Methods and apparatus for focus improvement in multiple liquid crystal cell lenses

A Liquid Crystal (LC) lens having an optical axis for use in convergence space a distance away from an image surface to project an incident image onto said image surface, said LC lens comprising:

• first and second birefringent LC cells in planes orthogonal to the optical axis, each cell having a corresponding frequency-dependent alignment layer and a corresponding non-uniform LC molecular director distribution characterized by a corresponding predominant director pre-tilt axis, respectively;
• wherein the first and the second predominant director pre-tilt axes are orthogonal to each other, respectively, defining first ordinary and extraordinary center ray axes and second ordinary and extraordinary center ray axes, respectively;
• and
• wherein the second cell is decentered with respect to the first cell by a vector offset based on differences between the first ordinary and extraordinary center ray axes at an emissive side of the first cell and between the second ordinary and extraordinary center ray axes at an emissive side of the second cell.

A Liquid Crystal (LC) lens having an optical axis for use in convergence space a distance away from an image surface to project an incident image onto said image surface, said LC lens comprising:

• first and second birefringent LC cells in planes orthogonal to the optical axis, each cell providing a first spatial modulation of light of one linear polarization;
• wherein said first and said second LC cells together provide spatial modulation of two linear polarizations including the first spatial modulation, and define first ordinary and extraordinary center ray axes and second ordinary and extraordinary center ray axes, respectively, said first and said second ordinary center ray axes corresponding to said optical axis of said first and said second birefringent LC cells, respectively;
• and
• wherein the second cell is decentered with respect to the first cell by a vector offset based on differences between the first ordinary and extraordinary center ray axes at an emissive side of the first cell and between the second ordinary and extraordinary center ray axes at an emissive side of the second cell.

A Liquid Crystal (LC) lens having an optical axis for use in convergence space a distance away from an image surface to project an incident image onto said image surface, said LC lens comprising:

• a pair of LC cells, each one of said cells having at least one alignment layer structurally defining a predominant director pre-tilt orientation, said director pre-tilt orientations of said LC cells being orthogonal to each other to act on corresponding orthogonal linear polarizations of incident light for modulating said incident light passing therethrough, each LC cell being birefringent configured to split said incident light into ordinary and extraordinary rays having mutually orthogonal light polarizations, each ordinary ray parallel to the optical axis being the direction of light propagation created by the LC of each cell, respectively, each LC cell configured to offset transversally non-uniform phase delay modulated light of its extraordinary ray by a corresponding birefringence-dependent offset distance from said optical axis at an exit surface of each LC cell, respectively,
• wherein at least one LC cell of said pair of LC cells is shifted relative to the other LC cell of said pair of LC cells in a direction within a plane between the LC cells equal to a direction of a vector sum of the offset distances to redirect corresponding offset center rays towards said optical axis at said image surface to compensate for said birefringence-dependent offset distances at the exit surfaces, respectively.