Minimized speckle noise in lens-less holographic projection by pixel separation

Acousto-optic holography for pseudo-two-dimensional dynamic light patterning

Optical systems use acousto-optic deflectors (AODs) mostly for fast angular scanning and spectral filtering of laser beams. However, AODs may transform laser light in much broader ways. When time-locked to the pulsing of low repetition rate laser amplifiers, AODs permit the holographic reconstruction of 1D and pseudo-two-dimensional (ps2D) intensity objects of rectangular shape by controlling the amplitude and phase of the light field at high (20-200 kHz) rates for microscopic light patterning. Using iterative Fourier transformations (IFTs), we searched for AOD-compatible holograms to reconstruct the given ps2D target patterns through either phase-only or complex light field modulation. We previously showed that phase-only holograms can adequately render grid-like patterns of diffraction-limited points with non-overlapping diffraction orders, while side lobes to the target pattern can be cured with an apodization mask. Dense target patterns, in contrast, are typically encumbered by apodization-resistant speckle noise. Here, we show the denoised rendering of dense ps2D objects by complex acousto-optic holograms deriving from simultaneous optimization of the amplitude and phase of the light field. Target patterns lacking ps2D symmetry, although not translatable into single holograms, were accessed by serial holography based on a segregation into ps2D-compatible components. The holograms retrieved under different regularizations were experimentally validated in an AOD random-access microscope. IFT regularizations characterized in this work extend the versatility of acousto-optic holography for fast dynamic light patterning.

Speckle noise suppression method in a holographic display based on pixel processing

In this paper, we propose a method to suppress the speckle noise in a holographic display based on pixel processing. Through the separation of object pixels in space, the recorded object is divided into multiple object point groups. The complex amplitude of the light field for each object point group is recorded as a sub-computer-generated hologram (sub-CGH). The phase of each pixel on a sub-CGH is optimized to generate the final sub-CGH. Therefore, the pixels of the recorded object and sub-CGH are processed. In the reconstruction process, the final sub-CGHs are loaded on the spatial light modulator sequentially. The speckle noise of the reconstructed image is suppressed by reducing the algorithm error and the overlapping area of adjacent image points. The experimental results prove the feasibility of the proposed method.

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.

Method of calculating speckle-reduced hologram data using a convergence light wave for a computer-generated hologram

In a computer-generated hologram, random phases are required for representing object surfaces; however, speckle noise occurs in the random phases. We propose a speckle reduction method for three-dimensional virtual images in electro-holography. The method does not have random phases but instead converges the object light on the observer's viewpoint. Optical experiments demonstrated that the proposed method greatly reduced speckle noise while maintaining a calculation time comparable to that of the conventional method.

Optimized phase-only hologram generation for high-quality holographic display

In holographic displays, the Gerchberg-Saxton (GS) method has been widely used to generate the phase-only hologram (POH). However, as the constraint strategy of the GS method cannot optimize the POH well enough, the display quality is degraded. Various methods have been proposed to solve this problem, such as introducing the dummy area, using an initial quadratic phase, and modifying the amplitude constraint strategy. This paper proposes a simple and effective iterative method to optimize POH for the high-quality reconstructed image, which is a combination of the above three methods. In the proposed method, the target image is padded with zeros, and the padded image is divided into the target and non-target region. The initial phase in the target region is reset to the quadratic phase, and the optimized parameters α and β are introduced to modify the amplitude constraint strategy. In the iterative process, this strategy is applied to the target region. Numerical and optical experiments were conducted to verify the effectiveness of the proposed method. The results show that the speckle noise is effectively suppressed, and the quality of the reconstructed image is improved.

Diffraction-engineered holography: Beyond the depth representation limit of holographic displays

Holography is one of the most prominent approaches to realize true-to-life reconstructions of objects. However, owing to the limited resolution of spatial light modulators compared to static holograms, reconstructed objects exhibit various coherent properties, such as content-dependent defocus blur and interference-induced noise. The coherent properties severely distort depth perception, the core of holographic displays to realize 3D scenes beyond 2D displays. Here, we propose a hologram that imitates defocus blur of incoherent light by engineering diffracted pattern of coherent light with adopting multi-plane holography, thereby offering real world-like defocus blur and photorealistic reconstruction. The proposed hologram is synthesized by optimizing a wave field to reconstruct numerous varifocal images after propagating the corresponding focal distances where the varifocal images are rendered using a physically-based renderer. Moreover, to reduce the computational costs associated with rendering and optimizing, we also demonstrate a network-based synthetic method that requires only an RGB-D image.

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.

Method of color holographic display with speckle noise suppression

In this paper, a method of color holographic display with speckle noise suppression is proposed. Firstly, the intensity information of the object is extracted according to the red, green and blue (RGB) channels. The band-limited phase is calculated and used as the initial phase for each color channel. Secondly, the double-step Fresnel diffraction algorithm is used to calculate the computer-generated holograms (CGHs), and a filter plane that dynamically adjusts the position of the filter in the optical path is designed. Then, a divergent spherical phase factor is added to the CGHs. Finally, the time average method is used to further reduce the speckle noise. When the CGHs of the RGB channels are loaded on the digital micromirror device and illuminated by the RGB lights emitting in a temporal sequence, the color reconstructed images with speckle noise suppression can be displayed. The validity of the proposed method is verified.

Artifact-free holographic light shaping through moving acousto-optic holograms

Holographic light modulation is the most efficient method to shape laser light into well-defined patterns and is therefore the means of choice for many intensity demanding applications. During the last two decades, spatial light modulators based on liquid crystals prevailed among several technologies and became the standard tool to shape light holographically. But in the near future, this status might be challenged by acousto-optic deflectors. These devices are well known for their excelling modulation rates and high optical power resilience. But only few scattered precedents exist that demonstrate their holographic capabilities, despite the many interesting properties that they provide. We implemented a holographic acousto-optic light modulation (HALM) system, that is based on displaying holograms on acousto-optic deflectors. We found that this system can eliminate the ubiquitous coherent artifacts that arise in holography through the inherent motion of acousto-optic holograms. That distinguishes our approach from any other holographic modulation technique and allows to reconstruct intensity patterns of the highest fidelity. A mathematical description of this effect is presented and experimentally confirmed by reconstructing images holographically with unprecedented quality. Our results suggest that HALM promotes acousto-optic deflectors from highly specialized devices to full-fledged spatial light modulators, that can compete in a multitude of applications with LC-SLMs. Especially applications that require large optical output powers, high modulation speeds or accurate gray-scale intensity patterns will profit from this technology. We foresee that HALM may play a major role in future laser projectors and displays, structured illumination microscopy, laser material processing and optical trapping.

Speckleless color dynamic three-dimensional holographic display based on complex amplitude modulation

In this paper, we propose a method to implement a speckleless color dynamic three-dimensional holographic display by modulating amplitude and phase distribution simultaneously. Computer-generated holograms are calculated with an initial uniform phase, and the speckle noise of reconstructed images is suppressed effectively. We perform both numerical simulations and optical experiments to demonstrate the effectiveness of the proposed method. The numerical simulations show that the proposed method can achieve speckleless reconstruction and the optical experiments provide a good color dynamic display effect. It is expected that the proposed method could be widely applied to realize high-quality color dynamic holographic displays in the future.

Phase hologram optimization with bandwidth constraint strategy for speckle-free optical reconstruction

An iterative method with bandwidth constraint strategy is proposed to design phase holograms for high-quality speckle-free optical reconstruction. The bandwidth properties of the reconstructed field are analyzed theoretically based on the sampling theory, which helps in properly allocating the sampling resources for efficiently describing the speckles and artifacts in the reconstructed field. Iterative calculation with bandwidth constraint strategy of the reconstructed field and quadratic initial phase can optimize the phase hologram without stagnation problem, which provides effective controls of the reconstructed intensity fluctuations and helps to suppress the speckles and artifacts. Numerical and optical experiments have been performed to validate the proposed method can achieve excellent image fidelity.

Adaptive weighted Gerchberg-Saxton algorithm for generation of phase-only hologram with artifacts suppression

In the conventional weighted Gerchberg-Saxton (GS) algorithm, the feedback is used to accelerate the convergence. However, it will lead to the iteration divergence. To solve this issue, an adaptive weighted GS algorithm is proposed in this paper. By replacing the conventional feedback with our designed feedback, the convergence can be ensured in the proposed method. Compared with the traditional GS iteration method, the proposed method improves the peak signal-noise ratio of the reconstructed image with 4.8 dB on average. Moreover, an approximate quadratic phase is proposed to suppress the artifacts in optical reconstruction. Therefore, a high-quality image can be reconstructed without the artifacts in our designed Argument Reality device. Both numerical simulations and optical experiments have validated the effectiveness of the proposed method.

Two-dimensional angle multiplexing by segmented spherical holography

The crosstalk noise produced in the multiplexing technology of curved computer-generated holograms has caused great damage to reconstructed objects. In order to solve this problem, we propose a method to realize three-dimensional object reconstruction with low crosstalk noise impact. By multiplexing the spherical holograms in the horizontal and vertical directions, the complex amplitudes of the multiple spherical holograms with different curvatures are added to form a composed hologram. The generated hologram records many unrelated scenes of the object. According to the different angles used to generate the hologram, the original object under different viewpoints can be rebuilt, and the multiview multiplexing and reconstruction of three-dimensional objects can be realized. Simulation and optical experiments verify the feasibility of this method.

Toward the next-generation VR/AR optics: a review of holographic near-eye displays from a human-centric perspective

Wearable near-eye displays for virtual and augmented reality (VR/AR) have seen enormous growth in recent years. While researchers are exploiting a plethora of techniques to create life-like three-dimensional (3D) objects, there is a lack of awareness of the role of human perception in guiding the hardware development. An ultimate VR/AR headset must integrate the display, sensors, and processors in a compact enclosure that people can comfortably wear for a long time while allowing a superior immersion experience and user-friendly human-computer interaction. Compared with other 3D displays, the holographic display has unique advantages in providing natural depth cues and correcting eye aberrations. Therefore, it holds great promise to be the enabling technology for next-generation VR/AR devices. In this review, we survey the recent progress in holographic near-eye displays from the human-centric perspective.

Method of curved composite hologram generation with suppressed speckle noise

In this paper, a curved composite hologram (CCH) generation method with suppressed speckle noise is proposed. The recorded 3D object is considered as many layers with different depths and the planar hologram (PH) for each layer is generated accordingly. Then the PH is transformed to curved hologram (CH). The CH of the recorded 3D object can be generated by superposing the CHs for all the layers. Also, the linear phase factor is superposed to the CH of the object. For different objects, the bending angle and linear phase factor of the hologram are different. The CCH is generated by superimposing the CHs of different objects. Finally, the CCH is encoded by using the error diffusion method and optimized by superposing of the digital lens. When the CCH is reproduced from different angles, the reconstructed images with suppressed speckle noise can be displayed. The experimental results verify the feasibility of the proposed method.

Spherical self-diffraction for speckle suppression of a spherical phase-only hologram

The spherical computer-generated hologram is inevitably suffered from the speckle noise since it is necessary to add random phase to the object to ensure the scattering characteristic of reconstructed image. The speckle noise seriously degrades the quality of reconstructed image especially for a spherical phase-only hologram (SPOH). In this paper, spherical self-diffraction iteration (SSDI) algorithm is proposed to suppress the speckle noise in the SPOH. The algorithm is based on spherical self-diffraction (SSD) model which is a special case of spherical back-propagation (SBP) model at limit condition. The correctness of SBP and SSD as well as the effectiveness of SSDI algorithm are verified by numerical simulations. Meaningfully, the proposed method significantly outperforms the conventional methods in speckle suppression performance and computing speed. As far as we known, models of SBP and SSD as well as conception of SSDI are firstly proposed and applied for speckle suppression of SPOH.

Three-dimensional visualization of brain tumor progression based accurate segmentation via comparative holographic projection

We propose a new optical method based on comparative holographic projection for visual comparison between two abnormal follow-up magnetic resonance (MR) exams of glioblastoma patients to effectively visualize and assess tumor progression. First, the brain tissue and tumor areas are segmented from the MR exams using the fast marching method (FMM). The FMM approach is implemented on a computed pixel weight matrix based on an automated selection of a set of initialized target points. Thereafter, the associated phase holograms are calculated for the segmented structures based on an adaptive iterative Fourier transform algorithm (AIFTA). Within this approach, a spatial multiplexing is applied to reduce the speckle noise. Furthermore, hologram modulation is performed to represent two different reconstruction schemes. In both schemes, all calculated holograms are superimposed into a single two-dimensional (2D) hologram which is then displayed on a reflective phase-only spatial light modulator (SLM) for optical reconstruction. The optical reconstruction of the first scheme displays a 3D map of the tumor allowing to visualize the volume of the tumor after treatment and at the progression. Whereas, the second scheme displays the follow-up exams in a side-by-side mode highlighting tumor areas, so the assessment of each case can be fast achieved. The proposed system can be used as a valuable tool for interpretation and assessment of the tumor progression with respect to the treatment method providing an improvement in diagnosis and treatment planning.

Optimized random phase tiles for non-iterative hologram generation

In this work, we introduce a technique for fast, high-quality, non-iterative generation of phase-only holograms from both 2D and 3D scenes. In this technique, we generate an optimized random phase tile which behaves like a small diffuser, spreading the amplitude of a section of the scene throughout the hologram plane. Each section of the scene is multiplied by this tile and then propagated to the hologram plane by means of the Fresnel transform. The contribution from each tile is added, resulting in a phase-only hologram of the scene. The optimized random phase tiles can be generated for any distance between the hologram plane and the object using an iterative Fresnel algorithm. Afterwards, this tile can be used to generate holograms from any number of objects without the need for further iterative algorithms. These holograms present increased quality after reconstruction compared to similar non-iterative hologram generation techniques. Both numerical and optical experiments are carried out, demonstrating the effectiveness of our proposal.

Fast hologram generation using intermediate angular-spectrum method for high-quality compact on-axis holographic display

In the angular-spectrum method-based computer-generated hologram, the zero-padding method is used to convert circular convolution into linear convolution. However, it will increase the calculation time and memory usage significantly. Therefore, a fast and simple method is proposed to solve the issue of the numerical convolution in the process of hologram generation by using the intermediate angular-spectrum method in this paper. Through replacing numerical Fourier transform by optical Fourier transform in the hologram generation, the calculation speed is approximately 6 times faster than that of the zero-padding method. And due to the scaling factors introduced by the Fourier lens and without the cropping operation, the reconstruction quality of the proposed method is improved significantly compared with the zero-padding method. Moreover, the optical reconstruction system is more compact than the 4-f filter system in the on-axis holographic reconstruction. Both numerical simulations and optical experiments have validated the effectiveness of the proposed method.

Synthetic amplitude for improved reconstruction of noniterative phase holograms

In this paper, we show how a specially designed synthetic amplitude can be used to obtain greatly improved reconstruction of objects only using the phase data of their Fourier or Fresnel transforms. The reconstruction of objects from phase-only information is of interest because phase modulation has much higher efficiency than amplitude modulation and can be achieved with a high degree of precision with current liquid-crystal-on-silicon spatial light modulators. However, direct reconstruction of an object from its phase information usually results in severely degraded outputs. Due to this issue, to achieve optimal reconstruction, the object information must be codified in a phase hologram by means of time-consuming algorithms. To avoid these kinds of algorithms, we propose using a synthetic amplitude, designed in such a way that, when multiplied with the phase information of the object, leads to high-quality reconstruction. This synthetic amplitude contains no information about the object and can be used to reconstruct a number of different inputs without further processing. We present experiments carried out in virtual and actual optical systems verifying the validity of our proposal for 2D, 3D, and dynamic scenes.

Holographic display method to suppress speckle noise based on effective utilization of two spatial light modulators

In this paper, a holographic display method to suppress the speckle noise is proposed. Firstly, the effective viewing area (EVA) of the reconstructed image is calculated. The object points are separated into groups by pixel separation. Then, the sub-computer-generated holograms (sub-CGHs) which can be reconstructed in the EVA are generated by calculating the principal fringe patterns. Finally, by loading the sub-CGHs on the two spatial light modulators respectively and using spatiotemporal multiplexing method, the reconstructed image can be displayed with lower speckle noise. Moreover, the calculation speed of the hologram is improved. Experimental results demonstrate the feasibility of the proposed method.

Image quality improvement of random phase-free holograms by addressing the cause of ringing artifacts

Holographic projectors utilize holography techniques, although there are several barriers to realizing holographic projections. One such challenge is the deterioration of the hologram image quality caused by speckle noise and ringing artifacts. Several methods designed to reduce the speckle noise and ringing artifacts have been proposed. However, these methods require multiple diffraction calculations and a significant amount of computational time. In this paper, we reveal that ringing artifacts are due to object light being recorded on the edge of the hologram and that the high-frequency component of the original image leaks outside of the recording area of the hologram when the random phase-free method is used. Therefore, this study proposes an object light centering method that prevents object light from being recorded on the edge of the hologram and prevents the high-frequency component of the original image from leaking outside the recording area of the hologram, which removes the ringing artifact and extends the random phase-free method to an off-axis hologram.

Electronic Tabletop Holographic Display: Design, Implementation, and Evaluation

Most of the previously-tried prototype systems of digital holographic display are of front viewing flat panel-type systems having narrow viewing angle, which do not meet expectations towards holographic displays having more volumetric and realistic 3-dimensional image rendering capability. We have developed a tabletop holographic display system which is capable of 360° rendering of volumetric color hologram moving image, looking much like a real object. Multiple viewers around the display can see the image and perceive very natural binocular as well as motion parallax. We have previously published implementation details of a mono color version of the system, which was the first prototype. In this work, we present requirements, design methods, and the implementation result of a full parallax color tabletop holographic display system, with some recapitulation of motivation and a high-level design concept. We also address the important issue of performance measure and evaluation of a holographic display system and image, with initial results of experiments on our system.

Fast method for ringing artifacts reduction in random phase-free kinoforms

In holographic projection, ringing artifacts and degradation appear when the speckle noise problem is solved based on the random phase-free method. In this paper, we present a fast method to suppress the ringing artifacts in random phase-free kinoforms. We first reduce the distance between the hologram plane and the focal plane, and keep the focal length of the convergence light unchanged in the random phase-free method. Next, the complex amplitude is modulated using a single spatial light modulator. Consequently, the ringing artifacts and speckle noise reduction in the reconstructed image can be achieved. At the same time, the computing speed can be increased with our proposed method. Numerical simulations and optical experiments have validated the feasibility of the proposed method.

Miniature holographic projector with cloud computing capability

A fully functional miniaturized projection head below 5  cm³ is presented, using computer-generated holograms dynamically displayed on a liquid-crystal spatial light modulator. Spatial division of the modulator is used for color projection without color breakup, and specially designed, anti-reflection coated prisms ensure simple light paths with small losses. Real-time calculations are performed on a remote server with on-the-fly compression of holographic fringes. Cloud computing allows 1 W of local electrical power usage and apparent image brightness equivalent to 15-500 lm/W efficiency, depending on the displayed content. The properties of the projector allow future applications in handheld displays.

Formulas of partially spatial coherent light and design algorithm for computer-generated holograms

Formulas of partially spatial coherent light are derived and its corresponding design algorithm is proposed for generating computer-generated holograms based on partially spatial coherent light. The partially coherent light is divided into two terms: spatially absolute coherent part and incoherent part. The former is propagated by angular spectrum method, while the latter is based on the optical transfer function. The related formulas are derived where the coherent function (degree of coherence) is related. A modified iterative algorithm is further developed for optimizing the phase distributions. Numerical simulations and optical experiments are both performed to verify the proposed algorithm. The results obtained by the proposed method and the traditional method are compared, and it is clear that the speckle contrasts in optical experiments are improved more than 46%, and the image quality is obviously improved. This method could also provide new applications for three-dimensional holographic display, beam shaping, and other wave-front modulation techniques.

Collective matrix of spatial light modulators for increased resolution in holographic image projection

We present a method to increase the resolution of holographically projected images by the use of a collective matrix of two phase-only spatial light modulators. As a result of fine alignment and common coherent illumination of the modulators, a synthetic aperture is formed with a doubled number of active pixels. In this paper we present theoretical analysis and numerical simulations which stand in good agreement for different distances between the apertures of modulators. We have achieved experimentally controlled field interference from both modulators on the projection screen, exhibiting increased resolution in one spatial direction and residual effects of the dead space between modulators. Then we have proved numerically possibility to extend our approach on bigger synthetic apertures consisted of more than two modulators.

Speeding up image quality improvement in random phase-free holograms using ringing artifact characteristics

A holographic projector utilizes holography techniques. However, there are several barriers to realizing holographic projections. One is deterioration of hologram image quality caused by speckle noise and ringing artifacts. The combination of the random phase-free method and the Gerchberg-Saxton (GS) algorithm has improved the image quality of holograms. However, the GS algorithm requires significant computation time. We propose faster methods for image quality improvement of random phase-free holograms using the characteristics of ringing artifacts.

Speckle reduced lensless holographic projection from phase-only computer-generated hologram

This paper presents a method for the implementation of speckle reduced lensless holographic projection based on phase-only computer-generated hologram (CGH). The CGH is calculated from the image by double-step Fresnel diffraction. A virtual convergence light is imposed to the image to ensure the focusing of its wavefront to the virtual plane, which is established between the image and the hologram plane. The speckle noise is reduced due to the reconstruction of the complex amplitude of the image via a lensless optical filtering system. Both simulation and optical experiments are carried out to confirm the feasibility of the proposed method. Furthermore, the size of the projected image can reach to the maximum diffraction bandwidth of the spatial light modulator (SLM) at a given distance. The method is effective for improving the image quality as well as the image size at the same time in compact lensless holographic projection system.

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.

Generation of complementary sampled phase-only holograms

If an image is uniformly down-sampled into a sparse form and converted into a hologram, the phase component alone will be adequate to reconstruct the image. However, the appearance of the reconstructed image is degraded with numerous empty holes. In this paper, we present a low complexity and non-iterative solution to this problem. Briefly, two phase-only holograms are generated for an image, each based on a different down-sampling lattice. Subsequently, the holograms are displayed alternately at high frame rate. The reconstructed images of the 2 holograms will appear to be a single, densely sampled image with enhance visual quality.

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

In this paper, we present a method for calculation of a computer-generated hologram (CGH) from a 3D object. A virtual wavefront recording plane (WRP) which is close to the 3D object is established. This WRP is nonuniformly sampled according to the depth map of the 3D object. The generation of CGH only involves two nonuniform fast Fourier transform (NUFFT) and two fast Fourier transform (FFT) operations, the whole computational procedure is greatly simplified by diffraction calculation from a 2D planar image instead of 3D object voxels. Numerical simulations and optical experiments are carried out to confirm the feasibility of our proposed method. The CGH calculated with our method is capable to project zoomable 3D objects without lens.

Speckle regularization and miniaturization of computer-generated holographic stereograms

Holographic stereograms produce multiple parallax images that are seen from multiple viewpoints. Because random phase distributions are added to the parallax images to remove areas where images cannot be seen in the viewing area, speckles are generated in the reconstructed images. In this study, virtual viewpoints are inserted between the original viewpoints (real viewpoints) to make the interval of the viewpoints smaller than the pupil diameter of the eyes in order to remove the areas without images. In this case, regular interference patterns appear in the reconstructed images instead of the speckle patterns. The proper phase modulation of the parallax images displayed to the real and virtual viewpoints increases the spatial frequencies of the regular interference patterns on retinas so that the eyes cannot perceive them. The proposed technique was combined with the multiview-based holographic stereogram calculation technique and was experimentally verified.

Holographic multi-projection using the random phase-free method

We demonstrated holographic multi-projection using the random phase-free method and the iterative method. Holographic multi-projection is a method of projecting multiple different images focused on different screens at the same time. The random phase-free method succeeded in improving the image quality. By applying the iterative method to the random phase-free method, the image quality was improved further. The results of our numerical reconstruction and optical experiments confirm that the proposed method improves the image quality. The peak signal-to-noise ratios of the reconstructed images using the proposed method and the conventional method are 30.66 and 13.61 dB, respectively.

Image magnification in lensless holographic projection using double-sampling Fresnel diffraction

Since the diffraction angle is limited by the spatial resolution of the spatial light modulator (SLM), the size of the optical image of the lensless holographic projection with a SLM is very small. Using a divergent spherical beam to illuminate a SLM is an effective method to physically increase the projection angle; nevertheless, the sampling ranges of the existing Fresnel diffraction algorithms with fast Fourier transform keep unchanged. In this paper, a double-sampling Fresnel diffraction algorithm to enlarge the sampling range is proposed when using a divergent spherical beam to illuminate a SLM, and the magnification of the optical image is realized in lensless holographic projection. The hologram can be easily optimized by the Gerschberg-Saxton algorithm. Simulation and experimental results with enlarged optical image are presented successfully.

Speckle-suppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg-Saxton algorithm

The Gerchberg-Saxton (GS) algorithm is widely used to calculate the phase-only computer-generated hologram (CGH) for holographic three-dimensional (3D) display. However, speckle noise exists in the reconstruction of the CGH due to the uncontrolled phase distribution. In this paper, we propose a method to suppress the speckle noise by simultaneously reconstructing the desired amplitude and phase distribution. The phase-only CGH is calculated by using a double-constraint GS algorithm, in which both the desired amplitude and phase information are constrained in the image plane in each iteration. The calculated phase-only CGH can reconstruct the 3D object on multiple planes with a desired amplitude distribution and uniform phase distribution. Thus the speckle noise caused by the phase fluctuation between adjacent pixels is suppressed. Both simulations and experiments are presented to demonstrate the effective speckle noise suppression by our algorithm.

Precise design of two-dimensional diffractive optical elements for beam shaping

Diffractive optical elements (DOEs) for beam shaping are widely used in many fields, and there are many kinds of optimization algorithms to design the DOEs for beam shaping. However, only the intensity distribution of the selected sampling points is controlled by these optimization algorithms. The intensity distribution of other points on the output plane is always far away from the ideal distribution. The reason is that the sampling interval on the output plane is not small enough. In this paper, a new modified GS algorithm is presented with a small enough sampling interval on the output plane. A two-dimensional DOE for beam shaping is designed, and the simulation results and the experimental results demonstrate the good performance of this algorithm.

Random phase-free kinoform for large objects

We propose a random phase-free kinoform for large objects. When not using the random phase in kinoform calculation, the reconstructed images from the kinoform are heavy degraded, like edge-only preserved images. In addition, the kinoform cannot record an entire object that exceeds the kinoform size because the object light does not widely spread. In order to avoid this degradation and to widely spread the object light, the random phase is applied to the kinoform calculation; however, the reconstructed image is contaminated by speckle noise. In this paper, we overcome this problem by using our random phase-free method and error diffusion method.

Enhancing the quality of reconstructed 3D objects by using point clusters

A novel algorithm for constructing computer-generated holograms using point clusters is presented. This method exploits the precalculated triangular meshes used in previous research and can reconstruct less noisy 3D objects. In addition, the high-speed property of a ferroelectric liquid crystal spatial light modulator is utilized to enhance the reconstruction quality. All 3D holograms generated in this paper are based on Fresnel propagation; thus, the Fresnel plane is treated as a vital element in producing the hologram. A GeForce GTX 770 graphics card with 2 GB memory was used to achieve parallel high-speed hologram generation.

Random phase-free computer-generated hologram

Addition of random phase to the object light is required in computer-generated holograms (CGHs) to widely diffuse the object light and to avoid its concentration on the CGH; however, this addition causes considerable speckle noise in the reconstructed image. For improving the speckle noise problem, techniques such as iterative phase retrieval algorithms and multi-random phase method are used; however, they are time consuming and are of limited effectiveness. Herein, we present a simple and computationally inexpensive method that drastically improves the image quality and reduces the speckle noise by multiplying the object light with the virtual convergence light. Feasibility of the proposed method is shown using simulations and optical reconstructions; moreover, we apply it to lens-less zoom-able holographic projection. The proposed method is useful for the speckle problems in holographic applications.

Speckle reduction in holographic projection by random pixel separation with time multiplexing

A speckle-reduction method with random locations of sparse object points is proposed for image quality improvement based on a time-multiplexing approach in holographic reconstruction. The object points of a reconstructed image are divided into groups of sparse object points. Pixel separation of the periodic location, in general, is used for the sparse object points. However, an unwanted periodic fringe pattern is caused, and it dominantly degrades the reconstructed image quality. The proposed random pixel separation enables the reconstructed image quality to improve more effectively. The numerical simulation and the optical experiment are presented to confirm the performance of the proposed method.

Real-time spatiotemporal division multiplexing electroholography with a single graphics processing unit utilizing movie features

We propose a real-time spatiotemporal division multiplexing electroholography utilizing the features of movies. The proposed method spatially divides a 3-D object into plural parts and periodically selects a divided part in each frame, thereby reconstructing a three-dimensional (3-D) movie of the original object. Computer-generated holograms of the selected part are calculated by a single graphics processing unit and sequentially displayed on a spatial light modulator. Visual continuity enables a reconstructed movie of the original 3-D object. The proposed method realized a real-time reconstructed movie of a 3-D object composed of 11,646 points at over 30 frames per second (fps). We also displayed a reconstructed movie of a 3-D object composed of 44,647 points at about 10 fps.

Large size three-dimensional video by electronic holography using multiple spatial light modulators

In this paper, we propose a new method of using multiple spatial light modulators (SLMs) to increase the size of three-dimensional (3D) images that are displayed using electronic holography. The scalability of images produced by the previous method had an upper limit that was derived from the path length of the image-readout part. We were able to produce larger colour electronic holographic images with a newly devised space-saving image-readout optical system for multiple reflection-type SLMs. This optical system is designed so that the path length of the image-readout part is half that of the previous method. It consists of polarization beam splitters (PBSs), half-wave plates (HWPs), and polarizers. We used 16 (4 × 4) 4K×2K-pixel SLMs for displaying holograms. The experimental device we constructed was able to perform 20 fps video reproduction in colour of full-parallax holographic 3D images with a diagonal image size of 85 mm and a horizontal viewing-zone angle of 5.6 degrees.

Speckle-suppression in hologram calculation using ray-sampling plane

Speckle noise is an important issue in electro-holographic displays. We propose a new method for suppressing speckle noise in a computer-generated hologram (CGH) for 3D display. In our previous research, we proposed a method for CGH calculation using ray-sampling plane (RS-plane), which enables the application of advanced ray-based rendering techniques to the calculation of hologram that can reconstruct a deep 3D scene in high resolution. Conventional techniques for effective speckle suppression, which utilizes the time-multiplexing of sparse object points, can suppress the speckle noise with high resolution, but it cannot be applied to the CGH calculation using RS-plane because the CGH calculated using RS-plane does not utilize point sources on an object surface. Then, we propose the method to define the point sources from light-ray information and apply the speckle suppression technique using sparse point sources to CGH calculation using RS-plane. The validity of the proposed method was verified by numerical simulations.

Image size scalable full-parallax coloured three-dimensional video by electronic holography

In electronic holography, various methods have been considered for using multiple spatial light modulators (SLM) to increase the image size. In a previous work, we used a monochrome light source for a method that located an optical system containing lens arrays and other components in front of multiple SLMs. This paper proposes a colourization technique for that system based on time division multiplexing using laser light sources of three colours (red, green, and blue). The experimental device we constructed was able to perform video playback (20 fps) in colour of full parallax holographic three-dimensional (3D) images with an image size of 63 mm and a viewing-zone angle of 5.6 degrees without losing any part of the 3D image.