Progressive multifocal lens and method of designing the same
To offer a novel combining formula for combining a progressive refractive surface and a toric surface, thereby to provide a novel progressive multifocal lens which has an eyesight correcting capability and an astigmia remedying capability on an identical refractive surface. Using a combining formula indicated by a combining formula (1) or (2), a refractive surface 2 on an eyeball side or a refractive surface 3 on an object side is made a combined refractive surface 14+15 in which an original progressive refractive surface 14 set only for the purpose of demonstrating a desired eyesight-correcting characteristic, and an original toric surface 15 set only for the purpose of demonstrating a desired astigmia-remedying characteristic are combined.
1. A progressive multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an eyeball side, said progressive refractive surface comprising:
a far-use portion,
a near-use portion having a refractive power different from the far-use portion, and
a progressive portion whose refractive power changes progressively between the far-use and near-use portions,
wherein the progressive refractive surface is a combination of an original progressive refractive surface for remedying only eyesight and an original toric surface for remedying only astigmia based on a following formula:
z
p
=
2
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
-
(
c
p
+
c
x
)
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
+
(
c
p
+
c
x
)
x
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
-
(
c
p
+
c
x
)
2
x
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from an object side onto the eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface, and
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and
C y is a curvature in a direction orthogonal to said cylinder axis.
2. A progressive multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an object side, said progressive refractive surface comprising:
a far-use portion,
a near-use portion having a refractive power different from the far-use portion, and
a progressive portion whose refractive power changes progressively between the far-use and near-use portions,
wherein the progressive refractive surface is a combination of an original progressive refractive surface for remedying only eyesight and an original toric surface for remedying only astigmia based on a following formula:
z
p
=
2
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
-
(
c
p
+
c
x
)
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
+
(
c
p
+
c
x
)
x
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
-
(
c
p
+
c
x
)
2
x
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from the object side onto an eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface,
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and C y is a curvature in a direction orthogonal to said cylinder axis.
3. A progressive multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an eyeball side, said progressive refractive surface comprising:
a far-use portion,
a near-use portion having a refractive power different from the far-use portion, and
a progressive portion whose refractive power changes progressively between the far-use and near-use portions,
wherein the progressive refractive surface is a combination of an original progressive refractive surface for remedying only eyesight and an original toric surface for remedying only astigmia based on a following formula:
z
p
=
2
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
-
(
c
p
+
c
y
)
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
+
(
c
p
+
c
y
)
y
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
-
(
c
p
+
c
y
)
2
y
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from an object side onto the eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface, and
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and
C y is a curvature in a direction orthogonal to said cylinder axis.
4. A progressive multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an object side, said progressive refractive surface comprising:
a far-use portion,
a near-use portion having a refractive power different from the far-use portion, and
a progressive portion whose refractive power changes progressively between the far-use and near-use portions,
wherein the progressive refractive surface is a combination of an original progressive refractive surface for remedying only eyesight and an original toric surface for remedying only astigmia based on a following formula:
z
p
=
2
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
-
(
c
p
+
c
y
)
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
+
(
c
p
+
c
y
)
y
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
-
(
c
p
+
c
y
)
2
y
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from the object side onto an eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface,
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and C y is a curvature in a direction orthogonal to said cylinder axis.
5. The progressive multifocal lens as defined in claim 1 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
6. The progressive multifocal lens as defined in claim 2 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.
7. The progressive multifocal lens as defined in claim 3 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
8. The progressive multifocal lens as defined in claim 4 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.
9. The progressive multifocal lens as defined in claim 1 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
10. The progressive multifocal lens as defined in claim 2 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.
11. The progressive multifocal lens as defined in claim 3 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
12. The progressive multifocal lens as defined in claim 4 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.
13. A method of designing a multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an eyeball side, said progressive refractive surface comprising a far-use portion, a near-use portion having a refractive power different from the far-use portion, and a progressive portion whose refractive power changes progressively between the far-use and near-use portions, the method comprising:
a) calculating an original progressive refractive surface for remedying only eyesight;
b) calculating an original toric surface for remedying only astigmia based;
c) calculating a combined refractive surface using a following formula:
z
p
=
2
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
-
(
c
p
+
c
x
)
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
+
(
c
p
+
c
x
)
x
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
-
(
c
p
+
c
x
)
2
x
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from an object side onto the eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface, and
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and
C y is a curvature in a direction orthogonal to said cylinder axis.
14. A method of designing a multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an object side, said progressive refractive surface comprising a far-use portion, a near-use portion having a refractive power different from the far-use portion, and a progressive portion whose refractive power changes progressively between the far-use and near-use portions, the method comprising:
a) calculating an original progressive refractive surface for remedying only eyesight;
b) calculating an original toric surface for remedying only astigmia based;
c) calculating a combined refractive surface using a following formula:
z
p
=
2
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
-
(
c
p
+
c
x
)
(
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
+
(
c
p
+
c
x
)
x
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
y
p
2
1
+
1
-
(
c
p
+
c
y
)
2
y
p
2
)
2
-
(
c
p
+
c
x
)
2
x
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from an object side onto the eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface, and
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and
C y is a curvature in a direction orthogonal to said cylinder axis.
15. A method of designing a multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an eyeball side, said progressive refractive surface comprising a far-use portion, a near-use portion having a refractive power different from the far-use portion, and a progressive portion whose refractive power changes progressively between the far-use and near-use portions, the method comprising:
a) calculating an original progressive refractive surface for remedying only eyesight;
b) calculating an original toric surface for remedying only astigmia based;
c) calculating a combined refractive surface using a following formula:
z
p
=
2
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
-
(
c
p
+
c
y
)
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
+
(
c
p
+
c
y
)
y
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
-
(
c
p
+
c
y
)
2
y
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from an object side onto the eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface, and
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and
C y is a curvature in a direction orthogonal to said cylinder axis.
16. A method of designing a multifocal lens for correcting an eyesight, said lens having a progressive refractive surface on an object side, said progressive refractive surface comprising a far-use portion, a near-use portion having a refractive power different from the far-use portion, and a progressive portion whose refractive power changes progressively between the far-use and near-use portions, the method comprising:
a) calculating an original progressive refractive surface for remedying only eyesight;
b) calculating an original toric surface for remedying only astigmia based;
c) calculating a combined refractive surface using a following formula:
z
p
=
2
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
-
(
c
p
+
c
y
)
(
(
c
p
+
c
x
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
+
(
c
p
+
c
y
)
y
p
2
1
+
(
1
-
(
c
p
+
c
x
)
(
c
p
+
c
y
)
x
p
2
1
+
1
-
(
c
p
+
c
x
)
2
x
p
2
)
2
-
(
c
p
+
c
y
)
2
y
p
2
where z-axis is an axis which passes through a center of the progressive refractive surface from an object side onto the eyeball side,
x-axis is in a direction of an cylinder axis of the original toric surface, and
y-axis is an axis which is orthogonal to the z-axis and the x-axis,
z p is any point P(x p , y p , z p ) of the combined refractive surface,
C p is an approximate curvature of the original progressive refractive surface, C x is a curvature in the direction of the cylinder axis of said original toric surface, and
C y is a curvature in a direction orthogonal to said cylinder axis.
17. The progressive multifocal lens as defined in claim 13 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
18. The progressive multifocal lens as defined in claim 14 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.
19. The progressive multifocal lens as defined in claim 15 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
20. The progressive multifocal lens as defined in claim 16 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.
21. The progressive multifocal lens as defined in claim 13 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
22. The progressive multifocal lens as defined in claim 14 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.
23. The progressive multifocal lens as defined in claim 15 wherein the refractive surface on the object side is a spherical surface or a rotationally-symmetric non-spherical surface.
24. The progressive multifocal lens as defined in claim 16 wherein the refractive surface on the eyeball side is a spherical surface or a rotationally-symmetric non-spherical surface.