Holographic search algorithms such as direct search (DS) and simulated annealing allow high-quality holograms to be generated at the expense of long execution times. This is due to single iteration computational costs of O ( NxNy ) and number of required iterations of order O ( NxNy ) , where Nx and Ny are the image dimensions. This gives a combined performance of order O(Nx2Ny2). We use a technique to reduce the iteration cost down to O ( 1 ) for phase-sensitive computer-generated holograms, giving a final algorithmic performance of O ( NxNy ) . We do this by reformulating the mean-squared error (MSE) metric to allow it to be calculated from the diffraction field rather than requiring a forward transform step. For a 1024 × 1024-pixel test images, this gave us a ≈50,000 × speed-up when compared with traditional DS with little additional complexity. When applied to phase-modulating or amplitude-modulating devices, the proposed algorithm converges on a global minimum MSE in O ( NxNy ) time. By comparison, most extant algorithms do not guarantee that a global minimum is obtained. Those that do, have a computational complexity of at least O(Nx2Ny2) with the naive algorithm being O [ ( NxNy ) ! ] .
Augmented and Mixed Reality promises another leap forward in productivity and lifestyle, offering benefits with a magnitude and impact matching that of the introduction of smartphones. However, to enable this, many significant technical challenges must be overcome. Here we review the state of the art, identifying key challenges established in the literature to consumer-wearable devices. In particular, we discuss: vergence-accommodation conflict (the detrimental effect of overlays that are optically inconsistent with the real-world objects they augment), the need to present overlays visible against the vast dynamic range that the human eye can process, and constraints surrounding the scalability and cost of manufacture of optics. We demonstrate that digital holography as a display mechanism not only provides an effective solution to the aforementioned challenges, but also that various hardware requirements become far less stringent. By operating in the Fourier Domain, holographic displays are freed of design compromises driven by the constraints of a pixelated screen. However, the computational cost of CGH has previously been considered prohibitive. We demonstrate that for real-world applications the latest advancements made by VividQ deliver sufficient focal accuracy at a computational cost within reach of personal mobile devices. We prove that it is now possible to clear the barriers preventing mass adoption of Augmented and Mixed Reality products with Computer-Generated Holography.