Calculating the Fresnel diffraction of light from a shifted and tilted plane

Miniaturization and image optimization of a full-color holographic display system using a vibrating light guide

In this study, a miniaturized full-color holographic reconstruction system that uses a single spatial light modulator to achieve full-color image reconstruction was developed. The reconstruction system uses a single light guide for light combination and is therefore less voluminous than conventional reconstruction systems. The experimental results demonstrated that the system had a full-color display, corrected light combination, and eliminated zero-order light. The vibrations of the light guide disrupted the temporal coherence of the laser beam, thus ensuring that the speckle in the reconstructed image was almost imperceptible to the human eye.

Light diffraction in slab waveguide lenses simulated with the stepwise angular spectrum method

A stepwise angular spectrum method (SASM) for curved interfaces is presented to calculate the wave propagation in planar lens-like integrated optical structures based on photonic slab waveguides. The method is derived and illustrated for an effective 2D setup first and then for 3D slab waveguide lenses. We employ slab waveguides of different thicknesses connected by curved surfaces to realize a lens-like structure. To simulate the wave propagation in 3D including reflection and scattering losses, the stepwise angular spectrum method is combined with full vectorial finite element computations for subproblems with lower complexity. Our SASM results show excellent agreement with rigorous numerical simulations of the full structures with a substantially lower computational effort and can be utilized for the simulation-based design and optimization of complex and large scale setups.

Effect of tilt on circular zone plate performance

Fresnel zone plates are frequently used as focusing and imaging optics in x-ray microscopy, as they provide the ease of use of normal incidence optics. We consider here the effects of tilt misalignment on their optical performance, both in the thin optics limit and in the case of zone plates that are sufficiently thick so that volume diffraction effects come into play. Using multislice propagation, we show that simple analytical models describe the tilt sensitivity of thin zone plates and the thickness at which volume diffraction must be considered, and examine numerically the performance of example zone plates for soft x-ray focusing at 0.5 keV and hard x-ray focusing at 10 keV.

Angle Multiplexing Optical Image Encryption in the Fresnel Transform Domain Using Phase-Only Computer-Generated Hologram

We propose an angle multiplexing method for optics-based image encryption using a phase-only computer-generated hologram (POCGH) in the tilted Fresnel transform (TFrT) domain. Modified Gerchberg-Saxton algorithms, based on the three types of rotation manipulation in both the hologram and reconstruction planes, are used with their corresponding TFrT parameters to extract the phase-only functions (POFs) of the target images. All the extracted POFs are then phase-modulated and summed to obtain the final POCGH, which is capable of multiplexing and avoiding overlap in the reconstructed images. The computer simulation results show that the images corresponding to the various rotation manipulations at the hologram and image reconstruction planes can be successfully restored with high correlation coefficients. Due to the encrypted nature of the multiplexed images, a higher system security level can be achieved, as the images can only be correctly displayed when all the required parameters in the TFrT are available. The angle sensitivity on the image quality for each manipulation is also investigated.

Coherent field propagation between tilted planes

Propagating electromagnetic light fields between nonparallel planes is of special importance, e.g., within the design of novel computer-generated holograms or the simulation of optical systems. In contrast to the extensively discussed evaluation between parallel planes, the diffraction-based propagation of light onto a tilted plane is more burdensome, since discrete fast Fourier transforms cannot be applied directly. In this work, we propose a quasi-fast algorithm (O(N³ log N)) that deals with this problem. Based on a proper decomposition into three rotations, the vectorial field distribution is calculated on a tilted plane using the spectrum of plane waves. The algorithm works on equidistant grids, so neither nonuniform Fourier transforms nor an explicit complex interpolation is necessary. The proposed algorithm is discussed in detail and applied to several examples of practical interest.

Effective information processing method to produce a computer-generated hologram based on a spatial light modulator

In this paper, we propose an effective information processing method to produce a computer-generated hologram (CGH) based on a spatial light modulator (SLM). The method generates CGHs according to the property of the field of view (FOV), which, to the best of our knowledge, has never been proposed before. The CGH is composed of essential interference patterns (EIPs). Each EIP records the information of different object points. The resolution of the EIP is reduced. In the reconstructed process, the boundaries of the diffraction light of each EIP and FOV of the reconstructed image are parallel with each other. Compared with the conventional method, the experiments here demonstrate that the effective reconstructed information in the FOV has no change, while the waste reconstructed information out of the FOV is decreased at any viewing distance. The CGH can reconstruct an image with high quality. Meanwhile, the computation burden of calculating the CGH is reduced with our method.

Three-directional motion-compensation mask-based novel look-up table on graphics processing units for video-rate generation of digital holographic videos of three-dimensional scenes

A three-directional motion-compensation mask-based novel look-up table method is proposed and implemented on graphics processing units (GPUs) for video-rate generation of digital holographic videos of three-dimensional (3D) scenes. Since the proposed method is designed to be well matched with the software and memory structures of GPUs, the number of compute-unified-device-architecture kernel function calls can be significantly reduced. This results in a great increase of the computational speed of the proposed method, allowing video-rate generation of the computer-generated hologram (CGH) patterns of 3D scenes. Experimental results reveal that the proposed method can generate 39.8 frames of Fresnel CGH patterns with 1920×1080 pixels per second for the test 3D video scenario with 12,088 object points on dual GPU boards of NVIDIA GTX TITANs, and they confirm the feasibility of the proposed method in the practical application fields of electroholographic 3D displays.

Accelerated one-step generation of full-color holographic videos using a color-tunable novel-look-up-table method for holographic three-dimensional television broadcasting

A color-tunable novel-look-up-table (CT-NLUT) for fast one-step calculation of full-color computer-generated holograms is proposed. The proposed method is composed of four principal fringe patterns (PFPs) such as a baseline, a depth-compensating and two color-compensating PFPs. CGH patterns for one color are calculated by combined use of baseline-PFP and depth-compensating-PFP and from them, those for two other colors are generated by being multiplied by the corresponding color-compensating-PFPs. color-compensating-PFPs compensate for differences in the wavelength between two colors based on their unique achromatic thin-lens properties, enabling transformation of one-color CGH pattern into those for other colors. This color-conversion property of the proposed method enables simultaneous generation of full color-CGH patterns, resulting in a significant reduction of the full color-CGH calculation time. Experimental results with test scenario show that the full color-CGH calculation time of the proposed CT-NLUT has been reduced by 45.10%, compared to the conventional NLUT. It has been further reduced by 96.01% when a data compression algorithm, called temporal redundancy-based NLUT, was used together, which means 25-fold reduction of its full color-CGH calculation time. Successful computational and optical reconstructions of full color-CGH patterns confirm the feasibility of the proposed method.

Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates

The shifted angular spectrum method allows a reduction of the number of samples required for numerical off-axis propagation of scalar wave fields. In this work, a modification of the shifted angular spectrum method is presented. It allows a further reduction of the spatial sampling rate for certain wave fields. We calculate the benefit of this method for spherical waves. Additionally, a working implementation is presented showing the example of a spherical wave propagating through a circular aperture.

Fast one-step calculation of holographic videos of three-dimensional scenes by combined use of baseline and depth-compensating principal fringe patterns

As a new approach for rapid generation of holographic videos, a so-called compressed novel-look-up-table(C-NLUT), which is composed of only two principal fringe patterns (PFPs) of baseline and depth-compensating PFPs (B-PFP, DC-PFP), is proposed. Here, the hologram pattern for a 3-D video frame are generated by calculating the fringe patterns for all depth layers only by using the B-PFP, and then transforming them into those for their depth layers by being multiplied with corresponding DC-PFPs. With this one-step calculation process, the computational speed (CS) of the proposed method can be greatly enhanced. Experimental results show that the CS of the proposed method has been improved by 30.2% on the average compared to that of the conventional method. Furthermore, the average calculation time of a new hybrid MC/C-NLUT method, in which both of motion-compensation (MC) and one-step calculation schemes are employed, has been reduced by 99.7%, 65.4%, 60.2% and 30.2%, respectively compared to each of the conventional ray-tracing, LUT, NLUT, and MC-NLUT methods. In addition, the memory size of the proposed method has been also reduced by 82 × 10(6)-fold and 128-fold compared to those of the conventional LUT and NLUT methods, respectively.

Speckle reduction by combination of digital filter and optical suppression in a modified Gerchberg-Saxton algorithm computer-generated hologram

A speckleless illuminated modified-Gerchberg-Saxton-algorithm-type computer-generated hologram, which adopts a lower frequency of the iterative algorithm and calculation time, is proposed to code a hologram with two signals and position a multiplexing phase-only function, which can reconstruct the left and the right viewing holograms on the pupillary-distance position after the decryption and still maintain the content with high contrast and definition. The reconstructed image quality presents root mean square error of 0.03, with a diffraction efficiency of 87%, and signal-to-noise ratio of 8 dB after the analysis. Furthermore, two denoising techniques for the digital filter and optical suppression are combined, in which the speckle suppression with pseudorandom phase modulation and a rotating diffuser are utilized for successfully reducing the speckle contrast, which was reduced to below 4%. The goal was to reduce visual fatigue for the viewers.

Stepwise angular spectrum method for curved surface diffraction

We present a method to calculate wave propagation between arbitrary curved surfaces using a staircase approximation approach. The entire curved surface is divided into multiple subregions and each curved subregion is approximated by a piecewise flat subplane allowing the application of conventional diffraction theory. In addition, in order to reflect the local curvature of each subregion, we apply the phase compensation technique. Analytical expressions are derived based on the angular spectrum method and numerical studies are conducted to validate our method.

Diffraction algorithm suitable for both near and far field with shifted destination window and oblique illumination

We propose a method for diffraction simulation with both shifted destination window and a large oblique illumination. Based on the angular spectrum theory, we first derive a generalized transfer function (GTF) and a generalized point-spread function (GSPF) suitable for free-space diffraction simulation when both a shifted destination window and a large oblique illumination are taken into account. Then we analyze the sampling error caused by sampling of the GTF and the GSPF for numerical simulation based on fast Fourier transform (FFT), and find out an analytical formula for determining a criteria distance of Zc. Theoretical analysis and simulation results prove that the FFT-based GTF sampling algorithm is valid for diffraction simulation with a diffraction distance less than or equal to Zc, while the FFT-based GSPF sampling is only suitable for the simulation with a distance larger than or equal to Zc. Based on theoretical analysis, we propose the hybrid GTF-GSPF algorithm suitable for simulation of both near- and far-field diffractions with shifted destination window and large oblique source illumination at the same time. Finally, some simulation results are given to verify the feasibility of the algorithm.