Lenses, devices, methods and systems for refractive error
The present disclosure is directed to lenses, devices, methods and/or systems for addressing refractive error. Certain embodiments are directed to changing or controlling the wavefront of the light entering a human eye. The lenses, devices, methods and/or systems can be used for correcting, addressing, mitigating or treating refractive errors and provide excellent vision at distances encompassing far to near without significant ghosting. The refractive error may for example arise from myopia, hyperopia, or presbyopia with or without astigmatism. Certain disclosed embodiments of lenses, devices and/or methods include embodiments that address foveal and/or peripheral vision. Exemplary of lenses in the fields of certain embodiments include contact lenses, corneal onlays, corneal inlays, and lenses for intraocular devices both anterior and posterior chamber, accommodating intraocular lenses, electro-active spectacle lenses and/or refractive surgery.
1. A lens for an eye, the lens having an optical axis, a focal distance and wherein the lens comprises:
an aberration profile along the optical axis, the aberration profile:
including higher order aberrations having at least one of a primary spherical aberration component C(4,0) and a secondary spherical aberration component C(6,0), herein the aberration profile provides, for a model eye with no aberrations and an on-axis length equal to the focal distance:
a retinal image quality (RIQ) with a through focus slope that degrades in a direction of eye growth; and
a RIQ of at least 0.3
wherein the RIQ is Visual Strehl Ratio measured substantially along the optical axis for at least one pupil diameter in the range 3 mm to 6 mm, over a spatial frequency range of 0 to 30 cycles/degree inclusive and at a wavelength selected from within the range 540 nm to 590 nm inclusive; and
wherein the average slope over a horizontal field of at least −20° to +20° degrades in a direction of eye growth.
2. The lens according to claim 1 , wherein the focal distance is a prescription focal distance for a myopic eye and wherein the focal distance differs from the focal distance for a C(2,0) Zernike coefficient of the aberration profile.
3. The lens according to claim 1 , wherein the lens is used for myopia control with or without astigmatism.
4. The lens according to claim 1 , wherein the higher order aberrations include at least two spherical aberration terms selected from the group C(4,0) to C(20,0).
5. The lens according to claim 1 , wherein the higher order aberrations include at least three spherical aberration terms selected from the group C(4,0) to C(20,0).
6. The lens according to claim 1 , wherein the magnitude of higher order aberrations included is at least 0.02 um over a 3 mm, 4 mm, 5 mm or 6 mm pupil diameter.
7. The lens according to claim 1 , wherein the average slope over a vertical field of at least −20° to +20° degrades in a direction of eye growth.
8. The lens according to claim 1 , wherein the aberration profile provides a RIQ of at least 0.3 at the focal length substantially across the pupil diameters in the range 3 mm to 6 mm.
9. The lens according to claim 1 , wherein the aberration profile provides a RIQ with a through focus slope that degrades in a direction of eye growth when primary or secondary astigmatism is added to the aberration profile.
10. The lens according to claim 1 , wherein the RIQ is characterised by:
RIQ
=
∫
∫
-
F
min
+
F
max
CSF
(
x
,
y
)
*
(
(
(
FT
(
FT
{
A
(
ρ
,
θ
)
*
exp
[
2
π
ⅈ
λ
*
W
(
ρ
,
θ
)
]
}
2
)
)
)
)
∫
∫
-
F
min
+
F
max
CSF
(
x
,
y
)
*
(
(
(
FT
(
FT
{
A
(
ρ
,
θ
)
*
exp
[
2
π
ⅈ
λ
*
Wdiff
(
ρ
,
θ
)
]
}
2
)
)
)
)
,
wherein:
Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;
CSF(x, y) denotes the contrast sensitivity function
CSF(F)=2.6(0.0192+0.114f)e −(0.114f)^1.1 ;
where f specifies the tested spatial frequency, in the range of F min to F max ;
FT denotes a 2D fast Fourier transform;
A(ρ,θ) denotes the pupil diameter;
W(ρ,θ) denotes wavefront phase of the test case measured for i=1 to 20;
W
(
ρ
,
θ
)
=
∑
i
=
1
k
a
i
Z
i
(
ρ
,
θ
)
Wdiff(ρ,θ) denotes wavefront phase of the diffraction limited case;
ρ and θ are normalised polar coordinates, where ρ represents the radial coordinate and θ represents the angular coordinate or azimuth; and λ denotes wavelength.
11. A lens for an eye, the lens having an optical axis, a focal distance and wherein the lens comprises:
an aberration profile along the optical axis, the aberration profile:
including higher order aberrations having at least one of a primary spherical aberration component C(4,0) and a secondary spherical aberration component C(6,0), herein the aberration profile provides, for a model eye with no aberrations and an on-axis length equal to the focal distance:
a retinal image quality (RIQ) with a through focus slope that degrades in a direction of eye growth; and
a RIQ of at least 0.3
wherein the RIQ is Visual Strehl Ratio measured substantially along the optical axis for at least one pupil diameter in the range 3 mm to 6 mm, over a spatial frequency range of 0 to 30 cycles/degree inclusive and at a wavelength selected from within the range 540 nm to 590 nm inclusive; and
wherein the average slope over a vertical field of at least −20° to +20° degrades in a direction of eye growth.
12. The lens according to claim 11 , wherein the focal distance is a prescription focal distance for a myopic eye and wherein the focal distance differs from the focal distance for a C(2,0) Zernike coefficient of the aberration profile.
13. The lens according to claim 11 , wherein the lens is used for myopia control with or without astigmatism.
14. The lens according to claim 11 , wherein the higher order aberrations include at least two spherical aberration terms selected from the group C(4,0) to C(20,0).
15. The lens according to claim 11 , wherein the higher order aberrations include at least three spherical aberration terms selected from the group C(4,0) to C(20,0).
16. The lens according to claim 11 , wherein the magnitude of higher order aberrations included is at least 0.02 um over a 3 mm, 4 mm, 5 mm or 6 mm pupil diameter.
17. The lens according to claim 11 , wherein the average slope over a horizontal field of at least −20° to +20° degrades in a direction of eye growth.
18. The lens according to claim 11 , wherein the aberration profile provides a RIQ of at least 0.3 at the focal length substantially across the pupil diameters in the range 3 mm to 6 mm.
19. The lens according to claim 11 , wherein the aberration profile provides a RIQ with a through focus slope that degrades in a direction of eye growth when primary or secondary astigmatism is added to the aberration profile.
20. The lens according to claim 11 , wherein the RIQ is characterised by:
RIQ
=
∫
∫
-
Fmin
-
Fmax
CSF
(
x
,
y
)
+
(
(
(
F
T
(
F
T
(
A
(
ρ
,
θ
)
+
exp
[
2
πi
λ
+
W
(
p
,
θ
)
]
}
2
)
)
)
)
∫
∫
-
Fmin
-
Fmax
CSF
(
x
,
y
)
+
(
(
(
F
T
(
F
T
(
A
(
ρ
,
θ
)
+
exp
[
2
πi
λ
+
Wdiff
(
ρ
,
θ
)
]
}
2
)
)
)
)
,
wherein:
Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;
CSF(x, y) denotes the contrast sensitivity function
CSF(F)=2.6(0.0192+0.114f)e −(0.114f)^1.1 ;
where f specifies the tested spatial frequency, in the range of F min to F max ;
FT denotes a 2D fast Fourier transform;
A(ρ,θ) denotes the pupil diameter;
W(ρ,θ) denotes wavefront phase of the test case measured for i=1 to 20;
W
(
ρ
,
θ
)
=
∑
i
=
1
k
a
i
Z
i
(
ρ
,
θ
)
Wdiff(ρ,θ) denotes wavefront phase of the diffraction limited case;
ρ and θ are normalised polar coordinates, where ρ represents the radial coordinate and θ represents the angular coordinate or azimuth; and λ denotes wavelength.
21. A lens for an eye, the lens having an optical axis, a focal distance and wherein the lens comprises:
an aberration profile along the optical axis, the aberration profile:
including higher order aberrations having at least one of a primary spherical aberration component C(4,0) and a secondary spherical aberration component C(6,0), herein the aberration profile provides, for a model eye with no aberrations and an on-axis length equal to the focal distance:
a retinal image quality (RIQ) with a through focus slope that degrades in a direction of eye growth; and
a RIQ of at least 0.3
wherein the RIQ is Visual Strehl Ratio measured substantially along the optical axis for at least one pupil diameter in the range 3 mm to 6 mm, over a spatial frequency range of 0 to 30 cycles/degree inclusive and at a wavelength selected from within the range 540 nm to 590 nm inclusive; and
wherein the aberration profile provides a RIQ with a through focus slope that degrades in a direction of eye growth when primary or secondary astigmatism is added to the aberration profile.
22. The lens according to claim 21 , wherein the focal distance is a prescription focal distance for a myopic eye and wherein the focal distance differs from the focal distance for a C(2,0) Zernike coefficient of the aberration profile.
23. The lens according to claim 21 , wherein the lens is used for myopia control with or without astigmatism.
24. The lens according to claim 21 , wherein the higher order aberrations include at least two spherical aberration terms selected from the group C(4,0) to C(20,0).
25. The lens according to claim 21 , wherein the higher order aberrations include at least three spherical aberration terms selected from the group C(4,0) to C(20,0).
26. The lens according to claim 21 , wherein the magnitude of higher order aberrations included is at least 0.02 um over a 3 mm, 4 mm, 5 mm or 6 mm pupil diameter.
27. The lens according to claim 21 , wherein the average slope over a horizontal field of at least −20° to +20° degrades in a direction of eye growth.
28. The lens according to claim 21 , wherein the average slope over a vertical field of at least −20° to +20° degrades in a direction of eye growth.
29. The lens according to claim 21 , wherein the aberration profile provides a RIQ of at least 0.3 at the focal length substantially across the pupil diameters in the range 3 mm to 6 mm.
30. The lens according to claim 21 , wherein the RIQ is characterised by:
RIQ
=
∫
∫
-
Fmin
-
Fmax
CSF
(
x
,
y
)
+
(
(
(
F
T
(
F
T
(
A
(
ρ
,
θ
)
+
exp
[
2
πi
λ
+
W
(
p
,
θ
)
]
}
2
)
)
)
)
∫
∫
-
Fmin
-
Fmax
CSF
(
x
,
y
)
+
(
(
(
F
T
(
F
T
(
A
(
ρ
,
θ
)
+
exp
[
2
πi
λ
+
Wdiff
(
ρ
,
θ
)
]
}
2
)
)
)
)
,
wherein:
Fmin is 0 cycles/degree and Fmax is 30 cycles/degree;
CSF(x, y) denotes the contrast sensitivity function
CSF(F)=2.6(0.0192+0.1140f)e −(0.114f)^1.1 ;
where f specifies the tested spatial frequency, in the range of F min to F max ;
FT denotes a 2D fast Fourier transform;
A(ρ,θ) denotes the pupil diameter;
W(ρ,θ) denotes wavefront phase of the test case measured for i=1 to 20;
W
(
ρ
,
θ
)
=
∑
i
=
1
k
a
i
Z
i
(
ρ
,
θ
)
Wdiff(ρ,θ) denotes wavefront phase of the diffraction limited case;
ρ and θ are normalised polar coordinates, where ρ represents the radial coordinate and θ represents the angular coordinate or azimuth; and λ denotes wavelength.