Simple calculation of a computer-generated hologram for lensless holographic 3D projection using a nonuniform sampled wavefront recording plane

Compact reconstruction of a Fourier hologram for a 3D object by scaling compensation

The Fourier holographic projection method is compact and computationally fast. However, since the magnification of the displayed image increases with the diffraction distance, this method cannot be used directly to display multi-plane three-dimensional (3D) scenes. We propose a holographic 3D projection method of Fourier holograms by scaling compensation to offset the magnification during optical reconstruction. To achieve a compact system, the proposed method is also used to reconstruct 3D virtual images with Fourier holograms. Different from traditional Fourier holographic displays, images are reconstructed behind a spatial light modulator (SLM) so that the observation position can be placed close to the SLM. The effectiveness of the method and the flexibility of combining it with other methods are confirmed by simulations and experiments. Therefore, our method could have potential applications in the augmented reality (AR) and virtual reality (VR) fields.

Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display

Holographic three-dimensional display is an important display technique because it can provide all depth information of a real or virtual scene without any special eyewear. In recent years, with the development of computer and optoelectronic technology, computer-generated holograms have attracted extensive attention and developed as the most promising method to realize holographic display. However, some bottlenecks still restrict the development of computer-generated holograms, such as heavy computation burden, low image quality, and the complicated system of color holographic display. To overcome these problems, numerous algorithms have been investigated with the aim of color dynamic holographic three-dimensional display. In this review, we will explain the essence of various computer-generated hologram algorithms and provide some insights for future research.

Acceleration and expansion of a photorealistic computer-generated hologram using backward ray tracing and multiple off-axis wavefront recording plane methods

Holograms can reconstruct the light wave field of three-dimensional objects. However, the computer-generated hologram (CGH) requires much calculating time. Here we proposed a CGH generation algorithm based on backward ray tracing and multiple off-axis wavefront recording planes (MO-WRP) to generate photorealistic CGH with a large reconstruction image. In this method, multiple WRPs were placed parallelly between the virtual object and the hologram plane. Virtual rays were emitted from the pixel of WRPs and intersect with the object. The complex amplitude of WRPs is then determined by illumination module, such as Phong reflection module. The CGH was generated by the shifted Angular Spectrum Propagation (ASP) from WRPs to the hologram plane. Experimental results demonstrate the effectiveness of this method, and the CGH generation rate is 37.3 frames per second (1 WRP) and 9.8 frames per second (2×2 WRPs).

Image quality improvement of holographic 3-D images based on a wavefront recording plane method with a limiting diffraction region

This study aims to improve the image quality of holographic three-dimensional (3-D) images based on the wavefront recording plane (WRP) method. In this method, we place a WRP close to the 3-D objects to reduce the propagation distance of light from the objects to the WRP. The conventional WRP method has been implemented only under conditions that did not cause aliasing noise. This study proposes a WRP method with a limiting diffraction region from the WRP to the hologram such that we can perform the WRP method under any condition. As a result, we succeeded in improving the image quality of the 3-D images based on the WRP method.

Acceleration of computer-generated hologram using wavefront-recording plane and look-up table in three-dimensional holographic display

In this paper, we propose a fast calculation method using look-up table and wavefront-recording plane. Wavefront-recording plane method consists of two steps: the first step is the calculation of a wavefront-recording plane which is placed between the object and the hologram. In the second step, we obtain the hologram by executing diffraction calculation from the wavefront-recording plane to the hologram plane. The first step of the previous wavefront-recording plane method is time consuming. In order to obtain further acceleration to the first step, we propose high compressed look-up table method based on wavefront-recording plane. We perform numerical simulations and optical experiments to verify the proposed method. Numerical simulation results show that the calculation time reduces dramatically in comparison with previous wavefront-recording plane method and the memory usage is very small. The optical experimental results are in accord with the numerical simulation results. It is expected that proposed method can greatly reduce the computational complexity and could be widely applied in the holographic field in the future.

Comparison of wavefront recording plane-based hologram calculations: ray-tracing method versus look-up table method

In this study, we compare the ray-tracing method with the look-up table (LUT) method in order to optimize computer-generated hologram (CGH) calculation based on the wavefront recording plane (WRP) method. The speed of the WRP-based CGH calculation largely depends on implementation factors, such as calculation methods, hardware, and parallelization method. Therefore, we evaluated the calculation time and image quality of the reconstructed three-dimensional (3D) image by using the ray-tracing and LUT methods in the central processing unit (CPU) and graphics processing unit (GPU) implementations. Thereafter, we performed several implementations by changing the number of object points and the distance from 3D objects to the WRP. Furthermore, we confirmed different characteristics between CPU and GPU implementations.

Accelerated near-field algorithm of sparse apertures by non-uniform fast Fourier transform

We present an accelerated algorithm for calculating the near-field of non-uniform sparse apertures with non-uniform fast Fourier transform (NUFFT). The distances of the adjacent units in non-uniform sparse apertures are unequal and larger than half a wavelength. The near-field of apertures can be calculated by the angular spectrum method and the convolution methods, and according to the different convolution kernels, the convolution methods can be divided as the Fresnel kernel convolution and the Rayleigh-Sommerfeld kernel convolution. The Fresnel kernel is the approximation of the Rayleigh-Sommerfeld kernel in the far regions of the near-field zone. In uniform apertures, the three methods can be accelerated by fast Fourier transform (FFT). However, FFT should be replaced by NUFFT for non-uniform sparse apertures. The simulation results reveal that the Rayleigh-Sommerfeld convolution with NUFFT (RS-NUFFT) can be applied to all aperture sizes, distributions and near-field distances. After investigating the error sources in RS-NUFFT, the techniques (padding zeros for apertures, increasing sampling rate for the convolution kernel) are developed for increasing the calculation accuracy of RS-NUFFT.

Scaling of Three-Dimensional Computer-Generated Holograms with Layer-Based Shifted Fresnel Diffraction

Holographic three-dimensional (3D) displays can reconstruct a whole wavefront of a 3D scene and provide rich depth information for the human eyes. Computer-generated holographic techniques offer an efficient way for reconstructing holograms without complicated interference recording systems. In this work, we present a technique for generating 3D computer-generated holograms (CGHs) with scalable samplings, by using layer-based diffraction calculations. The 3D scene is partitioned into multiple layers according to its depth image. Shifted Fresnel diffraction is used for calculating the wave diffractions from the partitioned layers to the CGH plane with adjustable sampling rates, while maintaining the depth information. The algorithm provides an effective method for scaling 3D CGHs without an optical zoom module in the holographic display system. Experiments have been performed, demonstrating that the proposed method can reconstruct quality 3D images at different scale factors.

Fast two-step layer-based method for computer generated hologram using sub-sparse 2D fast Fourier transform

Fast two-step layer-based and sub-sparse two-dimensional Fast Fourier transform (SS-2DFFT) algorithms are proposed to speed up the calculation of computer-generated holograms. In a layer-based method, each layer image may contain large areas in which the pixel values are zero considering the occlusion effect among the different depth layers. By taking advantage of this feature, the two-step layer-based algorithm only calculates the non-zero image areas of each layer. In addition, the SS-2DFFT method implements two one-dimensional fast Fourier transforms (1DFFT) to compute a 2DFFT without calculating the rows or columns in which the image pixels are all zero. Since the size of the active calculation is reduced, the computational speed is considerably improved. Numerical simulations and optical experiments are performed to confirm these methods. The results show that the total computational time can be reduced by 5 times for a three-dimensional (3D) object of a train, 3.4 times for a 3D object of a castle and 10 times for a 3D object of a statue head when compared with a conventional layer-based method if combining the two proposed methods together.

Accelerating computation of CGH using symmetric compressed look-up-table in color holographic display

The huge computational complexity is a challenge for computer-generated hologram (CGH) calculation in a holographic display. In this paper, we propose a symmetric compressed look-up-table algorithm to accelerate CGH computation based on the Fresnel diffraction theory and compressed look-up-table algorithm. In offline computation, the memory usage of horizontal and vertical modulation factors is reduced to the order of Kilobytes by using translational symmetric compression and wavelength separation. In online computation, we develop a one-time generation of color holograms method which is accelerated by matrix convolution operation. Numerical simulation results show at least 13 times faster than existing algorithms without sacrificing the computation precision. The optical experiments are performed to demonstrate its feasibility. It is believed that the proposed method is an effective algorithm to accelerate the computation of CGH in color holographic display.

Speckleless holographic display by complex modulation based on double-phase method

The purpose of this study is to implement speckle reduced three-dimensional (3-D) holographic display by single phase-only spatial light modulator (SLM). The complex amplitude of hologram is transformed to pure phase value based on double-phase method. To suppress noises and higher order diffractions, we introduced a 4-f system with a filter at the frequency plane. A blazing grating is proposed to separate the complex amplitude on the frequency plane. Due to the complex modulation, the speckle noise is reduced. Both computer simulation and optical experiment have been conducted to verify the effectiveness of the method. The results indicate that this method can effectively reduce the speckle in the reconstruction in 3-D holographic display. Furthermore, the method is free of iteration which allows improving the image quality and the calculation speed at the same time.