Multi-frame decomposition method for image rendering on multilayer displays

An apparatus comprising:

• a display device comprising one or more spatial light modulators including controllable-transparency pixels;
• and
• a processor configured to perform image rendering on the display device including at least:
• determining target beam values for exit light beams emitted from respective locations on the front surface of the display device, each of the exit light beams is formed by contributions from lights propagating along corresponding internal optical paths, each of the internal optical paths passes through at least one of the controllable-transparency pixels,
• for each of the exit light beams, partitioning the respective target beam value into beam value partitions, wherein each of the beam value partitions being associated with a corresponding one of the internal optical paths, and
• selecting transmittance values for the controllable-transparency pixels so that a sum of error terms is minimized, wherein an error term represents a difference between (i) a contribution from light propagating along an internal optical path to one of the exit light beam and (ii) a beam value partition associated with that internal optical path, and wherein the error term is represented as:
• (
• L
• i
• ,
• p
• -
• d
• i
• ,
• p
• ⁢
• L
• i
• target
• )
• 2
• ,
• wherein Li,p is a contribution to an exit light beam i by an internal optical path p,
• Litarget is a target beam value for an exit light beam i, and
• wherein Litarget is a target beam value for an exit light beam i, and
• wherein di,pLitarget is a beam value partition associated with an internal optical path p that contributes to an exit light beam i.