Optics: eye examining – vision testing and correcting – Spectacles and eyeglasses – Ophthalmic lenses or blanks
Reexamination Certificate
2001-05-09
2003-04-29
Sugarman, Scott J. (Department: 2873)
Optics: eye examining, vision testing and correcting
Spectacles and eyeglasses
Ophthalmic lenses or blanks
C351S159000
Reexamination Certificate
active
06554426
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to methods for designing and manufacturing a rotationally symmetrical single-vision spectacle lens whose at least one of front and back surfaces is an aspherical surface, and a manufacturing system thereof.
Many spectacle lenses employ aspherical surfaces at one of front and back surfaces. When a spectacle lens employs an aspherical surface, the curvature becomes smaller while keeping a predetermined power as compared with a lens whose front and back surfaces are spherical, which decreases the maximum thickness of the lens.
When a rotationally symmetrical single-vision spectacle lens is designed, lens material and a vertex power are given as a specification. According to this specification and additional specification, a combination of shapes of front and back surfaces is found such that optical aberrations are minimized. The shape of the lens surface is calculated using an optimizing algorithm such as a damped least squares method. In the optimizing process, one or more (five or six, in general) lens parameters are selected as variables from among a plurality of lens parameters that define the spectacle lens, and values of optical aberration at evaluation points whose distances from the optical axis are different to one another are employed as evaluation functions.
The lens parameters include refractive index of the lens material, a diameter of the lens, a radius of curvature of the front surface, a radius of curvature of the back surface, a center thickness, a conic coefficient and high-order aspherical surface coefficients. A few lens parameters are selected to be variables. The refractive index and the diameter of lens are usually set as constants. The center thickness is set as a constant when a minus lens is designed, and it should be a variable to keep an appropriate edge thickness when a plus lens is designed. While both of the radii of curvatures of the front and back surfaces may be variables, one of them is set as a constant and the other is set as a variable in general. Since the conic coefficient is closely related to the high-order aspherical surface coefficients, the conic coefficient is set as a constant and the high-order aspherical surface coefficients are set as variables.
On the other hand, a vertex power can be employed as the evaluation function at the center of the lens. At each evaluation point, optical aberrations such as power error, astigmatism and distortion, and a performance according to the lens shape such as a thickness of the lens and the aspherical amount can be employed as the evaluation functions. The power error can be selected from among meridional power error, sagittal power error and average power error defined as average of the meridional and sagittal power errors.
The weighted square of difference between the value of the evaluation function and a desired target value is calculated for each of the evaluation points, the best possible combination of variables, where a merit function that is the total sum of the weighted square of differences is minimized, is found. In the damped least squares process, the best possible combination of variables is found while damping the variations of variables in consideration of nonlinearity of the system and dependence among the variables. Equality constraints may be defined for a few evaluation functions.
Since a single-vision spectacle lens is assumed to be used for various object distances, the optical performance should be balanced within a range of the object distance from 30 cm to infinity. Thus, in a conventional design method of a single-vision spectacle lens, the aberrations at the infinite and finite object distances are used as the evaluation functions at the same time, and the lens parameters are optimized such that the merit function containing these evaluation functions is minimized.
Two examples of the conventional design methods with the damped leased squares method will be described.
FIGS. 27
to
30
D show data and performance of a spectacle lens that is designed by a first conventional design method. In this example, a spherical power (SPH) is −8.00 diopter, the front surface is spherical and the back surface is aspherical. A rotationally-symmetrical aspherical surface is expressed by the following equation:
X
(
h
)
=
h
2
c
1
+
1
-
(
1
+
κ
)
h
2
c
2
+
A
4
h
4
+
A
6
h
6
+
A
8
h
8
+
A
10
h
10
+
A
12
h
12
⋯
X(h) is a sag, that is, a distance of a curve from a tangential plane at a point on the surface where the height from the optical axis is h. Symbol c is a curvature (1/r) of the vertex of the surface, K is a conic coefficient, A
4
, A
6
, A
8
and A
10
are aspherical surface coefficients of fourth, sixth, eighth and tenth orders, respectively.
As shown in
FIG. 27
, the refractive index N, the lens diameter DIA, the radius of curvature R
1
of the front surface, the radius of curvature R
2
of the back surface, the center thickness CT, the conic coefficient &kgr; and the high-order aspherical surface coefficients A
4
, A
6
, A
8
, A
10
are the lens parameters. The parameters whose rightmost column “VARIABLE” are checked by marks “V” are the variables. Namely, R
2
and A
4
, A
6
, A
8
, A
10
are set as variables and the other parameters are constants. The numerical values of the variables in the column “VALUE” are the final values after optimization.
As shown in
FIG. 28
, the average power errors DAP and the astigmatisms AS at the infinite object distance on different evaluation points, and the average power errors DAP and the astigmatisms AS at the finite object distance −300 mm (the object distance takes minus value at a object side with respect to the lens) on the evaluation points are assigned to the evaluation functions as the optical aberrations, the vertex power AP at the lens center is added as the equality constraint. In the table of
FIG. 28
, “VE” denotes the evaluation function, “OD” denotes the object distance, “h” denotes the distance of the evaluation point from the optical axis and “TV” denotes the target value. The twenty evaluation points whose distances from the optical axis are different to one another are set on the lens surface. The center evaluation point is on the optical axis (the distance is 0 mm) and the distance of the farthest evaluation point is 40 mm. The interval of the evaluation points is 2 mm. The total number of the evaluation functions is 81 because four kinds of the optical aberration at the twenty evaluation points and the vertex power AP are employed. The target values of the evaluation functions regarding the optical aberration are zero. The target value of the evaluation function regarding the vertex power is set as −8.00. As shown by the values in the column “WEIGHT” of
FIG. 28
, evaluated values, which are the differences between the values of the evaluation functions and the target values, are weighted such that the weight decreases with the distance from the optical axis, and the variables are optimized using the damped least squares method.
FIGS. 29A-29D
are graphs showing the optical aberrations of the optimized spectacle lens of the first conventional design with respect to a visual angle &bgr; (unit: degrees) as the vertical axis;
FIG. 29A
shows the meridional power error DM,
FIG. 29B
shows the sagittal power error DS,
FIG. 29C
shows the average power error DAP and
FIG. 29D
shows the astigmatism AS. The solid line represents the aberration when the object visual diopter, which is a reciprocal of the object distance (unit: m), is 0 D (equivalent to the infinite object distance), the long dashed line represents the aberration when the object visual diopter is −2 D (the object distance −500 mm) and the short dashed line represents the aberration when the object visual diopter is −4 D (the object distance −250 mm).
Further,
FIGS. 30A-30D
are graphs showing the optical aberrations of the optimized spectacle lens of the first conventional design with respect to t
Greenblum & Bernstein P.L.C.
Pentax Corporation
Sugarman Scott J.
LandOfFree
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