Method for designing progressive addition lenses
View Patent ↗The invention provides a method for designing progressive surfaces and lenses produced using image blur to construct a merit function. The shape of a lens surface, or surfaces, is arbitrarily defined and optimized to minimize the image blur based merit function.
1. A method for designing a progressive addition lens, comprising a. ) describing a progressive addition surface; and b.) optimizing the surface using a merit function of the formula:
MF=MF blur +MF power +MF other
wherein:
MF blur is a merit function that controls image blur;
MF power is a merit function that controls the mean sphere power; and
MF other is a merit function that controls constraints on cosmetics and manufacturability wherein the surface is described as a continuous, a differentially continuous, or a twice differentially continuous surface.
2. The method of claim 1 , wherein the surface is described according to the equation:
sag
x
,
y
=
Delta
x
,
y
+
c
·
r
2
1
+
[
1
-
(
1
+
k
)
·
c
2
·
r
2
]
+
α
1
·
r
2
+
α
2
·
r
4
+
α
3
·
r
6
+
α
4
·
r
8
+
…
wherein:
c is a surface curvature;
r is a radial distance from an optical axis of the lens;
k is a conic constant;
α1, α2, α3, α4 each are a coefficient; and
Delta k,y is a delta sag that is a function of x and y.
3. A method for designing a progressive addition lens, comprising a.) describing at least two progressive addition surfaces; and b.) optimizing the surfaces using merit functions of the formula:
MF=MF blur +MF power +MF other
wherein:
MF blur is a merit function that controls image blur;
MF power is a merit function that controls the mean sphere power; and
MF other is a merit function that controls constraints on cosmetics and manufacturability.
4. The method of claim 3 , wherein the surfaces are each independently described as a continuous, a differentially continuous, or a twice differentially continuous surface.
5. The method of claim 3 , wherein the surfaces are each described according to the equation:
sag
x
,
y
=
Delta
x
,
y
+
c
·
r
2
1
+
[
1
-
(
1
+
k
)
·
c
2
·
r
2
]
+
α
1
·
r
2
+
α
2
·
r
4
+
α
3
·
r
6
+
α
4
·
r
8
+
…
wherein:
c is a surface curvature;
r is a radial distance from an optical axis of the lens;
k is a conic constant;
α1, α2, α3, α4 each are a coefficient; and
Delta x,y is a delta sag that is a function of x and y.
6. The method of claim 3 , 4 , or 5 , wherein MF power is:
MF
power
=
∑
θ
x
∑
θ
y
W
ϕ
θ
x
,
θ
y
·
(
Φ
θ
x
,
θ
y
-
P
θ
x
,
θ
y
)
2
+
Wadd
θ
x
,
θ
y
[
(
AddF
θ
x
,
θ
y
-
PF
θ
x
,
θ
y
)
2
+
(
AddB
θ
x
,
θ
y
-
PB
θ
x
,
θ
y
)
2
]
wherein
θ x is a horizontal eye rotation angle;
θ y is a vertical eye rotation angle;
RMS θx,θy is a RMS spot size calculated at an image of an eye lens;
Wrms θx,θy is a weight for a field position;
AddF θx,θy is a calculated add power on a front surface of the lens;
AddB θx,θy is a calculated add power on a back surface of the lens;
PF θx,θy is a target for an add power value for the front surface;
PB θx,θy is a target for an add power for the back surface; and
Wadd θx,θy is a weighting.
7. The method of claim 3 , 4 , or 5 , wherein MF power is:
MF
power
=
Wadd
far
[
(
AddF
far
-
PF
far
)
2
+
(
AddB
far
-
PB
far
)
2
]
+
[
∑
θ
x
∑
θ
y
W
ϕ
θ
x
,
θ
y
·
(
Φ
θ
x
,
θ
y
-
P
θ
x
,
θ
y
)
2
]
wherein
θ x is a horizontal eye rotation angle;
θ y is a vertical eye rotation angle;
RMS θx,θy is a RMS spot size calculated at an image of an eye lens;
Wrms θx,θy is a weight for a field position;
AddF θx,θy is a calculated add power on a front surface of the lens;
AddB θx,θy is a calculated add power on a back surface of the lens;
PF θx,θy is a target for an add power value for the front surface;
PB θx,θy is a target for an add power for the back surface; and
Wadd θx,θy is a weighting.
8. The method of claim 3 , 4 , or 5 , wherein MF blur is:
MF
blur
=
∑
θ
x
∑
θ
y
[
Wrms
θ
x
,
θ
y
·
(
RMS
θ
x
,
θ
y
)
2
+
Wast
θ
x
,
θ
y
·
(
AstF
θ
x
,
θ
y
-
AF
θ
x
,
θ
y
)
2
]
(
IX
)
wherein:
AstF θx,θy is either the surface astigmatism from the front surface or the contribution to the total lens astigmatism as seen by the eye from the front surface; and
Wast θx,θy are the weights placed on the unwanted astigmatism.
9. The method of claim 6 , wherein MF blur is:
MF
blur
=
∑
θ
x
∑
θ
y
[
Wrms
θ
x
,
θ
y
·
(
RMS
θ
x
,
θ
y
)
2
+
Wast
θ
x
,
θ
y
·
(
AstF
θ
x
,
θ
y
-
AF
θ
x
,
θ
y
)
2
]
(
IX
)
wherein:
AstF θx,θy is either the surface astigmatism from the front surface or the contribution to the total lens astigmatism as seen by the eye from the front surface; and
Wast θx,θy are the weights placed on the unwanted astigmatism.
10. The method of claim 7 , wherein MF blur is:
MF
blur
=
∑
θ
x
∑
θ
y
[
Wrms
θ
x
,
θ
y
·
(
RMS
θ
x
,
θ
y
)
2
+
Wast
θ
x
,
θ
y
·
(
AstF
θ
x
,
θ
y
-
AF
θ
x
,
θ
y
)
2
]
(
IX
)
wherein:
AstF θx,θy is either the surface astigmatism from the front surface or the contribution to the total lens astigmatism as seen by the eye from the front surface; and
Wast θx,θy are the weights placed on the unwanted astigmatism.
11. The method of claim 3 , further comprising c.) determining a set of coefficients to describe the lens surface to minimize e value of the merit function.
12. The method of claim 11 , wherein step c.) is carried out by (i) selecting optimization variables that are a curve for a front surface and a curve for e back surface of the lens; and (ii) minimizing MF other .