Lenses, devices and methods for ocular refractive error
A lens for an eye having an optical axis and an aberration profile along its optical axis, the aberration profile having a focal distance and including higher order aberrations having at least one of a primary spherical aberration component and a secondary spherical aberration component. The aberration profile may provide, for a model eye with no aberrations and an on-axis length equal to the focal distance: a peak, first retinal image quality (RIQ) within a through focus range that remains at or above a second RIQ over the through focus range that includes said focal distance, where the first RIQ is at least 0.35, the second RIQ is at least 0.1 and the through focus range is at least 1.8 Diopters.
1. A lens for an eye, the lens having an optical axis and an aberration profile about its optical axis, the aberration profile:
having a focal distance; and
including higher order aberrations having at least four spherical aberration components including at least one of a primary spherical aberration component (C(4,0)) and a secondary spherical aberration component (C(6,0)),
wherein 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 0.30;
wherein said RIQ is Visual Strehl Ratio measured 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 of at least 0.30 at the focal length for all pupil diameters in the range 3 mm to 6 mm.
2. The lens of claim 1 , wherein the higher order aberrations include at least two spherical aberration terms selected from the group C(8,20) to C(20,0).
3. The lens of claim 1 , wherein the average slope over a horizontal field of at least −20° to +20° degrades in a direction of eye growth.
4. The lens of claim 1 , wherein the aberration profile provides a RIQ with a through focus slope that degrades in a direction of eye growth when primary astigmatism is added to the aberration profile.
5. The lens of claim 1 , wherein the aberration profile provides a RIQ with a through focus slope that degrades in a direction of eye growth when secondary astigmatism is added to the aberration profile.
6. The lens of claim 1 , wherein said RIQ is
RIQ
=
∫
∫
-
Fmin
+
Fmax
CSF
(
x
,
y
)
*
(
(
(
FT
(
❘
"\[LeftBracketingBar]"
FT
{
A
(
ρ
,
θ
)
⋆
exp
[
2
π
i
λ
⋆
W
(
ρ
,
θ
)
]
}
❘
"\[RightBracketingBar]"
2
)
)
)
)
∫
∫
-
Fmin
+
Fmax
CSF
(
x
,
y
)
*
(
(
(
FT
(
❘
"\[LeftBracketingBar]"
FT
{
A
(
ρ
,
θ
)
⋆
exp
[
2
π
i
λ
⋆
Wdiff
(
ρ
,
θ
)
]
}
❘
"\[RightBracketingBar]"
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){circumflex over ( )}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
W
(
ρ
,
θ
)
=
∑
i
=
1
k
a
i
Z
i
(
ρ
,
θ
)
measured for i=1 to 20;
Wdiff(ρ, θ) denotes wavefront phase of the diffraction limited case;
ρ and θ are normalised polar coordinates, where p represents the radial coordinate and θ represents the angular coordinate or azimuth; and
λ denotes wavelength.