Optical lens design for flattening a through-focus curve
Described herein are systems and/or methods for forming an ophthalmic lens. An example method may comprise a step of determining a power profile based on a power profile function defined by a base optical power, an amount of spherical aberration at a radial distance from a geometric center of the lens, and a bump function. The example method may comprise a step of adjusting the power profile based at least on minimizing a shape metric of a through-focus curve.
1. An ophthalmic lens formed by a method comprising:
determining a power profile based on a power profile function defined by a base optical power, an amount of spherical aberration at a radial distance from a geometric center of a lens, and a bump function;
adjusting the power profile based at least on minimizing a shape metric comprising a through-focus flatness (TFF) metric of a through-focus curve; and
forming the lens to exhibit the adjusted power profile.
2. The lens of claim 1 , wherein forming a lens comprises configuring the geometric shape of the lens.
3. The lens of claim 1 , wherein the spherical aberration, and parameters of the bump function are configured to vary by refractive prescription.
4. The lens of claim 1 , wherein the spherical aberration, and parameters of the bump function are configured based on a characteristic of a target population.
5. The lens of claim 4 , wherein the characteristic is at least one of a pupil size or a vergence variance.
6. The lens of claim 1 , wherein the spherical aberration, and parameters of the bump function are configured based on pupil size and vergence variances for a specific prescription or target population.
7. The lens of claim 1 , wherein forming a lens comprises configuring an internal gradient refractive index profile of the lens.
8. The lens of claim 1 , wherein forming a lens comprises configuring a geometric shape of the lens and an internal gradient refractive index profile of the lens.
9. The lens of claim 1 , wherein forming a lens comprises configuring a main body of the lens such that a light propagating through the lens is refracted to exhibit the adjusted power profile.
10. The lens of claim 1 , wherein forming a lens further comprises configuring a main body of the lens such that at least an intensity of light propagating through the lens is changed to exhibit a target apodization profile.
11. The lens of claim 10 , wherein the intensity of light propagating through the lens is changed by apodizing the lens.
12. The lens of claim 11 , wherein the apodizing the lens is based on a transmittance profile defined by a continuous function, with a non-monotonically varying transmittance.
13. The lens of claim 12 , wherein a maximum of transmittance is at a pupil center and a minimum value is positioned less than an optical zone (OZ) radius.
14. The lens of claim 13 , wherein the transmittance is based on a polynomial function.
15. The lens of claim 12 , wherein a shape of the transmittance profile relative to a radial position on the lens is defined by a decrease from the center to a middle point and then an increase to a peripheral point.
16. The lens of claim 1 , wherein the TFF is defined by
TFF
=
∫
v
t
-
δ
v
t
+
δ
df
(
v
)
dv
dv
.
17. An ophthalmic lens comprising:
a main body configured to exhibit a power profile based on a power profile function defined by a base optical power, an amount of spherical aberration at a radial distance from a geometric center of a lens, and a bump function,
wherein the power profile is optimized based at least on minimizing a shape metric comprising a through-focus flatness (TFF) metric of a through-focus curve.
18. The lens of claim 17 , wherein the bump function comprises a multifocal function.
19. The lens of claim 17 , wherein the spherical aberration, and parameters of the bump function are configured to vary by refractive prescription.
20. The lens of claim 17 , wherein the spherical aberration, and parameters of the bump function are configured based on pupil size and vergence variances for a specific prescription or target population.
21. The lens of claim 17 , wherein the main body is configured by configuring a geometric shape of the lens.
22. The lens of claim 17 , wherein the main body is configured by configuring an internal gradient refractive index profile of the lens.
23. The lens of claim 17 , wherein the main body is configured by configuring a geometric shape of the lens and an internal gradient refractive index profile of the lens.
24. The lens of claim 17 , wherein the main body is configured such that a light propagating through the lens is refracted to exhibit the power profile.
25. The lens of claim 17 , wherein the main body is configured such that at least an intensity of light propagating through the lens is changed to exhibit a target apodization profile.
26. The lens of claim 25 , wherein the intensity of light propagating through the lens is changed by apodizing the lens.
27. The lens of claim 26 , wherein the apodizing the lens is based on a transmittance profile defined by a continuous function, with a non-monotonically varying transmittance.
28. The lens of claim 27 , wherein a maximum of transmittance is at a pupil center and a minimum value is positioned less than an optical zone (OZ) radius.
29. The lens of claim 28 , wherein the transmittance is based on a polynomial function.
30. The lens of claim 27 , wherein a shape of the transmittance profile relative to a radial position on the lens is defined by a decrease from the center to a middle point and then an increase to a peripheral point.
31. The lens of claim 17 , wherein the TFF is defined by
TFF
=
∫
v
t
-
δ
v
t
+
δ
df
(
v
)
dv
dv
.
32. An ophthalmic lens comprising:
a main body configured to exhibit a power profile based on a power profile function defined by a base optical power, an amount of spherical aberration at a radial distance from a geometric center of a lens, and a bump function,
wherein the power profile provides vision correction and is further optimized to slow myopia progression or treat presbyopia based at least on minimizing a shape metric comprising a through-focus flatness (TFF) metric of a through-focus curve.
33. The lens of claim 32 , wherein the main body is configured by configuring a geometric shape of the lens.
34. The lens of claim 32 , wherein the spherical aberration, and parameters of the bump function are configured to vary by refractive prescription.
35. The lens of claim 32 , wherein the spherical aberration, and parameters of the bump function are configured based on pupil size and vergence variances for a specific prescription or target population.
36. The lens of claim 32 , wherein the main body is configured by configuring an internal gradient refractive index profile of the lens.
37. The lens of claim 32 , wherein the main body is configured by configuring a geometric shape of the lens and an internal gradient refractive index profile of the lens.
38. The lens of claim 32 , wherein the main body is configured such that the a light propagating through the lens is refracted to exhibit the power profile.
39. The lens of claim 32 , wherein the main body is configured such that at least an intensity of light propagating through the lens is changed to exhibit a target apodization profile.
40. The lens of claim 39 , wherein the intensity of light propagating through the lens is changed by apodizing the lens.
41. The lens of claim 40 , wherein the apodizing the lens is based on a transmittance profile defined by a continuous function, with a non-monotonically varying transmittance.
42. The lens of claim 41 , wherein a maximum of transmittance is at a pupil center and a minimum value is positioned less than an optical zone (OZ) radius.
43. The lens of claim 42 , wherein the transmittance is based on a polynomial function.
44. The lens of claim 41 , wherein a shape of the transmittance profile relative to a radial position on the lens is defined by a decrease from the center to a middle point and then an increase to a peripheral point.
45. The lens of claim 32 , wherein the TFF is defined by
TFF
=
∫
v
t
-
δ
v
t
+
δ
df
(
v
)
dv
dv
.
46. A method of forming an ophthalmic lens, the method comprising:
determining a power profile based on a power profile function defined by a base optical power, an amount of spherical aberration at a radial distance from a geometric center of a lens, and a bump function;
adjusting the power profile based at least on minimizing a shape metric comprising a through-focus flatness (TFF) metric of a through-focus curve; and
forming a lens to exhibit the adjusted power profile.
47. The method of claim 46 , wherein forming a lens comprises configuring a geometric shape of the lens.
48. The method of claim 46 , wherein the spherical aberration, and parameters of the bump function are configured to vary by refractive prescription.
49. The method of claim 46 , wherein the spherical aberration, and parameters of the bump function are configured based on pupil size and vergence variances for a specific prescription or target population.
50. The method of claim 46 , wherein forming a lens comprises configuring an internal gradient refractive index profile of the lens.
51. The method of claim 46 , wherein forming a lens comprises configuring a geometric shape of the lens and an internal gradient refractive index profile of the lens.
52. The method of claim 46 , wherein forming a lens comprises configuring a main body of the lens such that the light propagating through the lens is refracted to exhibit the adjusted power profile.
53. The method of claim 46 , wherein forming a lens comprises configuring a main body of the lens such that at least an intensity of light propagating through the lens is changed to exhibit a target apodization profile.
54. The method of claim 53 , wherein the intensity of light propagating through the lens is changed by apodizing the lens.
55. The method of claim 54 , wherein the apodizing the lens is based on a transmittance profile defined by a continuous function, with a non-monotonically varying transmittance.
56. The method of claim 55 , wherein a maximum of transmittance is at a pupil center and a minimum value is positioned less than optical zone (OZ) radius.
57. The method of claim 56 , wherein the transmittance is based on a polynomial function.
58. The method of claim 55 , wherein a shape of the transmittance profile relative to a radial position on the lens is defined by a decrease from the center to a middle point and then an increase to a peripheral point.
59. The method of claim 46 , wherein the TFF metric is defined by
TFF
=
∫
v
t
-
δ
v
t
+
δ
df
(
v
)
dv
dv
.