Note: Descriptions are shown in the official language in which they were submitted.
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WIDE FIELD SPHERICAL LENSES AND
PROTECTIVE EYEWEAR
FIELD OF THE INVENTION
The present invention relates to improved ophthalmic lens elements and
eyewear, including prescription lenses, spectacles, sunglasses, laser
protective
eyewear, and frames, coatings and edgings therefor.
BACKGROUND
Most conventional prescription lenses have relatively flat base curves.
Such lenses provide a limited field of view due to peripheral distortion
and/or
physical size limitations. Their relatively flat shapes limit the amount of
eye
protection afforded by the lenses, particularly near the temples.
Wrap-around eyewear has been developed in an attempt to provide wider
fields of view and greater eye protection. Wrap-around design also permits
different and sometimes striking overall styles for the eyewear. However, wrap-
around eyewear is typically non-prescription. These products also typically
have
flat base curves between 6 and 10 D. Wrap (and sometimes rake) are achieved
by rotating and/or translating the optical axes of the lens in the as worn
orientation. See e.g. U.S. Patent No. 1,741,536 to Rayton; U.S. Patent No.
5,689,323 to Houston et al. This causes the line of sight of the wearer to
deviate
from the optical axis, and optical performance is often significantly
degraded.
Peripheral vision is typically poor.
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Early in the history of ophthalmic science, steeply curved prescription
lenses had been described, although not as vehicles for providing greater
field
of view or eye protection. A relationship between curvature and through power
is shown in the so-called "Tscherning's" ellipse. First described nearly 100
years ago, it attempts to identify combinations of lens curvature and lens
power
which have minimum abberation. The general form of the Tscherning ellipse is
shown in Figure 1. Figure 1 is given for assumed typical values for lens
parameters such as index of refraction, vertex distance, lens thickness, etc.
The
Tscherning ellipse retains its ellipsoid shape and inclined orientation for
various
assumed values of lens parameters, while the precise location of points on the
ellipse may change. The ellipse of Figure 1 is derived from the corrected von
Rohr equation (after Morgan) solved for point-focal (zero astigmatism)
distance
vision.
The lower portion 10 of the ellipse is the so-called "Ostwalt section"
which describes a selection of relatively flat front surfaces for lens powers
typically used in conventional prescription ophthalmic lenses. The upper
portion
12 of the curve, called the "Wollaston section", describes much more steeply
curved lenses which have never gained acceptance as lens forms, although there
are historical instances of attempts to make such objects (e.g. Wollaston
himself). See, M. Jalie, The PYinciples of Ophthalmic Leases p. 464 (4t'' Ed.
London, 1994). Because of difficulties in fabrication, such early lenses were
probably of small aperture and, consequently, perhaps, regarded as
unacceptable
for cosmetic reasons and because of their limited field of view.
Modern lenses with steeply curved front spherical surfaces have been
made for the treatment of aphakia (absence of the natural lens of the eye as
in the
case of surgical removal of the lens). The general form of these lenses is
shown
in Figure 2. See M. Jalie at p. 151. Such lenses serve essentially as an eye
lens
replacement and are characterized by great thickness and high plus power
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(greater than +5 D and typically +12 D or greater). The aperture A of these
lenses are of small size e.g. 26 or 28 mm in diameter. Typically such aphakic
lenses have a plano radial flange 14.
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.
Conventional Ostwalt section eyewear is sometimes covered, treated or
coated to provide specific reflective or anti-reflective properties. Most
familiar
are sunglasses which provided with coatings for selectively blocking portions
of
the incident light spectra. Some such lenses are designed to create pleasing
colors to an observer by selective selection or absorption of incident
spectral
wavelengths. Such coating may involve metallic mirror layers and/or stacks of
vacuum evaporated or sputter coated metal oxides. For example, coating for
sunglasses are disclosed in U.S. Patent No. 2.758,510 to Auwaxter. As another
example, certain mufti-layer antireflection coatings are disclosed in U.S.
Patent
No. 4,070,097 to Geller. See also U.S. Patent Nos. 5,719,705 and 5,959,518.
Conventional Ostwalt section lens are also sometimes specially coated to
protect
the wearer from intense ultraviolet or infrared radiation, or from laser
beams.
OBJECTS AND ADVANTAGES
OF THE INVENTION
Applicants have studied the properties of steeply curved lenses and
considered series of lenses having commonly prescribed plus or minus through
powers. Applicants observed that such lenses could, in principle, provide a
wide
field of view and eye protection. However, certain problems would interfere
with practical implementation of such wide-field lens. Generally there are
problems of fabrication and distortion, and problems of producing a range of
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common plus or minus power prescriptions with or without available common
astigmatism correction or "cyl" prescriptions.
A more subtle problem is presented by the wide range of front surface
powers which would be required to provide a range of common prescription
powers. For the lens assumptions of Figure 1, for example, the Wollaston
section would be understood to teach a variation in front surface power of
from
about 15 D to about 20 D for a product line through-power range of from +5 D
to -8 D. This corresponds to a variation in radius of front surface curvature
of
from about 29 to about 39 mm, which represents a large variation in overall
size
and shape for lenses large enough to provide a wide field of view. Such lens
cannot be fitted like panes into a single frame size, but, in fact, each
prescription
itself would dictate its own specialized frame size and style. While such
unique
styles have value, they are incompatible with providing mass-marketed eyewear
with a consistent appearance.
A broad object of the present invention is to provide ophthalmic lenses
with good vision properties.
It is another object of the present invention to provide a series of steep
base curve lenses which are readily manufactured and dispensed.
It is another object of the present invention to provide an ophthalmic lens
having good vision properties through a wide field of view.
It is another object of the present invention to provide a steeply curved
lens with reduced distortion in peripheral regions.
It is another object of the present invention to provide eyewear which
affords more effective eye protection.
It is another object of the present invention to provide steeply curved
lenses in common power and astigmatism prescriptions.
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It is another object of the present invention to provide eyewear for steeply
curved prescription lenses with a consistent appearance and frame
configurations
for a range of prescriptions.
Certain additional advantages may be realized through the teachings of
the present invention. The increased field of view allows the making of
eyewear
whose temporal edge is not visible to the wearer (apparent edgelessness). The
teachings of the present invention also permit reduction of magnification
effects
and associated distortion in some steeply curved lenses.
Other advantages involve providing the eyewear designer with options
heretofore unattainable in lens having good peripheral vision properties in
various prescriptions. These include the ability to use smaller outline
lenses,
topologically and cosmetically interesting three-dimensionally curved lens
edges
and spectacle rims, and edge thicknesses and surfaces which are more readily
hidden from view.
Other advantages involve the provision of novel sun lenses and protective
eyewear tailored to provide certain desired cosmetic properties and certain
reflectance and anti-reflectance properties.
These and other objects and advantages will be apparent from the
following text and drawings.
SUMMARY OF THE INVENTION
Generally, the present invention relates to eyewear and ophthalmic lens
elements therefor. Ophthalmic lens elements may include, according to context,
finished or edged ophthalinic lenses, semi-finished lenses, lens blanks or
molds
therefor. Also included are wafers for forming laminated lenses or lens blanks
The present invention is exemplified with reference to Figure 3 which
illustrates some geometric aspects of the steeply curved, concentric lenses of
the
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present invention. Figure 3 shows a horizontal cross-section of left and right
eyes (20 and 22 respectively). Each eye is shown having a centroid of
rotation,
24 and 26. The centroid of rotation may be understood as a volume within the
eyeball, having a diameter CD of roughly 1-2 mm, about which the eye appears
to rotate as the direction of gaze varies. As shown in Figure 3, left and
right
steeply curved lenses 28 and 30 are positioned about the eye. In the Figure,
the
optical axis of each lens is co-linear with the line of sight of each eye and
represented by the lines 32 and 34 for each eye. These lines also represent
the
z axis of coordinate systems later used in the text to describe certain lens
surfaces
(the x-y plane being normal to the plane of the Figure).
The lenses 28 and 30 are generally describable as spherical or spherically
based. In preferred embodiments, the front surface is spherical, having a
fixed
radius of less than 35 mm for all prescription values in the series. In other
embodiments, the lens is best described as having a spherical back, as
containing
a reference sphere or as lying within a defined spherical shell. In each case
the
radius of the reference sphere or shell and the location of the lens as worn
is
such that the center of the reference sphere or shell lies close to or within
the
centroid of rotation of the eye. The case in which the front surface is a
sphere
of radius R centered on the centroid of rotation of the left eye is
illustrated for
the left eye in Figure 3.
The selection of a spherical base of a given radius centered on or near the
centroid of rotation of the eye, places a constraint on the vertex distance
d,"
illustrated for the left eye of Figure 3 as the distance between the plane of
the
pupil 36 and the back surface 38 of the lens. Front surface radius and back
surface shape, in conjunction with other design parameters such as the lens
thickness and the index of refraction of the lens material determines the
optical
properties of the lens as described in detail below.
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Applicants have found that the lens design of the present invention may
be analyzed and described by a data array of a type illustrated in Figure 4.
The
diagram is called a "Morris-Spratt" diagram after two of the inventors.
In the diagram, each dot is at the center of a theoretical ray-trace plot
from a lens having properties of the grid point at the center of the dot. The
"y"
axis on the right gives the power of the front surface of the lens in diopters
(normalized for an index of refraction of n = 1.530). The "x" axis at the
bottom
shows the through power of the lens at its center. This corresponds to the
plus
or minus power prescription of the lens. For this Figure it is assumed that
each
lens is made of polycarbonate (n = 1.586) and has a center thickness of 1.8 mm
in minus power lenses, and a center thickness in plus lenses determined
individually for each prescription so that the minimum overall lens thickness
is
1 mm in the periphery of a 58 mm diameter lens blank. Each lens is positioned
relative to the eye such that the front surface is 33.1 mm from the centroid
of
rotation of the eye, which is concentric for lenses which have a front surface
power of 16.0 diopters.
At each individual grid point appears a ray trace result for eye rotation
angles up to 40 degrees. The dark area at each grid point represents the
region
of each lens that has less than 0.125 diopters of RMS power error relative to
the
prescription and allowing up to 0.375 diopters of accommodation. RMS power
error is defined mathematically below. This criterion is believed to be a good
indicator of lens performance.
The fully filled-in circles in Figure 4 represent lenses with less than 0.125
diopters of RMS power error over 40 degrees of eye rotation in any direction.
For dots with rings around them, the RMS power error rises above 0.125
diopters for some intermediate eye rotation angles then drops below that
threshold again for some small angular region.
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The elliptical outline of the locally largest dots corresponds roughly to a
Tcherning's ellipse generated for the special case of the lens parameters
selected
by applicants. Conventional wisdom dictates that the front surfaces of
spherical
lenses (lenses with spherical surfaces on the front and back) must follow
Tcherning's ellipse to produce high quality lenses. However, the Morris-Spratt
diagram illustrates that for appropriate selection of lens parameters there is
a
nearly horizontal region in this diagram where it is possible to produce
excellent
lenses. It ~S known that piano spherical lenses with high quality optics can
be
fabricated extending over a wide range of front surface curvatures (a fact
that
indicated by the vertical line of large dots near zero through power). Many
such
lenses are available in the market today. The novel idea that is illustrated
in the
Morris-Spratt diagram is that is it also possible through appropriate
selection of
lens parameters to fabricate high quality spherical lenses over a wide range
of
prescriptions using a single, steeply curved front surface or spherical
reference
surface or shell. Notice that the low RMS power error regions for lenses using
a front surface power of 16 diopters (grid points on line 40) have wide
angular
extent (nearly full or full circles) over a range of at least -6 to +4
diopters.
Over 95 % of all prescriptions fall within this range. Therefore, it is
possible to
produce high quality ophthalmic spherical lenses over a wide range of useful
prescriptions using a single, appropriately selected high power front surface
or
base curve. Moreover, as made clear by Figure 4, some small deviations from
the single power or from exact concentricity may be made while providing good
lens quality and a lens shape sufficiently consistent to use the same frame
style.
Figure 5 illustrates a series of good optical quality lenses of a preferred
embodiment of the present invention. In this embodiment, the front surface is
selected to be about 16 D ~ about 1/z D. This range lies between lines
horizontal 50 and 52. Particularly preferred embodiments provide series of
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lenses having prescription in the range -2 D to + 2 D (area 54), -6 D to +4 D
(areas 54 and 56), or -8 D to +5 D (areas 54, 56 and 58).
For comparison purposes, a portion of the Wollaston section of the
Tscherning ellipse 60 for this special case has been overlaid on the diagram
of
Figure 5. The Figure shows that the front curve and through power ranges
represented in the horizontal blocks are inconsistent with the Tscherning
ellipse
teaching which would indicate a 5 D variation in the front surface for -8 D to
+5
D through power and a far steeper curvature in the center of the through power
range.
Preferred embodiments of the present invention include series of lens
elements defined by a single reference sphere concentric with the centroid of
rotation of the eye of the wearer, where the sphere has a radius of curvature
in
the range of 25 to 50 mm, more preferably 30 to 35 mm and most preferably
about 33 mm ~ about 1 mm.
Advantageously, the series of lens elements are provided with the
appropriate prescribed power and cyl correction. In the embodiment where the
front surface is spherical, the back surface is configured to provide the
appropriate through power and cyl correction. In a preferred embodiment, a
series of lens elements would include through power through the above-
mentioned ranges in 1/4 D increments. Stock lens elements of each power would
be provided with each of various common astigmatism prescriptions, for
example, O D to -2 D in 1/4 D increments. It will be understood that because
of the spherical symmetry of the lens element, the angle of the cyl correction
can
be selected by appropriate rotation of the lens element during edging and
glazing.
Conventional astigmatism correction is based on toroid surfaces often
described in terms of principle meridia, i. e. orthogonal meridia centered at
the
optical axis of the lens, representing the locus of maximum and minimum
curvatures. Barrel toroids and donut toroids have both been used to provide
cyl
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corrections. As described below, applicants have developed novel astigmatism
correcting surfaces for steeply curved lens, which surfaces can be described
as
lying between a barrel toroid and donut toroid each having the same principle
meridia and the same power along the principle meridia. Two such surfaces are
the "all-circular meridia" surface and the "averaged-toroids" surface
described
in detail below.
The shape of lenses of the present invention will now be described. The
term "steep curvature" is used in this context to describe the overall shape
of the
lens or reference sphere or shell. In particular examples the curvature may be
quantified as an average radius of curvature of a surface or of a spherical
shell
lying inside or outside the lens or containing a surface of the lens.
Lenses of the present invention are also characterized in general shape by
their large angular field of view, often expressed as an angle between the
optical
axis and the temporal-most or nasal-most extremes of the edges. In accordance
with preferred embodiments of the present invention, the lens subtends an
angle
centered on the center of a front spherical surface, the angle being greater
than
80° and in preferred embodiments greater than 100°. It will be
understood that
such angles are indications of the field of view of the lens provided of
course that
the lens is optically usable in these peripheral regions.
The unique topological shape of the lenses of the present invention may
also be characterized by sagittal depth or "hollow" depth, which are generally
a measure of the three-dimensionality of the lens and lens edge. These depths
relate to the distance between the fronto-parallel plane of the lens and the
temporal most edge point, as described below. In accordance with preferred
embodiments of the present invention, there are provided lenses with an
average
radius of no more than 50 mm centered on the centroid of rotation of the eye
and
having a hollow depth of at least 8 mm. In a particularly preferred embodiment
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the radius of the front surface is about 33 mrn ~ about 1 mm and the hollow
depth is at least 10 mm.
The present invention also includes methods for providing prescription
eyewear. These methods employ lens elements having a steep curvature.
Preferred embodiments employ a front surface which lies within a spherical
shell
of a thickness no greater than 2 mm and a radius of no more than 50 mm. A
rear surface is formed in the lens element so that the lens element has a
prescribed through power and a prescribed astigmatism correction. The lens
element is positioned on the wearer so that the center of the spherical shell
lies
at or near the centroid of the eye by glazing into a frame having a standard
aperture corresponding to a radius of a spherical shell common to a series of
lens
elements having different through power, including the prescribed through
power. The eyewear provides the prescribed power and astigmatism correction
through the wearer's entire visual fixation field.
The present invention also includes specially designed spectacle frames.
In a preferred embodiment the spectacle frame is suitable for use with a
series
of ophthalinic lenses, each having a spherical surface of a single radius
between
25 and 35 mm, and a second surface selected to provide in conjunction with the
spherical surface various common prescriptions. In preferred embodiments the
frame is adapted to support left and right lenses on the wearer so that the
centers
of the spherical surfaces are located at or near the centroids of rotation of
the left
and right eyes, respectively. The spectacle frame may include temple pieces
and
rim portions for engaging the left and right lenses. The rim portion engaging
each lens may be formed in the shape of a closed curve lying on a reference
sphere having a radius approximately equal to the radius of said spherical
surface. In such spectacle frames, the nasal-most point and temporal-most
point
of the closed curve may subtend an arc of greater than 90 ° with a
vertex at the
center of the spherical surface.
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The spectacle frames may include a left temple piece, a right temple piece
and a nose bridge. In a preferred embodiment the nose bridge is of adjustable
length to allow horizontal adjustment of the lens separation to position the
centers of the spherical surfaces at the centroids of the eyes. In other
embodiments, rimless frames are provided with novel fitments and hinges for
supporting temple pieces, the hinges being adapted for direct attachment to
the
reference spherical surface at the temporal edges of the respective lens.
The present invention also includes novel lens edging which may be used
with steeply curved lenses particularly those having at least one spherical
surface
with a radius of curvature between about 31 mm and 33 mm.
In such a case the lens may be edged so that an edge surface of the lens
is approximately normal to the spherical surface of the lens. Eyewear made
with
such lenses may be rimless and the edge surface may be essentially invisible
to
the wearer because the edge surface lies approximately on the wearer's line of
sight when his gaze is cast in that direction. In addition, the appearance of
the
edge to an external observer is nlinitriized. Such edge surfaces may be
generated
by a mill rotated about an axis which intersects the center of curvature of
the
spherical surface. In preferred embodiments, the edge surface is cut so that
it
subtends a small arc with respect to the center of curvature of the spherical
surface where the arc lies in any plane which contains the optical axis of the
lens.
The present invention also includes methods for making steeply curved
lens elements adapted for mounting in eyewear. The method may involve
molding a lens blank having a radius of curvature along a principle meridian
of
less than 35 mm over a substantial portion of its front surface. After molding
a back surface is cut on the molded lens blank, which, together with the front
surface, provides a non-zero prescription through power. Finally, the lens
blank
is edged to provide an edged lens having a maximum hollow depth of at least ~
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mm. The cut back surface together with the front surface may be designed to
provide a non-zero astigmatism correction for the wearer.
In one embodiment, progressive surface power addition is molded on the
front of the lens blank. Alternatively, the progressive surface power addition
may be incorporated in the back surface cut in the lens blank.
Other aspects of the present invention relate to steeply curved sun lenses
such as the lenses with a spherical optical surface with a radius of curvature
less
than 35 mm described above. The suns lenses are made by coating and/or dying
the steeply curved lenses of the present invention. In a preferred embodiment,
an optical surface (for example the front surface) may be coated with a
partially
reflective dielectric stack which, in a particularly preferred embodiment, is
generally blue in color. The surface coating may be a sputter-deposited multi-
layer coating made up of alternating layers having relatively high and
relatively
low refractive indices. In particular the surface coating may be a stack of
silicon
and zirconium oxide layers, at least one of the zirconium oxide layers being
greater than about 10 nm in thickness. The coating is designed so that its
reflectance begins to decrease for incident light of a wavelength above about
4~0
nm and remains relatively low into the near infrared region.
The present invention also relates to protective eyewear including left and
right lenses each having a spherical surface. Each spherical surface
preferably
has a radius of curvature between about 31 mm and 35 mm. Frames support the
lenses on the face of the wearer so that the center of the spherical surface
of each
of the left and right lenses is located approximately on the centroid of
rotation
of the left and right eye, respectively.
Multilayer coatings may be formed on each lens for at least partially
blocking transmission to the respective eye of radiation incident on the lens.
The
layers have selected refractive indices and thicknesses for at least partially
blocking at least one selected portion of the spectrum of incident radiation.
In
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sun lens embodiments, ultraviolet light may be at least partially blocked.
Protection from laser radiation may also be provided by the eyewear in
industrial
or military settings. In this case coatings and/or dyes are provided to block
laser
light in a selected spectral range. In particular, infrared laser radiation
may be
at least partially blocked. Incident laser radiation is blocked sufficiently
to
reduce its power level to eye safe level. Off axis incident radiation is
blocked
by the stack, absorbed by a dye and/or has an optical path which does not
reach
the retina.
In the protective eyewear embodiments of the present invention,
advantageously each lens extends from the nasal margin of the orbital region
to
the temporal margin of the orbital region and from the lower to the upper
margins of the orbital region, so as to stand between incoming radiation from
all
directions which would reach the retina, while affording the wearer a wide
field
of view.
The foregoing is intended only as a summary of the invention, the scope
of the invention being determined by the literal language of the claims and
equivalents thereof.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a drawing of a Tscherning ellipse;
Figure 2 is a cross-sectional view of a prior art, high plus power "rotoid"
lens;
Figure 3 is a cross-sectional top view of a pair of human eyes, and lenses
configured in accordance with a preferred embodiment of the present invention;
Figure 4 is a Morris-Spratt diagram illustrating properties of series of
lens elements made in accordance with teachings of the present invention;
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Figure 5 is a diagram of front curves and through power ranges selected
in accordance with the present invention, with a portion of the Tscherning
ellipse
for this special case, overlaid thereon;
Figure 6(a), (b) and (c), 7, 8 and 9 are schematic diagrams illustrating
various aspects of the geometry of lens elements of embodiments of the present
invention;
Figures 10 (a), 10(b), 10(c) and 10(d) present a comparison of fields of
view for an example of a 6 base conventional lens and a lens and lens element
of the present invention;
Figures 11(a) and (b) illustrate surface astigmatism of a conventional
donut and a barrel toric when imposed on a steeply curved spherical lens
having
principle meridia shown in Figure 11(c);
Figures 12(a)-(d) are graphs of tangential and sagittal surface power as
a function of a polar angle for the donut and barrel torics of Figure 11;
Figures 13(a), 13(b), 14(a) and 14(b) are graphs of tangential and sagittal
surface power as a function of polar angle for the all-circular meridia and
the
averaged toric surfaces of the present invention;
Figures 15 and 16 are contour plots of surface astigmatism for lens
element surfaces employing the teachings of the present invention;
Figures 17(a), (b) and (c) illustrate an object grid and images thereof;
Figure 18 is a cross-sectional side view of a mold which may be used to
make lens elements of embodiments of the present invention;
Figures 19(a), 19(b), 19(c), 19(d), 19(e) and 19(fj contain plots of RMS
power error and distortion and a ray-traced grid calculated for three
conventional
low base lens and three steeply curved lens elements in accordance with the
present invention;
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Figures 20(a) and 20(b) contain plots of RMS power error and distortion
and a ray-traced grid calculated for a steeply curved lens with a conventional
toric back and for an all-circular meridia back;
Figure 21 and 22 are contour plots comparing a conventional 6D base
progressive lens, with a 16D base progressive lens in accordance with the
present invention;
Figures 23, 24, 25 and 25(a) illustrate various aspects of the appearance,
edging, and glazing of lens elements of the present invention and spectacle
frames for use therewith;
Figure 26 is a plan view of an eyewear embodiment of the present
invention;
Figure 26(a) is a detail of the embodiment of Figure 26 showing a
fitment, hinge and edged lens structure;
Figures 27(a)-(d) are illustrations of various lens edge surfaces employed
in preferred embodiments of the present invention;
Figure 28 is a pictorial view of an edged lens of the present invention
illustrating the thickness of the edge;
Figures 29(a)-(c) are illustrations of several lens edging techniques; and
Figures 30(a), (b) and (c) are is a cross sectional views of various lens
element with incident rays shown impinging their front surfaces;
Figures 31 and 32 are plots of reflection versus incident light wavelengths
for various coatings illustrating aspects of the present invention; and
Figures 33 and 34 are plots of optical density for an example of a band
block filter of a preferred embodiment of the present invention.
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DETAILED DESCRIPTION OF DRAWINGS AND EXAMPLES
OUTLINE
I. Basic Lens Geometry.
II. Correction Of Astigmatism.
III. Reduction Of Magnification Effects And Distortion.
IV. Lens Manufacture.
V. Calculated Performance Of Lens Design Examples.
VI. Glazed Lenses And Spectacle Frames.
VII. Coatings, Sun lenses and Protective Eyewear.
I. Basic Lens Geonzet~y
The basic geometry of Ienses made in accordance with the present
invention will first be discussed. Figures 6(a), 6(b) and 6(c) illustrate,
respectively, front, side and top views of an edged lens 100 in accordance
with
the present invention. The origin 102, in Figure 6(a), is the location of the
optical center of the lens and the design location of the center of the pupil
when
worn. The outline 104 of the edged lens is indicated from a front view
perspective in Figure 6(a). In Figure 6(b) the temporal edge 106 and nasal
edge
108 of the lens are shown. In Figure 6(c) the upper edge 110 and lower edge
112 of the lens are shown. In the lens embodiment of Figure 6, the front
surface
of the lens is a steep spherical curve, the right-most extent of which is
indicted
by the line 114.
The steeply spherical curvature of embodiments of the present invention
can be designed into the lens in a variety of ways. In the preferred
embodiment,
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discussed above, the front surface of the lens elements is a single radius
sphere
centered at or near the centroid of rotation of the eye. Alternatively, the
back
surface of the series of lens elements may be a constant steeply spherical
surface
and centered at or near the centroid of rotation. In these embodiments the
other
surface is of variable curvature, the curvature being selected to provide at
least
the appropriate through power for the wearer. For example, if a 16D spherical
front surface is selected for the lens element series, a rear surface with a
curvature of ZOD on its major meridian and 18D on its minor meridian may be
used to provide a -4D through power with a -2D cyl. Alternatively, if the
constant radius surface of the lens element is placed on the back surface,
then the
corresponding surface selected for the particular prescription may be placed
on
the front surface.
In other alternatives, the lens element or a surface is constrained to lie
within a spherical shell. This geometry is illustrated in Figure 7. Two
concentric spheres, 154 and 156 are defined by a center at Point P and two
radii
r1 and rZ where r2 > r1. Together, the spheres define a shell S. A lens 158 is
shown having a nasal-most edge point Q and a temporal-most edge point O. A
front surface 160 of the lens lies within the shell S.
A front surface of the optical lens element according to the present
invention may be a spherical, toric or rotationally symmetric aspheric
surface.
In order to improve vision further., the front and/or back surface of the
optical
lens element according to the present invention may deviate from a spherical
form to provide improved optical performance and/or cosmetic appearance. The
front and/or back surface, as described above, may be derived by the solution
of
the optimization problem to minimize a selected merit function representing a
measure of optical abberations seen by the wearer of the lens. The correction
may alternatively, or in addition, improve the cosmetic appearance of the lens
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element. Alternatively the surface within the shell may be a mufti-focal
progressive lens as described in greater detail below.
In a preferred embodiment, the lengths of radii rl and r2 differ by no
more than 2 mm, and in a more preferred embodiment one of the radii is about
33 mm and the difference in the lengths of the rl and r2 is about .1 mm or
less.
The front surface subtends an angle OPQ greater than 75 ° , preferably
greater
than 90 ° and more preferably greater than 100 ° . This angle is
a measure of the
wide field of view provided by the lens .
Alternatively, the lens may be defined to lie entirely within a shell
defined in a manner similar to the shell S of Figure 7, where the difference
in
length of rl and r2 is less than 6 mm.
Additionally and alternatively, the lens may be defined as containing a
portion of a steeply curved sphere such as the portion OQ of the sphere having
radius rl in Figure 7. The reference sphere may be a sphere which lies
intermediate the front and back surfaces of the lens element. In embodiments
of
the present invention this steeply curved sphere may define abutting surfaces
of
two lens wafers otherwise made in accordance with U.S. Patent No. 5,187,505
which is hereby incorporated by reference. In such a case the ophthalmic lens
or lens blank is formed as a laminate of back and front wafers. Because the
abutting surfaces of the wafers are spherical, it will be understood that the
wafers
may be rotated to achieve the desired orientation of a cyl correction applied
to
one of the surfaces. This is particularly useful in providing progressive
lenses.
Other aspects of the novel geometry of the lens elements of the present
invention are illustrated in Figure 8. A lens 170, with a steep spherical
curvature, approximately concentric with the centroid 172 of rotation of the
eye,
is shown. The fronto-parallel plane P is tangent to a spherical front surface
174
of the lens. The optical axis 176 of the lens is normal to the plane P and
passes
through the centroid of rotation of the eye. A back surface is identified by
the
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numeral 178. The lens extends in a temporal direction to a temporal edge 180.
The novel geometry of the lens is defined in part by a hollow depth ZH which
is
the perpendicular distance between the back surface 178 of the lens at the
optical
axis and the edge 180. A related dimension ZF, is the distance between the
fronto-parallel plane P and the edge 180.
It is instructive to consider the peripheral optical properties of the lenses
of the present invention, such as distortion. In such cases, reference may be
made as shown in Figure 9 to lens properties lying inside or outside of a cone
of
half angle c~ centered on an optical axis O. In Figure 9, ~ is shown as a 30
°
angle. In preferred embodiments of the present invention, the lens element of
the series has a surface astigmatism of less than .125D through a cone defined
by an angle 8 of at least 25 ° .
A lens element of the present invention may be such that for foveal vision
the RMS Power Error (defined below) is less than 3/8 D for eye rotation angles
less than 30°. Moreover the lens element may be such that for foveal
vision the
RMS Power Error is less than 1/a D for eye rotation angles greater than
30° and
less than 40 ° . Finally, the lens element may be such that for foveal
vision the
RMS Power Error is less than 3/4 D for eye rotation angles greater than
40° less
than 50 ° .
In preferred embodiments, the lens element may be configured such that
for peripheral vision where the eye is rotated and fixated at an angle of 30
°
temporally the RMS Power Error is less than 3/8 D for angles ~ 5 ° of
the fixed
position; the RMS Power Error is less than 0.65 D for angles ~ 10° of
the fixed
position; and the RMS Power Error is less than 1.0 D for angles ~ 30°
of the
fixated position.
Certain features of the present invention and a comparison with a
conventional lens are illustrated in Figure 10. Figure 10(a) illustrates a
plan
view outline selected for a conventional lens and a steeply curved spherical
lens
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of the present invention. A conventional 6 D base lens 200 is shown in Figure
10(b) and a 16 D base lens 202 in accordance with the present invention in
Figure 10(c), both having the same plan outline as in Figure 10(a). The
apparent
field of view is measured between edge rays centered on the center C of the
pupil
in the pupillary plane. The conventional base 6 lens 200 has an apparent field
of view of about 105 ° while the lens 202 has an apparent field of view
of about
130°. If a larger lens blank and plan outline are employed, a 16 D base
lens 204
of the approximate size of Figure 10(d) may be produced. Such a lens may
extend horizontally from the nasal margins 206 to the temporal margins 208 of
the orbital r egion producing an apparent field of view of about 170 °
. Such a
lens would have no temporal edge which could be seen by the wearer when
gazing straight ahead. Moreover, the temporal lens edge thickness 210, would
not be readily observed by other people because it curves in a posterior
direction, thus improving the cosmetic appearance of the lens. Finally, the
rear
surface 212 of the lens would clear eyelashes of normal length for a broad
range
of prescriptions.
IL Correction Of Astignzatisf~z
Steeply curved spherical lenses in accordance with the present invention
present particular problems when a cyl correction is part of the wearer's
prescription. Common toric back surfaces may not provide acceptable
performance. In particular, conventional torics do not work very well at the
periphery of steeply curved lenses.
The ideal back surface for a cyl Rx (neglecting things like ray obliquity)
would have a constant surface astigmatism appropriate for the prescription. No
such surface exists. Toric surfaces are a manufacturable approximation to this
ideal. There are two standard types of toric surfaces, sometimes referred to
as
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donut torics and barrel torics. Each is made by sweeping a circular arc around
a fixed axis. If the radius of the circle is smaller than its maximum distance
to
the fixed axis then it is a donut toric, otherwise it is a barrel toric. Both
types
of torics have circular cross sections along the two principal meridians.
Because
of this (and symmetry) the tangential power is correct everywhere along these
meridians. In addition each type of toric has a "preferred" meridian where the
sagittal power is correct. For the donut toric it is the lower tangential
power
meridian, for the barrel toric it is the higher tangential power meridian.
Zero
tangential and sagittal errors means the surface astigmatism is identically
zero
along the preferred meridian.
Examples of conventional torics in steeply curved lenses are shown in
Figures 11(a) and (b). Both examples have a tangential power of 18 diopters
(tea
n=1.530) on the equatorial 180 degree meridian and 20 diopters at 90 degrees,
for a nominal 2 cyl. The plots are 45 mm in diameter and have 0.1 diopter
contours. Circular principle meridional curvatures C1 and C2 are shown
pictorially in Figure 11(c). C1 and C2 intersect at a central point at the
pole P
at an angle of 90°. It will be understood that other "non-principle"
meridia may
be defined radiating from the central point.
The preferred axis is obvious from the plots of Figure 11. The tangential
and sagittal surface power for angles 0 to 90 degrees around radii 0, 10, and
20
mm from the center are shown in Figures 12(a)-(d).
From the Figures it may be noted that the donut and barrel torics both
have the correct tangential power at 0 and 90 degrees for all radii. The donut
toric has the correct sagittal power at 0 degrees, but an error at 90 degrees
that
increases with radius. The barrel toric has the correct sagittal power at 90
degrees and errors that increase with radius at 0 degrees.
There is something obviously asymmetrical about both of these torics;
they each have a preferred meridian. There are, however, functions that
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preserve the correct tangential powers along the main meridians but treat the
sagittal powers more symmetrically. One way to construct a function with the
desired tangential behavior is to force the cross section along every meridian
to
be circular. The function would have the form
~cr,e>=Rce>- Rce>2-r2
Where R(8) is the radius of curvature along the 8 Meridian, and r= x 2 +y 2 .
The values of R(0) and R(90) are fixed by the desired tangential powers and
the
powers at intermediate angles are determined by interpolating between these
end
values. A form for the interpolation comes from the recognition that the form
of the above power profiles are nearly sinusoidal. So a good first
approximation
for the R(8) would be
P(~)=P(0)+(P(90)-P(0))(1+cos28) / 2, and R(0)=(n-1) / P(8)
where P is the tangential power and n is the index of refraction needed to
convert
power to curvature. To add more control over the sagittal behavior, more
Fourier terms could be added to the interpolation. For more control over the
tangential behavior the power could be made polynominal in r. For a simple
surface no extra degrees of freedom would be required. The plots of Figure 13
show the tangential and sagittal powers as a function of angle as shown above
for
the torics. Notice that the tangential errors at intermediate angles are less
than
the donut and greater than the barrel torics. Notice also that the sagittal
power
is correct at 0 and 90 for r = 0 but starts missing on both meridia, more or
less
symmetrically, as the radius increases. For a surface that is not axially
symmetric there is a weak contribution from the angular behavior on the
tangential curvature. This is because the normal vector is not in the same
plane
as the circular cross section.
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Another way to produce an "unbiased" cyl correction surface is to
average the conventional donut and barrel torics together. Doing this gives
results that are similar to those for the surface constructed from circular
meridians. The angular plots for the averaged torics are shown in Figure 14 in
which z = aBZB + (1-aB)ZD where Z is the surface height of the lens, ZB is the
surface height of a conventional barrel toric; ZD is the surface height of a
conventional donut toric; and a$ is a weighting factor such that 1 > a$ > 0.
Figure
14 shows the specific case for a$ = 0.5.
It is difficult to tell from the plots of Figure 14, but there are significant
differences in the angular behavior of the tangential and sagittal powers for
these
circular meridia and averaged toric surfaces. The contour plots of Figure 15
compare the surface astigmatism of the averaged torics and the circular
meridian
functions. The plots have the same 0.1 diopter contours and 45 mm diameters
as before.
The astigmatism behaves more simply for the circular meridian surface
than for the averaged torics . To show the effect of adding Fourier terms to
the
angular interpolation, one extra coefficient can be adjusted to "round out"
the
elliptical looking contours. The results are shown in Figure 16. Note that the
meridians still all have circular cross sections, only the angular
interpolation has
been changed slightly.
The circular meridia and average toric surfaces have additional properties
of note. The surface astigmatism of the surface at any point off the principle
meridia is less than the larger of the surface astigmatism of the barrel toric
or the
donut toric at the same point. In addition, the average toric or circular
meridia
surfaces lie between (have an intermediate Z value) between the barrel toric
and
the donut toric of the same prescription.
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While the foregoing torics are preferred for use as back surfaces for
lenses of preferred embodiments of the present invention, it is possible to
use
conventional torics or generalized torics to provide for the lens.
Alternatively surface correction for lens elements of the present invention
may be provided by producing a back surface in accordance with the following
mathematical description of a symmetric polynomial:
n k
x k~~Y ~ ;
k=0,2... ,j=0,2... k-.7oJ
A number of measures of optical aberrations of a lens are defined as
follows:
+s
Mean Power Error (MPE) _ 11 22
2
1/2
Cyl Error - ( ( sll ~2z) 2+4 s12) )
~2 +2 ~2 +~2 1/2
RMS Power Error (RMS blur) - 11 12 22
2
_' 1 x/2
(mpe) 2+ 4 ( cy1 error) 2
where E is the focal error matrix and may be written
s ~
11 12
21 22
where Elz = ~2~ by the choice of the orthonormal basis set.
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Where these terms are calculated by considering specifically the optical
properties of the lens, the terms Optical Mean Power Error, Optical Cyl Error
and RMS Optical Power Error apply.
The merit functions) may be selected from the following functions
depending on the specific application of the optimized lens:
Ml - ~ (rms blur) a
a
M2 - ~ l(mpe) z+ ( cyl error) z'e
M3 ~ ~ 6 (mpe) z+ ( Cyl error) z
a
horizontal vertical obl ue
M4 ~ ( X11) e+ ~ ( ~zz) e+ ~ (mpe) a
MS - ~ (mpe) z+ 16 ( cyl error) z
a
where summations are over a number of eye rotations 8.
In the case of M4, there are different blur measures used depending upon
whether the sample point 8 represents a horizontal, vertical, or oblique
rotation
from the "straight ahead" position. This mode may provide some generalization
of the aspheric "minimum tangential error" design strategy.
The modes M3 and M5 represent "minimum astigmatic error" and
"minimum mean power error" strategies respectively.
In a still further embodiment, a term may be included in the merit
function that represents the cosmetics of the lens. For example, instead of
using
M alone, a modified merit function may be defined by
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V
M *=M+~leAz a
r1 r
where rye denotes the number of sample eye rotations 8 considered in M,
r is a specified lens radius, and V is the lens volume out to the radius r.
The
factor ~, is seen to be weighting on the average lens thickness.
III. Reduction Of Maghificatio~a Aud Distortion
Spectacle lenses either minify or magnify objects viewed through them.
This occurs because the principal planes of conventional spectacle lenses are
located close to the lens and do not coincide with the entrance pupil of the
eye.
In general, plus power lenses make things look bigger, and minus power lenses
make things look smaller. Magnification also changes the perceived direction
of objects in the peripheral field, and causes the apparent field of view to
differ
from the true field of view through the lens.
In addition to magnification, spectacle lenses also distort the shape of
objects viewed through them. For an eye looking straight ahead, minus lenses
create so-called "barrel distortion", in which rectangular objects appear
compressed in the periphery so that squares look like barrels. Conversely,
plus
powered lenses create "pincushion distortion" , which stretches out the
corners
of the squares.
The two effects add together to degrade the perception of object size,
shapes, and position. Textbooks on ophthalmic optics teach that it is not
practical to correct distortion in spectacle lenses, and are silent about the
desirability of reducing magnification effects. Yet one of the touted visual
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advantages of contact lenses is that the close fit of the lens to the eye
reduces
magnification and distortion effects, allowing a more natural correction of
vision.
It would seem desirable to reduce the magnification and distortion of
spectacle
lenses if it is possible.
For a distant object, the magnification effect is defined by the following
equation:
Relative Spectacle Magnification _ 1 1
( 1-dFy ) tFl
1-
n
where d (d,, in Figure 3) is the distance from the back surface of the lens to
the
entrance pupil of the eye, F~ is the back vertex power in diopters, t is the
thickness in meters, n is the index of refraction, and Fl is the front surface
power
in diopters.
The part of the equation inside the first set of brackets is often called the
"Power Factor" because it shows how much magnification is due to the lens
power. If d could be equal to zero, then the power factor would be equal to 1.
In other words, a lens in contact with the eye would have very little
magnification due to its power, and this is what happens with contact lenses.
Spectacle lenses are positioned away from the eye to avoid contact with the
eye,
eyelids, or eyelashes so this term is greater than 1 for plus lenses and less
than
1 for minus lenses. In other words, plus power spectacle lenses tend to
magnify
and minus lenses tend to minify. According to context, the term "magnification
effects" are used to describe both magnification and minification.
The part of the equation inside the second set of brackets is usually called
the "Shape Factor" because it shows how magnification varies with the
thickness
and curvature of the lens. If lenses had no thickness, then t would equal zero
and this term would be equal to 1. The ideal "thin lens" of third order optics
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would not have any magnification effect due to shape. Contact lenses come
close
to approximating this condition because they can be made extremely thin.
Spectacle lenses do have a significant thickness to avoid breakage and always
have positive front surface curvatures, so this term always is greater than 1.
In
other words, all positive meniscus spectacle lenses tend to magnify due to
their
shape.
To eliminate magnification effects, the equation must be set equal to 1,
so the product of the power and shape factors must be equal to 1. Since both
the
power factor and shape factor in plus lenses are each greater than one, their
product cannot equal 1, so no plus lens in a positive meniscus form can ever
be
free from magnification. On the other hand, minus lenses have power factor
less
than 1 and a shape factor greater than 1, so it is possible to force these
factors
to cancel.
To do this, we must solve this equation for unit magnification. After
doing so we get the following relationship:
n a' F
t _ Fs ( s -dF~) (1)
This equation specifies the lens thickness which eliminates spectacle
magnification effects. It works by placing the second principal plane of the
lens
at the entrance pupil of the eye. Achieving this in a practical thickness
requires
two things: a minus lens power and very steep curves.
Distortion
According to third order theory, distortion can only be eliminated within
lenses so steeply curved as to be impracticable. Jalie, M. The Principles of
Ophthalmic Lenses 4t'' Edition p. 461.
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Third Order theory in fact requires back surface curves in excess of 35
Diopters, which would be nearly concentric around the entrance pupil of the
eye;
such surfaces indeed would be impractical. A truly concentric lens design
which
has both surfaces concentric around the entrance pupil of the eye would have
no
distortion at all because the symmetry of the lens would ensure that all
bundles
of rays from oblique objects would encounter the same surface slopes as do
those
from central objects. While concentricity about the entrance pupil does
require
extremely steep curves, we have found that somewhat flatter curves also
drastically reduce distortion when they are combined with lenses which have
principal planes located close to the entrance pupil. This occurs with lenses
designed to reduce minification in minus power lenses, and result in lenses
which
are more nearly concentric around the centroid of rotation of the eye.
In fact, it is highly desirable to make the lens concentric about the center
of rotation of the eye, because this will improve the symmetry of the lens for
the
eye as it turns to view objects in the peripheral field, resulting in improved
resolution. If we strictly require that one surface of the lens be concentric
around the centroid of rotation of the eye, we can derive a thickness which
virtually eliminates distortion. In this case, a special form of the equation
for
lens thickness is required.
For example, in a lens which has its front surface concentric around the
centroid of rotation of the eye, we can solve for t in terms of the radius of
the
front surface, fitting distance, the index of refraction, the back vertex
power, and
the distance of the entrance pupil from the center of rotation of the eye. In
this
case
t- f F Ir -K +k ~-ll+ F (r -K +k ) -1 2 -4FZd k
I v1 1 a 1 v 1 a 1 v f 1
2F
v
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where
nr
s
s n-1
is a lens shape factor, r1 = radius of front surface; df = distance from the
front
lens surface to the plane of the entrance pupil; and Ke is the distance from
the
center of rotation of the eye to the entrance pupil of the eye as shown in
Figure
3.
Figures 17(a)-(c) show the advantage of this kind of design. Figure 17(a)
is a representation of a large grid to be viewed from a great distances such
that
the grid extends 45 degrees to the left and right of the viewer. Figure 17(b)
is
a calculated image of what a person wearing a conventional -5.00 D lens would
see: the grid appears smaller and distorted in shape. Figure 17(c) shows the
calculated image seen by a person wearing a lens designed to eliminate
distortion
according to the previous equations. The image appears almost identical to the
original object.
IV. Lens Manufacture
Ophthalmic lens elements according to the present invention may be
formulated from any suitable material. A polymeric material may be used. The
polymeric material may be of any suitable type. The polymeric material may
include a thermoplastic material such as polycarbonate or thermoset material
such as diallyl glycol carbonate type, e.g. CR-39 (PPG Industries) may be
used.
The polymeric article may also be formed from cross-linkable polymeric
casting compositions, for example as described in United States Patent
4,912,155
or United States Patent Application Serial No. 07/71,392, the entire
disclosures
of which are incorporated herein by reference.
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The polymeric material may include a dye, including, for example, a
photochromic dye, which may be added to the monomer formulation used to
produce the polymeric material.
The optical lens element according to the present invention may further
include standard additional coatings to the front or back surface, including
electrochromic and/or liquid crystal 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, the entire disclosure of which is incorporated herein
by
reference. To make sun lenses or to provide a desired cosmetic effect, a
partially reflective coating may be applied to the lens. The front lens
surface
may alternatively or additionally include an abrasion resistant coating, for
example of the type described in United States Patent 4,954,591, the entire
disclosure of which is incorporated herein by reference.
The front and back surfaces rnay further include one or more surface
treatments conventionally used in casting compositions such as inhibitors,
dyes
including thermochromic and photochromic dyes, fox example as described
above, polarizing agents, UV stabilizers and materials capable of modifying
refractive index.
Figure 18 illustrates a mold suitable for making a lens element in
accordance with teachings of the present invention. The mold includes a front
mold portion 300, a back mold portion 302 and closure flange portion 304. The
lens element may be formed in the cavity 306 between the mold halves by
injecting liquid lens matexial through port 308. Air escapes through port 310.
When the lens element is hard, the mold halves are separated. It will be
observed that the lens element as it leaves the mold will have a radial flange
312,
which may be removed in later processing.
Processes and apparatus for molding the lens elements of the present
invention are described in U.S. Patent Application Serial Number 09/658,496 to
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Kingsbury et al. filed September 8, 2000 entitled "PROCESS FOR MOLDING
THERMOPLASTIC LENSES AND STEEPLY CURVED AND/OR THIN LENSES
PRODUCED THEREBY", the contents of which are hereby incorporated by
reference in its entirety.
V. Calculated Performance Of Leas Design Exaf~aples
Example 1
Table 1 shows a comparison of the calculated performance of a
polycarbonate lens made in accordance with the present invention and a
conventional low base curve lens.
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Concentric Conventional
form
Index of refraction 1.586 1.586
Power -3.00 -3.00 diopters
Thickness 2.0 2.0 in mm
Front Surface Curvature16.00 4.00 diopters
(1.530
tooling index
Front Surface Radius 33.1 132.5 mm
Optical power of front 17.7 4.4 diopters (higher
surface due to
1.586index)
Paraxial Magnification 0.97 0.96
Apparent field of view 130 105 in degrees,
for the edge
outline of Figure
10(a)
Optical Values at 30
degree eye
rotation:
Distortion -1.10 % -3.10
Astigmatism 0.02 0.17 diopters
Mean Power Error 0.07 0.025 diopters
RMS Power Error 0.07 0.09
Chromatic Abberation 0.11 0.16 prism diopters
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Example 2
Figure 19 illustrates a calculated comparison between a series of steeply
curved spherical lens elements of -6 D, -3 D and +3 D power [Figures 19(a),
(c) and (e), respectively] with corresponding low base curve Sola Perma-
Poly''M
stock lenses [Figures 19(b), (d) and (f), respectively] .
The steeply curved spherical lens elements have essentially identical,
spherical front surfaces of 16D as shown in the lens cross sections 400.
Generally, the steeply curved spherical lens elements provide superior
peripheral
distortion. The lenses of Figures 19(a) and 19(c) also exhibit reduced RMS
power error in the minus prescriptions.
Example 3
Figure 20 illustrates a calculated comparison between two steeply curved
spherical lens elements with a 16D front surface -3 D through power and a back
surface cyl correction of -2.
The lens of Figure 20(a) has a conventional donut torus back; the lens of
Figure 20(b) has an all circular meridia back of the type described above. The
latter exhibits superior RMS power error and somewhat improved distortion.
Example 4
The final set of examples (Figures 21 and 22) are a calculated comparison
between a conventional base curve progressive lens and a progressive lens
according to the present invention.
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Figure 21 compares distance vision properties of a conventionally curved
Sola XL progressive lens, with a lens in which a similar progressive form is
placed on a lens element with steeply curved (16D) base curve.
Figure 22 compares near vision properties of the Sola XL progressive
lens with the steeply curved lens of Figure 21.
Generally speaking, progressive lenses made in accordance with the
present invention are characterized by a steeply curved reference sphere or
spherical shell approximately concentric with the centroid of rotation of the
wearer in the as worn position. Such lenses have an upper viewing zone for
distance vision; lower viewing zone, having a greater power than the upper
viewing zone for near vision and an intermediate zone connecting the upper and
lower zones, with power varying between the upper and lower zones, including
a corridor of relatively low surface astigmatism.
In one embodiment the steeply curved reference sphere corresponds to the
front surface of the central part of the upper viewing zone. In another
embodiment, the progressive surface is on the front surface of the lens and
lies
within a steeply curved spherical shell of thickness less than about 2 mm. In
both embodiments the radius of curvature of the shell or reference sphere may
be less than 50 mm, preferably between 30 and 35 mm, most preferably about
33 mm ~ about 2 mm. Suitable front surface designs for progressive lenses are
illustrated for example in applicant's patent application S.N. 08/782,493
filed
July 10, 1997, now LT.S. Patent No. 5,861,935.
VL Glazed Lenses Ahd Spectacle Frames
Spectacle frames for use in the present invention are adapted to hold
lenses of the present invention in the approximate positions shown in Figure
3.
The spectacle frame may be rimless, partial rim or full rim.
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In preferred embodiments the lenses, when mounted in the spectacle
frame, exhibit essentially no tilt or wrap angle. The spectacle frame may
include
an adjustable mechanism for altering the positions of the optical axes of the
lens
to correspond to the axes of straight-ahead vision of the wearer.
Figure 23 is a perspective view of eyewear 400 including lenses 402 and
404 and spectacle frames of the present invention. The lens shape creates a
cosmetically interesting object. The spectacle frame in Figure 23 is shown
with
a rim portion 406 and temple pieces 408 and 410. The rim of the spectacle
frame surrounding each lens is adapted to correspond to a closed curve lying
on
or near the steeply curved reference sphere of the lens. Because of the
consistency of this curvature through a range of prescriptions, a single frame
or
frame design may be fit to any prescription in the range.
Figure 24 is a side elevation of the eyewear of Figure 23 on the face of
the wearer. The Figure illustrates another aspect of the visual appearance of
the
eyewear due to the steep curvature of the lens and the complex three-
dimensional
shape of the lens edge. The Figure also illustrates that a lens of relatively
small
size provides a wide field of view and good eye protection.
Figure 25 is a front pictorial view of eyewear embodiment 412 according
to the present invention illustrating certain mechanical aspects of the
invention.
The spectacle frames of the embodiment of Figure 25 include a nose bridge 414
and hinged temple pieces 416 and 418. Together these components comprise a
three-piece, rimless spectacle frame.
The temple pieces 416 an 418 include hinges 420 and 422, and mounting
tabs 424 and 426. In a preferred embodiment, the tabs 424 and 426 are surface
mounted onto the spherical front surfaces of the lenses. It will be understood
that these mounting surfaces will have a consistent position and angular
relation
with respect to the frame, regardless of the prescribed through power and cyl
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correction of the lens. In a similar fashion, tabs 428 and 430 of the nose
bridge
414 may be surface mounted on the respective front surface edges of the lens.
The nose bridge 414 is shown in cross-section in Figure 25(a).
Advantageously, the nose bridge may be made an adjustable length to
compensate for different pupillary distances (PD in Figure 3) commonly found
in different wearers. This adjustable feature permits the optical axes of the
lenses to be aligned with the axes of vision of both wearer's eyes. One
mechanical structure suitable for producing this adjustable feature is shown
in
Figure 25(a), it being understood that other combinations of moving or
flexible
structures could be adapted to the purpose. In the embodiment of Figure 25(a),
the tabs 428 and 430 are each carried by members 432 and 434, respectively,
which are inserted into opposite ends of a tube 436. Set screws 438 and 440
hold the members 432 and 434 in position. The set screws may be loosened to
permit adjustment of the length of the nose bridge by sliding the members 432
and 434 within the tube to different positions.
Figure 26 is a plan view of an eyewear embodiment 500 of the present
invention. The eyewear is of the rimless type. A left lens 502 and a right
lens
504 are steeply curved, edged lenses. In preferred embodiments, they each have
an anterior optical surface 506 which is generally spherical with a radius of
curvature less than 50 mm and preferably less than 35 mm, as discussed above.
In the as worn position, the center of the radius of curvature of the
spherical
surface of each lens is positioned approximately at the centroids of rotation,
PL,
PR, of the respective eyes of the wearer.
Lenses 502 and 504 are joined by a nose bridge 508 for supporting the
lenses on the face of the wearer. Left and right temple pieces, 510 and 512
are
provided and attached to the temporal edges of the left and right lenses,
respectively. A preferred manner of attachment will now be discussed in
connection with Figure 26(a).
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Figure 26(a) is a detail of the embodiment of Figure 26 showing the
attachment of the right lens 504 to the right temple piece 512 by means of a
right
fitment 514 and hinge 516. In a preferred embodiment, the right fitment is
arcuate and generally continues along the spherical curvature of the anterior
surface of the lens 504. A nasal portion 518 of the fitment 514 overlies the
front
surface of the lens. A threaded fastening system such as bolt 520 and nut 522
rnay be used to hold the fitment in position on the lens. In a preferred
embodiment, an edge notch 524 in the lens may be provided to receive a
locating
protrusion 526 of the fitment to further secure the fitment and impede its
rotation
about a principal axis 528 of the bolt 520. In a preferred embodiment, the
principal axis 528 of the fastener lies on a radial line intersecting the
center of
curvature of the spherical surface of the lens.
A preferred edging of lens elements of the present invention is also shown
in detail in Figure 26(a). As shown, an edge surface 530 of the lens lies
approximately along a radial 532 of the spherical surface of the lens. In the
as
worn position this radial is centered approximately in the centroid of
rotation of
the eye, PR. This edge configuration makes the lens edge essentially invisible
to
the wearer, because the edge surface is viewed edge-on by the wearer when the
eye rotates so that the angle of regard is directed toward the lens edge. In
addition, the edge surface is reduced in size and minimized in appearance to
an
external observer. Particulars of this edging are illustrated in Figures 27
and 28.
Figures 27(a)-(d) illustrates several different edge contours which lie
approximately along a radial, R, of the spherical surface 534 of the lens. As
shown in the Figures, the cross section of the edge surface is approximately
perpendicular to a tangent T of the spherical surface at its perimeter, i.e.,
the
line of slight is approximately coplanar with the edge surface.
In Figures 27(a)-(d) the cross section of each edge surface lies within a
small angular range 0 with respect to the centroid of rotation P of the eye
and
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is therefore nearly invisible to the wearer. In the example of Figure 27(a),
the
cross section of the edge surface is a straight line 536 and 8 approaches
zero.
In the example of Figure 27(b) a slight rounding has been implemented to
eliminate sharp edges which might otherwise present a safety hazard. In the
example of Figure 27(c), a groove 538 has been cut in the edge which is
adapted
to interfit with a correspondingly shaped portion 540 of the rim of the
eyewear.
Finally, in the example of Figure 27(d), a bead 542 has been formed in the
edge
surface which is adapted to interfit with a channeled rim 544 of the eyewear
frames. In these later cases the edge surface is still largely invisible to
the
wearer.
In the case of the examples of Figures 27(b), (c) and (d), advantageously,
8 is less than about 5° around the entire perimeter of the lens. This
situation is
illustrated in Figure 28 which is a pictorial view of an edged lens 546 made
in
accordance with preferred embodiments of the present invention. The edge
surface 548 of the lens is an annulus perpendicular to tangents of the
spherical
surface 550 of the lens. The annulus is three-dimensional in the sense that it
does not lie entirely in one plane. The edge surface lies between two
generally
conical shapes 552 and 554 and subtends angle 0, which may vary somewhat at
different positions on the perimeter of the lens, but which is typically less
than
3° + 1.5°.
Figures 29(a)-(c) illustrate several lens edging techniques. Figure 29(a)
shows the edging of a conventional Ostwalt section lens 560 using a
conventional
mill 562 rotated about an axis 564 which is maintained parallel to a reference
axis 566 (which may be the optical axis of the lens blank). The axis 564 of
the
mill is moved around the perimeter of the lens as indicated by arrows 568 to
form the edge surface. The use of a similar technique to edge a steeply curved
lens 570 is shown in Figure 29(b). The result is an edged lens with sharp
edges
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572 and edge surfaces which will subtend a large angle in the wearer's
peripheral
field of view.
In accordance with a preferred embodiment of the present invention, as
shown in Figure 29(c), the edge surface 574 of a steeply curved lens 570 may
be
generated by a mill 562 rotated about an axis 576 which intersects a center of
curvature C of a spherical surface of the lens. Previously, such an
arrangement
had been employed only to edge non-steeply curved lenses.
VII. Coatings, Sun Lenses And Protective Eyewear
A. Coatings
Lens elements, such as those of the present invention, which have a
surface of high curvature, may be particularly difficult to coat with a film
for
controlling reflectance/transmittance. These difficulties are caused, at least
in
part, by the geometry of typical coating, evaporation and sputtering systems.
The systems are capable of forming relatively uniform films from center to
edge
of relatively flat lens elements. However, greater variation is observed with
the
steepening of the surface curvature. The perceived color of the lens element
will
change with film thickness. It may also vary across the lens due to change in
viewing angle. This effect is also more significant in the case of steeply
curved
lenses. These difficulties are sometimes referred to as "roll off".
Techniques for coating lens elements, particularly highly curved lens
elements, are disclosed in the above mentioned International Application No.
PCTlAU99/01029 entitled "Coated Lehs Exhibiting Substantially Balanced
Reflectance ". Also discussed are various types of coatings made up of a
"stack"
of multiple oxide film layers. Such a stack is illustrated generally in Figure
30(a). In this example, a steeply curved lens 600 has a spherical anterior
surface
602 coated with a multilayer film 604 (not drawn to scale).
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An example of an antireflectance coating which provides an appearance
which is a generally uniform pale blue color from the center to the edge of
the
coated, steeply curved lens element consists of a stack of five silicon and
zirconium oxide layers of various thicknesses. The stack is set forth in Table
I
below.
TABLE I
Material Thickness (nm)
Air
Si02 98.96
Zr02 132.79
Si02 36.96
Zr02 16.61
Si02 17.90
Lens
In addition to reducing roll off, the lens reduces the highlighting of
fingerprints
on the lens and is less susceptible to other systematic and non-systematic
manufacturing variations. These advantages may be achieved in conventional,
Ostwalt section lenses as well.
Techniques for sputter deposition of the aforementioned oxide coatings
are disclosed in U.S. Patent Application S.N. 09/605,401 to Burton et al.,
filed
June 28, 2000, the contents of which are hereby incorporated by reference in
its
entirety.
Figures 31 and 32 illustrate various aspects of the coatings of the present
invention. Figure 31 is a plot of reflection in percent as a function of light
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wavelength in nanometers. It compares the reflectance of the stack of Table I
with a more conventional stack having a greenish color (dashed line).
Variations of 3 % or more in deposited film thickness ordinarily cause
significant and noticeable color variations. The. green coloration, which is
an
effect of the "hump" 650 in the reflection spectrum (Figure 31) appears to
move
toward the blue end of the spectrum when viewed at an oblique angle. When
this happens, the reflectivity in the red end of the spectrum becomes more
intense. This will eventually result in a pink or purple color (rather than
the
desired yellow/green).
In contrast, the stack of Table I (blue) produces a reflectance spectrum
with a dominant amount of visible light reflectance in the blue portion of the
spectrum as represented by the peak or hump 652 in the in the spectrum
centered
at about 4~0 nm. The blue coating produces very low reflectances well into the
infra red region of the spectrum and is less than .5 % , preferably less than
.25
at 720 nm.
The effect of steep lens curvature is illustrated in Figure 32. As can be
seen, the reflectance at the red end of the spectrum at the center of each
lens is
higher for the green coating than for the blue coating. However, when the
reflection is measured towards the edge of the lens it is clearly seen that
the
green coating suffers greatly increased reflectivity in the red part of the
spectrum
while the blue coating remains stable at a low red reflectivity.
The result of this increase in red reflection towards the edge of a lens is
to turn the "green" coating into a bright purple color (Green + Red = Purple).
This effect does not occur to any significant extent in the case of the blue
coating. The net result of this decreased sensitivity to color roll off is
that the
need for standard lens curvature groupings to maintain color consistency
during
AR deposition is greatly reduced. It is apparent that steeply curved lens
surfaces
will maintain their color across either the whole surface, or across a greatly
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increased part of their surfaces (as compared to more conventional coatings
such
as the green coating) .
B. Suh Lenses
It is conventional to provide sun lenses or sun glasses that selectively
block wavelengths of light both in the visible and LTV ranges. Such lenses
have
applications both for eye protection and fashion design. The wavelengths of
light
passing through the lens may be selected by employing light absorbent dyes in
the plastic body. Alternatively, or in addition, mirror reflective coatings
may be
applied to the lens. These techniques may be applied to the steeply curved
lenses
of the present invention. Moreover, they may be used in conjunction with the
anti-reflection coatings described above. For example, the above described AR
coatings could be applied to the eye side optical surface of a lens containing
a
dye which partially blocks sunlight. Alternatively, the above described AR
coating could be applied to the eye side optical surface of the lens while the
anterior side optical surface is coated with a mirror coating, for example a
vivid
blue reflective coating.
C. Laser Protective Eyewear
The steeply curved, spherical surface lens elements described above may
advantageously be used in laser protective eyewear. In preferred embodiments
the eyewear is designed to locate the center of curvature of each lens on the
respective centroid of rotation of the eye with which it is used. Further, the
lens
may be edged so that the lens extends approximately from the nasal to the
temporal margins of the orbit and from the lower to the upper margins of the
orbit. Alternatively, the lenses may be mounted in eye wear frames which
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extend to said orbit margins. These configurations have several beneficial
effects. First, the lens can effectively surround the eye and reduce or
prevent the
leakage of stray light around the edges. Secondly, essentially all light
incident
on the lens which could be transmitted through the pupil will be within about
25 °
to 30° with respect to the normal to the tangent of the spherical
surface. Higher
angle incident light will not be directed through the pupil. Laser light
blocking
means on or in the lens can be tailored to block beams of laser light within
this
approximately 30 ° angular range of the normal to the tangent of the
spherical
surface.
It is known that band blocking optical filters can be sensitive to the
incident angle of the light to be blocked. Typically such filters use normal
incident light as a design center. The effectiveness of the filter typically
varies
and usually decreases with deviation in the incident angle from the normal.
This
geometry is illustrated in Figure 30(a) for two arbitrary rays Rl and R2 which
have angles of incidence ~1 and ~2, respectively. Angles cal and ~2 are
measured with respect to normals Nl and NZ at the point the rays Rl and RZ
intersect the surface of the lens. (The normals are perpendicular to tangent
planes Tl and TZ at their respective points of intersection). Generally, for
the
filters discussed above, the greater ~ is, the less effective the filtering
effect will
be.
The steeply curved lenses of the present invention typically present a
smaller range of relevant incidence angles ~, which will permit use of filters
with effective rejection angles up to, for example, about 30° from
normal. This
aspect of the steeply curved lenses is illustrated in a comparison of two lens
examples given in Figures 30(b) and 30(c). The lens 610 shown in Figure 30(b)
is a Ostwalt section, -4D base lens. The lens 612 shown in Figure 30(c) is a
steeply curved lens with -4D through power and a front spherical surface 614
of
about 15.5D. The analysis of incident rays assumes both lenses have refractive
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indices of 1.5 and center thicknesses of about 2 mm. It is also assumed that a
1 cm diameter pupil P is located 2 cm behind the point where the back surface
of the lens intersects its optical axis O-O.
Various incident rays are plotted in Figures 30(b) and 30(c). The rays
are selected from ray bundles which intersect a plane PT tangent to each lens
at
the optical axis O-O. Bundles are examined at distances of 0, 5, 10, 15 and
20 mm above and below the optical axis O-O. From each bundle, a ray is
selected which (i) has the largest angle ~ with respect to a normal to the
lens at
the point of incidence on the lens surface and (ii) which will reach the
lowest
point L of the pupil when refracted by the lens. These selected rays are
identified by their respective distances (e.g. 5 mm, 10 mm, etc.) above and
below the optical axis bn the plane PT.
The following table presents the calculated angle ~ for each of the
incident rays for the lenses of Figures 30(b) and 30(c):
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TABLE II
Ray in degrees for in degrees for
(mm from optical lens of Figure lens of Figure
axis) 30(b) 30(c)
20 53.3 15.8
IS 46.1 18.9
37.9 22.0
5 27.2 20.2
0 16.8 16.1
-5 3.0 10.9
-10 -9.4 6.4
-15 -22.6 3.1
-20 -3 3 . 3 2 . 8
(The angles ~ are expressed as both positive and negative angles. A positive
angle indicates a clockwise beam rotation from the lens normal as shown in the
Figure and a negative angle indicates a counter clockwise beam rotation from
the
lens normal. )
In the example, c~ for the Ostwalt section lens is greater than 30°
at many
locations and increases dramatically with distance from the optical axis to a
high
of 53.7 ° at the +20 mm location. In contrast, for the steeply curved
lens of
Figure 30(c), the angle ~ remains below 30°.
Selective blocking of laser light can be achieved with one or more optical
band block filters. A preferred way of producing selective blocking of laser
light
is to employ a thin film stack tailored to block potentially injurious laser
light.
The following is an example of a band filter which effectively blocks two
laser
light wavelengths frequently used in telecommunications: 1310 nm and 1550 nm
laser light. The optical filter is described in Table III in terms of layer
composition and thickness.
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TABLE III
Material Thicknesses (nm)
Air
Si02 125.42
Ti02 161.11
Si02 250.83
Ti02 161.11
Si02 250.83
Ti02 161.11
Si02 250.83
Ti02 161.11
Si02 250.83
Ti02 161.11
Si02 250.83
Ti02 161.11
Si02 250.83
Ti02 161.11
Si02 250.83
Ti02 161.11
Si02 , 250.83
TiOz 161.11
Si02 250.83
Ti02 161.11
Si02 250. 83
Ti02 161.11
Si02 250. 83
Ti02 161.11
Si02 125.42
Polycarbonate
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In optical design parlance, this stack is described by the expression:
"1.12(0.5L H 0.5L) 1.06(0.5L H 0.5L) 1.03(0.5L H 0.5L) (LHL)~6
1.03(0.5L H 0.5L) 1.06(0.5L H 0.5L) 1.12 (0.5L H 0.5L)"
where H and L denote the quarter wavelength optical thickness at the target
wavelength of the high refractive and low refractive index materials,
respectively. In the example of TABLE III the low refractive index material is
Silicon Dioxide and the high refractive index material is Titanium Dioxide. It
will be understood that various other stacks of conventional design can be
employed to provide a band block filter for protection from laser light.
Continuing with the example of TABLE III, the optical density (negative
of the logarithm of transmission percentage) is plotted as a function of
incident
light wavelength in Figure 33. As can be seen from the Figure, the blocked
band is a wide band centered at about 1400 nm. Most visible wavelengths are
passed (i.e. the optical density is near zero).
The plot of Figure 33 assumes a zero degree incidence angle ~ with
respect to a line N normal to a tangent T to the lens surface at the point of
incidence (see Figure 30(a)). The optical density of the stack is expected to
vary
as the incidence angle ~ increases from zero. The expected deviation for S and
P polarizations and incident light of 1310 nm and 1550 nm wavelengths are
plotted in Figure 34.
More specifically, in Figure 34 optical density is plotted as a function of
incidence angle ~ from 0 to 60 ° . It will be understood that as angle
of light
incidence increases, the whole block band will shift left (towards blue).
Because
of this the optical density increases for the 1310 nm wavelength. The optical
density of the 1550 line decreases as incident angle c~ increases. For the
stack
of TABLE III, at angles below 30 degrees, less than about 0.7 % of the light
is
transmitted and below 20 degrees, only about 0.2 % light is transmitted,
regardless of polarization. This is believed to be sufficient for commercial
safety
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applications, although military requirements might be more stringent and
require
a stack design with greater optical density in a particular bands.
It will be observed from Figure 34 that the transmittance of the stack
remains below 1 % for both wavelengths and polarizations at incident angles up
to about 33 ° . Incident angles higher than this would not be directed
toward the
retina in the steeply curved lenses described herein whose center of curvature
is
located at about the centroid of rotation of the eye being protected. However,
to insure against unwanted transmissions caused by strong reflections,
refractions
or light leaks, the lens body could also be molded from a thermoplastic
containing a radiation absorbing dye.
Accordingly, novel, high optical quality lens elements with steep
spherical curvature are provided with prescribed through-power and cyl
correction, and mounted in spectacle frames adapted for use therewith. These
designs are readily adapted for use in highly effective sunglasses and other
protective eyewear such as laser protective eyewear.
The present invention has been described in connection with various
embodiments and examples. However, the invention to be protected is defined
by the following claims and equivalents thereof recognized in law.
