Method for designing and manufacturing a monofocal ophthalmic lens and corresponding lens
A method for designing and manufacturing a monofocal ophthalmic lens and corresponding lens. A surface of the monofocal ophthalmic lens is defined by: f ( x,y )= a 1 +a 2 √{square root over (1− a 3 x 2 −a 4 y 2 )}+ a 5 exp{ a 6 x 4 +a 7 y 4 +a 8 x 2 y 2 } wherein x and y are perpendicular optical axes of the lens in a plane, wherein a 1 -a 8 are coefficients, and wherein a 5 is other than 0 and at least one of a 6 , a 7 and a 8 is other than 0, including a hyperbolic component and an exponential component. The coefficients can be calculated by an iterative calculation and the merit function as follows: fm = [ ∑ i α i m i 2 ( β ) ] 1 / 2 where m i is a value of an optical property at a specific viewing angle β with respect to an optical axis of the lens, and α i is a weighting value.
1. A method for making a monofocal ophthalmic lens, comprising the steps of:
defining a surface of the lens by the following formula (1):
f ( x,y )= a 1 +a 2 √{square root over (1 −a 3 x 2 −a 4 y 2 )}+ a 5 exp{ a 6 x 4 +a 7 y 4 +a 8 x 2 y 2 } (1)
wherein x and y are perpendicular optical axes of the lens in a plane, and
wherein a 1 , -a 8 are coefficients;
making a 5 other than 0 and at least one of a 6 , a 7 and a 8 other than 0;
receiving a monofocal ophthalmic lens; and
forming the surface on the lens according to the formula.
2. The method according to claim 1 , wherein said coefficients are calculated by an iterative calculation comprising the following steps:
[a] setting a value for a refractive index of the ophthalmic lens and for a base curve that will be used to manufacture the ophthalmic lens,
[b] setting sphere, cylinder and cylinder axis values for the ophthalmic lens,
[c] setting initial nominal values for a 1 -a 8 ,
[d] calculating at least one optical property of a lens with said values,
[e] calculating a value of a merit function by the following formula (2):
fm
=
[
∑
i
α
i
m
i
2
(
β
)
]
1
/
2
(
2
)
where m, is a value of said at least one optical property at a specific viewing angle β with respect to an optical axis of the lens, and α i is a weighting value,
[f] optimizing said merit function by setting new nominal values for said coefficients a 1 -a 8 , and
[g] repeating steps [c] to [f] until obtaining the desired optimization level.
3. The method according to claim 2 , wherein said merit function includes an oblique astigmatism value at 30°, and the α i value for the oblique astigmatism value is between 0.8 and 0.98.
4. The method according to claim 2 or 3 , wherein said merit function includes a curvature of field value at 30°, and the α i value for the curvature of field value is between 0.02 and 0.2.
5. The method according to any one of claims 1 , 2 , and 3 , wherein said surface is a concave surface of said lens.
6. The method according to claim 5 , wherein a i is equal to 0, a 2 is equal to a radius of curvature in a center of said surface, with a negative sign, and a 5 is equal to the radius of curvature in the center of said surface.
7. The method according to claim 1 , wherein a 6 is between 2×10 −8 and 5×10 −8 mm −4 .
8. The method according to claim 1 , wherein a 7 is between −2×10 −8 and 1.2×10 −7 mm −4 .
9. The method according to claim 1 wherein a 8 is between −2×10 −8 and 1.2×10 −7 mm −4 .
10. The method according to claim 1 , wherein each of the coefficients of the formula (1) has a value between +/−30% of a corresponding nominal value obtained from said optimization.
11. A lens, comprising:
a monofocal lens having a surface,
wherein said surface is defined by the following formula:
f ( x,y )= a 1 +a 2 √{square root over (1 −a 3 x 2 −a 4 y 2 )}+ a 5 exp{ a 6 x 4 +a 7 y 4 +a 8 x 2 y 2 }
wherein x and y are perpendicular optical axes of the lens in a plane,
wherein a 1 -a 8 are coefficients, and
wherein a 5 is other than 0 and at least one of a 6 a 7 and a 8 is other than 0.
12. The method according to claim 11 , wherein said coefficients are calculated by an iterative calculation comprising the following steps:
[a] setting a value for a refractive index of the ophthalmic lens and for a base curve that will be used to manufacture the ophthalmic lens,
[b] setting sphere, cylinder and cylinder axis values for the ophthalmic lens,
[c] setting initial nominal values for a 1 -a 8 ,
[d] calculating at least one optical property of a lens with said values,
[e] calculating a value of a merit function by the following formula (2):
fm
=
[
∑
i
α
i
m
i
2
(
β
)
]
1
/
2
(
2
)
where m i is a value of said at least one optical property at a specific viewing angle β with respect to an optical axis of the lens, and α i is a weighting value,
[f] optimizing said merit function by setting new nominal values for said coefficients a 1 -a 8 , and
[g] repeating steps [c] to [f] until obtaining the desired optimization level.
13. The method according to claim 11 , wherein said merit function includes an oblique astigmatism value at 30°, and the α i value for the oblique astigmatism value is between 0.8 and 0.98.
14. The method according to claim 11 , wherein a 1 is equal to 0, a 2 is equal to a radius of curvature in a center of said surface, with a negative sign, and a 5 is equal to the radius of curvature in the center of said surface.