U.S. patent number 3,722,986 [Application Number 05/190,058] was granted by the patent office on 1973-03-27 for high toric power ophthalmic lenses.
Invention is credited to Luc Andre Marcel Tagnon.
United States Patent |
3,722,986 |
Tagnon |
March 27, 1973 |
HIGH TORIC POWER OPHTHALMIC LENSES
Abstract
An ophthalmic aberration corrected toric lens which is derived
from a basic toric lens, said basic lens having on a block of
refringent material a spherical refracting surface and a toric
refracting surface, said basic lens further having first and second
main meridian planes at right angles to one another, said
ophthalmic aberration corrected toric lens having on a block of the
said refracting material two opposite refracting surfaces one of
which is identical to one of the two refracting surfaces of said
basic lens, while the other refracting surface of said aberration
corrected ophthalmic lens is a so-called aberration minimizing
surface and is shaped to maintain astigmatism and field curvature
aberrations of said ophthalmic lens less than .+-. 0.50
Diopters.
Inventors: |
Tagnon; Luc Andre Marcel
(Paris, FR) |
Family
ID: |
26180405 |
Appl.
No.: |
05/190,058 |
Filed: |
October 18, 1971 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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771143 |
Oct 28, 1968 |
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Foreign Application Priority Data
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Jul 26, 1968 [FR] |
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68160767 |
Oct 30, 1967 [FR] |
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67126369 |
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Current U.S.
Class: |
351/159.52 |
Current CPC
Class: |
G02C
7/02 (20130101) |
Current International
Class: |
G02C
7/02 (20060101); G02c 007/02 () |
Field of
Search: |
;351/176,159,169,177 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Rubin; David H.
Parent Case Text
This application is a continuation-in-part application of the now
abandoned patent application serial No. 771,143; filed Oct. 28,
1968, by the same applicant as that of the present invention.
Claims
What I claim is:
1. An ophthalmic aberration corrected toric lens which is derived
from a basic toric lens, said basic lens having on a block of
refringent material a spherical refracting surface and a toric
refracting surface, said basic lens further having first and second
main meridian planes at right angles to one another, said
ophthalmic aberration corrected toric lens having, on a block of
the said refracting material, two opposite refracting surfaces one
of which is identical to one of the two refracting surfaces of said
basic lens, while the other refracting surface of said aberration
corrected ophthalmic lens is a so-called aberration minimizing
surface and is shaped to maintain astigmatism and field curvature
aberrations of said ophthalmic lens less than .+-. 0.50 Diopters,
said ophthalmic lens further having first and second main meridian
planes coincident with said first and second main meridian planes
of said basic lens, respectively, said first and second main
meridian planes intersecting said aberration minimizing surface
along a first and a second meridian curve, respectively, which
divide said aberration minimizing surface into four quarters,
wherein: said first meridian curve is identical to a meridian curve
of a first aspheric surface of revolution adapted to minimize the
aberrations of a first spherical lens, the section of said first
spherical lens by a meridian plane thereof being identical to the
section of said basic lens by said first main meridian plane, said
first spherical lens being made of said refringent material, said
first meridian curve being determined by a first series of
discrepancies .epsilon..sub.x at several points of said first
meridian curve to a reference sphere centered on the optical axis
of said ophthalmic lens, said discrepancies .epsilon..sub.x being
measured along the radii of said reference sphere upon which are
situated said several points, respectively; said second meridian
curve is identical to a meridian curve of a second aspheric surface
of revolution adapted to minimize the aberrations of a second
spherical lens, the section of said second spherical lens by a
meridian plane thereof being identical to the section of said basic
lens by said second main meridian plane, said second spherical lens
being made of said refringent material, said second meridian curve
being determined by a second series of discrepancies
.epsilon..sub.y at several points of said second meridian curve to
said reference sphere, said discrepancies .epsilon..sub.y being
measured along the radii of said reference sphere upon which are
situated said several points, respectively, of said second meridian
curve and a random point of any one of said four quarters of the
aberration minimizing surface is situated firstly on a radius of
said reference sphere which makes an angle V.sub.i with said
optical axis and lies in a random meridian plane of said aberration
minimizing surface which makes an angle w with said first main
meridian plane, and secondly at a distance (discrepancy)
.epsilon..sub.wi from the surface of said reference sphere,
.epsilon..sub.wi being given by the formula:
.epsilon..sub.wi = .epsilon..sub.xi + (.epsilon..sub.yi -
.epsilon..sub.xi) [1 - f(w) ]
where .epsilon..sub.xi is the discrepancy of that one of the points
of said first main meridian curve which is situated on a radius of
said reference sphere making said angle V.sub.i with said optical
axis, .epsilon..sub.yi is the discrepancy of that one of the points
of said second main meridian curve which is situated on a radius of
said reference sphere making said angle V.sub.i with said optical
axis, and f(w) is a function of said angle w which varies from
0.degree. when said random meridian plane is coincident with said
first main meridian plane to 90.degree. when said random meridian
plane is coincident with said second main meridian plane, said
function being bound to the following conditions:
for w = 0.degree., f (w) = 1 and df(w)/dw = o
for w = 90.degree., f (w) = 0 and df(w)/dw = 0
whereby said one quarter is completely determined, the whole
aberration minimizing surface being completed by symmetries about
said first and second main meridian planes.
2. Ophthalmic toric lens according to claim 1, having a convex
refracting surface and a concave refracting surface, and which is
derived from a basic toric lens comprising a convex toric
refracting surface and a concave spherical refracting surface,
wherein said aberration minimizing surface is the concave surface
of the ophthalmic toric lens and has, in the close vicinity of the
optical axis, a spherical central portion identical to the relevant
central portion of said concave spherical refracting surface, said
aberration minimizing surface being gradually deformed towards the
outer periphery thereof while admitting as planes of symmetry said
first and second main meridian planes, said aberration minimizing
surface thereby presenting a toric character in the peripheral
portion thereof.
3. Ophthalmic toric lens according to claim 1, having a convex
refracting surface and a concave refracting surface, and which is
derived from a basic toric lens comprising a convex spherical
refracting surface and a concave toric refracting surface, wherein
said aberration minimizing surface is the concave surface of the
ophthalmic toric lens and has in the close vicinity of the optical
axis a toric central portion identical to the relevant central
portion of said concave toric refracting surface, said aberration
minimizing surface being gradually deformed towards the outer
periphery thereof while still admitting as planes of symmetry said
first and second main meridian planes and thereby preserving a
toric character.
4. Ophthalmic toric lens according to claim 1, having a concave
refracting surface and a convex refracting surface, and which is
derived from a basic toric lens comprising a concave toric
refracting surface and a convex spherical refracting surface,
wherein said aberration minimizing surface is the convex surface of
the ophthalmic toric lens and has, in the close vicinity of the
optical axis, a spherical central portion identical to the relevant
central portion of said convex spherical refracting surface, said
aberration minimizing surface being gradually deformed towards the
outer periphery thereof while admitting as planes of symmetry said
first and second main meridian planes, said aberration minimizing
surface thereby presenting a toric character in the peripheral
portion thereof.
5. Ophthalmic toric lens according to claim 1, having a concave
refracting surface and a convex refracting surface, and which is
derived from a basic toric lens comprising a concave spherical
refracting surface and a convex toric refracting surface, wherein
said aberration minimizing surface is the convex surface of the
ophthalmic toric lens and has in the close vicinity of the optical
axis a toric central portion identical to the relevant central
portion of said convex toric refracting surface, said aberration
minimizing surface being gradually deformed towards the outer
periphery thereof while still admitting as planes of symmetry said
first and second main meridian planes and thereby preserving a
toric character.
6. Ophthalmic toric lens according to claim 1, wherein the
aberrations which are minimized are those prevailing for an
infinite distance of vision.
7. Ophthalmic toric lens according to claim 1, wherein the
aberrations which are minimized are those prevailing for a finite
distance of vision.
8. Ophthalmic toric lens according to claim 1, wherein said
aberration minimizing surface is composed of several adjacent
aberration minimizing surface areas in each of which the
aberrations which are minimized are those prevailing for a
predetermined distance of vision.
9. Ophthalmic toric lens according to claim 1, wherein said
function f(w) is cos.sup.2 w.
Description
BACKGROUND OF THE INVENTION
This invention relates in general to ophthalmic high power lenses
and has reference more particularly to improvements in ophthalmic
toric lenses.
When the eye before which an ophthalmic lens is placed utilizes a
peripheral zone thereof, aberrations, astigmatism and notably field
curvature appear and reduce the quality of the eye ametropia
correction.
In practice, this defect is negligible in the case of negative
power lenses and low positive power lenses, provided that these
lenses have a suitable curvature. On the other hand, it limits the
useful vision of an eye provided with a high-power positive lens,
for the higher the lens power the smaller the useful area of the
lens.
It is known to resort to aspheric surfaces for reducing these
aberrations. The term "aspheric" usually denotes surfaces of
revolution such as paraboloids and ellipsoids, for example,
obtained by causing the same parabolic or elliptic curve to rotate
about the axis of the lens. These surfaces are currently used in
instrumental optics. They permit a certain correction of the
aberrations of ophthalmic lenses when these are designed for a
single type of vision, for instance distant vision. Moreover,
making such surfaces requires such elaborate machines and processes
that their cost is very expensive. Finally, in many cases the human
eye suffers from astigmatism, for example the post-operative
residual corneal astigmatism of a patient operated for cataract,
which entails the use of toric lenses, for example toric lenses
having a spheric radius +12.00 and a cylindrical radius + 3.00. It
will be readily understood that hitherto known aspheric surfaces of
revolution are not capable of correcting such lenses in a very
satisfactory manner. Either one main meridian will be properly
corrected for aberrations but not the other, or the aspheric
surface of revolution is designed to correct the aberrations in a
mean meridian but it leaves still too important aberrations
uncorrected in the main meridians.
On the other hand the applicant has been producing for more than
ten years progressive ophthalmic lenses. This type of lens usually
comprises, on a block of refringent material, two opposite
refracting surfaces: a first conventional refracting spherical or
toroidal surface and a second refracting surface, so called
progressive surface. This progressive surface cannot be simply
described in terms of circle, ellipse, etc.
Elementary optical calculation adapted to the manufacturing
processes permits to determine such progressive surfaces point by
point and to produce them at an economical industrial scale as
follows:
Every point A.sub.i of the desired progressive surface is
referenced on the one hand by the two spherical coordinates
(hereinafter referred to as V.sub.x and V.sub.Y) of the point of
intersection P with the basic sphere Q on the radius of sphere Q
passing by the considered point of the meridian, and, on the other
hand, by the distance .epsilon..sub.i between said considered point
A.sub.i of the meridian and said point P of intersection (See FIG.
5 of the enclosed drawings). Thus, the surface is determined by a
table of discrepancies or distances .epsilon..sub.i for a great
number of points of said surface, the distribution of which is
chosen to be uniform to allow an easy interpolation; for instance
V.sub.x and V.sub.y will be the spherical coordinates of the points
of intersection of regularly spaced meridian curves with regularly
spaced parallel curves of the basic sphere Q. Then, a high stress
resistant steel master pattern of the desired surface is ground,
point by point, by means of the diamond wheel grinding machine
disclosed in the U.S. Pat. No. 2,982,058 for the use of which the
discrepancy table must be transformed into a grinding table by
means of simple calculation taking into account the geometrical
features of the machinery such as for instance the diameter of the
grinding wheel. Then, this master pattern is reproduced by means of
the reproducing machine disclosed in the U.S. Pat. No. 3,041,789,
on a refringent material block to make a lens blank, or a suitable
material to make a mould which permits to obtain a lens by casting
a polymerizable material, or a hard refractory material used as a
stand upon which a glass block is caused to weigh down when put in
a temperature regulated furnace. The desired surface in then
smoothed by means of the machine disclosed in the U.S. Pat. No.
3,021,647 which does not alter its shape, then polished by means of
well known flexible polisher machinery. The same procedure may be
adhered to for determining and producing any kind of refracting
surface of an ophthalmic lens to obtain a given result. For
instance the applicant uses this procedure to determine and
industrially produce aspheric aberration correcting surfaces of
revolution, the meridian of which needs no longer to be of a known
curve. These surfaces lead to a better result which is mainly due
to the simplicity and the high precision of the manufacturing
process above recalled.
SUMMARY OF THE INVENTION
It is the essential object of the present invention to provide a
novel type of ophthalmic toric lens of which at least one of its
two refracting surfaces constitutes an aberration minimizing
surface which, by taking due account of the desired final
characteristics of a toric single-focus lens, on the one hand, and
on the other hand of the conditions of use of this lens, permits
the best correction of the aberrations. The aberration minimizing
surface of an ophthalmic lens according to this invention, designed
notably for equipping spectacles, is obtained mainly by properly
determining the distance or discrepancy between each point of said
surface and the corresponding point of a basic sphere, these
distances being counted on the radii of said sphere.
To this end, the invention provides an ophthalmic aberration
corrected toric lens which is derived from a basic toric lens, said
basic lens having on a block of refringent material a spherical
refracting surface and a toric refracting surface, said basic lens
further having first and second main meridian planes at right
angles to one another, said ophthalmic aberration corrected toric
lens having,on a block of the said refracting material, two
opposite refracting surfaces one of which is identical to one of
the two refracting surfaces of said basic lens, while the other
refracting surface of said aberration corrected ophthalmic lens is
a so-called aberration minimizing surface and is shaped to maintain
astigmatism and field curvature aberrations of said ophthalmic lens
less than .+-. 0.50 Diopters, said ophthalmic lens further having
first and second main meridian planes coincident with said first
and second main meridian planes of said basic lens, respectively,
said first and second main meridian planes intersecting said
aberration minimizing surface along a first and a second meridian
curve, respectively, which divide said aberration minimizing
surface into four quarters, wherein: said first meridian curve is
identical to a meridian curve of a first aspheric surface of
revolution adapted to minimize the aberrations of a first spherical
lens, the section of said first spherical lens by a meridian plane
thereof being identical to the section of said basic lens by said
first main meridian plane, said first spherical lens being made of
said refringent material, said first meridian curve being
determined by a first series of discrepancies .epsilon..sub.x at
several points of said first meridian curve to a reference sphere
centered on the optical axis of said ophthalmic lens, said
discrepancies .epsilon..sub.x being measured along the radii of
said reference sphere upon which are situated said several points,
respectively; said second meridian curve is identical to a meridian
curve of a second aspheric surface of revolution adapted to
minimize the aberrations of a second spherical lens, the section of
said second spherical lens by a meridian plane thereof being
identical to the section of said basic lens by said second main
meridian plane, said second spherical lens being made of said
refringent material, said second meridian curve being determined by
a second series of discrepancies .epsilon..sub.y at several points
of said second meridian curve to said reference sphere, said
discrepancies .epsilon..sub.y being measured along the radii of
said reference sphere upon which are situated said several points,
respectively, of said second meridian curve and a random point of
any one of said four quarters of the aberration minimizing surface
is situated firstly on a radius of said reference sphere which
makes an angle V.sub.i with said optical axis and lies in a random
meridian plane of said aberration minimizing surface which makes an
angle w with said first main meridian plane, and secondly at a
distance (discrepancy).epsilon. .sub.wi from the surface of said
reference sphere, .epsilon..sub.wi being given by the formula:
.epsilon..sub.wi = .epsilon..sub.xi + (.epsilon..sub.yi -
.epsilon..sub.xi) [1 - f(w)]
where .epsilon..sub.xi is the discrepancy of that one of the points
of said first main meridian curve which is situated on a radius of
said reference sphere making said angle V.sub.i with said optical
axis, .epsilon..sub.yi is the discrepancy of that one of the points
of said second main meridian curve which is situated on a radius of
said reference sphere making said angle V.sub.i with said optical
axis, and f(w) is a function of said angle w which varies from
0.degree. when said random meridian plane is coincident with said
first main meridian plane to 90.degree. when said random meridian
plane is coincident with said second main meridian plane, said
function being bound to the following conditions:
for w = 0.degree. , f (w) = 1 and df(w)/ dw = 0
for W = 90.degree. , f (w) = 0 and df(w)/w = 0
whereby said one quarter is completely determined, the whole
aberration minimizing surface being completed by symmetries about
said first and second main meridian planes.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects, features and advantages of the present invention
will appear more clearly as the following description proceeds with
reference to the accompanying drawing illustrating diagrammatically
by way of example various forms of embodiment of the ophthalmic
lenses according to the present invention. In the drawings:
FIG. 1 illustrates in diagrammatic form an eye with which a
corrector lens is associated, this eye looking successively at an
object point located at infinity and an object point located at a
finite distance;
FIG. 2 is a diagram showing the aberrations under distant-vision
conditions with a spherical lens having a + 12.00-diopter power, as
a function of the angle of vision to the horizontal;
FIG. 3 is a diagram illustrating the method of calculating the
discrepancies with respect to a reference sphere for obtaining a
meridian, of an aberration minimizing surface of an ophthalmic lens
according to the invention;
FIG. 4 is a diagram showing the aberrations of a toric lens of +
12.00 D (cylinder + 3.00 D);
FIG. 5 shows the reference system principle used for obtaining a
discrepancy table;
FIG. 6 is a diagram illustrating the calculation of the discrepancy
at a random point of an aberration minimizing surface of a first
type according to the invention;
FIG. 7 is a simplified illustration of the general shape of an
aberration minimizing surface of said first type;
FIG. 8 is a discrepancy table of a quarter of an actual exemplary
aberration minimizing surface for a toric lens + 12.00 D (cylinder
+ 3.00 D);
FIG. 9 shows the characteristics of the lens of the actual chosen
example, and the intersection of the aberration minimizing surface
of sais lens by the two main meridian planes thereof and by an
intermediate meridian plane at 45.degree. to the main meridian
planes.
FIG. 10 shows isodiscrepancy curves of the aberration minimizing
surface of the first type according to the invention, for the
chosen example.
FIG. 11 gives the performances of a toric lens having the same
focal power as that of the chosen example, but corrected according
to the previously known method by an aspheric surface of
revolution;
FIG. 12 illustrates the results of the correction of aberrations on
the spherical surface by a surface of the first type according to
the invention;
FIG. 13 is a simplified illustration of the general shape of an
aberration minimizing surface of a second type according to the
present invention;
FIG. 14 is a diagram illustrating the calculation of the
discrepancy at a random point of an aberration minimizing surface
of said second type;
FIG. 15 gives the general characteristics of a second exemplary
lens + 14.00 D (cylinder + 2.00 D) corrected by an aberration
minimizing surface of said second type, and shows the curves of
intersection of the aberration minimizing surface of said second
exemplary lens by the two main meridian planes thereof and by an
intermediate meridian plane at 45.degree. to the main meridian
planes;
FIG. 16 is the discrepancy table of a surface of the second type
according to the invention adapted to correct or minimize the
aberrations of the lens of the second chosen example, the
discrepancies being given with respect to the concave toric surface
of the basic toric lens, in the reference system of FIG. 5;
FIG. 17 shows isodiscrepancy curves illustrating the deformation
applied to the concave toric surface of the lens of the second
chosen example to obtain its aberration minimizing surface; and
FIG. 18 is a front view of a lens of which the upper and lower
halves are corrected for aberrations prevailing in distant vision
and reading vision, respectively.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring first to FIG. 1, an eye 1 looks at a point located at
infinity through its corrector lens 2 having an optical axis 3
passing through the center of rotation 0 of the eye, the axis of
vision forming an angle U with the optical axis 3. Assuming that if
U = 0 the ametropia correction is perfect, a point at infinity
gives an image (R.sub.o) which, when received by the optical
instrument constituted by the human eye, forms an image (Z.sub.o)
upon the retina. When, without altering its accommodation, the eye
rotates about 0, a point at infinity will be seen clearly,
irrespective of the value of angle U, if the image R of this point
describes a sphere 5 having a center 0 and a radius OR.
In practice, if the lens has to be shaped to have a spherical
surface, for example for any value of U other than 0, the light ray
from the object point lying at infinity will bear on a sagittal
focus S and a tangential focus T, and the circle of least confusion
lies at I. The field curvature IR and the astigmatism TS are the
main aberrations disturbing the correction of the eye's
ametropia.
FIG. 2 illustrates the aberrations of a spherical power lens of +
12.00 diopters as a function of the angle U for infinity
observation. These curves illustrate not the variation in the
position of the various images but the variaion of the reciprocals
of the distances in meters from said images to a same reference
point.
To simplify the following calculations the point of reference is
selected as customary at the intersection of the central ray of the
direction of vision with the circle centered at 0 and having a
radius OH of which the value, for all practical purposes, is of the
order of 27 to 28 millimeters (FIG. 1). This point is denoted K for
distant or infinity vision and G when the eye looks at an object
point M. Consequently, these reciprocals are as follows:
F.sub.T = 1/KT , F.sub.S = 1/KS, F.sub.I = 1/KI and F.sub.B = 1/KR
= 1/HRo
For infinity vision, the eye does not accommodate and F.sub.R is a
constant power.
FIG. 2 shows that a + 12.00-diopter spherical lens, if U =
30.degree., has a field curvature c = BC = F.sub.I -F.sub.R = 0.65
D, and an astigmatism a = AD =F.sub.T - F.sub.S = 4.50 D.
Let us consider a toric high power ophthalmic lens + 12.00 D
(cylinder + 3.00 D) to be corrected for aberrations and of which
the concave refracting surface is spherical. This toric lens has
aberrations represented in FIG. 4 as usual in the two main
meridians.
The sagittal power remains close to the desired value, that is to
say, in FIG. 1, S remains close to R or KS does not differ very
much from KR.
The tangential power increases with U, that is to say KT decreases
very much from its value HRo when U = 0 (FIG. 1). The rate of
increasing is very high and is responsible for the narrowing of the
field of view of such an aberration uncorrected lens.
In FIG. 1, for a spherical power lens, the reduction of astigmatism
can be illustrated by bringing KT close to KS and the reduction of
field curvature by bringing (KI + KS)/ 2 = KI close to KR. This
illustration can be easily transposed to illustrate the correction
of a toric lens as it is usual in the art. Due to the fact that an
ophthalmic lens is a simple optical system which has a too small
number of independent parameters it is well known in the art that
the correction of the aberrations leads to a compromise. Field
curvature error and parasitic astigmatism can only be brought
between acceptable limits which, for high power lenses and by way
of illustrating example, are usually .+-. 0.50 Diopters for U =
30.degree..
To correct the aberrations of the toric lens of the above example,
one can modify, for instance, the shape of its concave spherical
refracting surface, to reduce the tangential power while reducing
or maintaining the sagittal power within said acceptable limits,
and to obtain variations of FT and FS as functions of angle u
adapted to bring the field curvature within said acceptable
limits.
This is obtained by optical calculations as follows.
Referring to FIG. 3, let us consider the section of the to be
corrected toric lens by its + 12.00 D main meridian plane. Assuming
that this section is rotated around the optical axis of the lens,
it will generate a spherical single focus + 12.00 D lens which is
made of the same refringent material as that of said toric lens and
has a meridian section identical to that of the to be corrected
toric lens by the + 12.00 D main meridian plane thereof.
Considering now this spherical + 12.00 D lens,for as many values of
angle U as desired, the tangential and sagittal power along said
meridian section (1/KT and 1/KS) can be easily calculated by usual
optical calculation using the parameters represented in FIG. 3.
Thus, for each selected value of angle U one can calculate (1/KT) -
(1/KR) which is the excess of power to be cut off from the
tangential power.
Let us consider a reference sphere Q of which the center is Oo and
the radius ro, and which is tangent to the concave spherical
surface of the lens.
At every value of angle U corresponds a point A.sub.i of the
meridian curve of the desired aberration minimizing surface.
At every value of the angle U corresponds a power to be cut off
from tangential power along the sight axis to which corresponds a
power to be cut off from the tangential power along the axis
A.sub.i O.sub.o. Usual optical calculations permit to obtain the
tangential power and the excess power along A.sub.i O.sub.o from
tangential power and excess power along the sight axis.
For every point A.sub.i it is an easy matter to calculate the
decreasing of the radius of curvature of the concave meridian curve
which is needed to cut off the excess tangential power from the
tangential power.
So, step by step, a series of values is obtained which gives for
every point A.sub.i the value of the radius of curvature of the
concave meridian curve.
This leads to the profile of said concave meridian curve. The
aberration minimizing surface of said spherical + 12.00 D lens is
of course of revolution. It is easy to calculate the sagittal
radius of this surface along AiOo.
In the to be corrected toric lens of + 12.00 d (cylinder + 3.00 D)
the portion of the desired aberration minimizing surface on either
side of and in the vicinity of the + 12.00 D main meridian plane
can be considered, in first approximation, identical to the
aberration minimizing surface of the spherical + 12.00 D lens along
a meridian of which the values of the tangential and sagittal radii
are known at least at every chosen point A.sub.i of said concave
meridian curve.
Simple optical calculations lead to the tangential and sagittal
powers along the sight axis for the corresponding values of U.
Due to necessary approximations the profile of the meridian curve
of the concave aberration minimizing surface of the toric lens, in
the + 12.00 D meridian plane, is obtained after several
calculations as hereinabove explained which permits to know the
influence of this profile on the tangential and sagittal power
variations and to choose the best possible compromise. This profile
is known as a series of values of the radii of curvature of the
meridian curve at every point of said meridian curve corresponding
to every chosen point A.sub.i, that is as a function of angle U. It
is an easy step to obtain the actual shape of this curve and to
determine the discrepancies or distances .epsilon..sub.i to the
basic sphere Q of this curve at every point A.sub.i.
The meridian curve in the + 12.00 D main meridian plane of the
desired aberration minimizing surface is thus known as a first
series of discrepancies to the reference sphere Q in as many points
as desired.
To determine the meridian curve in the + 15.00 D main meridian
plane which is at right angles to the + 12.00 main meridian plane,
one follows exactly the same procedure. This leads to a second
series of discrepancies to the reference sphere Q in as many points
as desired.
FIG. 5 illustrates the principle of the reference system used and
how the discrepancies are posted up into a table. Usually, the
points A.sub.i are chosen to be spaced from one another every 2
millimeters measured on the surface of the reference sphere Q, and
are represented on the table in a point of which the coordinates
s.sub.x and s.sub.y corresponds to the curvilinear distances
S.sub.x and S.sub.y measured on the surface of the sphere Q in the
represented polar coordinates system.
At this point of the explanations the series of discrepancies of
the + 12.00 D main meridian of the aberration minimizing surface
according to the invention is posted up into the central vertical
column of the table, and the series of discrepancies of the + 15.00
D main meridian of the same aberration minimizing surface is posted
up into the horizontal central line of the table.
To obtain the complete discrepancy table of the aberration
correcting surface according to the invention one proceeds as
follows:
At a given distance s to the center of the table correspond a point
on the central column s.sub.y = s, s.sub.x = 0 and a point on the
central line (s.sub.y = 0, s.sub.x = s). Let us call those two
points the corresponding points of the central column and central
line of the table. A series of differences between the
discrepancies of these corresponding points for different values of
s is established.
The two main meridian planes of the toric lens divide the desired
aberration minimizing surface into four quarter. The discrepancy at
a point situated in any one of said four quarters at a distance s
from the center of the table and belonging to the curve of
intersection of the aberration minimizing surface by a meridian
plane making an angle w with the vertical meridian plane O P Y
(FIG. 6) is given by the formula :
.epsilon..sub.w = .epsilon..sub.x + (.epsilon..sub.y -
.epsilon..sub.x) [1 - f(w) ] (1)
where .epsilon..sub.w is the discrepancy at said point of the
intermediate meridian curve situated at the distance s from the
center of the table, .epsilon..sub.y is the discrepancy at the
point of the central vertical column located at a distance s from
the center of the table, .epsilon..sub.x is the discrepancy at the
point of the central horizontal line located at a distance s from
the center of the table, and f (w) is a chosen function of the
angle w which satisfies the following conditions
df(w)/dw = 0, f(w) = 0 for w = 90.degree.
df(w)/dw = 0, f(w) = 1 for w = 0
w is allowed to take any value between 0.degree. and 90.degree.,
the table being then completed by symmetries with respect to the
two main meridians.
f(w) is determined as follows:
Along one or several intermediate meridians corresponding to one or
several values of angle w, several profiles corresponding to
several series of values of .epsilon..sub.w are tried to obtain
different corrections of aberrations along said intermediate
meridians. This leads to the choice of the best value or values of
the function f (w) corresponding to this (or these) meridians.
Having thus determined different values of the function f(w), it is
an easy step to determine it.
For instance this function can be
f (w) = Cos..sup.2 (w)
then, it is easy, by interpolations, to obtain the discrepancy at
any point of the table of discrepancies of the surface according to
the invention. The above-described method of determining the
aberration minimizing surface of a toric lens leads to meridians
for which no hypotheses have been made as to their shape;
experience teaches that in the case of high-power lenses the
resulting tables of divergences lead to curves of which the shapes
can be described as elliptic shapes,at least for simplification
sake of the explanation. Thus, an example affording a clearer
understanding of the shape of the aberration minimizing surface can
be given with reference to FIG. 7. Since the aberration minimizing
surface is concave in this example, these ellipses or elliptic
portions revolve about their minor axis and admit the radius
(r.sub.o) of the concave spherical surface of the lens as the
radius of the osculating circle at the pole P of the aberration
minimizing surface.
Thus, in the first main meridian M.sub.1, the ellipse E.sub.1 will
be characterized by parameters a.sub.1 and b.sub.1 the values of
which, on the one hand, are chosen so that ellipse E.sub.1
approximates the above-determined main meridian curve corresponding
to the first series of discrepancies, and, on the other hand,
satisfy the well known relation between the radius of the
osculating circle at the tip of the minor axis of an ellipse and
the parameters thereof, that is, in the present case: a.sub.1.sup.2
/b.sub.1 = r.sub.o. Similarly, in the second main meridian M.sub.2,
the ellipse E.sub.2 will be characterized by a.sub.2 and b.sub.2
such that a.sub.2.sup.2 /b.sub.2 = r.sub.o . A random meridian
curve m.sub.i of the aspheric surface will thus be an ellipse
characterized by a.sub.i and b.sub.i such that, on the one hand,
a.sub.i.sup.2 /b.sub.i = r.sub.o and, on the other hand, a.sub.i =
A(w) and b.sub.i = B(w), where w denotes the angle formed between
the meridian involved and, for instance, the first main meridian,
and A(w) and B(w) are two functions of w , these two functions
being such that the discrepancy to the reference sphere Q at any
point A.sub.i of meridian curve m.sub.i satisfies the
above-mentioned formula (1).
The aberration minimizing surface will thus appear as constituting
the envelope of an ellipse E.sub.i revolving about its minor axis
and undergoing a deformation between two endmost ellipses E.sub.1
and E.sub.2 while preserving the same osculating circle at its
vertex or pole P.
FIG. 8 is the actual discrepancy table of the concave aberration
minimizing surface of the lens the actual characteristics of which
are given in FIG. 9. This discrepancy table is in fact a
discrepancy table of a quarter of the aberration minimizing surface
limited to one-half of the .+-. 12.00 D main meridian corresponding
to the column 50 of the table and to one-half of the .+-. 15.00 D
main meridian corresponding to the line 50 of the table. These
discrepancies are given in microns for curvilinear distances on the
surface of sphere Q of 4 mm between two adjacent points. The
intermediate values are easily obtained by interpolation, the
discrepancy table of the complete surface, of course being obtained
by symmetries with respect to the two main meridians since this
surface is symmetrical with respect to its two main meridian
planes.
In FIG. 9 is given a representation of the profile of the
intersection of the surface according to the invention by the two
main meridian planes of the lens and by the intermediate meridian
corresponding to w = 45.degree., the radius of the reference sphere
being conventionally assumed as having an infinite value in this
FIG. 9.
FIG. 10 shows the isodiscrepancy curves of one-half of the surface
according to the invention which appears as a surface having a
spherical central portion which is gradually deformed towards the
outer periphery, and admitting as its planes of symmetry the planes
of the main meridians of the toric lens, thus assuming the presence
of a toric character in this peripheral portion.
For this reason, the aberration minimizing surfaces illustrated in
FIG. 7 which correspond to the above description, are surfaces of a
first type of aberration minimizing surface according to the
invention and will be referred to as "atoric sphere" aberration
minimizing surfaces.
The interest of such aberration minimizing surfaces is illustrated
by the actual results obtained, readily measurable and represented
in FIG. 12 as compared to the results hitherto accepted represented
in FIG. 11. These results correspond to the actual chosen
example.
Let us consider as another example an aberration-uncorrected toric
lens consisting of a convex spherical refracting surface and a
concave torical refracting surface.
To correct the aberrations of such a lens one can modify the shape
of the concave torical surface of the lens into an aberration
minimizing surface of a second type. The explanations and the
calculation procedure given hereinabove are readily transposable
here.
As it has already been mentioned hereinabove, to simplify the
explanations and to give an idea of the shape of an aberration
minimizing surface of the second type according to the present
invention, let us assume that the meridian curves are or
approximate ellipses (FIG. 13). The main meridian curve m.sub.1
will be an ellipse E.sub.1 characterized by parameters a.sub.1 and
b.sub.1 such that a.sub.1.sup.2 /b.sub.1 = r.sub.1, the main
meridian curve m.sub.2 being an ellipse E.sub.2 characterized by
parameters a.sub.2 and b.sub.2 such that in this case a.sub.2.sup.2
/b.sub.2 = r.sub.2 ; and a random meridian curve m.sub.i being an
ellipse E.sub.i characterized by parameters a.sub.i and b.sub.i
such that a.sub.i.sup.2 /b.sub.i = r.sub.i, wherein r.sub.i is
determined by the elliptic indicatrix of the toric surface at its
vertex P, i.e. the curve representing r.sub.i = H (w) which at the
vertex P of the uncorrected concave toric surface is an ellipse. As
in the foregoing, a.sub.i and b.sub.i are two functions of w which
vary respectively from a.sub.1 to a.sub.2, and from b.sub.1 to
b.sub.2, these two functions of w being such that the discrepancy
to the reference sphere Q at any point A.sub.i of the random
intermediate meridian curve satisfies the above-mentioned formula
(1) considered with reference to FIG. 14 which corresponds to FIG.
6.
Let us consider the actual example of a + 14.00 cylinder + 2.00 D)
lens of which the characteristics are represented FIG. 15.
In the reference system represented in FIG. 5, one can easily
calculate the table of discrepancies of the concave toric
refracting surface (r.sub.1 = 168 mm and r.sub.2 = 504 mm) with
respect to the reference sphere Q which is tangent to said toric
surface at its point of intersection with the optical axis of the
lens and has a radius ro = 168.00 mm. It will be noted that in the
+ 14.00 D main meridian, the series of discrepancies contains zero
only since the radius r.sub.1 of the concave meridian is 168.00
mm.
The above-mentioned modification of the shape of this toric concave
surface to obtain the aberration minimizing surface is given by the
discrepancy table of FIG. 16. More precisely, the discrepancy
values plotted in table of FIG. 16 corresponds to discrepancies
with respect to the aberration-uncorrected toric surface which are
measured along the radii of the reference sphere Q. This
discrepancy table is in fact a discrepancy table of a quarter of
the aberration minimizing surface limited to one-half of the +
14.00 main meridian plane (column 50) and to one-half of the +
16.00D main meridian plane (line 50). These discrepancies are given
in microns and for curve distances on the sphere Q of 4 mm between
two adjacent points. The intermediate values can be easily obtained
by mere interpolation and the complete table can be easily obtained
by symmetries with respect to the two main meridians of the toric
lens since this surface is symmetrical with respect to these two
main meridian planes.
On FIG. 15 is given a representation of the profile of the
deformation of the toric surface (this toric surface being
conventionally assumed to be a plane) in the two main meridians and
in the intermediate meridian corresponding to w = 45.degree..
FIG. 17 shows the isodiscrepancy curves of this deformation brought
to the concave toric surface. It points out that this deformation
is of a nature identical to the nature of the deformation of the
concave spherical surface leading to the aberration minimizing
surface of the first type according to the invention.
To obtain the discrepancy table of the concave aberration
minimizing surface with respect to the sphere Q, one has to add for
every point of the desired aberration minimizing surface having
given coordinates the discrepancy with respect to sphere Q of the
point of the uncorrected toric surface having these given
coordinates and the discrepancy corresponding to the deformation to
be applied to this point of the uncorrected toric surface to obtain
the point of given coordinates of the desired aberration minimizing
surface. In other words, one has merely to superimpose the two
discrepancy tables and to add the discrepancies point by point.
It will be seen that the aberration minimizing surface is merged
into the initial toric surface in the vicinity of the central zone
of the lens and evolves towards the edges while preserving its
toric character, notably by preserving for its planes of symmetry
the main planes of the lens. For this reason, these aberration
minimizing surfaces of the second type according to the invention
will be referred to as surfaces of the "atoric tore" type.
It will be noted that ophthalmic toric lenses, according to the
invention, which are derived from a basic toric lens, can be
obtained by correcting the aberrations of said basic lens either by
altering the shape of its spherical surface into a first type
surface called "atoric sphere" surface, or by altering its toric
surface into a second type surface called "atoric tore" surface.
The corrections thus obtained are equivalent and the choice between
these two types is made from manufacturing considerations.
In the foregoing, it has been assumed in the two examples that the
aberration minimizing surface was obtained by altering the shape of
the concave spherical or toric surface of the basic toric surface
from which it derives into a surface of the first or second type,
respectively, but said aberration minimizing surface could as well
be obtained by altering the convex toric or spherical surface, as
may be the case, of said basic surface into a surface of the second
or first type, respectively, the same explanations applying also
here. As a matter of fact, the aberration minimizing surfaces of
the first and second type, which are diagrammatically illustrated
in FIGS. 6 and 7 and FIGS. 13 and 14, respectively, are represented
alone and could constitute the concave refracting surface of the
toric lens as well as the convex refracting surface thereof.
In all the foregoing the observation of an object point at infinity
was contemplated. Now when the eye is capable of accommodation such
toric lenses can also be used for reading. In this case they have
different aberrations which are sometimes not sufficiently
corrected by the distortion corresponding to infinity vision.
As shown in FIG. 1, it is an easy matter to determine according to
the same principles a lens corrected for observing at a finite
distance d = MN It is only necessary to adhere to the
above-described method.
It is even possible, without departing from the scope of the
present invention, to provide ophthalmic lenses provided on at
least one face with aberration minimizing surface areas determined
respectively in such a manner as to correct the aberrations
corresponding to a plurality of vision distances. The simplest case
illustrated in FIG. 18 is an unifocal lens of which the upper half
is corrected for aberrations prevailing in distant vision VL and
the lower half for aberrations prevailing in reading vision (VP);
the line separating these two surfaces being for example
discontinuous as in the case of a bifocal lens.
To manufacture lenses according to the invention, one can resort to
the method and machinery recalled in the foreword of the present
application. Usually these high-power lenses are thick and to save
weight one prefers to manufacture them by casting a polymerizable
material between conveniently shaped mold elements.
It would not constitute a departure from the invention to direct
the correction to field curvature only, parasitic astigmatism only,
distortion only or to any compromise between these aberrations.
Furthermore, it would not lie outside the scope of the invention to
associate in a same lens two aberration correcting surfaces in
order to obtain a better correction of the aberrations or to
incorporate the correction of another type of aberration.
* * * * *