Tunable cylindrical lenses and head-mounted display including the same
Systems include three optical elements arranged along an optical axis each having a different cylinder axis and a variable cylinder refractive power. Collectively, the three elements form a compound optical element having an overall spherical refractive power (SPH), cylinder refractive power (CYL), and cylinder axis (Axis) that can be varied according to a prescription (Rx).
1. A head-mounted display system, comprising:
a first optical element comprising a first refractive element arranged along an optical axis, the first refractive element having a first variable cylinder refractive power and a first cylinder axis along a first radial direction orthogonal to the optical axis;
a second optical element comprising a second refractive element arranged along the optical axis, the second refractive element having a second variable cylinder refractive power and a second cylinder axis along a second radial direction orthogonal to the optical axis;
a third optical element comprising a third refractive element arranged along the optical axis, the third refractive element having a third variable cylinder refractive power and a third cylinder axis along a third radial direction orthogonal to the optical axis, wherein the first, second, and third radial directions are different; and
an electronic controller configured to control the first, the second, and the third variable cylinder refractive powers, to form an optical element comprising the first, second, and third refractive elements and having an overall spherical refractive power (SPH), cylinder refractive power (CYL), and cylinder axis (Axis) according to a prescription (Rx).
2. The head-mounted display system of claim 1 , wherein the first optical element comprises a first pair of refractive elements, the first pair of refractive elements comprising the first refractive element,
wherein each refractive element of the first pair of refractive elements has a cubic profile oriented along an axis in the radial direction of the optical element, and
wherein refractive elements of the first pair of refractive elements are configured to slide in opposite directions orthogonal to the optical axis.
3. The head-mounted display system of claim 2 , wherein the second optical element comprises a second pair of refractive elements, the second pair of refractive elements comprising the second refractive element,
wherein each refractive element of the second pair of refractive elements has a cubic profile oriented along an axis in the radial direction of the optical element, and
wherein refractive elements of the second pair of refractive elements are configured to slide in opposite directions orthogonal to the optical axis.
4. The head-mounted display system of claim 3 , wherein the third optical element comprises a third pair of refractive elements, the third pair of refractive elements comprising the third refractive element,
wherein each refractive element of the third pair of refractive elements has a cubic profile oriented along an axis in the radial direction of the optical element, and
wherein refractive elements of the third pair of refractive elements are configured to slide in opposite directions orthogonal to the optical axis.
5. The head-mounted display system of claim 1 , wherein at least one of the first, second, and third refractive elements comprises:
a deformable transparent membrane adjacent a deformable optical material, the deformable transparent membrane and the deformable optical material aligned along the optical axis, wherein the cylinder refractive power of the at least one refractive element varies with changes in a shape of the deformable transparent membrane.
6. The head-mounted display system of claim 5 , wherein the deformable transparent membrane is formed of an elastomeric material.
7. The head-mounted display system of claim 6 , wherein the elastomeric material comprises a silicone elastomer.
8. The head-mounted display system of claim 5 , wherein the shape of the deformable transparent membrane is configured to change by bowing the deformable transparent membrane about the cylinder axis of the at least one of the first, second, and third refractive elements.
9. The head-mounted display system of claim 6 , wherein the deformable transparent membrane is configured to bow about the cylinder axis by pivoting the deformable transparent membrane.
10. The head-mounted display system of claim 1 , wherein an angular separation between the first and second radial directions is equal to an angular separation between the second and third radial directions.
11. The head-mounted display system of claim 10 , wherein, in a Cartesian coordinate system orthogonal to the optical axis, the first radial direction is at 30°, the second radial direction is at 90°, and the third radial direction is at 150°.
12. The head-mounted display system of claim 11 , wherein the first cylinder refractive power, C 30 , the second cylinder refractive power, C 90 , and the third cylinder refractive power, C 150 , and values for S, C, and A are related according to the formulae:
C
30
=
2
3
S
+
(
2
3
cos
2
A
+
2
3
3
cos
A
sin
A
)
C
C
90
=
2
3
S
+
(
sin
2
A
-
1
3
cos
2
A
)
C
C
150
=
2
3
S
+
(
2
3
cos
2
A
-
2
3
3
cos
A
sin
A
)
C
.
13. The head-mounted display system of claim 1 , wherein the cylinder refractive power of each of the first, second, and third optical elements is variable through a range from −5 D to +5 D.
14. The head-mounted display system of claim 1 , wherein each of the first, second, and third optical elements has an aperture having an area of 1 cm 2 or more, and wherein each of the refractive elements of the first, second, and third optical elements has a thickness along the optical axis of 10 mm or less.
15. The head-mounted display system of claim 1 , further comprising a see-through display along the optical axis.
16. The head-mounted display system of claim 15 , wherein the see-through display comprises an eyepiece comprising a waveguide configured to project visual imagery.
17. The head-mounted display system of claim 15 , wherein the second optical element is configured to be disposed between the see-through display and an eye of user of the head-mounted display system upon wearing of the head-mounted display by the user.
18. The head-mounted display system of claim 17 , wherein the first optical element comprises two variable cylindrical lenses having their respective cylinder axes orthogonal to each other.
19. The head-mounted display system of claim 1 , further comprising an eye-tracking module configured to detect a fixation location of eyes of a user of the head-mounted display system, wherein the electronic controller is programmed to vary the prescription based on of the fixation location.
20. The head-mounted display system of claim 1 , wherein the electronic controller is programmed to vary the prescription based on of the depth of the fixation location.