably within t0,5 D, more
preferably within X0.25 D, in the visual fixation field of the wearer.
Mean through power is the average of F; the through power in one
principal meridian along a given line of sight and Fz the through power in the
other principal meridian along that line of sight.
Mean through power s ~F', + F2
2
RMS Power Error is the root mean squared error of actual lens through
powers F,' and FZ in the principal meridians, compared with the desired
refractive
corrections FI and Fz
~Fn - Fu2 + ~Fz ' Fz ~Z
RMS Power Error a
2
By the term "significant deviation° in curvature from a standard
optical
surface, we mean that the shape of the surtace deviates sufficiently to
Introduce
optical distortions, e.g. astigmatism, to the lens surface. For example, the
curvature may deviate from a standard optical shape by at least 1.0 D along
the
horizontal meridian, preferably 3.0 D along any meridian, more preferably at
least
5.0 D, more preferably at least 6.0 D.
By the term "lens element° as used herein, we mean an optical or
ophthalmic lens, semi-finished lens, or lens wafer which may be utilised in
the
formation of an ophthalmic product. The optical lens element may be provided
in
the form of a semifinished lens, or lens blank, where the second or back
surface
of the optical lens element may be finished at a later time.
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By the term "visual fixation field", as used herein; we mean a region on the
lens surface defined by a set of points which are the intersection of the lens
surface and the wearer's sine of sight as he or she fixates on objects in the
median
plane.
5 By the tem~t "sagittal depth", as used herein, we mean the distance between
the fronto-parallel plane of the lens element and the temporal most edge
paint.
The sagittal depth provides generally a measure of the three-dimensionaltty of
the
lens element and lens edge.
In a particular preferred form the optical lens element includes front and
rear co~varying surfaces, at Isast one of which having a varying surface power
such that the mean through power of the lens element is constant to within
x.75 D
in the visual fixation field of the wearer with the optical axis of the lens
element
aligned with the visual axis of the wearer, said lens element conforming tv
the
shape of the face of the wearer and having a sagittal depth Z of at least 10
mm,
15 preferably between 10 and 20 mm.
By the term "co-varying surfaces" as used herein we mean two surfaces
which have corresponding points in close proximity which allow substantially
constant through-power even though the magnitude of the curvatures may vary
substantially. This is achieved by having the curvature changes across the
20 surfaces being nearly equal for each point of a corresponding pair. In this
way,
the curvatures at corresponding po(nts may be seen to track each other from
point
to point, even though the physical surfaces may diverge. Co-varying surfaces
may be defined by a set of mathematical constraints:
Constraints
25 For substantially ail corresponding points vn the front and back surfaces
of
the lens lying along tines passing through the center of rotation of the eye
in the
as-wom position;
P,n"~~"" + P"~",~ ~ F~ + kA
p~.~. + Pm~e~x ~ FZ + kA.
c
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for substantially all points an the lens, where P""" is the maximum surface
curvature in one principal meridian at a given point, Pmt" is the minimum
surface
curvature along the other principal meridian at that point, F, is the desired
prescription through-power in one principal meridian and F2 is the through-
power
in the other principal meridian such that the difference between F, and FZ
provides
the prescribed cyl correction; A = add in the progressive case (A _< 3 D} and
0 S k 51 (in the case of a piano lens both equations equal zero; in the case
where
there is no cylinder correction, F~-FZ; and where the lens is not progressive
of
varifocal, KA equals zero)
and
there exist regions of the lens such that for corresponding points
I P,~"=,,n", - P~;" ~", I > 025D
~p~~~ W'~~e~ f > ~~25D
and
there exist at (east two points P, and P2 on a surface of the lens (typically
16 horizontally spaced points within the useful aperture of the lens} such
that
IP,'P2 >3D
where P is the mean surface curvature at P~ and F~ is the mean surface
curvature at P2.
The optical lens elements of the present invention may be designed to have
an optical axis which passes through a sphere point or fitting point of at
least one
of the surfaces. The surface curvature of the surfaces) varies outwardly from
the
sphere point,
The lens elements of the present invention may be wom by a wearer with
an assumed line of sight: a visual axis substantially corresponding to the
wearer's
26 straight ahead gaze dirocted at an object at infinity. The lens elements
may be
designed to be glazed and wom so that the optical axis of the lens element is
parallel to, and preferably colinear with the line of sight of the wearer.
With respect to the "optical axis° it should be understood that for a
lens with
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two spherical surfaces, it simply is the line connecting the centers of
curvature of
the two surfaces. In a practical sense the optical ails is also the line about
which
the angle of refracted rays of light u' are least deflected from the angle of
incidence u. In lenses with covarying surfaces, the definition of an optical
axis is
5 not so simple and such s lens might have more than one axis nominally
satisfying
this definition. For this application we define a primary optical axis as the
line
passing through the fitting point P. Preferably, for such an axis, the average
slope
n
~rt
1
m=
n
of the rays r',....r'~ in a bundle of refracted rays is minimum. (See Figure
1) We
here take a 'bundle' of rays to be all of the rays surrounding the axis within
a
small circular portion of the xy plane and distributed uniformly such that the
snm of
all x and y values of the ray points within the plane are equal to zero.
One may usually locate the optical axis of a manufactured lens by
identifying the two points on the front and back surface which have coincident
~ 5 normals, for example by using an alignment telescope. These two points
define
the optical axis and in radially symmetric lenses with covarying surfaces this
will
be the correct procedure_ In ovaliform lenses with spiral curvatures there may
not
ba two such points so the optical axis must be located by finding the line
about
which bundles of incident and refracted rays has greatest symmetry. This might
20 be done for example using an optical bench with a source of a narrow bundle
of
rays located at the center of curvature of a spherical minor and the lens
located
between the source and mirror. In this method the lens could be tilled and
decentered until the returning rays are symmetrically centered upon the
source.
The optical axis is then defined by the points on the lens surface intersected
by
25 the line defined by the chief ray of the source.
in a particularly preferred aspect, the extent of deviation of the deviating
surface from a standard optical surface Is related to the radial distance from
the
optical axis of the lens element.
In one embodiment of the present invention, the extent of deviation varies
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linearly, sinusoidaily or a combination thereof, with radial distance. More
preferably, the optical lens element rnay be generally radiaify symmetric, and
in
particular may take the forth of a bowl, preferably an oblate or prolate bowl,
(n a
still further preferred form, the deviating surfaces) exhibits no more than 1
5 meridian being circular in section.
In a more preferred form, the lens element is a bowl shape, which is radially
symmetric about Its optical axis and defined by a pair of rotationally
symmetric, co-
varying surtaces. An oblate bowl has a flat central portion and becomes
increasingly steep away from the optical axis. A prolate bowl is most steeply
10 curved at or near the optical axis and flattens out away from the optics!
axis
toward the edge. The bowl may be defined by a radially symmetrtc spiral
curvature (i.e. a curvature varying monotonically from the fitting point).
Optionally
the rim or annulus of the bows may be blended smoothly into a region of
reduced
or zero power. The bowl shaped lenses have advantages arising from their
i 5 rotational symmetry. The lenses may be fabricated from two wafer elements
as
disclosed by applicants in United States patent no. 5,187,505. !f an
astigmatism
correction is provided by the lens, various prescribed cyl axis may be
obtained by
appropriate rotation, edging and glazing of a common lens blank, thus reducing
fens stock requirements.
20 As stated above, the lens element may be of ovaliform shape. This shape
may be selected in recognition of the fact that the human face has a strong
curvature temporal of the eyes but not in the vertical direction. The
ovaliform
shape has different overall curvature change in the vertical and horizontal
directions. This may be accomplished while maintaining colfnearity between the
25 optical axis of the lens and the wearer's line of sight thereby obviating
the need for
axis tilt or offset.
In the bowl and ovaliform shapes, the lens element surtaces may be
described as deviating from a reference sphere defined at a sphere point of
the
surtace. The deviation may be such that the curvature of the lens element
surface
30 becomes gradually less than the curvature of the reference sphere.
Altamatively,
the deviation may be such that the curvature of the surface becomes gradually
CA 02291548 1999-12-03
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more than that of the reference sphere, especially a curvature which would
spiral
inwarclly to a central point if extended. A prolate bowl may for example
deviate
from approximately 3 to 10 mm from the reference sphere at a location 30 mm
from tho sphere point.
Preferably the lens element has a temporat region outside the visual
fixation field wherein the mean through power of the lens is gradually
reduced.
More preferably along a horizontal meridian of the lens element, the surface
powers of co-varying surfaces Increase at a location temporal of the optical
axis,
then decrease in order to bend the lens element around the face of the wearer.
Alternatively, the surface powers of the co-varying surfaces vary along a
vertical meridian and local maxima of surface power occur at locations above
and
below the optical axis of the lens.
In a preferred aspect, wherein the optical lens element is of ovaliform
shape, and Is generally spherical in a central region up to approximately 20
mm,
preferably up to approximately 30 mm, sagittal depth, the curvature of the
surface
along the vertical meridian is maintained within approximately t0.5 D of the
curvature of the surface along~the horizontal meridian. Preferably the
curvature
along the vertical meridian is maintained within approximately t0.3 D of the
curvature of the surface along the horizontal meridian.
Applicants have discovered that for such ovaliform shaped lenses the mean
surface power may be permitted to deviate from the reference surface, as
required, without generating significant surface astigmatism.
Geometric Description
The preferred bowl-like lens elements are radially symmetric and may bQ
described in cylindrical coordinates (r,6,z) where the sagittal depth 2 is a
function
of r alone;
Z(r,B) = Z(r)
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The Sag is expressed in parametric form
4
Z(t) _ ~ Az" * r2n
Zn.O
which is of the generic form used to describe a spherical surface. Asphericity
as
normally introduced in lens design is achieved by selecting the parameters A~,
to
5 deviate from the relationship that specifies a surface systematically as
spherical,
namely
~ _ (Az)3~ ~ = 2 * (~)5~ and A8 = 5 t (A2)'
For a simple sphere, A2 is defined by the dioptric base curve D of the
sphere and the refractive index n,
10 A2 = D I 2(n-1 )
In the case of a bowl-shaped element of the presets invention, however, a
target surface may be set by making this parameter itself a systematic
function of
radial distance;
A2=Po+K(r)
wherein the function K(r) is desirably continuous, with well-behaved first or
second
derivatives according to the shapes of interest.
Surtace Power
The tangential power of a surface described in this way is
T(r) _ (n-1 ) " d2lJdrz " (1+(dZldr)21'~ and
the sagittal power is
S(r) _ (n_1) * dZldr * (1+(dZldr)2]''"~ / r.
Close to the axis (small values of r), the power equations may be expanded
in the following approximate eQuations;
T~r~o~ / (n-1 ) = 2(Pa+K(r)]-r4r * dKldr and
Sir-,o> I (n-~ ) = 2f Po+K(r)J+r * dKldr
which are equal at r,= 0. Every such surtace Is therefore spherical at the
axis r =
0, unless the function form chosen for K(r) has a discontinuity at the axis,
so that
its derivative diverges.
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The two components of power change steadily away from the axis
according to the following approximately equations;
dT/drt~~~ / (n-1 ) = 4dK/dr = 6 r' dZKldrz - 24 r [Po+K(r)] and
dS/dr~r~y ~ (n-1 ) - dKldr - r * d2K/drz - 8 r [Po+K(r)]
5 For a conventional surface where K is constant or zero, the tangential
power changes three times as fast as the saglttal power. For a surtace where
the
first derivative of K dominates the surface form, tangential power changes
four
times as fast as the sagittal power,
The particular convenience of this representation is that it allows a complex
surface to be seen as the departure from a model spherical or tonic form and
sets
up the mathematics) analysis in a form which is familiar in lens design.
However it
is by no means unique and similar ~resuits may be achieved by working with a
generalised set of polynomial coefficients Az" above (including odd and even
terms).
15 It may be seen that the tangential and saglttal powers vary to first order
in
the same form as the function K(r). If a linear ramp [for example K(r) ~ r] is
used,
the surface powers rise approximately linearly. If a sinusoidal form [K(r) ~
sin
(tcrl2ro)] is used, the surface powers rise approximately sinusoidally to a
maximum
at a radial position r_- ro. In practice, K(r) needs to be vary with a r over
a finite
20 area of a lens surface, for example within a disc or radius ra, but there
may also ba
areas where it is constant, for example in the annulus beyond ro. in order to
set
the value beyond ra, one needs to compute the exact power changes out to ra
and
then fit the appropriate value of K(r) to the outer region of the lens,
smoothing the
transition If required.
25 in this way, a pair of rotationally symmetric surfaces may be described and
analysed to bound a powered lens, both surfaces being reminiscent of the form
of
a bowl. An oblate bowl has a flat central portion and becomes increasingly
steep
away from the axis, optionally blending smoothly into a sph~rical edge or
annulus.
A prolate bowl is most steeply curved at the axis and flattens out away from
it
CA 02291548 1999-12-03
12
towards the edge. To zero order, the same function K(r) Is applied to both
surfaces bounding the lens body and the result is akin to physically bending a
powered lens from one notionally spherical shape to another of quite different
shape. To achieve best optics off~axis, however, one or other surface has to
be
5 optimised by systematic adjustment of the surface parameters to achieve the
best
distribution of mean through power and astigmatism, frequently judged by
constructing blur and RMS power error plots after ray trace analysis of the
lens.
Cyl correction
Lens elements designed as bowls may be provided with one surface,
10 typically the back surface, that caries the astigmatic correction required
to
complete an Rx. The considerations explained in the Untted States patent
application 09/223006, reterred to herein, apply equally in lenses of a bowl
configuration and analogous solutions may be employed to describe the
astigmatic correction applied to the mean through power of the powered lens,
15 such as describing the surface height function of the back surface as
Z(r,8)=R(r,8)- R(r,8)=r=
and where
R(r, 8) = R(r,0) * R(r, ~ I 2)
R(r8) sin ~ 8 t R(r,n~ ! 2} cos ~ 8
is the radial curvature along the meridian at 9, and the values 8 = 0 and zr/2
20 represent the principal meridians.
Selection of surface powers
In respect of the preferred rotationally symmetrical bowl-Ilke lens elements,
ans~ty5is of selection of surface powers may be Illustrated with resort to
Morris-
Spratt diagrams, whose properties are discussed in detail in the
aforementioned
25 United States patent application serial No. 09/223,OOfi.
Preferably the bowl-like lens elements are generally spherical in a centre)
region with a diameter of at least approximately 30 rnm.
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According to the Morris-Spratt diagram, Figure 2 hereto, there is
considerable freedom of choice for front surface power available over a range
of
prescription powers in the general region where the Ostwalt and Wollaston
sections of Tscheming's ellipse merge. Generally acceptable optical
5 performance, as judged by RMS blur analysis, can be expected for designs
which
fail between the two curves A and B in Figure 3. The design scheme for lenses
described in the aforementioned United States application fail generally
within the
oval C in Figure 3. There is another systematic field extending vertically at
taro
mean through power that is exploited widely in non-prescription eyewear. The
10 optical quality of different design options may be assessed by referring to
Figure
4. In a design such as those described in the aforementioned United States
patent application serial No. 09!223006, one may elect to set all front curves
constant across the Rx range, per line D in Schema 1, However, there are
extended areas in which design parameters may be set. For example In a
15 prescription range from approximately -1.5 to +4 D [outlined area C], we
Can
select curvatures between approximately 7 and 1i3 D with absolute confidence
in
the optics of the final optimised lens design. For lenses having a bowl
format, the
curvature may vary systematically within these limits and can occur follow the
same function change for all Rx's in the field. Outlined at A is a more
desirable
20 field in which to operate, defining bowls spanning Rx's from -4 to +4 D,
while
outlined area C extends the minus range to -& D with the prospect of some
compromise in the high minus prescription range for oblate bowls. Prolate
bowls
with central curvature of 14 D or above are preferred for the high minus Rx
range.
Back Surface Curvature
25 A very important consideration with the optical lens elements of the
present
invention for wrap around applications is the matter of clearance between the
eyelashes and the back surface of the lens, especially in the direction of
forward
gaze. Lens elements having plus Rx show greatest tendency for so-called "lash-
clash", because the back surfaces tend to be flatter as the Rx becomes more
30 positive. For example a +5 D Rx made from a fens with 8 D base curve has a
back surface curve of 3 D, whereas a ~5 D Rx made from a 2.50 D base curve
CA 02291548 1999-12-03
14
lens has a back surface curare of 7.50 0.
Scheme 2 in Figure 4 shows a sequence of lines along which a design
specification would move if selected to match a criterion of constant back
surface
curve, the numbers 4, 5, 10 and 15 denoting relevant curvatures. !n this case,
5 there would be different front curves for every fix. In Scheme 3 of Figure
4, we
show as the curve a, the actual design trajectory of conventional prescription
lenses sold by Applicants and thAir competitors. The rise of front curvature
with
increasingly positive Rx is not ~ aite as fast as would deliver a constant
back
surface curve, but does approach this condition. We have found that a similar
rise
10 in front curve Is necessary for bows lenses in the plus Rx range to provide
adequate clearance around the eyes and eye leashes. Twa appropriate design
target schemes for the mean front curvature of bowl type lenses are shown as
ihs
lines ~ and y in Scheme 3 of Figure 4.
Accordingly in a preferred aspect of the present invention there is provided
15 an optical lens element series wherein each lens element includes
a first surtace; and
a second surface of complementary curvature;
at least one surface exhibiting significant deviation In curvature from a
standard optical surface;
20 the first and second surfaces in combination defining an optical zone
exhibiting substantially constant mean through power along at least one
meridian
each lens element having
a front surface varying with mean through power required; and
a common back surface.
25 Preferably each lens element in this embodiment exhibits plus power.
Preferably each optical lens element is of radially symmetric, bow!-like
shape; the varying front surface and common back surfaces being select~d by
reference to the Morris-Spratt diagrams as herein described.
Altem~atively, in this preferred aspect, there is provided an optical lens
CA 02291548 1999-12-03
1S
element series wherein each lens element includes
a first surface; and
a second surface of complementary curvature;
at least one surface exhibiting significant deviation in curvature from a
standard optical surface;
the first and second surfaces in combination defining an optical gone
exhibiting substantially constant mean through power along at least one
meridian;
each lens element having
a common front surface; and
a back surtace varying with mean through power required.
Preferably each lens element in this embodiment exhibits minus power.
Preferably each optical lens element is of radially symmetric, bowl-like
shape; the common front surface and varying back surfaces being sel~cted by
reference to the Morris-Spratt diagrams as herein described.
The front and/or back surtaces may be selected by reference to the Morris
Spratt diagrams, Figures 2 and 3 hereto, as discussed in more detail below.
The lens element series, by providing constant front and/or back surfaces,
may permit a reduction in inventories. These inventories may be further
reduced
by forming the lens element as laminate from lens wafers, as discussed below.
The lens element series may be of the type described in Intematlona)
Patent Application PCT/EP97/00105, the entire disclosure of which is
incorporated
herein by reference.
Ovaliform lens elements and spiral bands
The designer's ability to achieve very extreme shapes with rotationally
symmetric bowls is limited by the strict relationship ensuing between
tangential
and sagittal powers, This becomes more evident the higher the changes imposed
on base curvature and the higher the lens mean through power required to suit
a
CA 02291548 1999-12-03
16
prescription (Rx). There is also the practical issue that the human face has
strong
curvature horizontally in the vicinity of the eyes, but not vertically.
Attractive and
useful non-corrective sunglass lenses and shields of wrap around style
frequently
employ different curvatures vertically and horizontally. In accordance with
this
5 aspect of the present invention, it is possible to achieve this object,
again
maintaining the correct orientation of the powered lenses and providing a high
quality prescription and having clear performance gains over the prior art.
In this embodiment, the optical lens element may not exhibit visual
symmetry. Rather the first and/or second surfaces may be seen to deviate from
toric surfaces, rather than from spheres,
Z(r.4~) = Z(x. Y)
The Sag is expressed in parametric form
< a
Z(x. y) _ ~ A2n * x2rt '~' ~ B2e * y2n
2n=O 2n-0
Where, for example
A2 - Po + K(x). and B2 = Po
so that there can be produced a changing base curvature in the direction of
the Ox
axis and the curvature orthogonal to it is held substantially constant. In
this case,
for example, the Ox axis corresponds to the horizontal axis and Oy is
vertical. In
an entirely analogous way to the shape changes of a BOWL as described above,
20 an optical lens element of this form remains somewhat flat in the vertical
sense
but reaches increasingly tightly in the horizontal direction to spiral in
towards the
temples to wrap around the field of vision and sit snugly against the face.
A useful aftemative representation of the above design form is to consid~r
the surface as a distortion of a sphere, whence
Z(x,y)=R- (R-2(x))=-y=
where R is the radius of the spherical surface and z(x) is tha surface height
variation along the Ox axis.
CA 02291548 1999-12-03
17
in a still further alternative aspect of the present invention, the deviating
surface may vary in both the orthogonal and horizontal direction. If closer
fit
against the cheeks is desired, a similar but less aggressive spiral bend may
be
imposed in the vertical direction also. It is important when designing such
spiral
5 bends to ensure that the vertical curvature does not crash into the eye
brows white
attempting to splrat in to the cheeks. Similarly, it is often desirable to
avoid inward
bending of the lens at the nasal limit, to create a lens form which is
relatively flat
from the nasal limit to the line of sight, beyond which the spiral takes
effect.
This is achieved mathematically by making the lens asymmetric, as for
example if
A2 =Po, forx50
=Pp+K(x) for0<x5xo
= Po f P, for xo < x
so that the base curvature has a first lower value to the nasal side of the
optical
axis (line of direct gaze) and a second high value toward the temporal Ilmit,
with a
smoothly increasing base curvature between the two.
15 In a still further alternative approach, the lens element may be designed
so
that its curvature is lowest at the nasal limit and changes continuously
across the
Ilne of direct gaze, for example;
A2 = Po - K(x) for x 5 0
= Po + K(x) for 0 < x ~ xo
=Po+Pv forxo<x
Jn a further aspect, the optical lens element may exhibit an optical
extension beyond the central optical zone. Accordingly, In this aspect of the
present invention, there Is provided an optical lens element including
a first surface; and
a second surface,
the first and second surfaces in combination defining
CA 02291548 1999-12-03
18
a central optical zone; and
an optical Zone extension extending from the central optical zone
towards the temporal region of the lens and wherein the absolute value of
mean through power of the Inns smoothly decreases gradually along at
feast a horizontal meridian across the extension such that unwanted optical
astigmatism is significantly reduced.
Preferably the optical lens element includes
a first surface; and
a second surtace of complementary curvature
10 the first and second surfaces in combination defining a centre) optical
zone
of substantially constant mean through power;
an optical zone extension extending from the ccntrai optical none towards
the temporal region of the fens.
Preferably the first and second surfaces exhibit a substantially equivalent
change of curvature in the optical zone extension such that the mean thraugh
power remains substantially constant.
More preferably the mean through power decreases to substantially zero
across the extension.
In a preferred aspect, the cental optical zone may be corrected for forward
distance vision. The central optical zone may bear a vertical meridian,
optionally
decentred relative to the optical centre of the lens element.
The optical Zone extension of the optical lens element may also be
corrected for distance vision. The optical zone extension may take the form of
a
channel, preferably a relatively broad channel, in which the curvature
decreases
25 smoothly towards the temporal region of the lens according to a
predetermined
mathematical tarmuta. This allows the lens to wrap around the forward visual
field
whilst giving direct control over the thickness and physical reach thereof
toward
the temporal limits.
CA 02291548 1999-12-03
19
In a preferred fiorm, the optical zvna extension tapers in width to avoid
contact with the wearer's temples,
The wearer is thus provided uninterrupted ability to detect and locate
distant objects throughout the channel. Optionally, the vertical width of the
channel
may decrease in accordance with the reducing need for vertical movement of the
eyes towards the temporal extreme of vision, Preferably the lens surfaces are
each substantially umbilic over the full length of the horizontal meridian of
the lens
element, especially within the temporal extension beyond the central optical
zone.
The mathematical formula may be such as to cause increasing
accentuation of the lens curvature toward the temporal region of the lens.
Consequently the optical lens element may wrap around the forward visual field
whilst allowing ample clearance between the eye lashes or temples of the
wearer
and the inner surface of the prescription tens.
The wearer may then be provided with uninterrupted prescription cvrreotivn
for distance vision throughout the optical zone extension.
In a further preferred aspect, the second or back surface of the optical lens
element will maintain constant curvature firom the centre of the lens to its
temporal
extreme and the changes in mean through power will be achieved by alteration
of
the front curve alone.
An optical lens element according to this aspect of the present invention is
schematically illustrated in Figure 5 below.
The optical lens element has two optical zones, both corrected for distance
vision, separated spatially along the horizontal meridian of the lens, 1-1'.
The
zones comprise firstly an optical zone OZ for forward vision which is
intersected by
the vertical meridian, 2-2', which meridian may be decentred with respect to
the
lens blank. The second zone, the optical zone extension, is a broad channel in
which the curvature changes smoothly according to a predetermined
mathematical formula in order tv cause smoothly decreasing mean through power
CA 02291548 1999-12-03
toward the temporal region of the lens,
The wearer is provided uninterrupted prescription correction for distance
vision throughout the channal. Optionally, the vertical width of the channel
may
decrease compared to that of the central zone CZ in accordance with the
reducing
5 need far vertical movement of the eyes towards the temporal extreme of
vision.
In a preferred aspect, the optical lens element may exhibit mirror symmetry
around the vertical meridian, e.g, fine 2-2', in Figure 5. In this embodiment,
the
finished lens cut-out exhibits a portion of the channel CZ reaching toward the
nasal side of the lens.
10 This has several practical advantages:
1. Lens elements may be provided with generally spherical symmetry about
the optical axis through the central optical zone, allowing the identification
of a surface of rotation wholly within the body of the lens element so that
the latter may be made in two separate wafers as discussed below. The
i 5 lens wafers may be oriented by rotation with respect to each other to
provide the desired orientation for a wearer's astigmatic correction. The
final lens may be completed by laminating the two parts together.
2. Many fashionable non-prescription sunglasses use dual lenses or unitary
lenses that conform to the human face both laterally and vertically by
20 having generally cylindrical (also called toric) shape or generally conical
shape. Lens elements with mirror symmetry about the central optical zone
meridian may thus provide Rx lenses for left or right eyes from one
inventory Item for each desired Rx.
In a further preferred embodiment, the central optical zone may be further
modified to be of the progressive type.
Accordingly, in this aspect of the present invention there is provided a
progressive optical lens element including
CA 02291548 1999-12-03
21
a first and
a second surface of complementary curvature;
at least one surtace exhibiting a deviation En curvature from a standard
optical surface,
the first and second surfaces defining
a central optical zone exhibiting substantially constant mean through
power; and
an optical zone extension extending from the centre! optical zone
towards the temporal region of the lens and wherein the mean through
power of the lens decreases gradually along a horizontal meridian across
the extension;
the central optical zone including
an upper viewing zone having a surface power to achieve a
refracting power corresponding to distance vision;
a tower viewing zone having a greater surface power than the upper
viewing zone to achieve a refracting power corresponding to near vision;
a corridor of relatively low surface astigmatism connecting the upper
and lower zones, said corridor having a surface power varying from that of
the upper viewing zone to that of the lower viewing zone.
The upper viewing or distance zone may be positioned primarily above the
horizontal meridian of the progressive optical lens element.
The lower viewing or reading zone may be positioned below the horizontal
meridian of the progressive optical lens element.
A progressive optical lens element according to this aspect is schematically
Illustrated In Figure 6 below. The central optical zone CZ of the optlcaf lens
element illustrated in Figure 5 is further modified, in this embodiment, to
provide a
progressive addition lens form.
This may be provided on the front and/or back surtace providing an upper
viewing or distance zone portion DP for distance viewing primarily above the
meridian 1-1' and a lower viewing or reading zone RP, optionally horizontally
insert
CA 02291548 1999-12-03
22
relative thereto, connected to the distance portion DP by an intermediate
portion
IP or corridor of increasing lens power accessible to the wearer in doom-gaze
below the horizontal median 1-1'.
Alternatively, but less desirably, the reading portion RP may be a physically
distinct segment such as a flat top bifocal or trifocal segment giving
functionality
for near work but lacking optical and cosmetic continuity with the distance
portion
within the central zone.
In a still further aspect of the present invention, the optical lens element
may further include a nasal optical zone exhibiting a change of curvature
across
10 substantially the entire width of the zone.
The nasal optical zone may extend from the nasal side of the central optical
zone to the edge of the optical fens element. Desirably, the nasal optical
zone
may be corrected for distance vision. The nasal optical zone may take the form
of
a channel, similar to the optical zone extension.
15 More preferably, the nasal optical zone may form a broad channel in which
the curvature decreases smoothly according to a predetermined mathematical
formula.
Consequently the optical lens element may exhibit increasing forward
accentuation of the surtace curvature of the lens thus causing it to avoid
physical
20 engagement or contact with the nasal comer of the eyes or the nasal bridge.
The
remainder of the optical lens element may maintain close proximity with the
facial
structure of the wearer. The optical lens element further maintains ample
clearance from the inner surface of the prescription lens.
The wearer is provided uninterrupted prescription correction for distance
25 vision throughout both channels. Obviously lenses of this form cannot be
made
with mirror symmetry about their vertical meridians. However, the physical
shapes
they offer are especially suited to fashionable prescription visors, wrap
around
shields, or dual lens renditions of similar fashion and style objectives.
CA 02291548 1999-12-03
23
Optionally the central optical zone of the optical lens element in this
embodiment may similarly be modified according to the scheme of Figure 3 to
exhibit a local progressive addition lens surface or mufti-focal lens segment
to
provide for close or near vision.
The optical lens elements according to the present invention may
accordingly provide one or more of the following features;
1. Full-field wrap around styling with flexible choice of the general shape of
the
product to appear spherical, conical, cylindrical and the like according to
conventlonaf non-prescription sunglass lens design principles whilst
nevertheless delivering a comprehensive Rx range to suit at feast 85% of
wearers,
2. Wrap style Tenses which depart substantially from all prior shape
conventions in ophthalmic lens design principles and which represent totally
new style options fvr Tenses and frames beyond any of those employed in
y 5 the non-prescription lens category and nevertheless deliver uncompromised
prescription optics,
3. No abrupt optical changes such as change in curvature or surface slope
that may be visible to an observer, thereby allowing use of products as
clear dress syewear, sports goggles and the tike if desired,
4. "Conventional" base curves in the region of the central optical zone,
meaning that the forward base curve is near or below the Ostwald section
of Tschering's ellipse, thereby eliminating bug-eyed appearance and
facilitating correct fit of the eyewear to the wearer's pupil locations,
5. The availability of progressive addition or multifocal correction in the
central
zone by lens surface alteration functionally identical to rendering those
features to a spectacle fens of conventional curvatures near or below the
Ostwald section,
CA 02291548 1999-12-03
24
6. Mean surface curvatures consistent with known art for applying anti-
reflective coatings, hard coatings or mirrors coatings to enhance the utility
and appeal of the products, and
7. Optical design beyond the optical zone extension may preserve accurate
recognition of objects in the extreme limits where the human visual can no
longer fixate objects but nevertheless depend upon their identification to
activate physical response stimuli (especially physical movement and re-
orientation of the direction of sight).
Optionally, the central curvature may be unusually high, In which case the
i 0 design between central optical zone and optical zone extension is
configured to
decrease the curvature smoothly according to a predetermined mathematical
function and so overcome physical contact between the rear prescription
surface
and the wearer's eyes or temples.
In a further aspect of the present invention, the curve or shape of at least
one surface of the optical lens element may be varied over a significant
range,
whilst maintaining the power of the lens substantially constant.
Convention in the prior art with respect to spectacles and sunglasses is to
employ conic sections as the basis of lens design. That is, lenses have to be
overall spherical, cylindrical, conicoidal or toroidal.
20 In contrast, Applicants have discovered a fundamental principle of lens
design which allows the specification 1n the first instance of unusualty
curved
surface shapes that may fit the above definitions or desirably , which are
totally
new shapes for the category of ophthalmic products.
In particular, Applicants have shown the ability to take lenses of known,
25 e.g. spherical or aspheric form, and bend them mathematically by
approximately
15 rnm at the limit of the visual fixation field (approximately 50° off
axis, which
corresponds to about 30 mm aperture width in the horizontal direction),
thereby
wrapping around Rx corrected temporal vision, and retain mean power and near
CA 02291548 1999-12-03
horizon blur within approximately 0.25D or less.
In this embodiment, the curvatures of the first and second surtaces are
smoothly varying functions that allow the surtaces of the optical lens element
to
deviate substantially from, for example, a conventional conic section whilst
5 providing between them substantially constant mean through power through the
lens.
Thus the first and/or second conventional functions may be of a
conventional conic type, defined as a conic section of rotation, given by the
following equatian describing the sagittal depth z of the lens in terms of
distance
10 from the optical axis OZ;
Z(x, Y) 4 2rt
~~.Z f~.2r~ Y
where rz = X2 + y2,
A2=1/2R,,A4=p18R3,As=p2/tfiRb,A$=5p31128R~,
R is the radius of curvature in millimetres,
15 D = (N-1)'103 I R is surface power , or Base Curve, in Dioptres, and
N is refractive index of the lens material.
The parameter p is an aspherizing coefficient. If p=1, the surtace is
spherical. If p-0, the surface is parabolic. For negative values of p, the
surface is
hyperbolic and for positive values of p it is elliptical. Most lens designers
use the
20 representation in terms of p for initial form functions only and prefer tv
optimise a
lens design by direct manipulation of the coefficients Az~ .
According to the present invention, Applicants achieve far greater control
over surface shape than manipulation of the coefficients allows.
Applicants employ a design approach wherein the curvatures of front and
25 back are smoothly varying functions that allow the surfaces of the lens to
depart
substantially from a conic section whilst still defining between them smoothly
varying mean through power through the lens.
CA 02291548 1999-12-03
26
That is to say, the optical lens element according to the present invention is
an Rx lens of conventional form within a central aperture which is distorted
mathematically so as to change their shape, without discontinuity in mean
through
power outside that aperture.
As stated above, the conventions( mathematical formulation of the first
andlor second surfaces may be modified by addition of a variable function,
Thus
in this embodiment, the first and/or second surfaces of the optics) lens
element
may be defined by the following formula:
2(x~ Y) _ ~ ~, Az~ x 2~ ~- f (x / Ro)~ ~ ~ ~ - Bz~ ~x ~ ,~ t ~ ~, A'x~ y s~
~t n.t ".t
Where the function f (x I Ro) is a conforming function which imposes a
second conic section with coefficients B~, on the first surtace with
coefficient Az".
Preferably, the second ( rear ) surface of the lens is defined in its entirety
by the
coefficients B~,.
The lens is distorted smoothly outside a central aperture x<Ro having
f 5 asymptotically vanishing effect at x=Ro and maximum effect at the lens
edges,
utilising the conforming function:
4
,f (r / Ro) = 0.75 ( 1 - ( 1 + ~ ,R (( r-Ro) ~ 2Ro )~" ] "' } for r y Ro
~.z z"
= 0 for r < Ro
This function and both its first and second derivatives vanish at r = Ro.
.20 Starting at x = 28 mm, the front surface of the optical lens element
begins
to deviate toward the rear prescription surface, thereby reducing the rate at
which
the difference in front arid back Sag depths grows. Simultaneously, the
curvature
of the front surface increases smoothly and approaches that of the back
surface
at the outermost horizontal distances on the lens.
25 An example of such a design is given in the following Figure 7 below for a
six base lens with -3 D mean through power.
CA 02291548 1999-12-03
27
Note the existence of precise control over the surfaces and corresponding
mean through powers out to the edge of the lens element, so that the Rx power
is
constant across the aperture of the central zone and thereafter declines in a
smooth fashion without discontinuity in the rate of change of power along the
entire axis t-1'.
(n an alternative embodiment of the present invention, where an optical lens
element, for example a progressive optical lens element, exhibits unwanted
optical
astigmatism in a region of the lens, for example towards the periphery of the
lens
element, the optical zone many simply function to reduce the excessive surface
power of the fens.
As stated above, the optical lens element may be a progressive optical lens
element. The peripheral optical zone may extend generally along the horizontal
meridian of the optical lens element. The peripheral optical zone may appear
on
opposite sides of the central optical zone generally along the horyzontal
meridian.
The optical zone extension may correspondingly extend from opposite
sides of the centraE optical zone of the lens element.
The optical zone extension may be represented by a suitable mathematical
formula including a conforming function selected to substantially balance the
unwanted optical astigmatism of the peripheral optical Zone.
20 Thus, in this embodiment localised surtace correction may be applied to a
progressive addition lens element near the ends of the horizontal meridian.
For
example, prior art lenses manutactured by severe! ophthalmic lens suppliers
such
as SOla4, Essilor, and AmeHcan Optical, show intruding ridges of excessive
front
surtace power extending inward from the ends of the meridian in narrowing
wedge
25 shaped forms. The effect is that a wearer exporiencas both growing
astigmatism
and unaccommodatable power that further decreases the utility of the lens In
the
peripheral horizon.
If the front surtace Z(x, y) near the horizon of such a lens element Is
CA 02291548 1999-12-03
28
represented in a perturbed form where change is preferably applied to the
temporal periphery as follows:
zw ~ zn
Z(x,y)=Z(x,y)+f~(ylR~o)*f(xlRo)~ ~ CZ~z +~ CzrY
-i
a
where f'(ylR'o) _ ( 1 - ~R' ( y l 2R'a )2" ] '"'
--z z~
The required surface modification may be interpreted as the reverse of the
design approach in Figure 7.
Direct measurement of lens elements designed according to this aspect of
the present invention wilt provide plots of horizontal and cross powers at the
meridian, of form somewhat similar to those created in the worked example for
10 Figure T. Suitable parameters Rz", G2" and m along the horizontal meridian
may
be determined by fitting the sagittal power in that direction to an
approximately
constant value defined by the power at the optical axis of the lens.
The formulation above preferably results in substantially equal cross power
correction at the meridian to that applied horizontally. However, the
intention is to
15 perturb the lens surface only fn an area close to the meridian and matching
as far
as possible the region of excessive surface power on the progressive lens.
Accordingly, the function ~''(ylRo) is next fitted as closely as possible to
the
excess power region, attempting at alt times to make surface adjustment which
introduces no additional astigmatism to the lens surtace. Accordingly, it will
not be
20 possible to eliminate the excess surface power entirely by such localised
surface
perturbation.
In a still further aspect of the present Invention the optical lens element
may
be designed such that the first and second surfaces each exhibit a
substantially
equivalent change of curvature in the optical zone extension such that the
mean
25 through power remains substantially constant.
Accordingly, in this aspect, there is provided an optical lens element
including a first and second surface, the first surface defining
CA 02291548 1999-12-03
29
a central optical zone; and
a optical zone extension extending from the central optical zone toward the
temporal region of the lens and exhibiting a relatively smooth change of
curvature
_across substantially the entire width of the zone;
5 the second surface being defined by a complementary surface function to
substantially balance the variation in the second optical zone of the first
surface,
the mean through power of the optical lens element remaining substantially
constant as the curvatures are varied beyond the central optical zone.
In a still further embodiment, the second optical zone may include a
temporal optical zone displaced laterally along the horizontal meridian of the
lens;
and an intecmedlate optical zone extending between the central optical zone
and
the temporal optical zone.
Accordingly, in this embodiment there is provided an optics! lens element
including
a first surface; and
a second surface of complementary curvature,
at least one surface exhibiting a deviation in curvature from a standard
optical surface;
the first and second surtaces in combination defining
a central optical zone exhibiting substantially constant mean through
power; and
an optical zone extension extending from the central optics! zone
towards the temporal region of the lens and exhibiting a change of
curvature in at least the horizontal direction across substantially the entire
width of the extension.
Thus in this embodiment both front and back surfaces are bent together
beyond the central optical zone so that the mean through power remains
substantially constant and the lens bends more or less steeply. In contrast,
other
examples herein of constant power lenses apply the bending epuations from R=0
outwards.
CA 02291548 1999-12-03
If the conforming function f (y/R'o) for a general lens form of the type
described above is either a slowly varying function of y or is set to unity,
and the
back surface is described by a complementary surface function, both surface
will
move together, banding away from the mean curve of the central optical zone.
5 If required, in a still further embodiment, the optical fens element may
further include a third zone in which to thin the extreme limits of the lens
by
allowing continuous decline of mean through power.
In an alternative embodiment, Figure 8 illustrates a further example of the
design approach illustrated in Figure 7, for a six base lens of +3 D mean
through
10 power.
Again starting at x a 28 mm, the front surface of the optical lens element
begins to deviate away from the rear prescription surface, thereby reducing
the
rate at which the difference in front and back Sag depths declines.
Simultaneously, the curvature of the front surface decreases smoothly and
i5 approaches that of the back surface at the outem~ost horizontal distances
on the
lens element.
Note the extension of the temporal edge beyond the limit of a simple
spherical lens of the same power and center thickness.
In a further preferred aspect of the present invention this extension may be
20 exaggerated further by increasing the curvatures of front and back surfaces
continuously across the optical zone in addition to changing the temporal
surfaces
at the axis 1-1'. In this embodiment, the first and second surfaces of the
optical
lens element, for example the front and back surfaces, are defined by the
following formulae:
25 zt (x) = S Aa, x2" + { 1 - [ 1 + ~ N ( r / 2No )z" ] 'm~ }" S G2" x~r'
rt-1 2n
and,
z2(x)=sB~,xz"+{1-[1+~M (r/2Mo)2")'"'')* SF2"xzn
~n
CA 02291548 1999-12-03
31
- f (xl Ro)[ ~ ~ A,~" -Bm ~xz~
~_~
wherein the coefficients Az" and Bz" are the chosen front and back curvatures
at
the optical axis.
The features of the consequent lens element design are shown In Figure 9
5 as lens [2j. Note the considerable temporal reach and length of the modified
lens
element compared to the spherical lens [1] to which it corresponds.
As elaborated In W097/35224 to Applicants, the entire disclosure of which
is incorporated herein by reference, the use of tilted alignment requires that
front
or back surface be further modified with atoric correction to eliminate mean
power
and astigmatic errors.
Corrections to physical shape that are net pravlded In the physical design
are achieved by horizontal displacement of viewing axis and optical axis. This
may
require prismatic correction to front or back surfape, as elaborated in
Australian
Provisional Application PP2612 to Applicants, the entire disclosure of which
is
15 incorporated herein by reference.
The optical lens element according to this aspect of the present invention
may be mounted directly in a spectacle frame, for example of the wrap around
or
shield type. When mounted, the optical lens element may be rotated temporally
about a vertical axis through the optical centre thereof (~tilt°), or
translated so that
2Q the line of sight remains parallel to the optical axis of the lens
(uoffset"), or a
combination of both tilt and offset as described below,
Preferably, the front andlor back surtace(s) of the optical lens element
include a compound spherical design to provide the desired prescription (Rx)
in
the prescription zone. More preferably, this prescription zone will extend
across
25 the full aperture of the spectacle frames being employed.
In a further preferred aspect the optical lens element In the region from the
nasal Limit to the optical centre may be generally of the meniscus type.
CA 02291548 1999-12-03
32
Alternatively, the nasal region of the optical lens element may be biconvex in
shape. The biconvex shape is preferred, particularly for lenses of high power,
due
to its ease of mounting and improved cosmetics for the wearer.
The lens element may be rotated temporally about a vertical axis through
the optical centre thereof or the optical axis may be decentrad relative to
the
geometric axis, or the lens element may be both rotated and decentred. Where
this is required, a surface correction to at least partially adjust for
optical errors,
may be appiied. Such corrections are described in detail in lntemational
application W097/35224 to Applicants, referred to above.
Preferably the front surface is capable of being mounted in a frame of
constant design curve of between 8.0 D and 9.0 D or above.
More preferably the front surface of the lens element has a high compound
curve extending from nasal to temporal limits, but the vert~al or orthogonal
generating curve is 6.0 D or below.
15 It will be understood that such vertical curves permit the final
prescription
lenses, preferably edged lenses, to be adapted to the shape of the wearer's
face
and so locate closely in a form of the wrap-around type (a so-called
"geometrically
toric" design for which the vertical curve of the back surface is selected to
maintain
the desired mean through power or Rx correction provided by the lens. This may
20 be distinguished from a conventional "optically toric" design wherein one
surface is
rvtativnally symmetric and the other is shaped to provide the sphere and
cylinder
components of the wearer's Fix without consideration of the facial form of a
wearer).
Alt~matively the optical lens elements may be adapted for mounting in a
25 frame of the shield type.
In a still further aspect of the present invention there is provided
prescription ophthalmic eyewear, including:
a frame for holding a pair of ophthalmic fens, preferably each of which
CA 02291548 1999-12-03
33
lenses have a non-zero mean through power, wherein each lens curves around
the face of the wearer toward one of the wearer's temples in an as-wom
configuration; and wherein each lens has
a front surface with a smoothly horizontal varying surface power, and
5 a concave rear surface which clears the wearers eyelashes in the as-wom
configuration, and which has a smoothly, horizontally varying surface power
providing, in combination with the front lens surface power, a mean through
power
constant to within 10.75 D, preferably t.50 D, horizontally between the
primary line
of sight through the lens in the a~-wom configuration and a peripheral line of
sight
rotated temporally at least 40° from the primary line of site
More preferably the mean through power Is constant to x.125 D up to
40°
off axis and declining to no more than t.25 D at 50° off axis.
In a still further preferred embodiment of the present invention, there is
provided an optical lens element including:
t 5 a first tans surface having a surface power varying radially symmetrically
from a sphere point and exhibiting high levels of surface astigmatism over
substantial portions of the lens such that the lens would be unusable as an
ophthalmic lens if combined with a second standard optical surface; and
a second lens surface such that the front and rear surfaces define an
20 optical body having an approximately constant mean through power and
ophthalmically acceptable properties over said substantial portion ef the lens
element.
Preterably the lens element is a prolate bowl such that the first surface
deviates from a reference sphere defined at the sphere point by at least 3 mm
at a
25 location 30 mm from the sphere point.
in a further embodiment, the present invention may provide a single vision,
prescription ophthalmic lens element having a relatively flat face portion,
and a
temporal portion curved to conform to the h~ad of the wearer including:
a front surface with a surface power which increases in temporal din3etion
30 by at least 3.0 D; and
CA 02291548 1999-12-03
34
a rear surface with a surface power which increases in a temporal direction
by at least 3.o D so that the fens has a non-zero mean through power constant
to
within t.75 D, preferably t0.5 D, more preferably 0.25 D,
Preferably, the lens element further includes a nasal portion curved to
confirm to the bridge of the nose of the wearer.
In a further aspect of the present invention, there is provided a method of
making an optical lens element including
a first surface; and
a second surface of complementary curvature;
10 at feast one surtace exhibiting significant deviation in curvature from a
standard optical surface;
the first and second surfaces In combination defining an optical zone
exhibiting substantially constant mean through power along at least one
meridian;
which method includes
providing
a mathematical or geometrical representation, of a first surface
exhibiting a deviation in curvature from a standard optical surface; and
a mathematical or geometrical representation of a second surface of
complementary curvature; the first and second surfaces in combination
defining an optical zone exhibiting substantially constant mean through
power;
forming a lens mould corresponding to the representations of the first and
second surfaces; and
casting an optical lens element from the mould.
25 In a preferred form, when the lens element is radially symmetric, the
sagittal
depth Is given by the formula
Z(r,6) = Z(r)
wherein r, 8, Z, are cylindrical coordinates
4
Z(r) _ ~ AZ~ * r ~"
1n~
CA 02291548 1999-12-03
wherein A4 = (A2)3~ As = 2 " (A2)s, and Aa = 5 " (A2)'
wherein Az = Po + K(r)
wherein the function K(r) is continuous.
Aitematively when the lens element deviates from a tonic surface, the
5 sagittal depth is given by the fom~ula
Z(r, gyp) = Z(x, y)
wherein r, cp are cylindrical co-ordinates
Z(x, y) = ~, ~~, * x2~ + ~ Bi" * y z~
z~-o
wherein
10 Az - Pa + K(x), and BZ = Po.
In a particularly preferred form, wherein when a surface carries a surtace
correction, the sagittal depth Is given by the formula
Z(r,8)=R{r,8)- R(r,6)ZrZ
and where
R(r,0) * R(r, ~c I 2)
15 R(r,6) =
R(r6) sin 2 8 + R(r,~ I 2) cos z 9
is the radial curvature along the meridian at 9, and the values 8 = 0 and ~/2
represent the principal meridians.
In a further preferred aspect the first and second surfaces further define an
optical zone extension extending from the central optical zone towards the
temporal region of the lens; the front surface exhibiting an Increase in
curvature
towards the temporal region of the ions such that the mean through power of
the
lens reduces gradually along a horizontal meridian across the extension such
that
unwanted optical astigmatism is significantly reduced. In this embodiment, the
sagittal depth may be given by the formula
CA 02291548 1999-12-03
36
z(x,Y)=Z(x,Y)'~f'(Y~R'o)*f(xlRo)( ~ CZnxIn+~ ynYZn
rtsl na1
s
where f'(yl R'o) _ ( 1 - ~ R' ( y l 2R'o )z" 1 "'
rt=1 2n
wherein the value of parameters R~,, C~, and rn are determined along the
horizontal meridian by fitting the sagittal power to an approximately constant
value.
In a preferred aspect of the present invention, as stated above, the optical
lens element may be formed as a laminate of a back and front lens element, as
described above.
It will be understood, in this embodiment, inventories may be reduced by
providing a single front lens wafer for a range of complementary back wafers
or
vice versa. Furthermore, the need to employ the most modem lens finishing
techniques as for example to complete an Rx from a semi-finished blank is
alleviated.
It will be understood further that any feature described as being included via
the front lens element may equally be included by the back lens element and
vice-
versa.
In a further preferred embodiment, In order to permit introduction of cyfi~der
correction, the mating surfaces of front and back lens elements may be
generally
rotationally symmetric about their respective optical axes through the central
optical zone of the laminate optical article. The lens wafers may be oriented
by
rotation with respect to each other to provide the desired orientation for a
wearer's
astigmatic correction. The final fens may be completed by laminating the two
parts together.
(n a particularly preferred form, the laminate optical article may include an
inner layer providing desired optical properties of the type described In
International Patent Application PCT/AUgfi/Ofl8Q5 to Applicants, the entire
disclosure of which is incorporated herein by reference.
CA 02291548 1999-12-03
37
The optical lens element may be fomlulated from any suitable material. A
polymeric material may be used. Ths polymeric material may be of any suitable
type. The polymeric material may include a thermoplastic or thermoset
material.
A material of the diallyl glycol carbonate type, for example CR-39 (PPG
Industries)
may be used.
The polymeric article may be formed from cross-finkable polymeric casting
compositions, for example as described in Applicants' United States Patent
4,912,155, United States Patent Application No. 071781,392, Australian Patent
Applications 50581/93, 50582/93, 81216/87, 74160/91 and European Patent
Specification 453159A2, the entire disclosures of which are incorporated
herein by
refen=nce.
The polymeric material may include a dye, preferably a photochromic dye,
which may, for example, be added to the monomer formulation used to produce
the polymeric material. The variation in depth of calour may be minimised by
incorporating a pigment or dye into one or more layers of the optical article.
The optical lens element according to the present invention may further
include standard additional coatings to the front or back surface or either of
the
mating surfaces of wafers for a laminated lens, including electrochromic
coatings.
The front lens surface may include an anti.reflective (AR) coating, for
example of the type described in United States Patent 5,704,692 to Applicants,
the entire disclosure of which is incorporated herein by reference.
The front tens surtace may include an abrasion resistant coating. e.g. of the
type described In United States Patent 4,954,591 to Applicants, the entire
disclosure of which is incorporated herein by reference.
The front and back surfaces may further Include one or more additions
conventionally used in casting compositions such as inhibitors, dyes including
thermochromic and photochromic dyes, e.g. as described above, polarising
agents, UV stabilisers and materials capable of modifying refractive index.
CA 02291548 1999-12-03
38
The present invention will now be more fully described with reference to the
accompanying figures and examples. it should be understood, however, that the
description following is illustrative only and should not be taken in any way
as a
restriction on the generality of the invention described above.
EXAMPLE 1 A
Figure 7a-d illustrates a six base optical fens element according to the
present invention with mean through power of -3 D beginning with Rx lens of
conventional form within a central aperture and are distorted mathematically
so
as to change their shape without discontinuity in mean through power outside
that
10 aperture based on the following formula:
1 n 1 1n
z(x,Y)=~ ~, Axn xi~ ~-f(xlRo)j ~ E AZWBen ~x~ ~+~ ~ A~'
n~I .~l n~l
where the function f (x l Ro) is a conforming function which imposes a second
conic section with coefficients Ba, on the first surface with coefficient Az".
The
second ( rear ) surface of the lens is in this example defined in its entirety
by the
i 5 coefficients BZ".
The lens is distorted smoothly outside a central aperture x__<Ro having
asymptotically vanishing effect at x=Ro and maximum effect at the lens edges,
utilising the conforming function:
f(rl Ro) = 0.75 {1 - ( 1 + ~ R (( r-Ro) I 2Ro )Z° ] '"' } for r ~ Ro
~~Z zn
~0 = 0 for r _< Ro
This function and both its first and second derivatives vanish at r = Ra.
Figure 7 shows the application of this formulation to a six base lens of -3D
mean through power, for which the coefficients are;
AZ = 5.12' 10-3 , A4 =1.34 " 10-~ , As = 7.02' 7 0-' 2, A° = 4.60' 10-'
°, and
25 Bo ;1 , BZ = 7.68*10~ , B~ = 4.52'10'° , BB =5.33'10-", Bs = 7.86
*10'~5
Ro=30, R2=0, Ra= 1.0, R°=-2.4, R°=0, m=2.
CA 02291548 1999-12-03
39
Since it is desirable for the temporal extension to be umbilic at least on the
horizontal meridian 1-1', the coefficients A'2 which define the local cross-
curve
vertically are computed at each value of x from the changing value of the
horizontal curvature (surface power) at the axis 1-1'. The remaining
coefficients
5 A'2" are detem~ined for chosen values of the asphericity coefficient p, as
defined
above. This creates an initial surface form to be optimised in terms of
astigmatic
and mean power errors, taking into account the chosen lens tilt or offset
displacement as required to locate the lens in a frame of the wrap around
type.
The variation of A'2 and the mean through power of the lens along the axis
1-1' aro shown also in Figure 7.
Note the existence of precise control over the surfaces and corresponding
mean through powers out to the edge of the lens element, so that the f~c power
is
constant across the aperture of the central zone and thereafter declines in a
smooth fashion without discontinuity in the rate of change of power along the
entire axis 1-1'.
The purpose of the design example is to show the freedom obtained by
eliminating circular symmetry in the lens and calculating the cross curve from
the
tangential power (the focus of which falls within the plane of the horizontal
sagittal
plane). Sagittal power as would be defined for rotational symmetry, would
20 introduce very large astigmatism levels.
The designs bring the through tangential power (and as a result the through
?gittal power) smoothly to zero at the edge of the lens.
EXAMPLE 1 B
in the event that a piano extension is required, this may be achieved
without prismatic jump by extending one or ether of the surfaces from the
established boundary of piano power outward to greater radii. An example is
calculated and depicted below in Figures 8a to d. Note that the tangential
curvature and power coefficients are continuous, but the surface has a
discernible
CA 02291548 1999-12-03
kink to it. Accordingly it would be visible to an observer. However, it is
free of local
power oscillations that would emerge from a discontinuity in sagittal power if
the
lens were rotationally symmetric.
EXAMPLE 2A
5 Figure 9a-d illustrates a six base optical lens element according to the
present invention with mean through power of +3 D. The .lens element was
designed fn a sirnllar manner to that described in Example 1 except that the
coefficients are as follows:
A2 - 5.12"10~ . A4 = 1.34 * 10'' , Aa = 7.02"1 p'~2, AB = 4.60*10''a, and
10 8Q - 4.5 , 82 = 2.56"10-3 , 84 ~ 1,68 *10'a , Ba =2.19*10''3, Be = 3.59 *1
p''a
Ro=30, R2a0, R4=1, Ra=-1.9, Ra=0, m=2.
The initial form coefficients A'2 which define the local cross-curve
vertically
are computed as before at each value of x from the changing value of the
horizontal curvature (surface power) at th~ axis 1-1'. The dependence of A'z
and
15 the mean through power of the lens element at the axis 1-1' are shown also
in
Figure 9.
Note the extension of the temporal edge beyond the limit of a simple
spherical lens of the same power and center thickness.
EXAMPLE 28
20 . In this example, a plan of extension is provided in a manner similar to
that
illustrated in Example 1 B attached. The resultant optical lens element Is
Illustrated
in Fgures 10a to d below.
EXAMPLE 3A
Figure 11 illustrates a modified form of the optical fens element of Figure 9
25 wherein the temporal extension is further exaggerated by increasing the
curvatures of front and back surfaces continuously across the optical zone in
CA 02291548 1999-12-03
41
addition to changing the temporal surfaces at the axis 1-1'.
tn this embodiment, the first and sxond surfaces of the optical lens
element, for example the front and back surfaces, are defined by the following
formulae:
4
5 z,(x)=SAz"xz"+{1-(1+~N (r/2No)2"]'rt'~}* SG~nx2"
=i a~
and,
d
z2(x) = S BZ" x2" + ( ,1 - ( 1 + ~M ( r l 2Mo )Z" ] '~'~ }' S Fz" x2"
n~1 1n
- f (xl Ro)~ ~ [ Aln ~ BZn ]
wherein the coefficients A2" and Ba, are the chosen front and back base curves
at
the optical axis. In this example the base curves are B D and 3 D to give an
Rx of
+3 0;
A2 = 5.12'10's , A4 = 1.34 * 10'' , Ag = 7.02*10'~2, AB = 4.60'10-~g, and
Bo = 5.5 , B2 = 2.56*10'3 , B4 = 1.68'10'8 , B6 =_2.19*1 Oos, Be = 3.59 'i 0oa
and the coefficients G~, and F2" correspond approximately to +10D base curves,
being
G2 = 8.53'10-3 , G4 = 4.65 ' 10'' , Ge =5.08'1 p'". Gs ° 6.96'"10-
,s, arid
F2 = 8.00'10 , F4 = 4,0'10-~ , Fe x.08*10'", Fe = 6.93*10''5.
The conforming coefficients are,
Na = 75, N2 = 0.415, N4 = 0.45, N8 = ~0.72, NB = 1.50, m' = 3
'20 Mo = 77.5, MZ = 0.50, Ma = 0.40, MB = -0.72, Me = 0,
Ro = 28, RZ = 0 , R4 = 2.75 , R6 =-2.0, R$ = 0, m = 2 .
The features of the consequent lens element design are shown In Figure
11 a as lens [2]. Note the considerable temporal reach and length of the
modified
lens element compared to the spherical lens ~1] to which it corresponds.
CA 02291548 1999-12-03
42
EXAMPLE 3B
In this example, a temporal extension may be provided with the geometric
appearance of an elongated piano region, as in Fig 11a. However, this is a
feature
of the sagittal power ( Fig ~ 1 b and Fig 11 c ), not of the tangential power
defined
by the surface curvature. The tangential power becomes highly negative in the
region of the extension ( Fig 11 d ) so that if, for example a rotationally
symmetric
lens of section like Fig 11 a were to be made, it would exhibit several
diopters of
astigmatism within the extension area.
The divergence of tangential power to highly negative values may be
controlled by a lens element design which draws back the physical length of
the
temporal extension, as shown below for parametric settings;
No = 82.5, N2 = 0.415, N4 = 0.45, N6 = -0.72, N8 = 1.5 end m=3
Mo s 82.5, M2 = 0.45, M4 = 0.4, Mg -- 0 and Mg = 0
Ro = 50, RZ = 0.45, R4 = 0.4, Re = 0 and Ra = 0
When corresponding cross-coefficients are applied to the vertical curve, the
resultant lens has a central Rx region outside of which the power declines to
zero
before stabilizing at a negative value in the outer extremities of the
temporal
extension. The image in this region will be essentially free of astigmatism
and
prism displacement, but will be blurred to a greater degree than the wearer is
used to experiencing with uncorrected vision. The resultant optical lens
element is
illustrated in Figures 12a and 12b,
The most desirable optics are provided by a lens design in which the
through tangential power declines smoothly to zero at the temporal edge. The
cross-coefficients for the vertical lens surface may then be calculated as In
Example 2 to achieve the desired asymmetric lens form with minimal
astigmatism.
Such a lens form is shown below, corresponding to the parameter values;
No = 75, N2 = 0.41 S, N~ = 0.45, Na = -0.72, N8 =1.5 and m=3
Mo = 77.5, M2 = 0.5, M4 = 0.4, M6 = -0.72 and MB = 0
CA 02291548 1999-12-03
as
Ro = 33.5, RZ = 0, R4 . 0,8, Rs - -2 and Re = 0
The resultant optical lens element is illustratEd in Figures 13a to 13c.
EXAMPL.f 4A
Figures 14 and 15 illustrate an optical lens element according to the
5 pr~sent Invention with rnean Through power of a-3 D.
The lens element was designed setting up the description of front and bi3ck
surtaces of a lens so that bEnding is occurring only in the horizontal plane (
x, z );
zi(x) _ >: Az" 5(2" + [Cos(n X /2Ra )~m t E Bzn x2"
z2(X) = E GZ~ Xx" t [CoS(~ X l2Ma )]"' ' E F2" xz"
t 0 The utility of the design approach Is depicted in Figures 15(a) and 15(b),
which shows lens cross-sections in the horizontal or (x,z) plane. The section
denoted [1] has constant front base curve of 14D, that dsneted [2J is the
current
variable curvature design, and that denoted (3J has constant front base curve
of
6D. All three lenses have mean through power of +3D over wide aperture ranges.
15 The variable base design [2j has equivalent capability to wrap around to
the
temples as the high base design [1J and provides much enhanced physical space
for the human eyes to sit behind the fens. The lower curvature design ~3J
reaches
across the field of vision but has relatively much less wra~ppMg tendency. If
this is
compensated by tilting the lens off axis, the flat rear surtace will truncate
the
ZO epees available to the eyes, clashing w(th the lashos end eye lids.
The numerical value of the base curve at me central optics! zone CZ is
defined by the sum A~"+B2". and that at the temples approaches th~ Ate, value.
in
the current exempla, the curvatur~ increases from CZ towards TZ because of the
choice of negative Bz~.
25 A2=1.203'10'2:Aa-22'10'~;Ao=4.4"10-~~;Ae=4.68"10''S
Bo = 0 ; 82 - -6.82 ' 103 ; Bd ~ _3,,18 ' 10'' ~ BQ = -2.96 ' 10't ~ ;
B8 ~ -3.45 ' 10'~s
CA 02291548 1999-12-03
44
Ro=120;m=3
Go=4 ~ GZ=$.9"10~; Ga=1.65"10'x; G6=.508' 10-to; GB-.693' 10''a
Fo = 0 ; Fz = -6.26 ' 10'~ ; F4 - -7.76 * 10$ ; F6 = -2.82 ' 10''z ; Fe =
.1.2$ " 10'ta
Mo~g1
5 If, on the other hand, AZ~ and Ba, are both positive, the curvature will
trend
appositely, being highest at the CZ, decreasing smoothly toward TZ.
EXAMPLE 4B
In this example, an alternative approach to designing the lens element of
example 4A is illustrated in which the function K(r) (introduced on page 10 at
line
14 above] has a convenient form, for example defining the front surtace of a
fens
via the expression;
A2(x) = 4(x) ' (10-311, i 70)
A(x)=QQ+Qt +42'x2+Qa*xs
B2(x) s P2(x) * (10'311.170)
P(x)=Po+Pt*x+P2*x2+P3*x3
A lens designed in this way, using the parametric values;
Qo = 6 ; Qt = .9 ' 10-' ; Qa - 0.17 ' 10'3 ; Q3 a 0.225 * 10N'
Po=3;Pt=0.9"10-';P~=0.15"10-3;P3e0w10'3;xo=40
has the features represented in the following figures 16a to 16c, The design
method ie more direct and convenient than the more complex formulations of
previous examples. Note that the decline in tangentEal through power toward
the
leris extremity is not as abrupt as the changes shown in Fig 14b.
EXAMPLE 5A
Figure 17 illustrates an optical lens element according to the present
CA 02291548 1999-12-03
45
invention with mean through power of +3 D based on an asymmetrical lens
design.
An example of an asymmetric optical lens element ~~sign with continuous
and smoothly varying curvature , and consequently, constant mean through power
5 notwithst~nding the design asymmetry can be created using thp following
mathematical formulae, defining the first and second surfaces of the optical
tens
element.
z, (x) ~ ~ A~" x~" for x < 0
z,(x) = F A2" xz" + [Cos(n x /2Ro )]"' * E B2~ x2" for x > o
t o z2(x) ~~ ~ G2"xz" for x < 0
z2(x) = E Ga, xz" + [Cos(~ x /2Mo )]m * ~ F~, x2" for x > 0
while z,(y) _ Eocz" y2" and z2(Y) = Er~Yz"
where tho coefficients are as defined above in Example 4A.
The features of the resultant element lens are Illustrated in Figure 17a to
15 t 7c.
EXAMPLE SB
The alternative approach to designing the lens element illustrated Example
4B vta the function K(x) also provides an asymmetric lens far an appropriate
selection of coefficients in plus and minus ranges of x. The formulation is
shown
20 as the second design in Example 4B and yields an asymmetric lens when x is
allowed to assume negative values without correction of the odd-powered terms
on P and Q, as shown below, The primary difference between this and th6 lens
element of Figure 17 is that the tangential surtace power is locally constant
for a
region about the optical axis, whereas in the present example, it varies
2b continuously across that axis.
Both lens designs in Example 5a and b show continuous tangential power
and continuous gradient in the power profile at the optical ails, Indicating
surfaces
that are continuous to the third derivative. However, the formulation based on
K(x)
CA 02291548 1999-12-03
~6
can, if desired Invohre continuity of the surface to the second demrativs with
a
discontinuity in the third derivative. The features of the resultant optical
lens
element ere illustrated in Figures 18a to~ 18c below.
EXAMPLE 6
S Ffgura 19 illustrat~s a modified form of the optical lens element of figure
17,
The horizontal lens section of Figure 17c is reproduced in Figure 19. The
fens front and back surtaces ers [1j and (2], An 8D curvo [3j is superimposed
between nasal and temporal limits. The back surface (2j intrudes approximately
10 1.5 mm behind the inner curve (3j. This provides satisfactory clearance for
tire
eyes when the lens Is mounted in a frame involving an off-axis tilt to achieve
the
desired degree of wrap. As elaborated In W097135224 to Applicants, the use of
tilted alignment requires that front or back surface be further modified w~h
atoric
correction to eliminate mean povuar and astigmatic errors.
15 EXAMPLE 7
Figure 20 illustrates a modified form of the opt~al lens element of Figure
19.
The first and second surtaces of the optics! lens elements are defined by
the tollowing~mathematical formulee
20 z,lix)=0 forx<0
z,(x) = E Aa, x~' - [Cos(n x /2Ro )j"' " ~ Ate, x2" for x > 0
Zz(x) = Ga for x < 0
zz(x) = E Ga, x2" - (Cos(~s X /2Ma )j"' '' E Az~ x2" for x > 0
while z, (y) _ ~, Yz" and Z2(y) = Erz"y2"
25 wherein the sign of the variable functions aro reversed.
Applicants have discovered therefore that a lens equivalent to that in
Figure 19 below may be created wherein the trout surfac~ has zero curvatur~ on
CA 02291548 1999-12-03
47
the nasal side of the optical axis. That is, the front surface is identical to
its own
tangent for x ~ 0.
EXAMPLE 8
Figure 21 illustrates a modified form of the optical lens element of Figure 20
in which the surface of the Figure 20 optical lens element design is displaced
increasingly forward In the nasal region.
The first and second surfaces of the optical lens element of Figure 21 ars
defined by the following mathematical formulae:
z~(x) = [Sin(n x 12R'o )j'n~ ' ~ B'z" x~' for x < 0
10 z~(x) = F A2n xz" - (Cos(~ x /2Ro )J'" " ~ A2n x~' for x> 0
zz(x) = Go+ (Sin(~n x 12M'o )]"'~ " E B'a, xa' far x < 0
zz(x) = E G2Wc~" - [Cos(n x /2Mo )j'" ' ~ A~, xZ" for x > 0
while Z~ (y) = F.a.~r, y~' and z2(y) = EYzn
where the various coefficients are as described above, and there being
additional parameters R'o, M'o and m' corresponding to Ro, Mo and m.
According to the choice of parameters, this representation may displace the
surface of the asymmetric tangent optical lens element illustrated in Figure
20
increasingly forward in the nasal region to a maximum forward displacement at
approximately x = - t.3 R'a. When these designs are set with R'o a M'o <
PDI2.6
20 where PD is the pupilliary distance for the wearer a pair of left and right
lenses is
created with a point of mirror symmetry corresponding to the center of the
nasal
bridge.
For the lens element Illustrated in Figure 21
m'=2
R'o = M'o = 25
B'2 = -2.56'10, H'4 = 1.68"10'6, B'6 a -2.19"10'", B'e - -3.58"'10''e
CA 02291548 1999-12-03
48
EXAMPLE 9
Figure 22 illustrates a modified form of the optical lens elements of Figures
14 and 15 wherein the conforming function is of the "Witch of Agnesi" type.
The first and second surface of the optical lens element of Figure 16 are
defined by the mathematical formulae
2n ~n~ "
z,(x)=EAa,xz"+{1-[1+~R (r/2Ro) ] } EB2"x~"
n=~ in
Z2(x) = E G2n X?r ~ { 1 - [ 1 + ~ M ( r I 2M0 )2" ] .m }* ~ F2n x2"
n~ 2n
Figures 22a to 22c shows the application of this formulation to the example
worked in connection with Figures l4~and 15.
10 The coefficients A~, and Ga, are the chosen front and back base curves at
the optical axis. in this example 6D and 3 D;
A2 = 5.12*10'3 , A4 = 1.34 ' 10'' , Ae = 7.02*10-'2, Aa =
4.80"10''°, and
Go = 4 , Ci2 = 2.56'10 , G4 =1.fi8 "10'8 , Ge =2.19*10'13, G8 = 3.59 "10-~a
and the coefficients Bz~ and F2~ correspond approximately to +10D base
curves, being
B2 = 25.5"10'3 , B,, = 4.65 * 10'' , Bs X5.08*10'", f38 = 6.96"10''s, and
F2 = 24.0*10'a , F4 = 4.0*10'~ , F6 =5.08*10-p FB = 6.93*l0ns .
The conforming coefficients are,
Ro = 100, R2 = 0.415, R4 = 0.45, RB = -0.75, Ra =1.50, m = 2
Mo = 82.5, M2 = 0.3075, M4 = 0.2, Ma = -0.75, Ms = 0,
'Note the existence of precise control over the tangential powers out to the
edge of the lens, so that the Rx power is constant across the entire lens
aperture.
The tangential power is within 10.03D of target across the entire fens
aperture.
CA 02291548 1999-12-03
49
EXAMPLE 10
Figure 23 illustrates a modified form of the optical lens element of Figure 22
wherein the conforming parameters are altered without change in the curvature
coefficients, whence
Ro = 100, RZ = 0.415, Ra = 0.45, R6 = -0.75, Rg = -3.0, m = 2
Mo = 82.5, MZ = 0.3075, M4 = 0.2, M6 = -0.75, Me = 1.8,
Note the more extensive wrap achieved by changing only the parameters
Re and Me .The Rx power commences to drop from a target at about 25 mm off:
axis and has fallen by 1.2D at 30 mrn off-axis.
1 Q EXAMPLE 1 i A
Figure 24 fltustrates an optical lens element having Rx of -3 D which is
flattened by 9 D between the optical axis and a point 30 mm off-axle.
The first and second surfaces of the optics! fens element are defined by the
following mathematical representation
z, (x)=FA2"xz" + [ 1 + ~R (r/2Ro)2")'"'' FB~,x~"
-r s"
a
12(x) = E a2" xz" + [ 1 + ~ M ( r I 2Mo )z~ J -m " ~ F2~ x2"
The coefficients A2" + B~" are the chosen front curve at the optical axis
(16.6 D) and Gz" + F~,. is the back curve, in this example 19.5 D for an Rx of
-3 D;
A2 ~ 5.97*10-3 , A4 . 2.13 * 10-' , As ~ 1.52'10-", A8 ~ 1.35'10''5, and
Go =1 , G2 = 8.53'10's , G,, = 4.65 '10'' , Gs a5.08' 10'", G$ = 6.93 *10''s
The coefficients B~, = F~, correspond approximately to +10D base curves,
being in this example;
B2 = 8.1'70'3 , B4 a 5.32 * 10'~ , Ba s6.99'10'", Bs = 1.15'10''x,
and the conforming coefficients are,
CA 02291548 1999-12-03
Ro = 27.5, R2 = 0.5, Rd = -0.03, Rs = 0.03, Re = 0.08, m = 2
Mo = 30, MZ = 0.5, M4 = -0.03, M6 = 0.03, MB = 0.08,
The curve marked [1 j in Figure 24 denotes the location of the front surface
if the curvature were to be held constant at 16.5D. It is seen that the front
surtace
5 of the lenses according to the cun-ent Invention are moved approximately 7
mm
outward, opening out the lens as it wraps around the eyes from an aperture of
23
mm to 30 mm as desired. It is also seen from the Rx tangential power plot that
the mean through power error is less than 0.3 D across the lens aperture.
EXAMPLE 1'!B
10 A very similar result may be achieved in which the front curve of a
rotationally symmetric lens element is flattened from 19.5D at the optical
axis to
9.5D 30mm off axis, using the representation
Where the Aa, and B~, are themselves functions of distance Er], per the
expressions;
z~(rJ = ~ (fix l rl *r~" ~ zZ(r) _ ~, (Bs~lrJ*r~' j
R~~
PIrJ =Po + P!'r + P2~'r~ and Q('rJ = Qo + Qr'r f Q2 *~,
Azlr~ = PIrJ'10'3/1.170, A4 = (A~3, A6 = 2(A2)6, Ae=$(Aa)~, and
Bzlrl = PIrJ'10-3/1,170, B4 = (~)3, Bs = 2(82)5, Ba=5(~)'
20 in this case, both sagittai and tangential powers decrease approximately
linearly from the optical axis, toward the edge of the lens.
The results of these adjustments are illustrated in Figures 25a to b which
correspond to the selections
CA 02291548 1999-12-03
51
Po = 19.5, P1 = -0.115, P2 = 0 and Qo = 16.5, Q~ _ -0. I 15 , Q2 = -1.5'" 10'~
The variation of sag and tan powers on front and back surfaces is closely
matched, in which case both components of through power remain close to ~.OD
5 from the axis to 30mm off axis. The difference between the two measures
astigmatism, and has a local maximum of 0.27D at about 20mm off axis,
subsequently reversing sign and growing to 0.33D at the edge of the lens (30mm
off axis ).
EXAMPLE 12
Bowl shapes
Examples of some bowl-shaped lens profiles are given in Figures 26, 27
and 28 for piano lenses having a 8 D base curvature at the optical axis,
increasing
via a range of functions to 16 D toward their outer edge. These are compared
with prior art spherical surfaces of 8 and 16 D curvature (Figures a and a in
each
15 case). To achiQVe wrap of an 8 D lens around the visual field, it is
necessary to
decanter the lens so that the forward line of sight is parallel to the optfcal
axis, but
not coincident with the axis or tilt the optical axis with respect the forward
line of
sight and apply atvric corrections to shapes allow for power and prism errors
thus
introduced. A lens element of high curvature such as 16 D may be mounted so
20 the optics) axis coincides with the tine of forward gaze of each eye but
the
curvature Is so extreme that lenses cannot actually reach beyond the temples
to
enclose the visual apparatus. Bowl-shaped lens elements designed according to
this method achieve the desired physical wrap and can also be fitted with
correct
alignment of the optical axis. They also provide greater volume in which to
fit an
25 Rx power correction between the front of the lens and the approximately
spherical
volume defined by the limits of the eye lashes, this being approximately 18 to
23 mm in radius from the center of rotation of the eye. In each case, Figures
(b)
to (d) illustrate the result on the lens designs of the 3 different selected
illustrative
tangential power profiles.
CA 02291548 1999-12-03
52
EXAMPLE 13
Figures 29(a) and (b) respectively illustrate a plan, side or top view of a
10.0 D base spherical fans (prior art) and an optical lens according to the
present
invention being a 10.0 D to 16.0 D base variable curvature, rotationally
symmetric
5 spiral oblate fens corresponding to the optical lens described In Figure
2fi(d)
above.
In Figure 29 the dotted lines represent the front surfaces of the lenses end
the solid lines represent the back ledges of the lenses.
The spiral optical lens according to Figure 29(b) may be contrasted with a
comparable prior art spherical lens of Figure 29(a}. It will be noted that the
lens
according tv the present invention axhlbfts a radical shape, with
significantly
increased curvature and sagittal depth, but still pem~itting mounting in a
frame
suitable for the prior art spherical lens.
EXAMPLE 14
j 5 Spiral bends
In this example axial symmetry is not maintained and the co-varying
surfaces are treated as deviations from tvric surfaces, rather than from
spheres.
Z(r~ 9~) = Z(x, y)
The Sag is expressed In parametric form
d a
20 Z(x~ y) _ ~, ~4z" * x2" ,~,~ ~ 82~ * y=~
2n-0 2h-9
Where, for example
Az = Po + K(x), and BZ s Po
so that there can be produced a changing base curvature in the direction of
the Ox
CA 02291548 1999-12-03
53
axis and the curvature orthogonal to it is held constant. In this case, for
example,
the Ox axis corresponds to the horizontal axis and Oy is vertical. In an
entirely
analogous way to the shape changes of a bowl as described above, a lens of
this
form remains somewhat fiat tn the vertical sense but reaches increasingly
tightly in
5 the horizontal direction to spiral in toward the temples to wrap around the
field of
vision and sit snugly against the face,
Designs and optical analysis of lenses designed according to this scheme
are given in Figure 30.
Figures 30(a) to (e) illustrate the general shape of the front surface (Figure
30(a)) and back surfaces (Figures 30(b) to (e) of the lens elements configured
as
spirals. The back surfaces are respectively piano (Figure 30(6)) or have
surface
powers of -3 D, -2 D and f2 D (Figures 30(c), (d) and (e)).
In each design the curve marked (1 ) is the reference sphere and the curve
marked (2) is the spiral surtace of the lens, thus illustrating the degree of
7 5 deviation.
In Figure 31 (a) to (c), plots of the RMS power error for spiral fens designs
according to the present invention are provided which illustrate a spiral lens
design
of -3 D mean through power optimized at 0 degrees (a) a prior art aspherical
design (b) and a spiral lens optimised at 45 degrees (c).
20 In the spiral lens designs the design in the left hemisphere is a spherical
design and in the right hemisphere is a spiral design.
EXAMPLE 15
Figure 32(a) illustrates the general shape (sagittal depth) of a front surface
of a lens element according to the present invention and substantially
corresponds
25 to the surface in Figure 30(a) below. Figure 32(b) illustrates the surface
power
profile of the deviating surface in Figure 32(a). In this case the reference
sphere
has a curvature of 8 D.
CA 02291548 1999-12-03
54
The deviating front surface has a curvature of 8 D at the centre and linearly
ramps up to 12 D over 27 mm along the "x" axis. It continues with j 2 D to the
edge. The resulting curvature and sag along the x axis of the surface are
shown
in Figure 32(a) below. Also shown is the sag of an 8 base sphere for
comparison.
5 The curvature gradient increases the sag by a little over 5 mm and
increases the slope from 37 to 53 degrees at 40 mm out. The curvature in the y
direction was kept constant at 8 D. The formula used for the surface depth was
Z(x,y)=R- (R-z(x))z -yz
where z(x) is the one x direction height described above and R is the 66.25 mm
1 t) radius corresponding to 8 D. The following sphere power plot Figure 33
shows the
vertical contours for this design. The contour interval is 1 D.
All subsequent contour plots will also have a range of t40 mm, or about 5B
degrees of eye rotation.
Piano lens
7 5 To make a piano lens element, a back surface was selected that had the
same form as the front, but with the central curvature slightly adjusted to
give zero
through power. The resulting RMS power error is shown below. For comparison
Figure 34(c) is a spherical piano fens element with an 8 base spherical front
and
appropriate spherical back. The contours are at 0.1 D intervals.
20 The plots in Figures 34(a) and (c) show that the deviating surfaces cause
only a slight increase in the error at extreme eye rotation angles on the
right side
of the lens. The left hemisphere of the accentuated surface is an 8 base
sphere
so p~rforms substantially identically to the spherical lens. Even without
optimization this provides a piano lens that pertorms essentially as welt as a
25 spherical lens w'tth an 8 base front. optimization was performed by adding
some
aspherical corrections to the back surtace. The optimization procedure is
described In more detait in Example 16 below. After optimization (Figure
34(b))
CA 02291548 1999-12-03
the performance is nearly perfect everywhere except for the extreme right edge
of
the lens. Qf course optimizing the back of the lens with the spherical front
would
give the performance shown on the left, spherical half of the lens.
EXAMPLE 16
Optlrnlzed minus two lens
A lens element was designed with an Rx of ~2 D using a deviatJng front
surface. The back surface consisted of three components; 1 ) the sag of the
front
surface 2) a spherical correction to give the proper Rx at the center and 3)
an
aspherical correction surface. The aspharical correction consisted of two
separate
10 10th order polynomials, one for the left hemisphere and one for the right.
The "left
hand' polynomial coefficients were adjusted by hand to minimize the RMS power
error along the negative half of the x axis. Separate coefficients were
similarly
determined for the right half optimizing along the positive x axis. The final
correction surface used was a linear superposition of these function
multiplied by
15 smoothly varying functions of angle (A ~ tan'' (ylx)). The right side
polynomial was
multiplied by cos2A out to t90 in the right hemisphere only. This has the
affect of
giving the polynomial full influence along the positive x axis and smoothly
tapering
it to zero along the y. The opposite function, sin26 in the right hemisphere,
was
used for the Isft side polynomial so that it has full effect on the left
hemiaphen=
20 and disappears along the positive x axis.
Figure 35(a) below shows the RMS power error for a lens with the back
surface design as described above. For comparison Figure 36(b) is from a
design
with a spherical 8 base front and an optimized asphere on the back. The left
side
polynomial from the accentuated lens was used for this asphere since, again,
that
25 lens is spherical in the left hemisphere.
At first glance the result is surprising. The power error along the positive x
axis is actually smaller than that along the negative (spherical front) axis,
and
therefore also less than for the optimized asphere. Figure 36 below compares
the
RMS power error along this axis in detail.
CA 02291548 1999-12-03
56
The error at 0 degrees, along the positive x axis, is lower for the complex
lens than for the spherical lens out to well past 30 mm.
Figure 35(c) and Figure 36 also illustrate the RMS power error at 45
degrees up from the x axis for the accentuated lens. This error is
significantly
5 higher than for the aspherical case, which is constrained to have the same
error
along ail axes. Sin°A and cos49 terms were added to the angular vamping
functions for the left and right side polynomials respectively. The new
co~fficient
was adjusted of the left side funqtion to minimize the error at 45 degrees (it
does
not affect the 0 degree Error). Then the coefficient of the cos~8 term was
until the
10 errors at 0 and 45 degrees were roughly equal. The result is shown in
Figure 37
below. Surprisingly the curves cross just at the level of the optimised
asphere.
In summary, it is possible to design a back surface that gave optical
pertormance essentially squat to a lens with a spherical front of similar
complementary curvature. !t showed that the pertomZance along one preferred
15 axis could actually be made better than the equivalent spherical front -
aspherical
back lens, It suggests that the angular averaged RMS emir may not be
significantly tower than the sphere-asphere combination.
EXAMPLE 17
Bowl shapes
20 Figures 38(a)-(c) Illustrate the genera) shapes of lens elements configured
as bowls. tt will be and~rstood that lens blanks may be made in the bowl forms
shown in Figures 39(a)-(c). When edged, the bowl may have a non-circular r1m
which is adapted to the spectacle frames or mountings desired.
A spherical bowl 500 has an edge or rim 502. It will be understood that the
25 lens elements disclosed in the above-mentioned United States Application
Serial
No. 091223,006 may have the general shape shown in Figure 29(a). Such lens
elements may be characterized by a generally constant radius of spherical
curvature of 35 mrn or less, centered on the centroid of rotation 504 of the
eye In
CA 02291548 1999-12-03
57
the as wom cvndttfon. An optical axis of the lens O-O is shown intersecting
the
centroid of rotation 504. The spherical bowl 500 is radially symmetric about
axis
O-O. When wom, it may require no optical axis tilt or offset frorr~ the visual
axis of
the wearer.
5 The bowl shapes of Figures 38(b) and 38(c) are also rad(ally symmetric
about their respective optical axes O-O. Figure 38{b) illustrates an oblate
bowl
510. It is characterized by a relatively gentle instantaneous spherical
curvature at
a sphere point 512 located at about the intersection of the optical axis O-O
with
the lens element. The curvature becomes steeper radially outwardly from the
axis
10 O-O. The effect is illustrated by a reference sphere indicated in cross-
section by
dashed line 514. The reference sphere has the same curvature as the
instantaneous curvature of the lens element at the sphere point 512. As shown
in
Figure 38(b) the lens element gradually deviates from the reference sphere as
radial distance increases. F~camples of various changes in curvature which
rnay
15 be used are illustrated in Figures 26-28.
The shape of a lens made from the lens element of Figures 38 may be
characterized by a sagittal depth Z. The depth may be measured from the fronto-
parallel plane 513 (a plane perpendicular to the axis O-O at the sphere point
512)
and a point 514 which represents the most radially distant temporal edge point
of
20 the edged lens. in preferred embodiments of the present invention this
distance
may be on the order of 20 mm at a 30 mm radial distance as illustrated more
expilc~ly in Figures 2fi-28.
The value DZ represent the perpendicular distance or deviation of the lens
element from the reference sphere. It will be understood that AZ will have its
25 maximum value in the edged lens at the radial distance corresponding to
point
514, In the oblate bowl examples of Figures 26-28, aZ is shown to range from
approximately 3 to 7 0 mm from the reference sphere at a location 30 mm from
the
axis O-O.
Figure 38(c) illustrates a prolate bowl-shaped lens element 520. It is
30 characterized by a relatively steep instantaneous spherical curvature at
the sphere
CA 02291548 1999-12-03
58
point 512. In contrast to the oblate bowl of Figure 38(b) the curvature
becomes
less steep radially outwardly from the axis O-O. In a preferred embodiment,
the
bowl of Figure 38(c) may take the form of one of the lens objects described in
United States Application Serial No. 09J223,006 such that it has steeply
curved
5 spherical shape in a visual fixation region approximately bounded by a cone
whose cross-section Is indicated by rays 522 and 524. At the edge of the
visual
fixation region the curvature begins to gradually change to produce a temporal
extension, in accordance with the preceding disclosure, in the lens region
between
ray 524 and the temporal edge point 514,
EXAMPLE 18
Ovatiform tens elements and spiral bends
Figures 39(a) and (b) are, respectively, top and side views of an ovaliform
lens 600 wKh a spiral bend in the horizontal direction. The lens Is
illustrated as
having an optical axis O-O, which, preferably, is eolinear with the wearer's
visuaE
15 axis. The temporal-most edge point of the lens is indicated at 602. The
shape of
the lens in the horizontal plane of Figure 39(a) Is characterized by a spiral
bend
(l.e. a monotonic curvature increasing in at least the temporal direction).
For
illustration purposes, this curvature increase is continued beyond the lens
edge
point 602 and is indicated by the spiralling dashed line 604.
20 The eye 606 and eyelashes 608 of the wearer are also shown in Figure
39(a). A line 610 represents a cross-section of a three dimensional surface
which
contains the frontal-most possible locations of the eyelashes and lids. This
surtace 610 preferably lies completely behind the rear surface of the lens to
avoid
eyelash/lid clash.
25 Figure 39(b) is a side perspective view in partial cross-section of the
lens
600 and eye 606 of Figure 39(a). Figures 39(a) and (b) illustrate that the
vertical
curvature of lens is different than the horizontal curvature of the lens. The
lens is
not radialiy symmetric and better described as an ovaliform shape than as a
bowl.
CA 02291548 1999-12-03
59
The vertical shape of the lens 600 is characterized by bends 612 and 614
located above and below the axis O-0, respectively. The change in vertical
curvature may be tailored to avoiding eyalash/lid clash and providing
protection for
the eye above and below the optical axis 0-O.
5 It will be understood that the invention disclosed and defined in this
specification extends to ail alternative combinations of two or more of the
individual features mentioned or evident from the text or drawings. All of
these
different combinations constitute various alternative aspects of the
invention.
