U.S. patent number RE42,781 [Application Number 12/887,731] was granted by the patent office on 2011-10-04 for ophthalmic lens.
This patent grant is currently assigned to Essilor Internationale (Compagnie Generale d'Optique). Invention is credited to Bernard Bourdoncle, Bruno Decreton.
United States Patent |
RE42,781 |
Bourdoncle , et al. |
October 4, 2011 |
Ophthalmic lens
Abstract
A progressive multifocal ophthalmic lens has a complex surface
having a prism reference point, a fitting cross, a progression
meridian having a power addition greater than or equal to 1.5
diopters. The lens has, under conditions when being worn: a reduced
root mean square, normalized to the addition prescription, of less
than 0.65 microns per diopter in a zone delimited by a circle
centred on the prism reference point and with a diameter
corresponding to a sweep of vision of 80.degree., a progression
length of less than or equal to 25.degree., and a difference in
normalized reduced root mean square between pairs of symmetrical
points relative to a vertical axis passing through the fitting
cross of less than 0.12 microns per diopter in a zone delimited by
a semi-circle centred on the fitting cross and with a radius
corresponding to raising viewing by 25.degree..
Inventors: |
Bourdoncle; Bernard (Paris,
FR), Decreton; Bruno (Charenton Cedex,
FR) |
Assignee: |
Essilor Internationale (Compagnie
Generale d'Optique) (Charenton Cedex, FR)
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Family
ID: |
36778200 |
Appl.
No.: |
12/887,731 |
Filed: |
September 22, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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Reissue of: |
11450913 |
Jun 9, 2006 |
7427134 |
Sep 23, 2008 |
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Foreign Application Priority Data
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Nov 29, 2005 [FR] |
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05 12063 |
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Current U.S.
Class: |
351/159.17;
351/159.78 |
Current CPC
Class: |
G02C
7/061 (20130101); G02C 7/065 (20130101); G02C
7/025 (20130101); G02C 7/028 (20130101); G02C
2202/22 (20130101) |
Current International
Class: |
G02C
7/06 (20060101) |
Field of
Search: |
;351/169,177 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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0 990 939 |
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Apr 2000 |
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EP |
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2 683 642 |
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May 1993 |
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FR |
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2 699 294 |
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Jun 1994 |
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FR |
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2 704 327 |
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Oct 1994 |
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FR |
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2 770 000 |
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Apr 1999 |
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FR |
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2 277 997 |
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Nov 1994 |
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GB |
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WO 98/12590 |
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Mar 1998 |
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WO |
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WO 03/048841 |
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Jun 2003 |
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WO |
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Other References
Eloy, A. Villegas et al., "Spatially Resolved Wavefront Aberrations
of Ophthalmic Progressive-Power Lenses in Normal Viewing
Conditions", Optometry and Vision Science, vol. 80, No. 2, pp.
106-114 (Feb. 2003). cited by examiner .
W.N. Charman et al., "Astigmatism, Accomodation, and Visual
Instrumentation", Applied Optics, vol. 17, No. 24, pp. 3903-3910
(Dec. 15, 1978). cited by examiner .
Rainer G Dorsch et al., "Coma and Design Characteristics of
Progressive Addition Lenses", Vision Science and Its Applications,
Tehnical Digest Series vol. 1, Santa Fe, New Mexico pp.
SaA3-1/68-SaA3-4/71 (Feb. 6-9, 1998). cited by examiner.
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Primary Examiner: Schwartz; Jordan M.
Attorney, Agent or Firm: HKH Law, LLC
Claims
What is claimed is:
1. Progressive multifocal ophthalmic lens with a complex surface
having: .[.a prism reference point;.]. a fitting cross.[.situated
8.degree. above the prism reference point.].; a substantially
umbilical progression meridian having a power addition greater than
or equal to 1.5 diopters between a far-vision reference point and a
near-vision reference point; the lens having, under wearing
conditions and with reference to a plane prescription in far vision
by adjustment of the radii of curvature of at least one of its
faces: a reduced root mean square, normalized to the addition
prescription, of less than 0.65 microns per diopter, in a zone
delimited by a circle .[.centred.]. .Iadd.centered .Iaddend.on
.[.the prism reference.]. .Iadd.a .Iaddend.point .Iadd.located
8.degree. below the fitting cross .Iaddend.and with a diameter
corresponding to a sweep of vision of 80.degree., the reduced root
mean square being calculated by cancelling the coefficients of
order 1 and the coefficient of order 2 corresponding to the
defocusing in the decomposition into .[.Zemicke.]. .Iadd.Zernicke
.Iaddend.polynomials of a wave front passing through the lens; a
progression length less than or equal to 25.degree., the
progression length being defined as the angle of lowered viewing
from the fitting cross to the point of the meridian at which the
wearer's optical power reaches 85% of the addition prescription; a
normalized reduced root mean square difference of less than 0.12
microns per diopter calculated in absolute values as the difference
in root mean square values between pairs of symmetrical points
relative to a vertical axis passing through the fitting cross, in a
zone which includes the far-vision control point and delimited by a
semi-circle centred on the fitting cross and with a radius
corresponding to a raised viewing of 25.degree..
2. The lens of claim 1, characterized in that said root mean square
difference between two symmetrical points in said semi-circle is
less than or equal to 0.12 microns per diopter below a
substantially horizontal line situated 8.degree. above the fitting
cross.
3. The lens of claim 1, characterized in that the semi-circle has a
substantially horizontal base passing through the fitting
cross.
4. The lens of claim 1, characterized in that the axis of symmetry
of the semi-circle substantially coincides with the progression
meridian.
5. A visual device including at least one progressive multifocal
ophthalmic lens with a complex surface having: .[.a prism reference
point;.]. a fitting cross.[.situated 8.degree. above the prism
reference point.].; a substantially umbilical progression meridian
having a power addition greater than or equal to 1.5 diopters
between a far-vision reference point and a near-vision reference
point; the lens having, under wearing conditions and with reference
to a plane prescription in far vision by adjustment of the radii of
curvature of at least one of its faces: a reduced root mean square,
normalized to the addition prescription, of less than 0.65 microns
per diopter, in a zone delimited by a circle centered on .[.the
prism reference.]. .Iadd.a .Iaddend.point .Iadd.located 8.degree.
below the fitting cross .Iaddend.and with a diameter corresponding
to a sweep of vision of 80.degree., the reduced root mean square
being calculated by cancelling the coefficients of order 1 and the
coefficient of order 2 corresponding to the defocusing in the
decomposition into Zernicke polynomials of a wave front passing
through the lens; a progression length less than or equal to
25.degree., the progression length being defined as the angle of
lowered viewing from the fitting cross to the point of the meridian
at which the wearer's optical power reaches 85% of the addition
prescription; a normalized reduced root mean square difference of
less than 0.12 microns per diopter calculated in absolute values as
the difference in root mean square values between pairs of
symmetrical points relative to a vertical axis passing through the
fitting cross, in a zone which includes the far-vision control
point and delimited by a semi-circle centred on the fitting cross
and with a radius corresponding to a raised viewing of
25.degree..
6. A method for correcting the vision of a presbyopic subject,
which comprises providing the subject with, or the wearing by the
subject of, a visual device including at least one progressive
multifocal ophthalmic lens with a complex surface having: .[.a
prism reference point,.]. a fitting cross.[.situated 8.degree.
above the prism reference point.].; a substantially umbilical
progression meridian having a power addition greater than or equal
to 1.5 diopters between a far-vision reference point and a
near-vision reference point; the lens having, under wearing
conditions and with reference to a plane prescription in far vision
by adjustment of the radii of curvature of at least one of its
faces: a reduced root mean square, normalized to the addition
prescription, of less than 0.65 microns per diopter, in a zone
delimited by a circle .[.centred.]. .Iadd.centered .Iaddend.on
.[.the prism reference.]. .Iadd.a .Iaddend.point .Iadd.located
8.degree. below the fitting cross .Iaddend.and with a diameter
corresponding to a sweep of vision of 80.degree., the reduced root
mean square being calculated by cancelling the coefficients of
order 1 and the coefficient of order 2 corresponding to the
defocusing in the decomposition into .[.Zemicke.]. .Iadd.Zernicke
.Iaddend.polynomials of a wave front passing through the lens; a
progression length less than or equal to 25.degree., the
progression length being defined as the angle of lowered viewing
from the fitting cross to the point of the meridian at which the
wearer's optical power reaches 85% of the addition prescription; a
normalized reduced root mean square difference of less than 0.12
microns per diopter calculated in absolute values as the difference
in root mean square values between pairs of symmetrical points
relative to a vertical axis passing through the fitting cross, in a
zone which includes the far-vision control point and delimited by a
semi-circle centred on the fitting cross and with a radius
corresponding to a raised viewing of 25.degree..
.Iadd.7. The lens of claim 1, wherein the complex surface has a
prism reference point located 8.degree. below the fitting
cross..Iaddend.
.Iadd.8. The visual device of claim 5, wherein the complex surface
of the lens has a prism reference point located 8.degree. below the
fitting cross..Iaddend.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
Pursuant to U.S.C. .sctn. 119, this application claims the benefit
of French Patent Application 05 12 063, filed Nov. 29, 2005. The
contents of the prior application is incorporated herein by
reference in its entirety.
TECHNICAL FIELD
This invention relates to an ophthalmic lens.
BACKGROUND
Any ophthalmic lens intended to be held in a frame involves a
prescription. The ophthalmic prescription can include a positive or
negative power prescription as well as an astigmatism prescription.
These prescriptions correspond to corrections enabling the wearer
of the lenses to correct defects of his vision. A lens is fitted in
the frame in accordance with the prescription and with the position
of the wearer's eyes relative to the frame.
In the simplest cases, the prescription is nothing more than a
power prescription. The lens is said to be unifocal and has a
rotational symmetry. It is fitted in a simple manner in the frame
so that the principal viewing direction of the wearer coincides
with the axis of symmetry of the lens.
For presbyopic wearers, the value of the power correction is
different for far vision and near vision, due to the difficulties
of accommodation in near vision. The prescription thus comprises a
far-vision power value and an addition (or power progression)
representing the power increment between far vision and near
vision; this comes down to a far-vision power prescription and a
near-vision power prescription. Lenses suitable for presbyopic
wearers are progressive multifocal lenses; these lenses are
described for example in FR-A-2 699 294, U.S. Pat. No. 5,270,745 or
U.S. Pat. No. 5,272,495, FR-A-2 683 642, FR-A-2 699 294 or also
FR-A-2 704 327. Progressive multifocal ophthalmic lenses include a
far-vision zone, a near-vision zone and an intermediate-vision
zone, a principal progression meridian crossing these three zones.
They are generally determined by optimization, based on a certain
number of constraints imposed on the different characteristics of
the lens. These lenses are all-purpose lenses in that they are
adapted to the different needs of the wearer at the time.
Families of progressive multifocal lenses are defined, each lens of
a family being characterized by an addition which corresponds to
the power variation between the far-vision zone and the near-vision
zone. More precisely, the addition, referenced A, corresponds to
the power variation between a point FV of the far-vision zone and a
point NV of the near-vision zone, which are respectively called
far-vision control point and near-vision control point, and which
represent the points of intersection of viewing with the surface of
the lens for far distance vision and for reading vision.
In one family of lenses the addition varies from one lens to the
other in the family between a minimum addition value and a maximum
addition value of 0.25 diopter and by 0.25 diopter from one lens to
the other in the family.
Lenses with the same addition differ in the value of the mean
sphere at a reference point, also called a base. It is possible to
choose for example to measure the base at the point FV for
measuring far vision. Thus the choice of a pair (addition, base)
defines a group or set of aspherical front faces for progressive
multifocal lenses. Generally, it is thus possible to define 5 base
values and 12 addition values, i.e. sixty front faces. In each of
the bases an optimization is carried out for a given power.
Starting from semi-finished lenses, of which only the front face is
formed, this known method makes it possible to prepare lenses
suited to each wearer, by simple machining of a spherical or toric
rear face.
Progressive multifocal lenses thus usually comprise an aspherical
front face, which is the face away from the person wearing the
glasses and a rear spherical or toric face directed towards the
person wearing the glasses. This spherical or toric face allows the
lens to be adapted to the user's ametropia, so that a progressive
multifocal lens is generally defined only by its aspherical
surface. As is well known, an aspherical surface is generally
defined by the altitude of all of its points. The parameters
constituted by the minimum and maximum curvatures at each point are
also used, or more commonly their half-sum and their difference.
This half-sum and this difference multiplied by a factor n-1, n
being the refractive index of the lens material, are called mean
sphere and cylinder.
A progressive multifocal lens can thus be defined, at every point
on its complex surface, by geometric characteristics including a
mean sphere value and a cylinder value, given by the following
formulae.
In a manner known per se, at any point of a complex surface, a mean
sphere D given by the formula:
.times. ##EQU00001##
is defined, where R.sub.1 and R.sub.2 are the maximum and minimum
local radii of curvature expressed in meters, and n is the index of
the material constituting the lens.
A cylinder C, given by the formula:
.times. ##EQU00002##
is thus defined.
The characteristics of the complex face of the lens can be
expressed using the mean sphere and the cylinder.
Moreover, a progressive multifocal lens can also be defined by
optical characteristics taking into account the situation of the
wearer of the lenses. In fact, the laws of the optics of ray
tracings mean that optical defects appear when the rays deviate
from the central axis of any lens. Conventionally, the aberrations
known as power defects and astigmatism defects are considered.
These optical aberrations can be generically called obliquity
defects of rays.
Obliquity defects of rays have already been clearly identified in
the prior art and improvements have been proposed. For example, the
document WO-A-98 12590 describes a method for determination by
optimization of a set of progressive multifocal ophthalmic lenses.
This document proposes defining the set of lenses in consideration
of the optical characteristics of the lenses and in particular the
wearer power and oblique astigmatism under wearing conditions. The
lens is optimized by ray tracing, using an ergorama linking a
target object point with each direction of viewing under wearing
conditions.
EP-A-0 990 939 also proposes to determine a lens by optimization
taking into account the optical characteristics instead of the
surface characteristics of the lens. For this purpose the
characteristics of an average wearer are considered, in particular
as regards the position of the lens in front of the eye of the
wearer in terms of curving contour, pantoscopic angle and lens-eye
distance.
It is thus possible to consider, in addition to the obliquity
defects of rays described previously, the so-called higher order
optical aberration such as spherical aberrations or coma by
studying the deformations which are undergone by a non-aberrant
spherical wave front passing through the lens.
It is considered that the eye rotates behind the lens in order to
sweep over all of its surface. Thus, at each point, an optical
system composed of the eye and the lens is considered, as will be
explained in detail below with reference to FIGS. 1 to 3. The
optical system is therefore different at each point of the surface
of the lens because the relative positions of the principle axis of
the eye and of the lens are in fact different at each point due to
the rotation of the eye behind the lens.
In each of these successive positions, the aberrations undergone by
the wave front which passes through the lens and is limited by the
pupil of the eye are calculated.
The spherical aberration results for example from the fact that the
rays which pass at the edge of the pupil do not converge in the
same plane as the rays which pass close to its centre. Moreover,
the coma represents the fact that the image of a point situated
outside the axis has a tail, due to the power variation of the
optical system. Reference can be made to the article by R. G.
Dorsch and P. Baumbach, "Coma and Design Characteristics of
Progressive Addition Lenses" R. G. Dorsch, P. Baumbach, Vision
Science and Its Applications, Santa Fe, February 1998 which
describes the effects of coma on a progressive multifocal lens.
SUMMARY
The deformations of the wave front passing through the multifocal
lens can be described in a global manner by the root mean square or
RMS. The RMS is generally expressed in microns (.mu.m) and, for
each point on the complex surface, indicates the difference in the
resulting wave front relative to a non-aberrant wave front. The
invention proposes controlling the RMS value in order to determine
a progressive multifocal lens defined by its optical
characteristics under wearing conditions in order to limit the
optical aberrations perceived by the eye.
In particular when the progressive multifocal lens has a large
power addition, for example greater than or equal to 1.5 diopters,
the aberrations affecting the wave front become more significant
due to the power progression between the far-vision zone and the
near-vision zone. These optical aberrations perceived by the wearer
adversely affect the comfort in peripheral vision and in dynamic
vision. A need therefore exists for a progressive multifocal lens
which better satisfies the needs of wearers.
The invention proposes a progressive multifocal lens which is
easier to adapt to than the standard ophthalmic lenses; it has a
very smooth power progression in order to provide the wearer with
excellent perception in dynamic vision and in peripheral vision. It
is proposed to limit the RMS over the whole of a central zone of
the lens while guaranteeing good accessibility to the powers
required in near vision. Such a lens is particularly suitable for
the comfort of hypermetropic wearers who require a large power
addition, greater than or equal to 1.5 diopters.
Consequently, the invention proposes a progressive multifocal
ophthalmic lens with a complex surface having:
a prism reference point;
a fitting cross situated 8.degree. above the prism reference
point;
a substantially umbilical progression meridian having a power
addition greater than or equal to 1.5 diopters between a far-vision
reference point and a near-vision reference point;
the lens having, under wearing conditions and with reference to a
plane prescription in far vision by adjustment of the radii of
curvature of at least one of its faces:
a reduced root mean square, normalized to the addition
prescription, of less than 0.65 microns per diopter, in a zone
delimited by a circle centred on the prism reference point and with
a diameter corresponding to a sweep of vision of 80.degree., the
reduced root mean square being calculated by cancelling the
coefficients of the order of 1 and the coefficient of the order of
2 corresponding to the defocusing in the decomposition into
Zernicke polynomials of a wave front passing through the lens; a
progression length less than or equal to 25.degree., the
progression length being defined as the angle of lowered vision
from the fitting cross to the point on the meridian at which the
wearer's optical power reaches 85% of the addition prescription; a
normalized reduced root mean square difference of less than 0.12
microns per diopter calculated in absolute values as the difference
in root mean square values between pairs of symmetrical points
relative to a vertical axis passing through the fitting cross, in a
zone which includes the far-vision control point and delimited by a
semi-circle centred on the fitting cross and with a radius
corresponding to a raised viewing of 25.degree..
According to one characteristic, the root mean square difference
between two symmetrical points in said semi-circle is less than or
equal to 0.12 microns per diopter below a substantially horizontal
line situated 8.degree. above the fitting cross.
According to one characteristic, the semi-circle has a base which
is substantially horizontal passing through the fitting cross.
According to one characteristic, the axis of symmetry of the
semi-circle substantially coincides with the progression
meridian.
The invention also relates to a visual device including at least
one lens according to the invention and a method for correcting the
vision of a presbyopic subject, which comprises providing the
subject with, or the wearing by the subject of, such a device.
DESCRIPTION OF DRAWINGS
Other advantages and characteristics of the invention will become
apparent on reading the following description of the embodiments of
the invention, given by way of example and with reference to the
drawings which show:
FIG. 1, a diagram of an eye-lens optical system, top view;
FIGS. 2 and 3, perspective diagrams of an eye-lens system;
FIG. 4, a graph showing the wearer's optical power along the
meridian of a lens according to a first embodiment of the
invention;
FIG. 5, a map of the wearer's optical power for the lens of FIG.
4;
FIG. 6, an oblique astigmatism amplitude map of the lens of FIG.
4;
FIG. 7, a map of normalized reduced RMS of the lens of FIG. 4;
FIG. 8, a map representing the differences in RMS between pairs of
symmetrical points of the lens of FIG. 7;
FIG. 9, a graph showing the wearer's optical power along the
meridian of a lens according to a second embodiment of the
invention;
FIG. 10, a map of the wearer's optical power for the lens of FIG.
9;
FIG. 11, an oblique astigmatism amplitude map of the lens of FIG.
9;
FIG. 12, a map of normalized reduced RMS of the lens of FIG. 9;
FIG. 13, a map representing the differences in RMS between pairs of
symmetrical points of the lens of FIG. 12;
FIG. 14, a graph showing the wearer's optical power along the
meridian of a lens according to a prior art;
FIG. 15, a map of the wearer's optical power for the lens of FIG.
14;
FIG. 16, an oblique astigmatism amplitude map of the lens of FIG.
14;
FIG. 17, a map of normalized reduced RMS of the lens of FIG.
14.
DETAILED DESCRIPTION
In a conventional manner, for a given lens, characteristic optical
variables are defined, namely a power and an astigmatism, under
conditions when being worn. FIG. 1 shows a diagram of an
eye-and-lens optical system in a side view, and shows the
definitions used hereafter in the description. The centre of
rotation of the eye is called Q'; the axis Q'F' represented in the
figure by a chain-dotted line is the horizontal axis passing
through the centre of rotation of the eye and continuing in front
of the wearer--in other words the axis Q'F' corresponds to the
primary viewing direction. This axis cuts, on the front face, a
point on the lens called the fitting cross FC, which is marked on
the lenses in order to allow their positioning by an optician. The
fitting cross is generally situated 4 mm above the geometrical
centre of the front face. Let point O be the point of intersection
of the rear face and this axis Q'F'. A sphere of the vertices is
defined, with a centre Q', and a radius q', which cuts the rear
face of the lens at the point O. By way of example, a radius q'
value of 27 mm corresponds to a current value and produces
satisfactory results when the lenses are worn. The section of the
lens can be drawn in the plane (O, x, y) which is defined with
reference to FIG. 2. The tangent to this curve at the point O is
inclined relative to the axis (O, y) at an angle called the
pantoscopic angle. The value of the pantoscopic angle is currently
8.degree.. The section of the lens can also be drawn in the plane
(O, x, z). The tangent to this curve at the point O is inclined
relative to the axis (O, z) at an angle called the curving contour.
The value of the curving contour is currently 0.degree..
A given viewing direction--represented by a solid line in FIG.
1--corresponds to a position of the eye in rotation about Q' and to
a point J on the sphere of the vertices; a viewing direction can
also be marked, in spherical coordinates, by two angles .alpha. and
.beta.. The angle .alpha. is the angle formed between the axis Q'F'
and the projection of the straight line Q'J over the horizontal
plane containing the axis Q'F'; this angle appears in the diagram
of FIG. 1. The angle .beta.0 is the angle formed between the axis
Q'F' and the projection of the straight line Q'J over the vertical
plane containing the axis Q'F'. A given viewing direction therefore
corresponds to a point J of the sphere of the vertices or to a pair
(.alpha.,.beta.).
In a given viewing direction, the image of a point M in the object
space situated at a given object distance forms between two points
S and T corresponding to minimum and maximum distances JS and JT
(which are sagittal and tangential focal distances in the case of
revolution surfaces, and of a point M at infinity) The angle
.gamma. marked as the axis of astigmatism is the angle formed by
the image corresponding to the smallest distance with the axis
(z.sub.m), in the plane (z.sub.m,y.sub.m) defined with reference to
FIGS. 2 and 3. The angle y is measured in counterclockwise
direction when looking at the wearer. In the example of FIG. 1, on
the axis Q'F', the image of a point of the object space at infinity
forms at the point F'; the points S and T coincide, which is
another way of saying that the lens is locally spherical in the
primary viewing direction. The distance D is the rear front end of
the lens.
FIGS. 2 and 3 show perspective diagrams of an eye-lens system. FIG.
2 shows the position of the eye and of the reference frame linked
to the eye, in the principal viewing direction, .alpha.=.beta.=0,
called the primary viewing direction. The points J and O thus
coincide. FIG. 3 shows the position of the eye and of the reference
frame which is linked to it in one direction (.alpha.,.beta.). In
FIGS. 2 and 3 a fixed reference frame {x, y, z} and a reference
frame {x.sub.m,y.sub.m,z.sub.m} linked to the eye are represented,
in order to show the rotation of the eye clearly. The origin of the
reference frame {x, y, z} is the point Q'; the axis x is the axis
Q'F'--the point F' is not represented in FIGS. 2 and 3 and passes
through the point O; this axis is orientated from the lens towards
the eye, in agreement with the direction of measurement of the axis
of astigmatism. The plane {y, z} is the vertical plane; the y axis
is vertical and orientated upwards; the z axis is horizontal, the
reference frame being directly orthonormalized. The reference frame
{x.sub.m y.sub.m, z.sub.m} linked to the eye has the point Q' as
its centre; the axis x.sub.m is given by the direction JQ' of
viewing, and coincides with the reference frame {x, y, z} for the
primary direction of viewing. Listing's law gives the relationships
between the coordinate systems {x, y, z} and {x.sub.m, y.sub.m,
z.sub.m}, for each direction of viewing, see Legrand, Optique
Physiologique, Volume 1, Edition de la Revue d'Optique, Paris
1965.
Using these data, an optical power of the wearer and an astigmatism
can be defined in each viewing direction. For a viewing direction
(.alpha.,.beta.), an object point M at an object distance given by
the ergorama is considered. The points S and T between which the
image of the object forms are determined. The image proximity IP is
then given by
.times. ##EQU00003##
while the object proximity OP is given by
##EQU00004##
The power is defined as the sum of the object and image
proximities, i.e.
.times. ##EQU00005##
The amplitude of the astigmatism is given by
##EQU00006##
The angle of the astigmatism is the angle .gamma. defined above: it
is the angle measured in a reference frame linked to the eye,
relative to the direction z.sub.m, with which the image T forms, in
the plane (z.sub.m,y.sub.m). These definitions of power and of
astigmatism are optical definitions, under wearing conditions and
in a reference frame linked to the eye. Qualitatively, the
thus-defined power and astigmatism correspond to the
characteristics of a thin lens, which, fitted instead of the lens
in the viewing direction, provides the same images locally. It is
noted that, in the primary viewing direction, the definition
provides the standard value of the astigmatism prescription. Such a
prescription is produced by the ophthalmologist, in far vision, in
the form of a pair formed by an axis value (in degrees) and an
amplitude value (in diopters).
The thus-defined power and astigmatism can be experimentally
measured on the lens using a frontofocometer; they can also be
calculated by ray tracing under wearing conditions.
The invention proposes to consider not only the standard
aberrations of the wave front, namely the power and the
astigmatism, but to take into account all of the higher order
aberrations which affect the wave front.
The invention thus proposes a progressive multifocal ophthalmic
lens having the advantages of an excellent perception in dynamic
vision and in peripheral vision while limiting the optical
aberrations in a central zone of the lens covering the far-vision
zone, the near-vision zone and the intermediate-vision zone. The
proposed solution also provides a good accessibility to the powers
required in near vision, allowing the wearer to see satisfactorily
at distances equal to approximately 40 cm without obliging him to
lower his eyes very much, the near-vision zone being accessible
from 25.degree. below the fitting cross. The lens has a
prescription such that the powers prescribed for the wearer in far
vision and in near vision are achieved on the lens. The proposed
lens is particularly suited to hypermetropic wearers, but it may
also be intended for myopic or emmetropic wearers. In each of the
figures below, the case of nil power in far vision is considered,
which corresponds to emmetropic wearers.
The lens according to the invention is described below with
reference to two embodiments and compared with a lens of the prior
art which does not satisfy the criteria of the invention (FIGS. 14
to 17).
The lens of FIGS. 4 to 8 is suited to presbyopic wearers having a
power progression prescription of 2 diopters.
FIGS. 4 to 8 show a lens of diameter 60 mm with a progressive
multifocal front face and comprising a prism of 1.15.degree. with a
geometric base orientated at 270.degree. in the TABO reference. The
plane of the lens is inclined 8.degree. relative to the vertical
and the lens has a thickness of 3 mm A value of q' of 27 mm (as
defined with reference to FIG. 1) was considered for the
measurements on the lens of FIGS. 4 to 8.
In FIGS. 5 to 8, the lens is represented in a system with spherical
coordinates, the beta angle being plotted on the abscissa and the
alpha angle on the ordinates.
The lens has a substantially umbilical line, called a meridian, on
which the astigmatism is practically nil. The meridian coincides
with the vertical axis in the upper part of the lens and has an
inclination on the nasal side in the lower part of the lens, the
convergence being more marked in near vision. In the lenses of the
applicant, the meridian represents the line of intersection of the
viewing and the lens when the wearer looks ahead from a point in
the far distance to a target point in near vision.
The figures show the meridian as well as reference points on the
lens. The fitting cross FC of the lens can be geometrically marked
on the lens by a cross or any other mark such as a point surrounded
by a circle produced on the lens, or by any other appropriate
means; this is a centring point produced on the lens which is used
by the optician to fit the lens in the frame. In spherical
coordinates, the fitting cross FC has the coordinates (0,0) as it
corresponds to the point of intersection of the front face of the
lens and the primary viewing direction, as defined previously. The
far-vision control point FV is situated on the meridian and
corresponds to a raised viewing of 8.degree. above the fitting
cross; the far-vision control point FV has the
coordinates)(0,-8.degree.) in the predefined spherical reference.
The near-vision control point NV is situated on the meridian and
corresponds to a lowered viewing of 35.degree. below the fitting
cross; the near-vision control point NV has the coordinates
(6.degree.,35.degree.) in the predefined spherical coordinate
system.
A lens also has a prism reference point PRP corresponding to the
geometrical centre of the lens. On the lens of the applicant, the
fitting cross FC is situated 8.degree. above the prism reference
point; or, in the case of a surface characterization of the lens, 4
mm above the geometrical centre (0,0) of the lens.
FIG. 4 shows a graph of the optical power of the wearer along the
meridian; the angle .beta. is plotted on the ordinates and the
power on the abscissa in diopters. The minimum and maximum optical
powers corresponding respectively to the quantities 1/JT and 1/JS
defined previously are shown by dotted lines, and the optical power
P by a solid line.
It is then possible to note in FIG. 4 an optical power of the
wearer which is substantially constant around the far-vision
control point FV, an optical power of the wearer which is
substantially constant around the near-vision control point NV and
a regular progression of the power along the meridian. The values
are shifted to zero at the origin where the optical power is
actually -0.05 diopters corresponding to a lens prescribed for
presbyopic emmetropic wearers.
The intermediate-vision zone generally begins, for a progressive
multifocal lens, at the fitting cross FC; it is here that the power
progression begins. Thus the optical power increases, from the
fitting cross to the near-vision control point NV, for values of
the angle .beta. of 0 to 35.degree.. For angle values beyond
35.degree., the optical power becomes substantially constant again,
with a value of 2.11 diopters. It is noted that the progression of
optical power of the wearer (2.17 diopters) is greater than the
prescribed power addition A (2 diopters). This difference in power
value is due to the oblique effects.
It is possible to define on a lens a progression length PL which is
the angular distance--or the difference in ordinates--between the
fitting cross FC and a point on the meridian at which the power
progression reaches 85% of the prescribed power addition A. In the
example of FIG. 4, a progression of optical power of 0.85.times.2
diopters, i.e. 1.7 diopters, is obtained for a coordinate point of
angle .beta.=approximately 24.5.degree..
The lens according to the invention thus has a good accessibility
to the powers required in near vision with a moderate lowered
vision, less than or equal to 25.degree.. This accessibility
guarantees comfortable use of the near-vision zone.
FIG. 5 shows the contour lines of the optical power of the wearer
defined in a direction of viewing and for an object point. As is
usual, the isopower lines have been plotted in FIG. 5 in a
spherical coordinate system; these lines are formed by the points
having the same value of optical power P. The 0 diopter to 2
diopter isopower lines are represented.
FIG. 6 shows the contour lines for the amplitude of the oblique
astigmatism under conditions when being worn. As is usual, the
isoastigmatism lines have been plotted in FIG. 6 in a spherical
coordinate system; these lines are formed by the points having the
same astigmatism amplitude value as defined previously. The 0.25
diopter to 1.75 diopter isoastigmatism lines are represented.
FIG. 7 shows the contour lines for the normalized reduced RMS
calculated under conditions when being worn. The RMS is calculated
for each viewing direction and thus for each point on the glass of
the lens, with a ray tracing method. Initially, for each viewing
direction and therefore each point of the lens, the wave front is
calculated after having passed through the lens and the wearer's
prescription--power, axis and amplitude of astigmatism--is
subtracted from it in a vectorial manner in order to determine the
resulting wave front. A diameter of the wearer's pupil
approximately equal to 5 mm was considered. The RMS represents, for
each point of the lens corresponding to a viewing direction, the
difference between the resulting wave front and a non-aberrant
spherical reference wave front corresponding to the desired power
for the viewing direction linked to this point of the lens. The RMS
values shown in FIG. 7 were calculated for the lens of FIGS. 4 to
6, i.e. for a lens with plane power in far vision and having a
prescription for 2 diopter power addition, prescribed for
presbyopic emmetropic wearers.
A possible fitting in order to measure the aberrations of a wave
front passing through the lens as perceived by the eye of the
wearer is described in the article by Eloy A. Villegas and Pablo
Artal, "Spatially Resolved Wavefront Aberrations of Ophthalmic
Progressive-Power Lenses in Normal Viewing Conditions", Optometry
and Vision Science, Vol. 80, No. 2, February 2003.
In a known manner, a wave front which has passed through an
aspherical surface can be decomposed by Zernicke polynomials. More
precisely, a wave surface can be approximated by a linear
combination of polynomials of the type: z(x, y,
z)=.SIGMA..sub.ia.sub.ip.sub.i9x, y, z)
where the P.sub.i are Zernicke polynomials and the a.sub.i are real
coefficients.
The decomposition of the wave front into Zernicke polynomials and
the calculation of the aberrations of the wave front were
standardized by the Optical Society of America; the standard being
available on the web site of Harvard University
ftp://color.eri.harvard.edu/standardization/Standards
TOPS4.pdf.
The RMS is calculated in this way, under wearing conditions. The
RMS is then reduced, i.e. the coefficients of order 1--which
correspond to the prismatic effects--and the coefficient of order 2
corresponding to the defocusing in the decomposition of the wave
front into .[.Zemicke.]. .Iadd.Zernicke .Iaddend.polynomials are
cancelled. The optical aberrations caused by power defects are
therefore not included in the calculation of reduced RMS; on the
other hand the coefficients of order 2 corresponding to the
residual astigmatism of the lens are retained. The RMS is then
normalized, i.e. divided by the prescribed power addition.
In FIG. 7, the normalized reduced RMS, expressed in microns per
diopter, is represented. The 0.1 .mu.m/D to 0.5 .mu.m/D iso RMS
lines are represented. In FIG. 7 a circle is also marked out
centred on the prism reference point--i.e. the geometrical centre
of the lens before trimming and positioning in a frame. In
spherical coordinates, the prism reference point PRP has the
coordinates (0,-8.degree.) because it is situated 8.degree. or 4 mm
below the fitting cross FC. This circle also has a diameter
corresponding to a sweep of vision of 80.degree.--i.e. of
approximately 40 mm diameter if a surface characterization of the
complex surface of the lens is considered. In the zone of the lens
covered by this circle, which includes the far-vision control point
FV, the near-vision control point NV and consequently all of the
intermediate-vision zone, the normalized reduced RMS is limited to
0.65 .mu.m/D. Imposing a small RMS value over all of this central
zone of the lens provides the wearer with optimal comfort of visual
perception in peripheral vision and in dynamic vision.
In FIG. 8, contour lines representing the difference in normalized
reduced RMS values between symmetrical points relative to a
vertical axis passing through the fitting cross FC are represented.
The map of FIG. 8 is constructed point by point by considering all
the pairs of symmetrical points on either side of the predefined
vertical axis and by calculating the difference in normalized
reduced RMS between these two points. The absolute value of this
difference is then shown on the map of FIG. 8. It is noted that all
the normalized reduced RMS isodifference lines are symmetrical
relative to this vertical axis passing through the fitting cross
FC.
A semi-circle centred on the fitting cross FC and including the
far-vision control point is also marked out in FIG. 8. This
semi-circle has a radius corresponding to a raised viewing of
25.degree.--i.e. of approximately 12.5 mm radius if a surface
characterization of the complex surface of the lens is considered.
This semi-circle can have a substantially horizontal base passing
through the fitting cross; the base can however be inclined
according to the methods of fitting the lens in a frame which
depend on the lens manufacturers. The semi-circle defined above
must include the far-vision control point FV and the horizontal
zone of the lens which is used most often in far vision.
In the zone delimited by this semi-circle, the difference in
normalized reduced RMS on either side of the axis of symmetry is
less than 0.12 microns per diopter.
The lens according to the invention also has a small difference in
normalized reduced RMS between the temporal and nasal parts of the
far vision zone. This characteristic ensures optimal wearer comfort
in far vision. In fact, when the wearer looks into the distance by
shifting his eyes slightly horizontally, he looks through the nasal
part of a lens with one eye and through the temporal part of the
other lens with the other eye. For good binocular balance it is
important that the perspective qualities are substantially the same
for both eyes, i.e. that the optical aberrations perceived by each
eye are substantially the same. By guaranteeing normalized reduced
RMS values which are substantially symmetrical on either side of a
vertical axis in far vision it is ensured that the wearer's left
eye and right eye encounter substantially the same optical defects,
which ensures a good balance of perception between the two
eyes.
A substantially horizontal line situated 8.degree. above the
fitting cross--i.e. approximately 4 mm above the fitting cross in
surface characterization of the lens, is also marked out in FIG. 8.
For the lenses of the applicant, this horizontal line therefore
passes beneath the far-vision control point as has been defined
previously.
In said semi-circle and beneath said horizontal line, the
difference in normalized reduced RMS between the nasal and temporal
zones is less than 0.12 microns per diopter. This very small
difference in normalized reduced RMS value allows optimal comfort
in binocular vision because it is this horizontal zone just above
the fitting cross which is most used by a wearer when he looks at a
point in far vision while moving his eyes laterally behind his
lenses.
In FIG. 8 it is seen that the vertical axis of symmetry between the
nasal and temporal parts of the lens substantially coincides with
the progression meridian in far vision. In fact, in the lenses of
the applicant, the progression meridian is defined as the line of
vision without lateral movements of the eyes from a target point in
far vision to a target point in near vision. It is understood that
other definitions can be envisaged for the progression meridian and
that the vertical axis of symmetry cannot then coincide with the
meridian as is the case in FIG. 8.
The lens of FIGS. 9 to 13 is another example of a lens according to
the invention; the lens of FIGS. 9 to 13 is suitable for presbyopic
wearers having a prescription for a 2.5 diopter power
progression.
FIGS. 9 to 13 show a lens of diameter 60 mm with a progressive
multifocal front face and comprising a prism of 1.44.degree. with a
geometric base orientated at 270.degree. in the TABO reference. The
plane of the lens is inclined 8.degree. relative to the vertical
and the lens has a thickness of 3 mm A value of q' of 27 mm (as
defined with reference to FIG. 1) was considered for the
measurements on the lens of FIGS. 9 to 13.
FIG. 9 shows a graph of the optical power of the wearer along the
meridian. The values are shifted to zero at the origin, where the
optical power is actually -0.06 diopters corresponding to a plane
lens in far vision prescribed for presbyopic emmetropic
wearers.
As in FIG. 4, a progression length PL is defined which is the
angular distance--or the difference in ordinates--between the
fitting cross FC--and a point on the meridian at which the power
progression reaches 85% of the prescribed power addition A. In the
example of FIG. 9, an optical power progression of 0.85.times.2.5
diopters, i.e. 2.125 diopters, is obtained for a coordinate point
of angle .beta.=approximately 24.50. The lens according to the
invention thus has a good accessibility to the powers required in
near vision with a moderate lowering of viewing, less than or equal
to 25.degree.. This accessibility guarantees comfortable use of the
near-vision zone.
FIG. 10 shows the contour lines for the optical power of the wearer
defined in a viewing direction and for an object point. In FIG. 10,
the 0 diopter to 2.50 diopter isopower lines are plotted in a
reference with spherical coordinates.
FIG. 11 shows the contour lines for the amplitude of the oblique
astigmatism under wearing conditions. In FIG. 11, the 0.25 diopter
to 2.25 diopter isoastigmatism lines are plotted in a reference
with spherical coordinates.
FIGS. 12 and 13 are similar to FIGS. 7 and 8 described above. It is
noted in FIGS. 12 and 13 that the values of normalized reduced RMS
and of difference in normalized reduced RMS between nasal and
temporal zones depend only to a small extent on the prescribed
addition value.
The lens of FIGS. 14 to 17 is an example of a lens of the prior
art, marketed by Essilor under the name Varilux Comfort.RTM.. The
lens of FIGS. 14 to 17 is suitable for presbyopic emmetropic
wearers having a prescription for a 2 diopter power
progression.
FIG. 17 shows the normalized reduced RMS iso lines. It is noted in
FIG. 17 that the normalized reduced RMS exceeds the value of 0.65
microns per diopter in the central zone of the lens.
A smooth and regular variation in the power between the far-vision
zone and the near-vision zone compared with FIG. 15 is also noted
in FIGS. 5 and 10. This smooth variation makes it possible to limit
the optical aberrations, in particular astigmatism, in order to
maintain a normalized reduced RMS which is not very great over all
of the central zone of the lens as shown in FIGS. 7 and 12 compared
with the lens of FIG. 17.
A regular and symmetrical distribution of the isoastigmatism lines
on either side of the meridian as well as lower levels of
astigmatism compared with FIG. 16 are also seen in FIGS. 6 and 11.
These characteristics of the astigmatism make it possible to limit
the optical aberrations and to maintain a normalized reduced RMS
which is not very great over all of the central zone of the lens,
compared with the lens of FIG. 17.
The lens according to the invention is prescribed by considering
the prescriptions of the wearer in far vision and in near vision
which determines the necessary addition. When the complex surface
is on the front face of the lens, the necessary power can be
obtained, as in the state of the art, by machining the rear face in
order to ensure that the power is identical to the prescribed
power.
The fitting of the lens in a visual device can take place in the
following manner. The horizontal position of the wearer's pupil in
far vision is measured, i.e. the interpupillary half-distance only,
and the overall height of the dimensions of the frame of the visual
device is determined. The lens is then fitted in the visual device
with the fitting cross positioned in the measured position.
In this regard reference can be made to the patent application
FR-A-2 807 169 describing a simplified method for fitting
ophthalmic lenses in a frame. This document in particular describes
the different measurements made by opticians and proposes to
measure only the interpupillary half-distance in order to carry out
the fitting of the lenses in the frame using the overall height of
the dimensions of the frame.
The fitting of the lens therefore only requires a standard
measurement of the interpupillary half-distance for far vision as
well as a measurement of the height of the dimensions of the frame
in order to determine the height at which the fitting cross must be
placed in the frame. The lens is then cut out and fitted in the
frame in such a way that the fitting cross is situated in a
determined position. The determination of the vertical position of
the fitting cross can of course be carried out in a standard manner
through measurement of the fitting height by measuring the position
in the frame of the subject's vision in far vision; this
measurement takes place in a standard manner, the subject wearing
the frame and looking into the far distance.
The lens according to the invention allows improved tolerance for
the fitting described above. This tolerance is provided by limiting
the optical aberrations around the fitting cross. In particular the
normalized reduced RMS value and the differences in normalized
reduced RMS symmetry are limited around the fitting cross.
The lens described above can be obtained by optimization of a
surface according to the optimization methods known per se and
described in the above-mentioned documents of the state of the art
relating to progressive multifocal lenses. In particular
optimization software is used in order to calculate the optical
characteristics of the lens-eye system with a predetermined merit
function. For the optimization, one or more of the criteria set out
in the above description can be used, and in particular:
a reduced RMS normalized to the addition prescription of less than
0.65 microns per diopter, in a zone delimited by a circle centred
on the prism reference point PRP and with a diameter corresponding
to a sweep of vision of 80.degree..
a progression length less than or equal to 25.degree.,
a difference in normalized reduced RMS of less than 0.12 microns
per diopter, calculated in absolute values as the difference in
normalized reduced RMS values between pairs of symmetrical points
relative to a vertical axis passing through the fitting cross, in a
zone including the far-vision control point FV and delimited by a
semi-circle centred on the fitting cross FC and with a radius
corresponding to raising viewing by 25.degree..
These criteria can be combined with others and in particular with a
difference in normalized reduced RMS of less than or equal to 0.12
microns per diopter below a substantially horizontal line situated
8.degree. above the fitting cross.
The choice of these criteria makes it possible to obtain a lens by
optimization. A person skilled in the art readily understands that
the lens in question does not necessarily have values corresponding
exactly to the set criteria; for example, it is not essential for
the upper value of the normalized reduced RMS to be obtained.
In the above examples of optimization it is proposed to optimize
only one of the faces of the lenses. It is clear that in all of
these examples, the roles of the front and rear surfaces can easily
be switched once optical targets similar to those of the lens
described are obtained.
* * * * *