Varifocal lens

A varifocal lens is a camera lens with variable focal length in which focus changes as focal length (and magnification) changes, as compared to parfocal ("true") zoom lens, which remains in focus as the lens zooms (focal length and magnification change). Many so-called "zoom" lenses, particularly in the case of fixed lens cameras, are actually varifocal lenses,[1] which give lens designers more flexibility in optical design trade-offs (focal length range, maximum aperture, size, weight, cost) than parfocal zoom. These are practical because of auto-focus, and because the camera processor can automatically adjust the lens to keep it in focus while changing focal length ("zooming") making operation practically indistinguishable from a parfocal zoom. Varifocal lenses can be used for image display as well as capture, and Oculus VR has confirmed developing a varifocal display for virtual reality.[2]

A varifocal lens. Left image is at 2.8 mm, in focus. Middle image is at 12 mm with the focus left alone from 2.8 mm. Right image is at 12 mm refocused. The close knob is focal length and the far knob is focus.
You can create a variable focal lens by overlapping two asymmetric phase plates (with the correct profile) and adjusting their relative angle.

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