  Creating immersive 3D stereoscopic, autostereoscopic, and lightfield
experiences are becoming the center point of optical design of future head
mounted displays and lightfield displays. However, despite the advancement in
3D and light field displays; there is no consensus on what are the necessary
quantized depth levels for such emerging displays at stereoscopic or monocular
modalities. Here we start from psychophysical theories and work toward defining
and prioritizing quantized levels of depth that would saturate the human depth
perception. We propose a general optimization framework, which locates the
depth levels in a \emph{globally optimal} way for band limited displays. While
the original problem is computationally intractable, we manage to find a
tractable reformulation as maximally covering a region of interest with a
selection of hypographs corresponding to the monocular depth of field profiles.
The results show that on average 1731 stereoscopic and 8 monocular depth levels
(distributed from 25 cm to infinity) would saturate the visual depth
perception. Also the first 3 depth levels should be allocated at (148), then
(83, 170), then (53, 90, 170) distances respectively from the face plane to
minimize the monocular error in the entire population. The study further
discusses the 3D spatial profile of the quantized stereoscopic and monocular
depth levels. The study provides fundamental guidelines for designing optimal
near eye displays, light-field monitors, and 3D screens.
