Effective generation of digital holograms of three-dimensional objects using a novel look-up table method

Abstract

Several approaches for increasing the speed in computation of the digital holograms of three-dimensional objects have been presented with applications to real-time display of holographic images. Among them, a look-up table (LUT) approach, in which the precalculated principal fringe patterns for all possible image points of the object are provided, has gained a large speed increase in generation of computer-generated holograms. But the greatest drawback of this method is the enormous memory size of the LUT. A novel approach to dramatically reduce the size of the conventional LUT, still keeping its advantage of fast computational speed, is proposed, which is called here a novel LUT (N-LUT) method. A three-dimensional object can be treated as a set of image planes discretely sliced in the z direction, in which each image plane having a fixed depth is approximated as some collection of self-luminous object points of light. In the proposed method, only the fringe patterns of the center points on each image plane are precalculated, called principal fringe patterns (PFPs) and stored in the LUT. Then, the fringe patterns for other object points on each image plane can be obtained by simply shifting this precalculated PFP according to the displaced values from the center to those points and adding them together. Some experimental results reveal that the computational speed and the required memory size of the proposed approach are found to be 69.5 times faster than that of the ray-tracing method and 744 times smaller than that of the conventional LUT method, respectively.

Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

“…On the other hand, it must be taken into account that images corresponding to the set of tuples are sparse and this can also minimize the additive computational complexity. Digital holograms of partial images corresponding to the set of tuples are named "partial holograms" and they are denoted by ( ) which can be obtained by (15) and the methodology of [9]. Since the transformed images to generate the corresponding holograms are linear, according to (8), the hologram corresponding to the set of tuples can be presented as follows:…”

“…Unlike other works, it successfully explores the use of the global mathematical symmetry, a key consideration which allows reducing the MCC, which in turn contributes to increasing the speed of digital hologram generation. The memory size used to generate the hologram is the same as that reported [9]. The time to generate a hologram point is 0.009 ms compared to the N-LUT algorithm which takes 0.0170 ms. By this method, the computational complexity is reduced by approximately the half with respect to the N-LUT method.…”

Recent progress in computer-generated holography for three-dimensional scenes

“…Therefore, by pre-calculating the optical fields for every distance and storing them, the LUTs can be constructed. The hologram of a 3D object can be obtained simply by adding the LUTs that are shifted according to the lateral position and multiplied with the complex amplitude of the 3D object points, as shown in Figure 3(a) [21,22]. In the case of a moving 3D scene, the temporal redundancy can also be considered to reduce the computational load.…”

Reference Functions for Synthesis and Analysis of Multiview and Integral Images

“…4,[6][7][8][9] can be found, e.g., in [13,16]. In common with the patterns of the digital holography [24,25], the proposed reference functions depend on the distance only; the discrete displacement within a plane does not affect their shape. Especially important for this analysis is the projection, because the period of cells is identical for all planes in the projected form but varies from plane to plane in the regular coordinates.…”