Participants: A. Alkan Gulses, B. Keith Jenkins
In diffractive optics and computer holography, generally, a common and well-studied scenario is using one computer-generated hologram plane (or one diffractive optical element plane) to generate a single image plane. In our project, we have extended this scenario in two ways: using multiple diffractive optical element planes in cascade, to reconstruct multiple image planes in depth. With this approach, the information in any one optical element plane contributes to the information in all image planes, similar to how a small portion of a single hologram can reconstruct an entire scene, albeit with reduced resolution.
We have developed iterative algorithms for the design of the pixel-states of the set of optical elements, given a desired (target) set of image plane intensities. One algorithm is deterministic and is an extension of the well-known Gerchberg-Saxton algorithm typically used for the case of one optical element and one image plane; we call it the extended iterative Fourier Transform algorithm (or extended IFTA). The other algorithm is stochastic and is based on a simulated annealing approach; we call it the extended simulated annealing (or extended SA) algorithm. Numerical simulations from both algorithms show that using more optical element planes improves generated-image quality in all image planes. With other things being held constant, increasing the number of image planes results in a decrease in image quality in each image plane (due to information limits); thus, using more optical element planes can be equivalently thought of as allowing the generation of more image planes, with a similar quality per image plane.
In addition to expanding the optical elements in the longitudinal (out-of-plane) dimension, we have also simulated a technique that extends the optical elements in the lateral (in-plane) dimensions. Adapting a method used by others for single-optical-element systems, we can use larger (higher pixel count) optical elements in each plane, and add a “don’t care” region bordering around each image plane. This further improves generated image quality, or equivalently, allows generation of a larger number of image planes for a given image quality.
Follow-on and future work includes applying this multiplane approach to 3D informational displays, in areas such as automotive 3D head-up displays, wearable 3D displays including those for augmented reality, and printed 3D-information displays. Additionally, we have recently improved the iterative design algorithms themselves to reduce the computation time by two orders of magnitude, showing that real-time operation would likely be feasible with additional efforts on more efficient coding and hardware implementation.