Tunable cylindrical lenses and head-mounted display including the same

An optical system, comprising:

• a plurality of refractive elements each arranged along an optical axis, each of the plurality of refractive elements having an associated variable cylinder refractive power and an associated cylinder axis, wherein the associated cylinder axis of each of the refractive elements extends along different radial directions orthogonal to the optical axis;
• wherein the plurality of refractive elements comprises:
• a first refractive element, wherein the first refractive element is part of a first pair of refractive elements along the optical axis,
• wherein each refractive element of the first pair of refractive elements has a cubic profile oriented along a radial direction of the first refractive element, and
• wherein refractive elements of the first pair of refractive elements are configured to slide in opposite directions orthogonal to the optical axis;
• a second refractive element, wherein the second refractive element is part of a second pair of refractive elements along the optical axis,
• wherein each refractive element of the second pair of refractive elements has a cubic profile oriented along a radial direction of the second refractive element, and
• wherein refractive elements of the second pair of refractive elements are configured to slide in opposite directions orthogonal to the optical axis;
• and
• a third refractive element, wherein the third refractive element is part of a third pair of refractive elements along the optical axis,
• wherein each refractive element of the third pair of refractive elements has a cubic profile oriented along a radial direction of the third refractive element, and
• wherein refractive elements of the third pair of refractive elements are configured to slide in opposite directions orthogonal to the optical axis;
• and
• an electronic controller configured to control the variable cylinder refractive powers, to form an optical element comprising the plurality of refractive elements and having an overall spherical refractive power (SPH), cylinder refractive power (CYL), and cylinder axis (Axis) according to a prescription (Rx).