Method of minimizing the maximum thickness of a unifocal ophthalmic lens and gradient index unifocal ophthalmic lens obtained by application of this method

A unifocal ophthalmic lens has part-spherical concave and convex surfaces. Its refractive index varies radially from its optical axis to its periphery. The variation of the refractive index is governed by a law such that the absolute value of the optical power of the lens is significantly greater than its geometrical power when the optical power is computed using the refractive index of the lens on its optical axis.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention is generally concerned with unifocal ophthalmic 
lenses, that is to say constant power lenses, whether they are convergent 
(positive power) lenses or divergent (negative power) lenses. 
It is more particularly directed to lenses in which the convex front 
surface and the concave rear surface are both part-spherical. 
2. Description of the prior art 
These lenses have the advantage of being relatively easy to machine. 
They give rise to two problems, however. 
The first relates to the fact that for relatively high powers their maximum 
or critical thickness, which is the thickness at the center for a positive 
power or the thickness at the periphery for a negative power, is 
relatively high, which is detrimental from the esthetic point of view and, 
given their resulting weight, from the user comfort point of view. 
The second problem relates to the fact that, especially for higher powers, 
abberations and in particular astigmatism and field curvature abberations 
become increasingly important as the user's axis of vision moves away from 
the optical axis of the lens. 
To minimize such abberations an aspherical surface is usually employed for 
at least one surface of the lens, at the cost of complicated machining 
thereof. 
Also, the refractive index of the material contituting ophthalmic lenses is 
usually uniform. 
In the case of ophthalmic lenses with part-spherical concave and convex 
surfaces the power is then geometrically determined by the refractive 
index, the radius of curvature of the surfaces and the thickness at the 
center. 
However, it has already been proposed to vary the refractive index of an 
ophthalmic lens radially from its optical axis to its periphery. 
This is the case, for example, in British Patent No 1 571 930 and also in 
published French patent application No 2 599 157. 
In both cases this is essentially to correct abberations. 
In more precise terms, in British patent No 1 571 930, in which the 
refractive index varies in a quasi linear manner, the preferential 
arrangement is such that, given this variation in the refractive index, 
the concave and convex surfaces of the lens concerned are still 
effectively part-spherical. 
In published French patent application No 2 599 157, in which the concave 
and convex surfaces are necessarily part-spherical, it is in principle a 
question of minimizing the critical thickness of the lens. 
However, the examples described in this document show that the refractive 
index does not necessarily vary in any significant manner in the central 
part of the lens, which is the most used part, and most importantly that 
the optical power of the lens does not differ in any significant way from 
its geometrical power. 
The present invention is based on the fact, not previously demonstrated, 
that by appropriately varying the refractive index it is possible to 
modify significantly the optical power of a lens relative to its 
geometrical power, while achieving satisfactory correction of astigmatism 
and field curvature. 
It is directed to the manufacture of unifocal ophthalmic lenses which 
advantageously have accurately part-spherical concave and convex surfaces 
and are therefore easy to machine, which achieve sufficient correction of 
astigmatism and field curvature aberrations, and which advantageously have 
a reduced maximum thickness. 
SUMMARY OF THE INVENTION 
In one aspect, the present invention consists in a method of minimizing the 
maximum thickness of a unifocal ophthalmic lens with part-spherical convex 
and concave surfaces and a refractive index that varies radially from the 
optical axis of the lens to its periphery, in which method the variation 
of the refractive index is governed by a law such that the absolute value 
of the optical power of the lens is significantly greater than its 
geometrical power when the optical power is computed using the refractive 
index of the lens on its optical axis. 
In practise, in accordance with the invention, the absolute value of this 
optical power is at least 1.5 times the geometrical power. 
The result of this is the required minimizing of the maximum thickness, to 
the benefit of esthetic appearance and weight. 
For a given optical power it is then possible in accordance with the 
invention to implement unifocal ophthalmic lenses with spherical concave 
and convex surfaces with the maximum thickness reduced as compared with 
that of a conventional ophthalmic lens of the same type and the same 
power, although the astigmatism and field curvature aberrations are 
sufficiently corrected to be acceptable. 
In another aspect, the present invention consists in a unifocal ophthalmic 
lens having part-spherical concave and convex surfaces and a refractive 
index that varies radially from the optical axis of the lens to its 
periphery, in which lens the variation of the refractive index is governed 
by a law such that the absolute value of the optical power of the lens is 
significantly greater than its geometrical power when the optical power is 
computed using the refractive index of the lens on its optical axis. 
In essence, the present invention makes it possible to combine 
advantageously the use of part-spherical concave and convex surfaces, a 
reduced maximum thickness and good image quality.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIGS. 1 through 3 show the application of the invention to a convergent 
(positive power) ophthalmic lens. 
It has a convex front surface 10 and concave rear surface 11. 
Both are part-spherical. 
R.sub.CX denotes the radius of the convex surface 10 and R.sub.CV denotes 
that of the concave surface 11. 
e.sub.0 denotes the thickness at the center as measured along the optical 
axis X of the lens. 
If the refractive index of the material from which the lens concerned is 
made is uniform and has the value n.sub.0 then the power of the lens is 
exclusively determined by its geometry, depending on, in addition to the 
refractive index n.sub.0, the radii R.sub.CX and R.sub.CV of its convex 
and concave surfaces and on its thickness at the center e.sub.0. 
Let P.sub.G denote this power, referred to hereinafter as the geometrical 
power, which in practise is determined by the following equation: 
##EQU1## 
in which 
EQU D.sub.1 =(n.sub.0 -1)/R.sub.CX and 
EQU D.sub.2 =(n.sub.0 -1)/R.sub.CV. 
In the case of a convergent unifocal ophthalmic lens the thickness at the 
centre e.sub.O is the maximum or critical thickness. 
To minimize this maximum thickness it has been proposed, other conditions 
being equal, notably the power, to use a refractive index n that varies 
radially from the optical axis X of the lens towards its periphery. 
Because the refractive index n varies as a function of the distance r to 
the optical axis X, in practise in the same sense as the thickness e of 
the lens as measured parallel to the optical axis X, the actual power of 
the lens, referred to hereinafter as its optical power P.sub.O, differs 
slightly from its geometrical power P.sub.G, because the refractive index 
n is involved in its computation. 
In accordance with the invention, the law governing the variation of the 
refractive index n is chosen so that the absolute value of the optical 
power P.sub.O of the lens is significantly greater than its geometrical 
power P.sub.G, the optical power P.sub.O being computed using the 
refractive index n.sub.O of the lens on its optical axis X. 
The variation law is preferably chosen so that the absolute value of the 
optical power P.sub.O is at least 1.5 times the geometrical power P.sub.G. 
Thus in accordance with the invention the variation in the refractive index 
is used to "create" the optical power. 
In practise the law governing the variation of its refractive index n is 
chosen so that at each point on the lens: 
##EQU2## 
in which, as previously explained, r is the distance from any point on the 
lens to the optical axis X. 
This equation implies that at every point on the lens, including points in 
its central area, the variation in the refractive index n is not linear, 
but rather features a certain gradient. 
Therefore in accordance with one characteristic of the invention it is by a 
gradient effect and not by a distribution effect that the variation of the 
refractive index is caused to "create" the optical power. 
Of course, aberrations must be corrected, and in particular aberrations of 
astigmatism and field curvature. 
However, in accordance with the invention the corresponding corrections are 
limited in that they are not pushed to the extreme but rather made just 
sufficient for the aberrations to remain within limits of tolerance 
usually regarded as sufficient, such as apply to conventional ophthalmic 
lenses of the same type. 
Thus in accordance with the invention the variation in the refractive index 
n is chosen to favor increasing the absolute value of the power rather 
than to correct aberrations, to yield unifocal ophthalmic lenses which, 
while having part-spherical concave and convex surfaces, and which are 
therefore easy to machine, are advantageously lighter and of better 
esthetic appearance, because of the resulting increase in power, but which 
nevertheless have sufficient astigmatism and field curvature aberration 
correction for the latter aberrations to be no worse than what is usually 
regarded as acceptable. 
In practise, it suffices in implementing the invention to determine the 
geometrical characteristics of the required lens, in this instance the 
radii R.sub.CX and R.sub.CV of its convex and concave surfaces and its 
thickness, for those skilled in the art to know how to choose the law 
governing the variation in the refractive index n which, while making it 
possible to obtain an optical power P.sub.O significantly greater than the 
geometrical power P.sub.G, provides sufficient correction of astigmatism 
and field curvature aberrations. 
The law governing the variation in the refractive index n may be expressed 
as follows, for example: 
##EQU3## 
n.sub.O being the refractive index on the optical axis X, a.sub.j being 
numerical coefficients and, as already mentioned hereinabove, r being the 
distance to the optical axis. 
There will now be given by way of non-limiting example numerical values for 
two possible embodiments of a convergent unifocal ophthalmic lens. 
EXAMPLE 1 
R.sub.CX =160 mm 
R.sub.CV =237 mm 
e.sub.O =3 mm 
For this geometry with a refractive index n.sub.O of 1.5 the geometrical 
power is: 
P.sub.G =1 dpt 
In accordance with the invention the variation in the refractive index is 
such that the coefficients a of the corresponding law are as follows: 
EQU a.sub.1 =-4.0761.times.10.sup.-4 
EQU a.sub.2 =-10.sup.-8 
EQU a.sub.3 =0 
EQU a.sub.4 =-5.times.10.sup.-13 
EQU a.sub.5 =6.times.10.sup.-16 
With this kind of variation of the refractive index the optical power 
P.sub.O obtained is: 
P.sub.O =3.5 dpt. 
It is therefore 3.5 times higher than the geometrical power P.sub.G. 
The refractive index n at a point situated at a radial distance of 15 mm 
from the optical axis X (this radial distance corresponds in practise to 
an angle of vision in the order of 30.degree. relative to the optical 
axis) is: 
n.sub.15 mm =1.417 
The difference .DELTA.n between this refractive index n and the refractive 
index n.sub.O on the optical axis X is therefore 0.083. 
It is therefore greater in absolute terms than 0.07. 
The astigmatism and field curvature aberrations that the resulting 
convergent ophthalmic lens produces emerge from the FIG. 2 diagram. 
In this diagram the horizontal axis shows the optical power P.sub.O in 
diopters and the vertical axis shows the angle of vision A relative to the 
optical axis X in degrees. 
As is known, this angle of vision A is established relative to the center 
of rotation CR of the eye, with the ophthalmic lens assumed to be placed 
so that its concave rear surface 11 is at a distance of substantially 25 
mm from the center of rotation CR. 
In the FIG. 2 diagram the curve S corresponds to the sagittal focal length, 
which is that contained in the plane of FIG. 1, and the curve T 
corresponds to the tangential focal length, which is that contained in the 
plane perpendicular to the previous plane. 
As is known, the difference T-S corresponds to the astigmatism Ast and the 
expression [(T+S)/2-P.sub.O ] corresponds to the field curvature CC. 
The FIG. 2 diagram, which has deliberately been limited to 30.degree., 
shows that this angle of vision corresponds normally to the maximum 
vertical scanning of the human eye, that the astigmatism Ast is less that 
0.21 diopters, reaching this value at 30.degree., and that the field 
curvature CC, in absolute terms, remains below 0.14 diopters, reaching 
this value at 25.degree.. 
Thus: 
EQU Ast.sub.max =0.21 dpt at 30.degree., and 
EQU CC.sub.max =-0.13 dpt at 25.degree.. 
These values for astigmatism and field curvature aberrations are perfectly 
acceptable. 
Also, as the field curvature is negative it can readily be compensated for 
by accommodation. 
EXAMPLE 2 
R.sub.CX =100 mm 
R.sub.CV =4815 mm 
e.sub.O =7 mm 
whence 
EQU P.sub.G =5 dpt for n.sub.O =1.5 
EQU a.sub.1 =-4.83.times.10.sup.-4 
EQU a.sub.2 =-2.3.times.10.sup.-7 
EQU a.sub.3 =2.times.10.sup.-10 
EQU a.sub.4 =-5.times.10.sup.-3 
EQU a.sub.5 =-5.times.10.sup.-16 
EQU n.sub.O =1.5 
whence 
P.sub.O =12 dpt n.sub.15 mm =1.39 
.DELTA.n=-0.11 
Ast.sub.max=- 0.17 at 25.degree. 
CC.sub.max=- 0.63 at 30.degree. 
It will be noted that although the corresponding convergent ophthalmic lens 
is of high power the correction is sufficient. 
The S and T curves for example 2 are shown in FIG. 3. 
FIGS. 4 through 6 show the application of the invention to the 
implementation of a divergent (negative power) unifocal ophthalmic lens. 
Two practical embodiments of same will be described hereinafter, given the 
same conditions as apply hereinabove. 
EXAMPLE 3 
R.sub.CX =160 mm 
R.sub.CV =100 mm 
e.sub.O =2 mm 
whence 
EQU P.sub.G =-2 dpt for n.sub.O =1.5 
EQU a.sub.1 =5.33.times.10.sup.-4 
EQU a.sub.2 =-4.5.times.10.sup.-7 
EQU a.sub.3 =0 
EQU a.sub.4 =5.times.10.sup.-3 
EQU a.sub.5 =10.sup.16 
EQU n.sub.O =1.5 
whence 
P.sub.O =-4 dpt n.sub.15 mm=1.586 
n=+0.086 
Ast.sub.max =-0.23 dpt at 30.degree. 
CC.sub.max =-0.03 dpt at 15.degree. 
FIG. 5 shows the S and T curves for example 3. 
EXAMPLE 4 
R.sub.CX =200 mm 
R.sub.CV =77 mm 
e.sub.O =3 mm 
whence 
EQU P.sub.G =-4 dpt for n.sub.O =1.5 
EQU a.sub.1 =5.017.times.10.sup.-4 
EQU a.sub.2 =-5.times.10.sup.-7 
EQU a.sub.3 =0 
EQU a.sub.4 =5.times.10.sup.-13 
EQU a.sub.5 =1.5.times.10.sup.-16 
EQU n.sub.O =1.5 
whence 
P.sub.O =-7 dpt n.sub.15 mm =1.577 
n=+0.077 
Ast.sub.max =-0.25 dpt at 20.degree. 
CC.sub.max =-0.15 dpt at 20.degree. 
FIG. 6 shows the S and T curves for example 4. 
As previously, the aberrations are going in the right direction and remain 
within acceptable limits. 
The table on the next page summarises the main parameters for the previous 
example and adds thereto additional parameters for further examples 5 
through 10. 
Note that the difference n between the refractive index on the optical axis 
and at a point at a radial distance of 15 mm therefrom is always greater 
______________________________________ 
P.sub.O 
P.sub.G Ast.sub.max 
CC.sub.max 
(diop- 
(diop- .DELTA.n (diop- 
(diop- 
ters) ters) (n.sub.15mm - n) 
ters) ters) 
______________________________________ 
EXAMPLE 1 3.5 1 -0.083 0.21 -0.13 
EXAMPLE 2 12 5 -0.11 -0.17 -0.63 
EXAMPLE 3 -4 -2 0.092 -0.23 -0.03 
EXAMPLE 4 -7 -4 0.083 -0.25 -0.15 
EXAMPLE 5 10 3.5 -0.119 -0.15 -0.51 
EXAMPLE 6 7 2 -0.10 0.09 -0.37 
EXAMPLE 7 4.5 1.5 -0.07 0.27 -0.12 
EXAMPLE 8 -3 -1 0.088 -0.14 -0.03 
EXAMPLE 9 -6 -3 0.094 -0.28 -0.14 
EXAMPLE 10 
-10 -5 0.079 -0.29 -0.13 
______________________________________ 
than 0.07, in absolute value, being usually in the order of 0.1. 
Note also that the ratio of the optical power P.sub.O to the geometrical 
power P.sub.G is as much as 3.5 in examples 1 and 6. 
The usual techniques in this art are employed for the practical implemental 
of the index variation law adopted. 
These techniques do not form any part of the present invention and will not 
be described here. 
Applied to a bar, for example, they produce cylindrical iso-index surfaces 
and the bar treated in this way is then cut into blanks for machining into 
ophthalmic lenses. 
Of course, the invention is not limited to the examples given but 
encompasses any variant execution thereof. 
Also, although it has been assumed in the foregoing description, in order 
to simplify the latter, that a unifocal lens in accordance with the 
invention formed an entity in itself, it goes without saying that the 
invention can be applied equally well to multifocal lenses, for example to 
bifocal lenses, and could contribute to the formation of a multifocal lens 
of this kind, itself forming only part thereof.