U.S. patent number 3,623,800 [Application Number 04/867,433] was granted by the patent office on 1971-11-30 for ophthalmic lens of changing power.
Invention is credited to David Volk.
United States Patent |
3,623,800 |
Volk |
November 30, 1971 |
OPHTHALMIC LENS OF CHANGING POWER
Abstract
An optical lens is provided, having a convex aspheric front
surface useful for the correction of presbyopia. This front surface
is a nonaxial portion of a convex surface of revolution, all
meridian sections of which are identical elliptical arcs and all
sections of this surface other than those sections normal to the
axis of revolution being noncircular, the axis of revolution of
said convex surface coinciding with a straight portion of the
modified evolute of said elliptical arc. This front surface is
characterized by having a substantially constant difference in
principal curvatures at all points along all meridional sections
providing a substantially constant astigmatism at all points
outside the vertical principal meridian, while both principal
curvatures along any elliptical arc meridian section change
continuously and regularly by substantially equal amounts to
provide an accelerating surface. This novel front surface is
intended for use in a lens having a negatively curved
spherocylindrical back surface optically coacting with the front
surface and at least neutralizing the constant astigmatism of the
front surface.
Inventors: |
Volk; David (Pepper Pike,
OH) |
Family
ID: |
25349764 |
Appl.
No.: |
04/867,433 |
Filed: |
October 16, 1969 |
Related U.S. Patent Documents
|
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
|
518848 |
Jan 5, 1966 |
|
|
|
|
292380 |
Jul 2, 1963 |
3239967 |
Mar 15, 1966 |
|
|
Current U.S.
Class: |
351/159.21;
351/159.42; 65/39; 65/37 |
Current CPC
Class: |
B24B
13/065 (20130101); G02C 7/065 (20130101); G02C
7/061 (20130101) |
Current International
Class: |
B24B
13/00 (20060101); G02C 7/02 (20060101); B24B
13/06 (20060101); G02c 007/06 () |
Field of
Search: |
;351/169,171,176,177 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
|
|
|
|
|
|
|
775,007 |
|
May 1957 |
|
GB |
|
219,767 |
|
Jan 1959 |
|
AU |
|
557,424 |
|
May 1957 |
|
BE |
|
Other References
Volk, "The Omnifocal Lens for Presbyopia" Article in American
Archives of Ophthalmology Dec. 1962, pp. 776-784 cited..
|
Primary Examiner: Rubin; David H.
Parent Case Text
This application is a streamline continuation of my application
Ser. No. 518,848, filed Jan. 5, 1966 now abandoned, and which was a
continuation-in-part of my copending application Ser. No. 292,380,
filed July 2, 1963 for LENS SURFACE GENERATOR now U.S. Pat. No.
3,239,967, granted Mar. 15, 1966.
Claims
What is claimed is:
1. An optical lens of transparent optical material, useful for the
correction of presbyopia, having a convex aspheric front surface
which is a nonaxial portion of a surface of revolution having an
apical cusp, all meridian sections of said convex lens surface
being identical elliptical arcs with the least curved portion of
the elliptical arc in the upper portion of the lens, all sections
of said convex lens surface other than those sections normal to the
axis of revolution being noncircular, the axis of revolution of
said convex surface coinciding with a straight portion of a
modified evolute of said elliptical arc determined by first
determining a series of modified evolutes by adding for each
modified evolute to be determined a different fixed increment of
curvature units to the value of the curvature at each point along
said ellipse and using the reciprocals of said sums at each point
as distances measured along normals from each of said points of
said ellipse toward said modified evolute as the locus of each said
modified evolute, then taking a base curve point on said ellipse
corresponding to the vertical elliptical meridian in the upper part
of the lens, for far vision, and selecting an add point in the
lower part of the lens, for reading, corresponding to the added
positive spherical power for the correction of a wearer's
presbyopia at a chord distance of predetermined length across said
vertical elliptical meridian from said base curve point, then
drawing normals from said base curve point and from said add point
through all of said modified evolutes, and finally selecting that
modified evolute which is substantially a straight line between
said two last named normals, so that said surface is characterized
by having a substantially constant difference in principal
curvatures at all points along all meridian sections providing a
substantially constant astigmatism at all points on said surface,
with the transmeridional power being greater than the meridional
power, while both principal curvatures along any elliptical arc
meridian section change continuously and regularly and by
substantially equal amounts to provide an accelerating surface,
said lens having a negatively curved back surface optically
coacting with said front surface, there being a common normal to
both surfaces through the geometrical center of the front aspheric
surface and through the midpoint of said chord, said back surface
at least neutralizing said constant astigmatism of the front
surface at the common normal, and the difference in dioptric powers
between said base curve and add points being the added power
required for the correction of the wearer's presbyopia.
2. A lens as defined in claim 1 wherein said lens back surface is
negatively curved with a radius of curvature approximately 8 mm.
less than the transmeridional radius of curvature of the aspheric
convex surface at its geometrical center, the thickness of the lens
along the common normal being approximately 8 mm.
3. A lens as defined in claim 1 wherein said back surface is toric
and negatively curved in both principal meridians, said normal
coinciding with an equatorial axis of symmetry of the toric
surface, the principal directions of the back toric surface and the
front aspheric surface coinciding along the common normal to both
surfaces, the astigmatism of the back surface neutralizing that
resulting from the front surface at the common normal, there being
a minimum of unneutralized astigmatism away from the common normal
for light rays in a plane containing the common normal and a
meridian of the front aspheric surface and a principal meridian of
the back surface, there being astigmatism for light rays through
the lens at points lateral to said plane with principal directions
at 45.degree. and 135.degree. to said plane, the amount of said
astigmatism increasing with increasing lateral distance of said
points from said plane, the amount of astigmatism, V, in diopters
for a given distance h, in meters from said plane, at the level of
point P(a, b) along the elliptical arc meridian section of the
front aspheric surface contained in said plane, being:
where a is the coordinate of the point P(a, b) on the elliptical
arc in the direction of the semimajor axis of the ellipse, OA, of
length A, and b is the coordinate of the point P(a, b) on the
elliptical arc in the direction of the semiminor axis of the
ellipse, OB, of length B, all distances being measured in meters,
the origin of the Cartesian coordinates being the point 0 at the
geometrical center of the ellipse, said lens being of usual
spectacle lens thickness.
4. A lens as defined in claim 1 wherein said back surface is toric
and negatively curved in both principal meridians, said normal
coinciding with an equatorial axis of symmetry of the toric
surface, the principal directions of the back toric surface and the
front aspheric surface being noncoinciding along the common normal
to both surfaces, the toric back surface being mathematically
resolvable into two components: (1) an astigmatic component
neutralizing that of the front aspheric surface at the common
normal and approximately neutralizing the astigmatism for points
along the meridian section of the front aspheric surface
intersected by the common normal, and (2) a sphero-cylindrical
component in which, when the meridian of the front aspheric surface
which contains the normal to said surface at its geometrical center
is oriented vertically in front of the eye, the cylinder portion
and its axis found in this component is that of a patient's
prescription, and the spherical portions of said sphero-cylindrical
component is that of the patient's prescription to which has been
added the negative of the dioptric power at the base curve point,
said lens being of usual spectacle lens thickness.
5. A lens as defined in claim 1 wherein the excess of said
transmeridional over said meridional power at a given level is 1.00
diopter.
Description
This invention relates to an improved ophthalmic lens primarily
intended for the relief of presbyopia. Ordinarily the optical
treatment of presbyopia is accomplished with either simple reading
glasses, bifocals, or trifocals. In the lens of this invention, the
change in optical power required to supplement the failing
accommodation of the presbyopia is accomplished in a continuous and
regular manner, without discontinuities in the field of vision
through the lens, without localized distortion in the field. The
design of the lens is such that, in level straightforward gaze at
distant objects through the upper portion of the lens as it is worn
in spectacles, vision is clear, and as objects are observed through
lower and lower portions of the lens, they must be brought closer
and closer to the wearer to be seen clearly.
The continuous and regular change in power from the top to the
bottom of the lens results from the combination of an ordinary
toric or spherical back surface and a unique front surface,
hereinafter termed the accelerating surface, which is a nonaxial
portion of a surface of revolution designed such that meridian
sections of said accelerating surface are elliptical arcs, said
accelerating surface having the quality of substantially constant
astigmatism at all points on the surface.
In the drawings
FIG. 1 is a diagrammatic showing of the parameters of an ellipse
involved in the design and construction of the improved lens of
this invention;
FIG. 2 is a central sectional view through a workpiece mounted on a
work holder for carrying out the method of producing the lens of
this invention;
FIG. 3 is a diagrammatic showing of a circular cam and follower in
proper relation with a grinding tool and workpiece for carrying out
the present invention and indicating the relationship between the
various parts and values utilized in the description of this
invention;
FIG. 4 is a side elevational view of a machine adapted to carry out
the method of this invention in making the lens taught herein;
FIG. 5 is an enlarged side elevational view of a cam follower used
in the machine of FIG. 4, the same being partly broken away in
central section to show the friction reducing character
thereof;
FIG. 6 is a central sectional view through the workpiece utilized
in carrying out this invention and illustrating the location of the
accelerating lens surface of this invention;
FIG. 7 is a diagram showing the location of the base and add points
of this invention along various ellipses;
FIG. 8 is a diagram illustrating graphically how I determine the
work line of this invention which is a modified evolute of the
basic elliptic curve wherein the series of points representing the
transmeridianal centers of curvatures fall on practically a
straight line which practically minimizes any deviations from
constant astigmatism in the utilized zone of the accelerated
surface of this invention;
FIG. 9 is a diagram plotting, for one series of lenses, the
vertical meridian power of the accelerating surface of this
invention against the distance from the base curve point of the
lens for surfaces having various adds at a fixed chord
distance;
FIG. 10 is a top plan view of the workpiece of this invention
illustrating the manner in which useful lenses are cut therefrom
and marked for use in an ophthalmic laboratory;
FIG. 11 shows an elevational view of a lens of this invention
marked for use in completing the patient's prescription; while
FIG. 12 is a flat mapping of the front surface of a lens of this
invention showing how the meridian lines of the accelerating
surface converge towards a point on the axis of revolution of the
surface.
As will be disclosed in the description which follows, the
elliptical arc plays the primary role in the design and manufacture
of the accelerating surface of the lens of this invention, as
follows:
1. The elliptical arc is readily obtained from the edge of an
inclined circle.
2. By suitable inclinations of a circle of a given diameter, a
series of elliptical arcs of the appropriate shape, useful for a
series of ophthalmic lens accelerating surfaces, can be
obtained.
3. A simple cam-following generator in which the circular edge of a
right circular cylinder suitably inclined and positioned serves as
the cam, is used to generate the accelerating lens surface of the
lens of this invention. Said cam following generator is disclosed
in my invention LENS SURFACE GENERATOR, Ser. No. 292,380, filed
July 2, 1963, now U.S. Pat. No. 3,239,967, granted Mar. 15, 1966.
An alternative method of generating the accelerating surface of the
lens of this invention is disclosed in my invention LENS GENERATING
METHOD, Ser. No. 218,601, filed Aug. 22, 1962, now U.S. Pat. No.
3,218,765, granted Nov. 23, 1965, and LENS GENERATING APPARATUS,
Ser. No. 480,726, filed Aug. 18, 1965, now U.S. Pat. No. 3,267,617,
granted Aug. 23, 1966, in which the suitably inclined and
positioned circular edge of a circular cup wheel, fed into the work
material, is used to generate the surface directly without the
interposition of a cam.
The planar projection of a circle oblique with respect to the said
plane is an ellipse, whose eccentricity, e, is given by the
equation:
e = sin .phi. (1)
where .phi. is the inclination of the plane of the circle with
respect to the plane of projection. The major axis of the
elliptical projection of the inclined circle corresponds to that
diameter of said circle which is parallel to the plane of
projection. With the plane of projection vertical, the major axis
of the elliptical projection and the corresponding diameter of the
inclined circle, hereinafter called the cam axis, will form an
angle with the horizontal which shall be defined as azimuth and
will be symbolized by .alpha..
The semimajor axis, OA, of length A, of the projected 22, ellipse
is equal to the radius of the inclined circle, hereinafter called
the cam circle, and the semiminor axis, OB, of length B of the
ellipse is equal to Acos.phi.. The radius, r, at any point P(a,b)
along the ellipse, where a is the coordinate in the direction of
the semimajor axis from the origin 0, at the geometrical center of
the ellipse, and b is the coordinate in the direction of the
semiminor axis, is given by the equivalent equations: ##SPC1##
A second vertical plane, hereinafter called the center plane,
intersects normally the vertical plane of projection, hereinafter
called the principal section, the vertical line of intersection
being defined as the work axis. For the generation of the
accelerating surface of the lens of this invention, the center of
the inclined cam circle on the inclined circular cam, hereinafter
called the cam circle center, and the corresponding geometrical
center of the elliptical projection of the inclined cam circle,
will be at a distance s from the center plane, of the skewness such
that the center plane intersects the upper semimajor axis which is
at angle .alpha. with the horizontal. In FIG. 1 I have shown the
elliptical projection of the inclined cam circle, the semimajor
axis of the projected ellipse, skewness, and azimuth.
In the generation of the accelerating surface by my method, there
are only four variables; viz, A (radius of the cam circle), .phi.
(inclination of the cam circle), .alpha. (azimuth of the cam axis),
and s (skewness of the cam circle center). For the generation of a
limited series of accelerating surfaces of the lens of this
invention, one of the variables may be kept constant, while the
other three are adjusted to predetermined values for each of the
surfaces of the series. In a lens series later to be used for
illustration, I have used, for generation, a circular cam with a
cam circle of fixed radius A, each of the accelerating surfaces in
the series being generated with adjusted values of .phi., .alpha.,
and s.
In the generation of the accelerating surface of the lens of this
invention, the workpiece, from which several identical lenses may
be obtained, consists of a portion of a substantially spherical
optical glass or plastic bowl, or a similar shaped bowl which has
been molded to a shape such that its outer convex surface is
approximately the same as the desired final shape. The workpiece is
mounted by means of pitch or adhesive, or by mechanical means,
pitch being preferred, to a work holder which in turn is attached
by taper fit or by screw fit to a revolving axle or shaft in such a
way that there is a common axis of revolution, the previously
mentioned work axis, for the axle, work holder, and work. In FIG. 2
I have shown a typical workpiece, mounted by means of pitch to a
typical work holder having a metal flange whose upper face is
perpendicular to the axis of the work holder and whose outer
circumference, concentric to the work axis, is equal to the outer
circumference of the bowl-shaped workpiece. The general convexity
of the work holder reduces the amount of pitch required for
adherence of the workpiece to the work holder while the flange aids
in the placing of the workpiece in a symmetrical position with
respect to the work axis.
The cam-follower, which rolls freely along the inclined and skew
cam circle, is an elongated right circular cylinder, freely
rotatable by means of bearings, about a cylindrical shaft, the tool
shaft, both the cam follower and the tool shaft being concentric to
an axis, the tool axis (FIG. 4). Along the tool shaft is a circular
grinding tool which has a cylindrical grinding edge embedded with
diamond dust. The grinding edge, concentric to the tool axis,
rigidly attached to the tool shaft and straddling the principal
section, is of the same diameter as the cylindrical cam follower.
By means of appropriate shafts and linkages, later described, the
tool shaft and its axis are always maintained perpendicular to the
principal section, as the cam follower rolls along the cam circle,
with the tool shaft and attached grinding tool rapidly rotating
about the tool axis.
In FIG. 3 I have shown the relationship between the various planes,
axes, angles, and positions of the elements of the generator and
workpiece, as described previously. Vertical center plane 18 and
vertical principal section 16, intersect normally in the vertical
work axis 15. A trace of the work holder and workpiece, symmetrical
to the work axis, is shown in the principal section. Cam circle
19a, of radius A, is shown in cam circle plane 20, which is
inclined at angle .phi. with respect to plane 21 which is parallel
to principal section 16. Cam axis 23 is shown at azimuth angle
.alpha. with respect to horizontal plane 22 (line 24 is in plane
22). Cam center 19b is adjustable in position along horizontal
skewness axis 24, though in FIG. 3 skewness is set at 0. Elongated
cam follower of radius "d," in contact with cam circle 19a, and
grinding tool of radius "d," straddling the principal section, are
both concentric to tool axis 17, which is always maintained
parallel to the center plane as the cam follower rolls along the
cam circle.
In FIG. 4 I have shown the apparatus for generating the workpiece,
which apparatus incorporates those features of FIG. 3 and its
description.
Referring to FIG. 4, a pair of seats 56 are bolted to the base 25
and bearings 57 are bolted to their respective seats and a shaft 58
is rotatably mounted in the bearings. Parallel links 59 are
rotatably mounted on shaft 58 and held in position by collars 60.
At their upper ends, links 59 support shaft 61 which in turn
carries a pair of parallel links 62 extending at an angle to the
links 59. These links are freely rotatable on shaft 61. At their
outer ends, links 62 mount shaft 49 for rotation therein by means
of motor 63 which is here shown as mounted on the links 62 although
the motor might be connected in any other suitable position in
order to provide its driving function. As here shown, the motor
drives a pulley 64 which through belt 65 drives a pulley 66 rigidly
fixed to shaft 49. Preferably, a counter weight is provided at 67
so as to substantially balance the weights on opposite sides of the
shaft 61. To accurately control the position of shaft 41, cam
follower 201 and grinding wheel 200, a bracket 68 is fixed to the
base 25 and carries at its upper end a rotatably mounted screw 69
which has a threaded connection with a nut 70 which is mounted by a
trunnion 71 in one of the links 59. Rotation of the screw 69 by
means of handwheel 72 then varies the angular position of the links
59 with respect to the base 25 so as to carry the cam follower 48
in any desired direction as it rolls across the cam 202. Thus,
energization of motor 63 will cause shaft 49 and grinding wheel 200
to rotate rapidly as the grinding wheel follows the pattern
provided by the cam follower 201 rolling over the cam 202. For
further details of this machine one may refer to my copending
application Ser. No. 292,380, filed July 2, 1963, now U.S. Pat. No.
3,239,967, granted Mar. 15, 1966.
The drive shaft 49 has a grinding wheel 200 fixed to turn with the
shaft in a position closer to the driving mechanism. Farther to the
right, a cam roller 201 is mounted on shaft 49, as shown in FIG. 5.
Cylindrical cam follower 201 of the same outside diameter as
grinding wheel 200 rolls on cam 202. This circular cam is fixed to
a manipulating hub 203 having a cylindrical extension 203a which
fits rotatably in a suitable socket in an arm 204 so that the cam
202 may be rotated about a diametrical axis, this adjustment being
read by pointer 205 on indicia 206 and the adjustment held as
desired by a thumb screw 207. The arm 204 is bent at right angles
and fixed to a trunnion pin 208, the central axis of which lies on
a projected diameter through the circular cam 202. Trunnion pin 208
is mounted in a suitable bearing 209a at the upper end of bracket
209 which in turn is secured to the base 25. The arm 204 may be
oscillated about the trunnion pin 208 and this position is read by
means of a pointer 210 which moves with arm 204 across indicia
carried by a plate 211 which is fixed to the bracket 209. This
position is held by means of a thumb screw 212. In this form of the
invention, the inclination .phi. is read directly on indicia 206
and the azimuth .alpha. is read directly on the indicia at 211.
A skewness adjustment is provided in connection with the bracket
209. The bracket 209 is movable in ways 45' by means of a screw
manipulated by handwheel 47' so as to move the bracket 209
crosswise of the base 25 or at right angles to a vertical plane
passing through the axis of shaft 49'.
The workpiece to be shaped, indicated at 213, is mounted in a work
holder 214 which in turn is connected to a vertical shaft 215
rotatable by means of a motor 216. This whole work holding device
is held in a bracket 217 which has a stub shaft 218 preferably
rotatably mounted in a bracket 219 fixed to the base 25. A pin 220
is provided to hold the work in the position with shaft 215
vertical as shown in FIG. 4 or, alternatively, to rotate the same
90.degree. and hold the shaft 215 in a generally horizontal
position.
Consider the surface generated on the workpiece with the following
adjustment of the variables:
A= 100 mm.
.phi. = 44.027.degree.
.alpha. = 40.349.degree.
s = 26.663 mm.
After adjusting the work holder so that the uppermost portion of
the workpiece is slightly above the level of the cam circle where
it would be intersected by the center plane, the cam follower is
caused to roll slowly along that portion of the circular edge of
the cam which is on the same side of the center plane as the cam
circle center, while the grinding tool, rotating rapidly about the
tool axis, contacts the workpiece, rotating rapidly about the work
axis, removing material from the work as the cam follower moves
along the cam, until the entire surface of the workpiece has been
generated.
The surface generated, shown in section in FIG. 6, will be spindle
shaped with an apical cusp. Within the broad surface area contained
within a zone limited by parallel planes perpendicular to the work
axis at 2.124 mm. and 18.183 mm. from the apical cusp of the
surface, which surface area is more than 42 mm. in chord length
along a meridian between the two said planes, the meridianal
refracting power of a glass surface of index of refraction 1.523
increases continuously and regularly from 3.872 diopters at the
lower level to 5.008 diopters at the upper level of the zone, while
the transmeridianal power at any level between the limits of the
zone is always 1.000.+-. 0.011 diopters greater than the meridianal
power at that level. Table 1 contains data on this surface, showing
the meridianal and transmeridianal powers and their differences at
several points along a meridian. Since all meridians in a surface
of revolution are identical, it is obvious that the entire surface
within the aforementioned zone is of substantially constant
astigmatism. The .+-. 0.011 diopter difference from the designated
value of 1.000 diopters is well within the tolerances accepted in
standard ophthalmic practice.
In the lens of this invention, a range of accelerating front
surfaces can be readily designed to an accuracy comparable to that
of the above example. However, in order to systemize the production
of series of accelerating surfaces, so that a single circular cam
may serve for the production of several surfaces in a series, and
so that the accelerating surfaces so produced will be compatible
with the usual standard graded powers of the back surfaces, I have
set an upper limit of tolerances of .+-. 0.04 diopters for the
accuracy of the accelerating front surface constant astigmatism, a
value which is comparable to the tolerances of standard ophthalmic
lens practice.
In the determination of the actual values of the adjustable
variables for a series of lenses, the following factors must be
considered:
1. The radius of the cam circle must be such that with each setting
of inclination, the projected ellipse must contain the required
curvature values at specific chord distances.
2. The values of azimuth and skewness must be so determined that
the transmeridianal power of the generated accelerating surface
will be greater than the meridianal power thereof, within the given
tolerances, by a predetermined amount, for those portions of the
workpiece from which the spectacle lens is obtained, and in
particular for those portions of the finished spectacle lens which
are used in straightforward vision at eye level and thence downward
to a portion of the lens used for near work such as reading. The
vertical distance referred to above is about 30 mm., but, as in the
example of the generated surface in which astigmatism of the
accelerating surface was maintained well within tolerances for more
than 42 mm., azimuth and skewness for the lens series of this
invention have been adjusted so that accelerating surface
astigmatism is within the tolerance for a chord length of more than
40 mm.
For a given cam circle of radius A, each successive increase in
inclination of the cam circle (for a series of lenses) results in
the projected ellipse having a shortened semiminor axis and a
consequent longer radius of curvature at the end of the minor axis,
r.sub.m, and a shortened radius of curvature at the end of the
semimajor axis, r.sub.M. Between the two extreme values of radius
of curvature along the ellipse, the radius of curvature changes
continuously and progressively from r.sub.m to r.sub.M according to
equation (2a, b). Once inclination has reached a sufficiently large
value, then the minimum curvature at the end of the minor axis will
be equal to some preassigned value C.sub.base. With each increase
in .phi., the preassigned value C.sub.base will be at a greater
distance from the minor axis of each successive ellipse. The
intervals of .phi. are such that at each successive value of .phi.,
the difference in curvature between C.sub.base and C.sub.add, where
C.sub.base and C.sub.add represent two points on the ellipse
separated by a chord distance of 30 mm., will result in an increase
in refractive power by a definite increment, 0.25 diopters for
example, where n = 1.523. Illustrating the above is FIG. 7 which is
a drawing of a series of elliptical arcs, each formed with A
constant at 100 mm. but .phi. differing. Also shown in FIG. 7, by
means of two short curved lines intersecting the elliptical arcs,
are the position of C.sub.base and C.sub.add on each elliptical
arc, with the dioptric power of each C.sub.base point equal to 4.10
diopters, when n = 1.523, while for each successive pair of
C.sub.base and C.sub.add points, the power difference, hereinafter
termed the add, increases by 0.25 diopters, with the range of adds
extending from 0.50 to 2.50 diopters. The values of .phi. and the
coordinates for each pair of C.sub.base and C.sub.add points on
each elliptical arc, and the adds for each pair of said points, are
listed in table 2.
For any given elliptical curve, normals to the ellipse form an
envelope, the evolute of the ellipse, which is convex towards that
portion of the ellipse from whose normals it is formed. The
curvature R at any point along the ellipse is the reciprocal of the
distance r along the normal from said point on the ellipse to its
point of tangency to the evolute, 1/r.
In the discussions following, it is to be assumed that the optical
material is ophthalmic crown glass of n = 1.523. Since refracting
power of a refracting surface in air is R(n - 1), where r is
measured in meters, it will be convenient to discuss the refracting
surfaces in terms of units of curvature, it being understood that
one unit of curvature will result in a refracting power of 0.523
diopters, so that 0.50 diopters of refracting power will result
when the curvature is 0.956 curvature units.
If a fixed increment of curvature units is added to the value of
the curvature at each point along the ellipse, the reciprocals of
the sums, measured in meters along the normals from said points of
the ellipse towards the evolute, is the locus of a new curve
related to the evolute, which new curve will hereinafter be termed
in the specification and claims as the modified evolute. Said
modified evolute will differ from the evolute in that it falls
between the evolute and the ellipse, and that it has a point of
inflection, so that it is both concave and convex towards the
elliptical arc from which it was derived. By adding a series of
fixed increments of curvature to the curvature values of the
ellipse, a series of modified evolutes can be obtained, each
differing somewhat from the adjacent modified evolute.
In FIG. 8 I have drawn elliptical arc BA, one of the elliptical
arcs of FIG. 7 and table 2, for which A= 10, .phi. = 48.072, and
for which the add is 1.50 diopters. Also drawn is the evolute EE'
for arc BA, and a series of modified evolutes, 1, 1', through 7,
7', each modified evolute being separated from the adjacent
modified evolute by 0.956 curvature units or 0.50 diopters, with
the exception of 4, 4' which is 0.478 curvature units, 0.25
diopters, from 3, 3' and 5, 5'. Also drawn are the normals to the
elliptic arc from the points C.sub.base and C.sub.add to the
evolute E, E'. By inspection it can be seen that modified evolutes
1, 1', 2, 2', and 3, 3', between the two said normals, are
generally convex towards said elliptical arc segment C.sub.base,
and C.sub.add, while modified evolutes 5, 5', 6, 6', and 7, 7' are
generally concave towards said elliptical arc segment, and modified
evolute 4, 4' is practically a straight line between the two said
normals, and beyond. This is the "straight portion of the modified
evolute" referred to in the claims. Through that portion of
modified evolute 4, 4' between and beyond the two said normals, and
tangent to 4, 4' at its point of inflection n, I have drawn a
straight line WL, hereinafter termed the work line, said work line
thus representing the locus of those points, the reciprocals of
whose distances along the normals from arc segment C.sub.base,
C.sub.add is greater, by practically a constant, than the
corresponding values of curvature along said arc segment, and
beyond. Note the normal to the ellipse Nn lies approximately half
way between the normals at C.sub.base and C.sub.add.
For the purpose of this example, the modified evolutes have been
drawn no closer than 0.478 curvature units, but the coordinates for
a series of modified evolutes of any desired degree of closeness
may be easily determined by modern computer techniques. To the data
so determined for each series of coordinates of a portion of a
modified evolute, corresponding to a specified portion of an
elliptical arc, one may apply the method of least squares and find
that modified evolute most closely approaching a straight line in
the required portion, while said straight line, from which the sums
of the squared deviations of the points in the modified evolute are
minimized, would be the optimum work line. However, from the
practical standpoint such precision in the determination of the
work line is not required, in view of the tolerances previously
specified, and graphical methods such as represented in FIG. 8 have
been utilized with the desired accuracy.
Again referring to FIG. 8, the slope m of the work line, with
respect to the major axis of the ellipse, can be determined quite
simply from the graph by selecting any two points (b', a'), (b, a)
on the modified evolute through which the work line passes, and
applying the formula:
m=(b'-b)/(a'-a) (3)
By applying the coordinates of one of the two points and slope m to
the standard equation of a line:
b=ma+ x (4)
the value of the constant x, where x is the value of the ordinate b
when a = 0, is obtained.
One may also obtain the value of x simply and directly by reading
its value on the ordinate where the extended work line WL crosses
the ordinate, while the slope of WL is accurately determined by
means of equation (3) utilizing the coordinates of any two widely
separated points along WL.
If the ellipse is oriented so that the work line WL is vertical,
then the angle .alpha. (see FIG. 3) which the major axis of the
ellipse makes with a horizontal plane, which is the angle between
the work line WL and the minor axis of the ellipse, OB in FIG. 8,
is (90 - tan.sup.-.sup.1 m.), and skewness s= x sin .alpha.. In the
example of FIG. 8, .alpha. is 49.87.degree. and s = 29.05 mm. In
the generation of the work surface by the methods and apparatus
described previously, the position and orientation of the
elliptical projection on the principal section, of the inclined cam
circle of radius A and inclination .phi., is such that the work
line coincides with the work axis when azimuth is set at .alpha.
and skewness is set at s. When this is done, the transmeridianal
radius of curvature, at any point on the generated surface, within
the zone containing the base and add points, will be greater,
within the given tolerances, than the meridianal curvature at said
point, by that amount of curvature units which has been added to
that of the meridianal curvature in producing the utilized modified
evolute and associated work line. This is true since the
transmeridianal curvature of any point on a surface of revolution
is the reciprocal of the distance along the normal from said point
to the axis of revolution of the surface.
In the above example, generating the work surface with
.alpha.=49.87.degree. and s = 29.05 mm. results in a substantially
constant astigmatism of 1.75 diopters in the desired zone of the
generated surface. In the present state of the art of ophthalmic
spectacle lens grinding by prescription shops, the grinding tools
are designed for refracting power at one-eighth diopter intervals.
Furthermore, the grinding tools are designed for refractive
material of index of refraction 1.530 whereas the ophthalmic crown
glass used has an index of refraction of 1.523. Since standard
prescription shop tools are to be used for the processing of the
back surface of the lens of this invention, the dioptric power of
the astigmatism of the accelerating surface must be compensated for
lens thickness and the actual dioptric power which the tool grinds
on the back surface. These factors of specific power intervals,
lens thickness, and the index of refraction of the optical
material, have been taken into account in the design of the
accelerating surface, so that the actual dioptric power of the
astigmatism of the accelerating surface is slightly less than the
named value, by the compensating amount, the named values being at
the one-eighth and one-fourth diopter intervals. The increment of
curvature units added to those of the elliptical arc in producing
the modified evolute of FIG. 8 is such that the dioptric power of
the astigmatism of the generated accelerating surface in the
desired zone, will be the required compensated value for each
accelerated surface of the lens series of this invention.
In FIG. 8, I have drawn line W'L', which is the actual work line
for the compensated accelerating surface, the modified evolute
corresponding to W'L' being obtained by adding 3.25 curvature units
to those of the elliptical arc, so that the dioptric power of the
compensated front surface astigmatism is actually about 1.70
diopters. The portion of the modified evolute used for the
determination of work line W'L', for the required portion of the
elliptical arc, is practically coincident with a straight line, so
that the value of the astigmatism of the accelerating surface, at
all points within the required zone, will be well within the
specified tolerances of .+-. 0.04 diopters.
Ophthalmic spectacle lenses of multifocal type may be supplied to
the prescription shop in one or more forms: (1) They may be
completed on both sides with standard surfaces and be of average
center thickness and of relatively large diameter or area, so that
all that is required for the filling of a prescription for glasses
is the shaping of the lens by the removal of excess peripheral
glass so that it may be used in the spectacle frame. Such lenses
are called finished-uncut, and they have spherical powers only; and
(2) They may be completed on both sides with standard surfaces and
be of excessive thickness and relatively large diameter, so that
the operations in the prescription shop may include the process of
generating, grinding, and polishing one of the surfaces for the
filling of a prescription, thereby reducing the thickness of the
lens to conventional thickness, in addition to the other procedures
of shaping the lens for the spectacle frame. Such lenses are called
semifinished, since one of the surfaces must be refinished, as
described above, by the prescription shop.
In the production of the finished-uncut and semifinished ophthalmic
lens of this invention for commercial use, the accelerated surface
is standardized in terms of 4.25, 6.25, 8.25, etc., diopter base
curve series, wherein the base curve designation refers to the
compensated vertical meridian power at a single point along the
vertical meridian, said point having been referred to previously as
the base curve point. The standardization of the accelerating
surface into such base curve series has been done for the purpose
of minimizing such aberrations as are manifested in oblique gaze
through the periphery of the finished spectacle lens, in a manner
analogous to the standardization of commercial finished-uncut and
semifinished bifocals and trifocals into base curve series, wherein
such base curve designations refer to the compensated front surface
dioptric power, the compensation taking into account the range of
lens refractive powers for which a base curve is used, lens
curvatures, refractive index of the lens material used in
relationship to the refractive index for which the tools were
designed, and center thickness of the finished lens.
In the finished-uncut lens of this invention, the specific
compensated base curve accelerating surface which is used for a
specific lens, is in accordance with the dioptric power of the lens
for light rays through the lens at both the base curve point and
the add point. In general, negative power lenses require the weaker
base curves, while positive power lenses require the stronger base
curves. Since the average curvature of the total accelerating
surface increases as the add increases, with the average curvature
at the base curve point also being increased, the range of lens
refractive powers for which a specific base curve series is
recommended is, in general, shifted toward the less negative or
more positive powers as the adds are increased from the weakest to
the strongest.
For the processing of the semifinished lens of this invention, the
prescription shop is instructed as to what base curve lens is
appropriate for the powers of the prescription, taking into account
the effects of prescription cylinder power and axis, and the add,
so that when the processing of the lens is completed, aberrations
will be minimized in oblique gaze through the lens.
Referring to FIG. 7 and table 2, the series of elliptical arcs
shown are an example of the curves which may be used in a 4.25
diopter compensated series of lens accelerating surfaces. The base
curve point is found along the vertical elliptical meridian in the
upper part of the lens, and the additional power corresponding to
the added positive spherical power required for the correction of
presbyopia is at a chord distance across the vertical elliptical
meridian 30 mm. from the base curve point. In each of the
accelerated lens surfaces above the base curve point, the
meridianal dioptric power of a point on the vertical elliptical
meridian is less than that of the base curve point, while for a
point on the vertical elliptical meridian below the add point, the
dioptric power of the accelerated surface in the meridianal
direction is greater than that of the add point. In FIG. 9, I have
shown graphically the meridianal dioptric power at various chord
distances along the elliptical vertical meridian for seven of the
nine accelerated surfaces of the 4.25 diopter compensated series.
The compensated power at the base curve point is shown as about
4.10 diopters. The amount of power added to that of the base curve
point at any chord distance from the base curve point, for each of
the seven vertical meridians shown, can be obtained from FIG.
9.
In table 3 I have listed the values of the adjustable variables for
the production of the sample 4.25 diopter compensated series of the
accelerating lens surfaces so far described, along with the nominal
power of the astigmatism of the accelerating surface and the actual
dioptric power of said astigmatism. It is obvious that by applying
the same principles and method of this invention already described,
other 4.25 diopter series may be designed in which, for example,
the chord separation of the base curve and add points on the
accelerated surface might be 25 mm. or 20 mm. instead of the 30 mm.
described for the sample series. Referring to FIG. 9 and the curve
labeled "2.00 add," the power difference between the base curve
point and a point at a chord distance of 25 mm. is about 1.50
diopters. The same lens might well be considered one of a series in
which the base curve and add points are separated by a chord
distance of 25 mm., in this case the add being 1.50 diopters. Other
accelerating lens surfaces may be designed, according to this
invention, to complete a series of nine lens surfaces, for adds
from 0.50 to 2.50 diopters, all having a chord separation of 25 mm.
between the base curve and add points.
After completing the generation of a workpiece by the method
described, there remain many small pits and scratches which must be
removed prior to polishing the surface. For the removal of these
scratches and pits, I use the invention of my copending U.S. Pat.
application, LENS GRINDING APPARATUS, Ser. No. 337,514, filed Nov.
14, 1962, which utilizes a grinding tool having a slitted flexible
sheet metal backed by a resilient material such as sponge rubber.
The previously generated workpiece is mounted on a vertical spindle
and caused to rotate about the work axis. The grinding tool with
its slitted flexible grinding surface is caused to oscillate along
a meridian of the rotating work, while a slurry of fine grinding
compound is continuously fed to the work surface, and grinding is
continued until the pits and scratches are removed.
The ground surface can then be polished with a sheet of nylon or
cotton cloth which conforms to and completely covers a sector of
the surface from the apex to the periphery, said cloth being
oscillated across the surface in a substantially meridianal
direction, while the workpiece is rotating about the work axis.
Cerium oxide suspension is continuously fed to the work surface
during the polishing operation.
After the workpiece is polished, it is removed from the work holder
by chilling both the work holder and the workpiece, which causes
the workpiece to separate from the pitch.
For the production of semifinished lenses, the inner surface of the
finished workpiece is then ground and polished to a precise
standard negative curvature, each specific base curve and add
requiring a specific negative inner, or back, surface. The radius
of curvature of the negative surface is 8 mm. less than that of the
transmeridianal radius of curvature at a point on the generated
surface corresponding to the midpoint of the chord between the base
curve point and the add point. As will be later described, said
point on the generated workpiece will be at the geometrical center
of the accelerating lens surface; and the normal to said point,
which is also the normal to a standard negative spherical back
surface, will be defined as the optic axis of the lens. The
individual lenses may then be cut out of the bowl. An alternative
method of completing the lens is to first cut the finished
workpiece into circular discs or wedge-shaped sections, and then
grind and polish the back surface to a precise standard concave, or
negative, spherical surface.
In FIG. 10 I have shown in a diagrammatic top view the location of
three lenses on the surface of a workpiece finished as described
above. Each lens is 58 mm. in diameter, a size convenient for use
by prescription shops, of both the finished-uncut and the
semifinished lens. In one of the lens locations, I have drawn the
outline of a typical finished ophthalmic spectacle lens which
includes within its confines the zone of substantially constant
astigmatism on the accelerating lens surface, previously referred
to, and have also drawn a meridian line A' through the middle of
the lens, said meridian line to be the vertical meridian line of
the finished prescription lens when it is inserted into a spectacle
frame. The three lenses are then cut out of the workpiece with a
circularly cylindrical diamond edged saw, the inner spherical
surface having been ground and polished previously as described.
With the precise spherical back surface the lenses can be tested
optically through various points on the accelerating surface, thus
providing a means for measuring the accelerating lens surface for
both quality and power. The 8 mm. center thickness of the
semifinished lenses is sufficient thickness for generating and
grinding the back surface by prescription shops, when modifying the
lens to meet the specifications of a prescription.
The finished-uncut lens of this invention, which is supplied to the
prescription shops with a toric surface on the back, as will be
later described, is marked on its accelerating surface with a thin
line of waterproof ink along a meridian which bisects the front
surface into symmetrical halves. Short lines crossing the marked
vertical meridian B' in FIG. 11 are used to identify the base curve
point, the geometrical center of the lens, and the add point. The
lens so marked is packaged and the carton labeled to identify power
of the lens through the base curve point, and the add. The
semifinished lens of this invention is marked on the accelerating
surface in the same manner as the finished-uncut lens. The lens so
marked is packaged and the carton labeled to identify the base
curve, the add, and the dioptic power of the astigmatism of the
accelerating surface. FIG. 11 is a drawing of a lens marked as
described above.
Semifinished lenses of different base curves and different adds are
supplied to the prescription shop for the incorporation of a
patient's distance prescription and for the additional refractive
power required for the correction of presbyopia. In a semifinished
lens with the appropriate accelerating surface which lens is to be
modified by the prescription shop to incorporate a patient's
prescription, the astigmatism resulting from the excess of
transmeridianal refracting power of the accelerated surface over
the meridianal refracting power, at any point along the marked
vertical meridian, must be neutralized at the back surface by
cylindrical refracting power, the axis of said cylindrical
refracting power being vertical when its power is negative. In the
incorporation of patient's distance prescription into the lens of
this invention, said astigmatism neutralizing cylindrical
refracting power must be combined with the cylindrical refracting
power of the patient's prescription, and the resulting
sphero-cylindrical refracting power be combined with the spherical
refracting power of the patient's prescription. In those instances
in which the patient's prescription is for spherical power and add
only, the prescription shop may choose to grind the required back
toric surface instead of utilizing a finished-uncut lens. As an
example, consider the following prescription: -1.00 diopter sphere,
add +1.50 diopters. Reference to table 3 shows that the 4.25
diopter base curve, 1.50 diopter add, semifinished lens has a
nominal front surface astigmatism of 1.75 diopters. The
neutralizing cylindrical refracting power is therefore -1.75
diopters and the back surface is ground with a toric tool which
grinds curves resulting in refractive power of -5.25 diopters in
the vertical meridian and -7.00 diopters in the horizontal
meridian, as calculated for optical material of n = 1.53. The power
of the lens through the base curve point will then be -1.00 diopter
and through the add point, +0.50 diopters. It is to be understood
that a lens finished by the factory, in the manner thus described,
is the finished-uncut lens of this invention.
Now consider a prescription similar to the one above except that
the prescription calls for cylindrical refractive power in addition
to the spherical refractive power. For example, consider the
following prescription: -1.00 diopter sphere combined with -1.75
diopter cylinder axis 60.degree., add 1.50 diopters. The
semifinished lens is a 4.25 diopter base curve, 1.50 diopter add
lens requiring -1.75 diopters of cylindrical refracting power axis
90.degree. at the back surface for neutralizing the astigmatism
produced by the accelerating front surface along the vertical
meridian. The angle .gamma. between the neutralizing cylinder and
the prescription cylinder is 30.degree.. The resultant cylinder C
is obtained by the following formula:
C = (A.sup.2 + B.sup.2 + 2ABcos2.gamma.)1/2 (5)
where A is the power of the neutralizing cylinder and B is the
power of the prescription cylinder, so that C = -3.03 diopters,
which, to the nearest one-eighth diopter interval, is -3.00
diopters. The sphere power, D, resulting from combining the
neutralizing cylinder and the prescription cylinder is:
D= (A+ B - C)/2 (6) so that D = -0.24 diopters, which to the
nearest one-eighth diopter interval, is -0.25 diopters. The total
sphere power required is that of the patient's prescription plus
the sphere power resulting from the combination of the cylinders
and is -1.25 diopters. The angle .beta. between the vertical
meridian and the axis of the resultant cylinder is obtained by the
following formula:
.beta. = (arc sinB/C) [sin(180- 2.gamma.)]/2 (7)
so that .beta. = 15.degree., with the resultant cylinder axis
falling between the axis of the neutralizing cylinder and that of
the prescription cylinder, so that the axis of the resultant
cylinder is 75.degree.. The base curve of the lens being 4.25
diopters (compensated) the powers ground on the back surface are
then -5.50 in the 75.degree. meridian and -8.50 diopters in the
165.degree. meridian as calculated for n = 1.53. The powers at the
base curve point of the finished lens will then be that of the
patient's distance prescription and the powers at the add point
will be that of the patient's distance prescription plus the add,
within the tolerances permitted for ophthalmic prescription lenses,
which is the order of .+-. 0.06 diopters.
Along the vertical meridian, the lens will have the astigmatism
correction in the amount and at the axis called for in the
prescription. On either side of the vertical meridian, there will
be astigmatism other than that called for in the prescription and
required for the correction of the patient's ocular astigmatism.
This said other astigmatism results from the fact that the
principal directions of the cylindrical component of the back
surface for neutralizing the astigmatism due to the accelerating
surface of the front surface can coincide with the principal
directions of the accelerating surface only along one meridian
line, the vertical meridian. Consider the vertical meridian section
of the accelerating surface, and its containing plane, which I have
called the principal plane. Now consider the neutralizing
cylindrical component of the back surface with its axis in the said
principal plane, with said axis parallel to a plane tangent to the
vertical meridian section of the accelerating surface at the
geometrical center of the lens. The normal to the tangent plane at
its point of contact with the accelerating surface, which is also
perpendicular to the back surface, coinciding with an equatorial
axis of symmetry of the back surface, is analogous to the optic
axis of an ordinary lens, and only at the normal common to both
surfaces, can the principal directions of the accelerating surface
and those of the neutralizing cylinder component of the back
surface coincide. Elsewhere along the vertical meridian line of the
accelerating surface, above and below the normal common to both
surfaces, the principal directions of the accelerating surface of
the front surface and those of the neutralizing cylinder component
of the back surface, are close, but do not coincide, and
appropriate bending or coflexure of the two surfaces are used to
minimize lens aberrations in the completed lens along the vertical
meridian, in a manner analogous to the bending or coflexure of
ordinary "corrected curve" ophthalmic spectacle lenses. This aspect
of minimizing aberrations has been discussed earlier in relation to
the use of multiple base curves for minimizing aberrations. On
either side of the vertical meridian line, meridian lines of the
accelerating surface, shown diagrammatically as a flat mapping in
FIG. 12, converge towards a point on the axis of revolution of the
surface, with a resulting tilting of their containing planes and
obliquity of their principal directions with respect to those of
the neutralizing cylinder component of the back surface which are
substantially vertical and horizontal. The optical effect of
combining the cylinder component of the accelerating front surface,
whose principal directions at any point on the accelerating
surface, become progressively oblique and tilted with increasing
distance from the vertical meridian line, with the neutralizing
cylinder component of the back surface, whose principal directions
remain substantially vertical and horizontal, is astigmatism, with
principal direction in the 45.degree. and 135.degree. meridians,
which increases progressively in proportion to the distance
laterally from the vertical meridian and to the rate of change in
refractive power along the vertical principal meridian at the
specified level.
The amount of said astigmatism, V, in diopters, for light rays
through the lens through a given point on the accelerating surface,
said point being at a given distance, h, in meters, lateral to the
vertical elliptical meridian at the level of point P(a,b) is
where n is the index of refraction of the optical material, A and B
are the semimajor and semiminor axes, respectively, of the ellipse
whose arc is that of the vertical meridian of the accelerated
surface, and a and b are the coordinates of the given point P(a, b)
on the elliptical arc.
The said other astigmatism which is present everywhere in the lens
of this invention, except along the vertical meridian, has the
effect of blurring vision in lateral gaze through the lens, but the
amount of blurring is of sufficiently small magnitude near the
vertical meridian, that clear and useful vision can be obtained
through the lens along and in the immediate vicinity of the
vertical meridian. Vision through lateral portions of the lens is
useful, though not as clear as through the lens along the vertical
meridian.
Although the lens of this invention has been described as made of
glass, it is to be understood that it may be made of any other
useful optical material, such as optical plastic.
The sample 4.25 diopter series used as an example is by way of
illustration only. Other 4.25 diopter series, as well as other base
curve series, may be designed having chord separations of the base
curve point and the add point other than 30 mm., and in which the
compensated dioptric power of the base curve point is slightly
different for each of the various adds. The use of a single cam for
the production of a series is convenient and economical, though
more than one cam, or a series of cams, may need to be used for
some series. ##SPC2## ##SPC3## ##SPC4##
* * * * *