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 system, comprising:
a first optical element comprising a first refractive element arranged along an optical axis, and a first actuator arranged to vary a cylinder refractive power of the first refractive element in response to a first control signal, the first refractive element having a first cylinder axis associated with the first refractive element along a first radial direction orthogonal to the optical axis;
a second optical element comprising a second refractive element arranged along the optical axis, and a second actuator arranged to vary a cylinder refractive power of the second refractive element in response to a second control signal, the second refractive element having a second cylinder axis associated with the second refractive element along a second radial direction orthogonal to the optical axis;
a third optical element comprising a third refractive element arranged along the optical axis, and a third actuator arranged to vary a cylinder refractive power of the third refractive element along a third radial direction orthogonal to the optical axis in response to a third control signal, where the first, second, and third radial directions are different; and
an electronic controller in communication with the first, second, and third actuators, the electronic controller being configured, during operation, to provide the first, second and third control signals to the first, second, and third actuators, respectively, so that the first, second, and third refractive elements collectively form an optical element having an overall spherical refractive power (SPH), cylinder refractive power (CYL), and cylinder axis (Axis) according to a prescription (Rx).
2. The 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.
3. The system of claim 1 , wherein, for 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°.
4. The system of claim 3 , wherein the first cylinder refractive power, CC 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
3
0
=
2
3
S
+
(
2
3
cos
2
A
+
2
3
3
cos
A
sin
A
)
C
C
9
0
=
2
3
S
+
(
sin
2
A
-
1
3
cos
2
A
)
C
C
1
5
0
=
2
3
S
+
(
2
3
cos
2
A
-
2
3
3
cos
A
sin
A
)
C
5. The system of claim 1 , wherein at least one of the refractive elements comprises a deformable optical material comprising a solid optical material.
6. The system of claim 5 , wherein the solid optical material is an elastomeric material comprising a silicone elastomer.
7. The system of claim 5 , wherein the at least one of the refractive elements comprises a deformable transparent membrane adjacent the deformable optical material, the actuator of the at least one refractive element being arranged to deform a shape of the deformable transparent membrane to vary the cylinder refractive power of the at least one refractive element.
8. The system of claim 7 , wherein the actuator bows the membrane about the cylinder axis of the at least one refractive element to vary the cylinder refractive power of the at least one refractive element.
9. The system of claim 7 , wherein the at least one of the refractive elements comprises a rigid transparent substrate adjacent the deformable optical material on an opposing side of the refractive element from the deformable optical material.
10. The system of claim 7 , wherein the optical element of the at least one of the refractive elements comprises a rigid gasket at an edge of the deformable optical material and the deformable transparent membrane pivots on the rigid gasket when acted upon by the actuator.
11. The 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.
12. The system of claim 1 , wherein the optical element has an aperture having an area of 1 cm 2 or more and wherein each of the refractive elements has a thickness along the optical axis of 10 mm or less.
13. The system of claim 1 , wherein each optical element comprises a pair of refractive elements, each refractive element of the pairs having a cubic profile oriented along an axis in the radial direction of the optical element, the actuator of the corresponding optical element being arranged to slide the pair of refractive elements in opposite directions orthogonal to the optical axis.
14. A head-mounted display system, comprising:
a first optical element having a variable spherical refractive power (SPH);
a second optical element having a variable SPH, a variable cylinder refractive power (CYL), and a variable cylinder axis (Axis);
a see-through display arranged between the first optical element and the second optical element; and
an electronic controller in communication with the first optical element, the second optical element, and the see-through display, the electronic controller being programmed to adjust the SPH of the first optical element and the SPH, CYL, and Axis of the second optical element according to a prescription (Rx) of an individual user of the head-mounted display.
15. The head-mounted display of claim 14 , further comprising a frame for mounting the first optical element, second optical element, and see-through display relative to each other and, during use, relative to a user of the head-mounted display.
16. The head-mounted display of claim 14 , wherein the second optical element is arranged between the see-through display and the user during use of the head-mounted display, and wherein the first optical element comprises two variable cylindrical lenses having their respective cylinder axes orthogonal to each other.
17. The head-mounted display of claim 14 , further comprising an eye-tracking module, the electronic controller being programmed to vary the prescription of the second optical element based on information about where a user of the head-mounted display is looking from the eye-tracking module.
18. The head-mounted display of claim 17 , wherein the electronic controller is programmed to vary the SPH, CYL, and Axis of the second optical element from a near-vision prescription to a distance-vision prescription depending on where the user is looking.
19. The head-mounted display of claim 14 , further comprising a biometric identification module, the electronic controller being programmed to identify a user based on information from the biometric identification module and adjust a prescription of the second optical element based on the user's identity.
20. The head-mounted display of claim 19 , wherein the biometric identification module is an iris identification module.